Sample records for accurate mathematical description

  1. The first accurate description of an aurora

    NASA Astrophysics Data System (ADS)

    Schröder, Wilfried

    2006-12-01

    As technology has advanced, the scientific study of auroral phenomena has increased by leaps and bounds. A look back at the earliest descriptions of aurorae offers an interesting look into how medieval scholars viewed the subjects that we study.Although there are earlier fragmentary references in the literature, the first accurate description of the aurora borealis appears to be that published by the German Catholic scholar Konrad von Megenberg (1309-1374) in his book Das Buch der Natur (The Book of Nature). The book was written between 1349 and 1350.

  2. Mathematical Description and Mechanistic Reasoning: A Pathway toward STEM Integration

    ERIC Educational Resources Information Center

    Weinberg, Paul J.

    2017-01-01

    Because reasoning about mechanism is critical to disciplined inquiry in science, technology, engineering, and mathematics (STEM) domains, this study focuses on ways to support the development of this form of reasoning. This study attends to how mechanistic reasoning is constituted through mathematical description. This study draws upon Smith's…

  3. Mathematical Proof. Description of Teacher Inservice Education Materials.

    ERIC Educational Resources Information Center

    National Education Association, Washington, DC. Project on Utilization of Inservice Education R & D Outcomes.

    The learning module described here is designed to help teachers plan and present a lesson on mathematical proof to pupils. The main topics covered are structure, hypothesis and conclusion, analysis, contrapositive, proof by contradiction, part proof worksheet, and conclusion and posttest. This descriptive report provides information on the…

  4. Connecting Intonation Labels to Mathematical Descriptions of Fundamental Frequency

    ERIC Educational Resources Information Center

    Grabe, Esther; Kochanski, Greg; Coleman, John

    2007-01-01

    The mathematical models of intonation used in speech technology are often inaccessible to linguists. By the same token, phonological descriptions of intonation are rarely used by speech technologists, as they cannot be implemented directly in applications. Consequently, these research communities do not benefit much from each other's insights. In…

  5. Comparative Validity of the Descriptive Tests of Mathematical Skills (DTMS) and SAT-Mathematics (SAT-M) for Predicting Performance in Freshman College Mathematics Courses: Prefatory Report

    ERIC Educational Resources Information Center

    McLoughlin, M. Padraig M. M.; Bluford, Dontrell A.

    2004-01-01

    This study investigated the predictive validity of the Descriptive Tests of Mathematical Skills (DTMS) and the SAT-Mathematics (SAT-M) tests as placement tools for entering students in a small, liberal arts, historically black institution (HBI) using regression analysis. The placement schema is four-tiered: for a remedial algebra course, college…

  6. Towards a Bernsteinian Language of Description for Mathematics Classroom Discourse

    ERIC Educational Resources Information Center

    Straehler-Pohl, Hauke; Gellert, Uwe

    2013-01-01

    This article aims at developing an external language of description to investigate the problem of why particular groups of students are systematically not provided access to school mathematical knowledge. Based on Basil Bernstein's conceptualisation of power in classification, we develop a three-dimensional model that operationalises the…

  7. Factors Related to White, Black, and Hispanic Women's Mathematics Attainments: A Descriptive Study.

    ERIC Educational Resources Information Center

    Rothschild, Susan J. S.; Lichtman, Marilyn

    Virtually no research conducted on women and mathematics is longitudinal in scope, generalizable in extent, and ethnic-race specific in nature. This descriptive study begins to fill the gap by examining the effects of background, school, and social-psychological factors on Hispanic, black, and white women's mathematics attainments. Data for the…

  8. Practice; criteria; provisions; mathematical descriptions: Examples

    NASA Astrophysics Data System (ADS)

    Wijdieks, J.

    1983-06-01

    Waterhammer is defined as the appearance of pressure changes in closed conduits caused by velocity changes with time of the flow. Therefore waterhammer may occur in all kinds of pipelines in which flow changes occur over time: long or short pipelines for oil, sewage, drinking water, cooling water, slurry, coal slurry, chemicals, and in fresh water or city heating networks. The phenomenon of waterhammer is discussed herein. Specific parameters addressed include: the practical causes of waterhammer, cavitation flow, overpressure, vapor pressures, bulk modulus, continuous and discontinuous flow, and provisions to prevent waterhammer. Calculation of waterhammer is presented along with a mathematical description thereof. Hydraulic equipment (valves, pumps, surge towers) is also discussed.

  9. Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth

    PubMed Central

    Benzekry, Sébastien; Lamont, Clare; Beheshti, Afshin; Tracz, Amanda; Ebos, John M. L.; Hlatky, Lynn; Hahnfeldt, Philip

    2014-01-01

    Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic. PMID:25167199

  10. Classical mathematical models for description and prediction of experimental tumor growth.

    PubMed

    Benzekry, Sébastien; Lamont, Clare; Beheshti, Afshin; Tracz, Amanda; Ebos, John M L; Hlatky, Lynn; Hahnfeldt, Philip

    2014-08-01

    Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic.

  11. Short description of mathematical support programs for space experiments in the Interkosmos program

    NASA Technical Reports Server (NTRS)

    Elyasberg, P. Y.

    1979-01-01

    A synopsis of programs of mathematical support designed at the Institute for Cosmic Research of the USSR Academy of Sciences for cosmic experiments being conducted in the Interkosmos Program is presented. A short description of the appropriate algorithm is given.

  12. Simple Mathematical Models Do Not Accurately Predict Early SIV Dynamics

    PubMed Central

    Noecker, Cecilia; Schaefer, Krista; Zaccheo, Kelly; Yang, Yiding; Day, Judy; Ganusov, Vitaly V.

    2015-01-01

    Upon infection of a new host, human immunodeficiency virus (HIV) replicates in the mucosal tissues and is generally undetectable in circulation for 1–2 weeks post-infection. Several interventions against HIV including vaccines and antiretroviral prophylaxis target virus replication at this earliest stage of infection. Mathematical models have been used to understand how HIV spreads from mucosal tissues systemically and what impact vaccination and/or antiretroviral prophylaxis has on viral eradication. Because predictions of such models have been rarely compared to experimental data, it remains unclear which processes included in these models are critical for predicting early HIV dynamics. Here we modified the “standard” mathematical model of HIV infection to include two populations of infected cells: cells that are actively producing the virus and cells that are transitioning into virus production mode. We evaluated the effects of several poorly known parameters on infection outcomes in this model and compared model predictions to experimental data on infection of non-human primates with variable doses of simian immunodifficiency virus (SIV). First, we found that the mode of virus production by infected cells (budding vs. bursting) has a minimal impact on the early virus dynamics for a wide range of model parameters, as long as the parameters are constrained to provide the observed rate of SIV load increase in the blood of infected animals. Interestingly and in contrast with previous results, we found that the bursting mode of virus production generally results in a higher probability of viral extinction than the budding mode of virus production. Second, this mathematical model was not able to accurately describe the change in experimentally determined probability of host infection with increasing viral doses. Third and finally, the model was also unable to accurately explain the decline in the time to virus detection with increasing viral dose. These results

  13. Langley Atmospheric Information Retrieval System (LAIRS): System description and user's guide

    NASA Technical Reports Server (NTRS)

    Boland, D. E., Jr.; Lee, T.

    1982-01-01

    This document presents the user's guide, system description, and mathematical specifications for the Langley Atmospheric Information Retrieval System (LAIRS). It also includes a description of an optimal procedure for operational use of LAIRS. The primary objective of the LAIRS Program is to make it possible to obtain accurate estimates of atmospheric pressure, density, temperature, and winds along Shuttle reentry trajectories for use in postflight data reduction.

  14. Mathematical description and program documentation for CLASSY, an adaptive maximum likelihood clustering method

    NASA Technical Reports Server (NTRS)

    Lennington, R. K.; Rassbach, M. E.

    1979-01-01

    Discussed in this report is the clustering algorithm CLASSY, including detailed descriptions of its general structure and mathematical background and of the various major subroutines. The report provides a development of the logic and equations used with specific reference to program variables. Some comments on timing and proposed optimization techniques are included.

  15. A mathematical function for the description of nutrient-response curve

    PubMed Central

    Ahmadi, Hamed

    2017-01-01

    Several mathematical equations have been proposed to modeling nutrient-response curve for animal and human justified on the goodness of fit and/or on the biological mechanism. In this paper, a functional form of a generalized quantitative model based on Rayleigh distribution principle for description of nutrient-response phenomena is derived. The three parameters governing the curve a) has biological interpretation, b) may be used to calculate reliable estimates of nutrient response relationships, and c) provide the basis for deriving relationships between nutrient and physiological responses. The new function was successfully applied to fit the nutritional data obtained from 6 experiments including a wide range of nutrients and responses. An evaluation and comparison were also done based simulated data sets to check the suitability of new model and four-parameter logistic model for describing nutrient responses. This study indicates the usefulness and wide applicability of the new introduced, simple and flexible model when applied as a quantitative approach to characterizing nutrient-response curve. This new mathematical way to describe nutritional-response data, with some useful biological interpretations, has potential to be used as an alternative approach in modeling nutritional responses curve to estimate nutrient efficiency and requirements. PMID:29161271

  16. THE SHEFFIELD ALCOHOL POLICY MODEL - A MATHEMATICAL DESCRIPTION.

    PubMed

    Brennan, Alan; Meier, Petra; Purshouse, Robin; Rafia, Rachid; Meng, Yang; Hill-Macmanus, Daniel; Angus, Colin; Holmes, John

    2014-09-30

    This methodology paper sets out a mathematical description of the Sheffield Alcohol Policy Model version 2.0, a model to evaluate public health strategies for alcohol harm reduction in the UK. Policies that can be appraised include a minimum price per unit of alcohol, restrictions on price discounting, and broader public health measures. The model estimates the impact on consumers, health services, crime, employers, retailers and government tax revenues. The synthesis of public and commercial data sources to inform the model structure is described. A detailed algebraic description of the model is provided. This involves quantifying baseline levels of alcohol purchasing and consumption by age and gender subgroups, estimating the impact of policies on consumption, for example, using evidence on price elasticities of demand for alcohol, quantification of risk functions relating alcohol consumption to harms including 47 health conditions, crimes, absenteeism and unemployment, and finally monetary valuation of the consequences. The results framework, shown for a minimum price per unit of alcohol, has been used to provide policy appraisals for the UK government policy-makers. In discussion and online appendix, we explore issues around valuation and scope, limitations of evidence/data, how the framework can be adapted to other countries and decisions, and ongoing plans for further development. © 2014 The Authors. Health Economics published by John Wiley & Sons Ltd. © 2014 The Authors. Health Economics published by John Wiley & Sons Ltd.

  17. Accurate Energies and Orbital Description in Semi-Local Kohn-Sham DFT

    NASA Astrophysics Data System (ADS)

    Lindmaa, Alexander; Kuemmel, Stephan; Armiento, Rickard

    2015-03-01

    We present our progress on a scheme in semi-local Kohn-Sham density-functional theory (KS-DFT) for improving the orbital description while still retaining the level of accuracy of the usual semi-local exchange-correlation (xc) functionals. DFT is a widely used tool for first-principles calculations of properties of materials. A given task normally requires a balance of accuracy and computational cost, which is well achieved with semi-local DFT. However, commonly used semi-local xc functionals have important shortcomings which often can be attributed to features of the corresponding xc potential. One shortcoming is an overly delocalized representation of localized orbitals. Recently a semi-local GGA-type xc functional was constructed to address these issues, however, it has the trade-off of lower accuracy of the total energy. We discuss the source of this error in terms of a surplus energy contribution in the functional that needs to be accounted for, and offer a remedy for this issue which formally stays within KS-DFT, and, which does not harshly increase the computational effort. The end result is a scheme that combines accurate total energies (e.g., relaxed geometries) with an improved orbital description (e.g., improved band structure).

  18. Mathematical Description of Dendrimer Structure

    NASA Technical Reports Server (NTRS)

    Majoros, Istvan J.; Mehta, Chandan B.; Baker, James R., Jr.

    2004-01-01

    Characteristics of starburst dendrimers can be easily attributed to the multiplicity of the monomers used to synthesize them. The molecular weight, degree of polymerization, number of terminal groups and branch points for each generation of a dendrimer can be calculated using mathematical formulas incorporating these variables. Mathematical models for the calculation of degree of polymerization, molecular weight, and number of terminal groups and branching groups previously published were revised and elaborated on for poly(amidoamine) (PAMAM) dendrimers, and introduced for poly(propyleneimine) (POPAM) dendrimers and the novel POPAM-PAMAM hybrid, which we call the POMAM dendrimer. Experimental verification of the relationship between theoretical and actual structure for the PAMAM dendrimer was also established.

  19. Focus group discussion in mathematical physics learning

    NASA Astrophysics Data System (ADS)

    Ellianawati; Rudiana, D.; Sabandar, J.; Subali, B.

    2018-03-01

    The Focus Group Discussion (FGD) activity in Mathematical Physics learning has helped students perform the stages of problem solving reflectively. The FGD implementation was conducted to explore the problems and find the right strategy to improve the students' ability to solve the problem accurately which is one of reflective thinking component that has been difficult to improve. The research method used is descriptive qualitative by using single subject response in Physics student. During the FGD process, one student was observed of her reflective thinking development in solving the physics problem. The strategy chosen in the discussion activity was the Cognitive Apprenticeship-Instruction (CA-I) syntax. Based on the results of this study, it is obtained the information that after going through a series of stages of discussion, the students' reflective thinking skills is increased significantly. The scaffolding stage in the CA-I model plays an important role in the process of solving physics problems accurately. Students are able to recognize and formulate problems by describing problem sketches, identifying the variables involved, applying mathematical equations that accord to physics concepts, executing accurately, and applying evaluation by explaining the solution to various contexts.

  20. Molecular acidity: An accurate description with information-theoretic approach in density functional reactivity theory.

    PubMed

    Cao, Xiaofang; Rong, Chunying; Zhong, Aiguo; Lu, Tian; Liu, Shubin

    2018-01-15

    Molecular acidity is one of the important physiochemical properties of a molecular system, yet its accurate calculation and prediction are still an unresolved problem in the literature. In this work, we propose to make use of the quantities from the information-theoretic (IT) approach in density functional reactivity theory and provide an accurate description of molecular acidity from a completely new perspective. To illustrate our point, five different categories of acidic series, singly and doubly substituted benzoic acids, singly substituted benzenesulfinic acids, benzeneseleninic acids, phenols, and alkyl carboxylic acids, have been thoroughly examined. We show that using IT quantities such as Shannon entropy, Fisher information, Ghosh-Berkowitz-Parr entropy, information gain, Onicescu information energy, and relative Rényi entropy, one is able to simultaneously predict experimental pKa values of these different categories of compounds. Because of the universality of the quantities employed in this work, which are all density dependent, our approach should be general and be applicable to other systems as well. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

  1. A mathematical description of the inclusive fitness theory.

    PubMed

    Wakano, Joe Yuichiro; Ohtsuki, Hisashi; Kobayashi, Yutaka

    2013-03-01

    Recent developments in the inclusive fitness theory have revealed that the direction of evolution can be analytically predicted in a wider class of models than previously thought, such as those models dealing with network structure. This paper aims to provide a mathematical description of the inclusive fitness theory. Specifically, we provide a general framework based on a Markov chain that can implement basic models of inclusive fitness. Our framework is based on the probability distribution of "offspring-to-parent map", from which the key concepts of the theory, such as fitness function, relatedness and inclusive fitness, are derived in a straightforward manner. We prove theorems showing that inclusive fitness always provides a correct prediction on which of two competing genes more frequently appears in the long run in the Markov chain. As an application of the theorems, we prove a general formula of the optimal dispersal rate in the Wright's island model with recurrent mutations. We also show the existence of the critical mutation rate, which does not depend on the number of islands and below which a positive dispersal rate evolves. Our framework can also be applied to lattice or network structured populations. Copyright © 2012 Elsevier Inc. All rights reserved.

  2. Mathematical modeling in realistic mathematics education

    NASA Astrophysics Data System (ADS)

    Riyanto, B.; Zulkardi; Putri, R. I. I.; Darmawijoyo

    2017-12-01

    The purpose of this paper is to produce Mathematical modelling in Realistics Mathematics Education of Junior High School. This study used development research consisting of 3 stages, namely analysis, design and evaluation. The success criteria of this study were obtained in the form of local instruction theory for school mathematical modelling learning which was valid and practical for students. The data were analyzed using descriptive analysis method as follows: (1) walk through, analysis based on the expert comments in the expert review to get Hypothetical Learning Trajectory for valid mathematical modelling learning; (2) analyzing the results of the review in one to one and small group to gain practicality. Based on the expert validation and students’ opinion and answers, the obtained mathematical modeling problem in Realistics Mathematics Education was valid and practical.

  3. Mathematical Description of the Uptake of Hydrocarbons in Jet Fuel into the Stratum Corneum of Human Volunteers

    PubMed Central

    Kim, David; Farthing, Matthew W.; Miller, Cass T.; Nylander-French, Leena A.

    2008-01-01

    The objective of this research was to develop a mathematical description of uptake of aromatic and aliphatic hydrocarbons into the stratum corneum of human skin in vivo. A simple description based on Fick’s Laws of diffusion was used to predict the spatiotemporal variation of naphthalene, 1- and 2-methylnaphthalene, undecane, and dodecane in the stratum corneum of human volunteers. The estimated values of the diffusion coefficients for each chemical were comparable to values predicted using in vitro skin systems and biomonitoring studies. These results demonstrate the value of measuring dermal exposure using the tape-strip technique and the importance of quantifying of dermal uptake. PMID:18423910

  4. Mathematics Teachers' Use of Ethnomathematics Approach in Mathematics Teaching in Edo State

    ERIC Educational Resources Information Center

    Aikpitanyi, Lucky Aiwuyor; Eraikhuemen, Lucy

    2017-01-01

    The study investigated mathematics teachers' use of ethnomathematics approach to teaching. Descriptive survey research was used with a target population of all mathematics teacher in all public secondary schools in Oredo, Egor and Ikpoba-Okha local government areas of Edo State out of which 121 mathematics teachers in 42 randomly selected public…

  5. A Descriptive Qualitative Study Exploring Teacher and Parental Perceptions of African-American Middle School Male Students Related to Mathematics Performance

    ERIC Educational Resources Information Center

    Fowler, Crystal Nicole

    2013-01-01

    This qualitative descriptive case study explored the perceptions of parents and teachers of the academic achievement gap in mathematics between African-American middle school males and their White counterparts. Ten parents, both African-American and White, with students attending middle school in the Cherokee County School District and 5 teachers…

  6. The Mathematical Sciences: A Report.

    ERIC Educational Resources Information Center

    National Academy of Sciences, Washington, DC.

    Presented are position statements for the support of the mathematical sciences and a description of the present state of both research and education in mathematics and related disciplines. The report calls attention to the penetration of mathematics and mathematical modes of thought into many new areas of scholarship and the resultant increase in…

  7. Teaching Mathematics as Agape

    ERIC Educational Resources Information Center

    Amidon, Joel C.

    2011-01-01

    What happens when the problem of inequitable access to mathematics is addressed by agape (pronounced agapa) or attending to the relationships students develop with mathematics? To respond to this question, this paper offers a description of the journey towards teaching mathematics as agape. First, I organized examples of equity pedagogy around the…

  8. The written mathematical communication profile of prospective math teacher in mathematical proving

    NASA Astrophysics Data System (ADS)

    Pantaleon, K. V.; Juniati, D.; Lukito, A.; Mandur, K.

    2018-01-01

    Written mathematical communication is the process of expressing mathematical ideas and understanding in writing. It is one of the important aspects that must be mastered by the prospective math teacher as tool of knowledge transfer. This research was a qualitative research that aimed to describe the mathematical communication profile of the prospective mathematics teacher in mathematical proving. This research involved 48 students of Mathematics Education Study Program; one of them with moderate math skills was chosen as the main subject. Data were collected through tests, assignments, and task-based interviews. The results of this study point out that in the proof of geometry, the subject explains what is understood, presents the idea in the form of drawing and symbols, and explains the content/meaning of a representation accurately and clearly, but the subject can not convey the argument systematically and logically. Whereas in the proof of algebra, the subject describes what is understood, explains the method used, and describes the content/meaning of a symbolic representation accurately, systematically, logically, but the argument presented is not clear because it is insufficient detailed and complete.

  9. Mathematical and Numerical Techniques in Energy and Environmental Modeling

    NASA Astrophysics Data System (ADS)

    Chen, Z.; Ewing, R. E.

    Mathematical models have been widely used to predict, understand, and optimize many complex physical processes, from semiconductor or pharmaceutical design to large-scale applications such as global weather models to astrophysics. In particular, simulation of environmental effects of air pollution is extensive. Here we address the need for using similar models to understand the fate and transport of groundwater contaminants and to design in situ remediation strategies. Three basic problem areas need to be addressed in the modeling and simulation of the flow of groundwater contamination. First, one obtains an effective model to describe the complex fluid/fluid and fluid/rock interactions that control the transport of contaminants in groundwater. This includes the problem of obtaining accurate reservoir descriptions at various length scales and modeling the effects of this heterogeneity in the reservoir simulators. Next, one develops accurate discretization techniques that retain the important physical properties of the continuous models. Finally, one develops efficient numerical solution algorithms that utilize the potential of the emerging computing architectures. We will discuss recent advances and describe the contribution of each of the papers in this book in these three areas. Keywords: reservoir simulation, mathematical models, partial differential equations, numerical algorithms

  10. Mathematical, Constitutive and Numerical Modelling of Catastrophic Landslides and Related Phenomena

    NASA Astrophysics Data System (ADS)

    Pastor, M.; Fernández Merodo, J. A.; Herreros, M. I.; Mira, P.; González, E.; Haddad, B.; Quecedo, M.; Tonni, L.; Drempetic, V.

    2008-02-01

    Mathematical and numerical models are a fundamental tool for predicting the behaviour of geostructures and their interaction with the environment. The term “mathematical model” refers to a mathematical description of the more relevant physical phenomena which take place in the problem being analyzed. It is indeed a wide area including models ranging from the very simple ones for which analytical solutions can be obtained to those more complicated requiring the use of numerical approximations such as the finite element method. During the last decades, mathematical, constitutive and numerical models have been very much improved and today their use is widespread both in industry and in research. One special case is that of fast catastrophic landslides, for which simplified methods are not able to provide accurate solutions in many occasions. Moreover, many finite element codes cannot be applied for propagation of the mobilized mass. The purpose of this work is to present an overview of the different alternative mathematical and numerical models which can be applied to both the initiation and propagation mechanisms of fast catastrophic landslides and other related problems such as waves caused by landslides.

  11. Mathematical String Sculptures: A Case Study in Computationally-Enhanced Mathematical Crafts

    ERIC Educational Resources Information Center

    Eisenberg, Michael

    2007-01-01

    Mathematical string sculptures constitute an extremely beautiful realm of mathematical crafts. This snapshot begins with a description of a marvelous (and no longer manufactured) toy called Space Spider, which provided a framework with which children could experiment with string sculptures. Using a computer-controlled laser cutter to create frames…

  12. Description and Application of a Mathematical Method for the Analysis of Harmony

    PubMed Central

    Zuo, Qiting; Jin, Runfang; Ma, Junxia

    2015-01-01

    Harmony issues are widespread in human society and nature. To analyze these issues, harmony theory has been proposed as the main theoretical approach for the study of interpersonal relationships and relationships between humans and nature. Therefore, it is of great importance to study harmony theory. After briefly introducing the basic concepts of harmony theory, this paper expounds the five elements that are essential for the quantitative description of harmony issues in water resources management: harmony participant, harmony objective, harmony regulation, harmony factor, and harmony action. A basic mathematical equation for the harmony degree, that is, a quantitative expression of harmony issues, is introduced in the paper: HD = ai − bj, where a is the uniform degree, b is the difference degree, i is the harmony coefficient, and j is the disharmony coefficient. This paper also discusses harmony assessment and harmony regulation and introduces some application examples. PMID:26167535

  13. Deadline rush: a time management phenomenon and its mathematical description.

    PubMed

    König, Cornelius J; Kleinmann, Martin

    2005-01-01

    A typical time management phenomenon is the rush before a deadline. Behavioral decision making research can be used to predict how behavior changes before a deadline. People are likely not to work on a project with a deadline in the far future because they generally discount future outcomes. Only when the deadline is close are people likely to work. On the basis of recent intertemporal choice experiments, the authors argue that a hyperbolic function should provide a more accurate description of the deadline rush than an exponential function predicted by an economic model of discounted utility. To show this, the fit of the hyperbolic and the exponential function were compared with data sets that describe when students study for exams. As predicted, the hyperbolic function fit the data significantly better than the exponential function. The implication for time management decisions is that they are most likely to be inconsistent over time (i.e., people make a plan how to use their time but do not follow it).

  14. The Nature of Mathematics Anxiety.

    ERIC Educational Resources Information Center

    Cemen, Pamala Byrd

    This paper attempts to generate a comprehensive description of the nature of mathematics anxiety through a synthesis of: (1) the general and test anxiety literatures applied to mathematics anxiety; (2) the mathematics anxiety literature, and (3) case studies developed through in-depth interviews. The indepth interviews were conducted with seven…

  15. Student Perceptions about Applied Mathematics.

    ERIC Educational Resources Information Center

    Keif, Malcolm G.; Stewart, Bob R.

    Background information on the history and rationale for Tech Prep introduces the description of a study that examines the perceptions of students enrolled in Applied Mathematics 1 and Applied Mathematics 2 courses which are based on the Center for Occupational Research and Development's (CORD) applied mathematics curriculum. The primary goal is to…

  16. The X3LYP extended density functional for accurate descriptions of nonbond interactions, spin states, and thermochemical properties

    PubMed Central

    Xu, Xin; Goddard, William A.

    2004-01-01

    We derive the form for an exact exchange energy density for a density decaying with Gaussian-like behavior at long range. Based on this, we develop the X3LYP (extended hybrid functional combined with Lee–Yang–Parr correlation functional) extended functional for density functional theory to significantly improve the accuracy for hydrogen-bonded and van der Waals complexes while also improving the accuracy in heats of formation, ionization potentials, electron affinities, and total atomic energies [over the most popular and accurate method, B3LYP (Becke three-parameter hybrid functional combined with Lee–Yang–Parr correlation functional)]. X3LYP also leads to a good description of dipole moments, polarizabilities, and accurate excitation energies from s to d orbitals for transition metal atoms and ions. We suggest that X3LYP will be useful for predicting ligand binding in proteins and DNA. PMID:14981235

  17. Current problems in applied mathematics and mathematical physics

    NASA Astrophysics Data System (ADS)

    Samarskii, A. A.

    Papers are presented on such topics as mathematical models in immunology, mathematical problems of medical computer tomography, classical orthogonal polynomials depending on a discrete variable, and boundary layer methods for singular perturbation problems in partial derivatives. Consideration is also given to the computer simulation of supernova explosion, nonstationary internal waves in a stratified fluid, the description of turbulent flows by unsteady solutions of the Navier-Stokes equations, and the reduced Galerkin method for external diffraction problems using the spline approximation of fields.

  18. The Emergence of Objects from Mathematical Practices

    ERIC Educational Resources Information Center

    Font, Vicenc; Godino, Juan D.; Gallardo, Jesus

    2013-01-01

    The nature of mathematical objects, their various types, the way in which they are formed, and how they participate in mathematical activity are all questions of interest for philosophy and mathematics education. Teaching in schools is usually based, implicitly or explicitly, on a descriptive/realist view of mathematics, an approach which is not…

  19. Internet Connections to Mathematics Education.

    ERIC Educational Resources Information Center

    Day, Roger

    1995-01-01

    Presents Internet connections appropriate for mathematics education; provides descriptions of ways that mathematics educators can access electronic resources such as e-mail, discussion groups, gopher servers, and transfer of files; and provides hints and examples from classroom connections and professional applications. (18 references) (Author/MKR)

  20. Goddard trajectory determination subsystem: Mathematical specifications

    NASA Technical Reports Server (NTRS)

    Wagner, W. E. (Editor); Velez, C. E. (Editor)

    1972-01-01

    The mathematical specifications of the Goddard trajectory determination subsystem of the flight dynamics system are presented. These specifications include the mathematical description of the coordinate systems, dynamic and measurement model, numerical integration techniques, and statistical estimation concepts.

  1. Problem-solving rubrics revisited: Attending to the blending of informal conceptual and formal mathematical reasoning

    NASA Astrophysics Data System (ADS)

    Hull, Michael M.; Kuo, Eric; Gupta, Ayush; Elby, Andrew

    2013-06-01

    Much research in engineering and physics education has focused on improving students’ problem-solving skills. This research has led to the development of step-by-step problem-solving strategies and grading rubrics to assess a student’s expertise in solving problems using these strategies. These rubrics value “communication” between the student’s qualitative description of the physical situation and the student’s formal mathematical descriptions (usually equations) at two points: when initially setting up the equations, and when evaluating the final mathematical answer for meaning and plausibility. We argue that (i) neither the rubrics nor the associated problem-solving strategies explicitly value this kind of communication during mathematical manipulations of the chosen equations, and (ii) such communication is an aspect of problem-solving expertise. To make this argument, we present a case study of two students, Alex and Pat, solving the same kinematics problem in clinical interviews. We argue that Pat’s solution, which connects manipulation of equations to their physical interpretation, is more expertlike than Alex’s solution, which uses equations more algorithmically. We then show that the types of problem-solving rubrics currently available do not discriminate between these two types of solutions. We conclude that problem-solving rubrics should be revised or repurposed to more accurately assess problem-solving expertise.

  2. Improving students’ mathematical representational ability through RME-based progressive mathematization

    NASA Astrophysics Data System (ADS)

    Warsito; Darhim; Herman, T.

    2018-01-01

    This study aims to determine the differences in the improving of mathematical representation ability based on progressive mathematization with realistic mathematics education (PMR-MP) with conventional learning approach (PB). The method of research is quasi-experiments with non-equivalent control group designs. The study population is all students of class VIII SMPN 2 Tangerang consisting of 6 classes, while the sample was taken two classes with purposive sampling technique. The experimental class is treated with PMR-MP while the control class is treated with PB. The instruments used are test of mathematical representation ability. Data analysis was done by t-test, ANOVA test, post hoc test, and descriptive analysis. The result of analysis can be concluded that: 1) there are differences of mathematical representation ability improvement between students treated by PMR-MP and PB, 2) no interaction between learning approach (PMR-MP, PB) and prior mathematics knowledge (PAM) to improve students’ mathematical representation; 3) Students’ mathematical representation improvement in the level of higher PAM is better than medium, and low PAM students. Thus, based on the process of mathematization, it is very important when the learning direction of PMR-MP emphasizes on the process of building mathematics through a mathematical model.

  3. A knowledge-based potential with an accurate description of local interactions improves discrimination between native and near-native protein conformations.

    PubMed

    Ferrada, Evandro; Vergara, Ismael A; Melo, Francisco

    2007-01-01

    The correct discrimination between native and near-native protein conformations is essential for achieving accurate computer-based protein structure prediction. However, this has proven to be a difficult task, since currently available physical energy functions, empirical potentials and statistical scoring functions are still limited in achieving this goal consistently. In this work, we assess and compare the ability of different full atom knowledge-based potentials to discriminate between native protein structures and near-native protein conformations generated by comparative modeling. Using a benchmark of 152 near-native protein models and their corresponding native structures that encompass several different folds, we demonstrate that the incorporation of close non-bonded pairwise atom terms improves the discriminating power of the empirical potentials. Since the direct and unbiased derivation of close non-bonded terms from current experimental data is not possible, we obtained and used those terms from the corresponding pseudo-energy functions of a non-local knowledge-based potential. It is shown that this methodology significantly improves the discrimination between native and near-native protein conformations, suggesting that a proper description of close non-bonded terms is important to achieve a more complete and accurate description of native protein conformations. Some external knowledge-based energy functions that are widely used in model assessment performed poorly, indicating that the benchmark of models and the specific discrimination task tested in this work constitutes a difficult challenge.

  4. Mathematics Framework, Kindergarten-Grade 12.

    ERIC Educational Resources Information Center

    Texas Education Agency, Austin.

    This publication should help educators provide a mathematics program that emphasizes productive time on task and active involvement of students in mathematics activities. The focus on problem solving is stressed. Time allotments are stated, followed by descriptions of essential elements for kindergarten through grade 8: understanding numbers and…

  5. Mathematics Teachers' Criteria of Dimension

    ERIC Educational Resources Information Center

    Ural, Alattin

    2014-01-01

    The aim of the study is to determine mathematics teachers' decisions about dimensions of the geometric figures, criteria of dimension and consistency of decision-criteria. The research is a qualitative research and the model applied in the study is descriptive method on the basis of general scanning model. 15 mathematics teachers attended the…

  6. NNLOPS accurate associated HW production

    NASA Astrophysics Data System (ADS)

    Astill, William; Bizon, Wojciech; Re, Emanuele; Zanderighi, Giulia

    2016-06-01

    We present a next-to-next-to-leading order accurate description of associated HW production consistently matched to a parton shower. The method is based on reweighting events obtained with the HW plus one jet NLO accurate calculation implemented in POWHEG, extended with the MiNLO procedure, to reproduce NNLO accurate Born distributions. Since the Born kinematics is more complex than the cases treated before, we use a parametrization of the Collins-Soper angles to reduce the number of variables required for the reweighting. We present phenomenological results at 13 TeV, with cuts suggested by the Higgs Cross section Working Group.

  7. Mathematical Description of THE Traction Characteristics of the Driving Devices at Spatial Stiffness Compensators of the Vibration Isolation Installations

    NASA Astrophysics Data System (ADS)

    Gurova, E. G.

    2016-08-01

    During the researches the mathematical description of the traction characteristics of the stiffness compensators of the vibration isolation devices, relatively of the each axis, has been done. Representation of the compensators properties considers the variable load, thereby provide the wide enough spectrum of the action of the suggested vibration isolators. The derived expressions are valid for all three axes of space at the different stiffnesses, i.e. basic basic and two compensating. The research was supported by the scholarships of Russian Federation President for young scientists №184 from 10th of March 2015.

  8. Accurate Descriptions of Hot Flow Behaviors Across β Transus of Ti-6Al-4V Alloy by Intelligence Algorithm GA-SVR

    NASA Astrophysics Data System (ADS)

    Wang, Li-yong; Li, Le; Zhang, Zhi-hua

    2016-09-01

    Hot compression tests of Ti-6Al-4V alloy in a wide temperature range of 1023-1323 K and strain rate range of 0.01-10 s-1 were conducted by a servo-hydraulic and computer-controlled Gleeble-3500 machine. In order to accurately and effectively characterize the highly nonlinear flow behaviors, support vector regression (SVR) which is a machine learning method was combined with genetic algorithm (GA) for characterizing the flow behaviors, namely, the GA-SVR. The prominent character of GA-SVR is that it with identical training parameters will keep training accuracy and prediction accuracy at a stable level in different attempts for a certain dataset. The learning abilities, generalization abilities, and modeling efficiencies of the mathematical regression model, ANN, and GA-SVR for Ti-6Al-4V alloy were detailedly compared. Comparison results show that the learning ability of the GA-SVR is stronger than the mathematical regression model. The generalization abilities and modeling efficiencies of these models were shown as follows in ascending order: the mathematical regression model < ANN < GA-SVR. The stress-strain data outside experimental conditions were predicted by the well-trained GA-SVR, which improved simulation accuracy of the load-stroke curve and can further improve the related research fields where stress-strain data play important roles, such as speculating work hardening and dynamic recovery, characterizing dynamic recrystallization evolution, and improving processing maps.

  9. The Mathematics of Global Change

    ERIC Educational Resources Information Center

    Kreith, Kurt

    2011-01-01

    This paper is a descriptive and preliminary report on recent efforts to address two questions: 1) Can school mathematics be used to enhance our students' ability to understand their changing world? and 2) What role might computer technology play in this regard? After recounting some of the mathematical tools that led to a better understanding of…

  10. Beauty as Fit: A Metaphor in Mathematics?

    ERIC Educational Resources Information Center

    Raman, Manya; Öhman, Lars-Daniel

    2013-01-01

    Beauty, which plays a central role in the practice of mathematics (Sinclair 2002), is almost absent in discussions of school mathematics (Dreyfus and Eisenberg 1986). This is problematic, because students will decide whether or not to continue their studies in mathematics without having an accurate picture of what the subject is about. In order to…

  11. Descriptions of Free and Freeware Software in the Mathematics Teaching

    NASA Astrophysics Data System (ADS)

    Antunes de Macedo, Josue; Neves de Almeida, Samara; Voelzke, Marcos Rincon

    2016-05-01

    This paper presents the analysis and the cataloging of free and freeware mathematical software available on the internet, a brief explanation of them, and types of licenses for use in teaching and learning. The methodology is based on the qualitative research. Among the different types of software found, it stands out in algebra, the Winmat, that works with linear algebra, matrices and linear systems. In geometry, the GeoGebra, which can be used in the study of functions, plan and spatial geometry, algebra and calculus. For graphing, can quote the Graph and Graphequation. With Graphmatica software, it is possible to build various graphs of mathematical equations on the same screen, representing cartesian equations, inequalities, parametric among other functions. The Winplot allows the user to build graphics in two and three dimensions functions and mathematical equations. Thus, this work aims to present the teachers some free math software able to be used in the classroom.

  12. A HALF CENTURY OF TEACHING SCIENCE AND MATHEMATICS.

    ERIC Educational Resources Information Center

    ISENBARGER, KATHARINE U.; AND OTHERS

    MAJOR DEVELOPMENTS IN SCIENCE AND MATHEMATICS EDUCATION DURING THE PERIOD 1900-50 ARE REVIEWED. AN EARLY CHAPTER IS DEVOTED TO A DETAILED DESCRIPTION OF THE FORMATION AND SUBSEQUENT DEVELOPMENT OF THE CENTRAL ASSOCIATION OF SCHOOL SCIENCE AND MATHEMATICS TEACHERS AND THE JOURNAL, "SCHOOL SCIENCE AND MATHEMATICS." OTHER SECTIONS INCLUDE (1)…

  13. From The Cover: The X3LYP extended density functional for accurate descriptions of nonbond interactions, spin states, and thermochemical properties.

    PubMed

    Xu, Xin; Goddard, William A

    2004-03-02

    We derive the form for an exact exchange energy density for a density decaying with Gaussian-like behavior at long range. Based on this, we develop the X3LYP (extended hybrid functional combined with Lee-Yang-Parr correlation functional) extended functional for density functional theory to significantly improve the accuracy for hydrogen-bonded and van der Waals complexes while also improving the accuracy in heats of formation, ionization potentials, electron affinities, and total atomic energies [over the most popular and accurate method, B3LYP (Becke three-parameter hybrid functional combined with Lee-Yang-Parr correlation functional)]. X3LYP also leads to a good description of dipole moments, polarizabilities, and accurate excitation energies from s to d orbitals for transition metal atoms and ions. We suggest that X3LYP will be useful for predicting ligand binding in proteins and DNA.

  14. From The Cover: The X3LYP extended density functional for accurate descriptions of nonbond interactions, spin states, and thermochemical properties

    NASA Astrophysics Data System (ADS)

    Xu, Xin; Goddard, William A., III

    2004-03-01

    We derive the form for an exact exchange energy density for a density decaying with Gaussian-like behavior at long range. Based on this, we develop the X3LYP (extended hybrid functional combined with Lee-Yang-Parr correlation functional) extended functional for density functional theory to significantly improve the accuracy for hydrogen-bonded and van der Waals complexes while also improving the accuracy in heats of formation, ionization potentials, electron affinities, and total atomic energies [over the most popular and accurate method, B3LYP (Becke three-parameter hybrid functional combined with Lee-Yang-Parr correlation functional)]. X3LYP also leads to a good description of dipole moments, polarizabilities, and accurate excitation energies from s to d orbitals for transition metal atoms and ions. We suggest that X3LYP will be useful for predicting ligand binding in proteins and DNA.

  15. Science, technology, engineering, mathematics (STEM) as mathematics learning approach in 21st century

    NASA Astrophysics Data System (ADS)

    Milaturrahmah, Naila; Mardiyana, Pramudya, Ikrar

    2017-08-01

    This 21st century demands competent human resources in science, technology, engineering design and mathematics so that education is expected to integrate the four disciplines. This paper aims to describe the importance of STEM as mathematics learning approach in Indonesia in the 21st century. This paper uses a descriptive analysis research method, and the method reveals that STEM education growing in developed countries today can be a framework for innovation mathematics in Indonesia in the 21st century. STEM education integrate understanding of science, math skills, and the available technology with the ability to perform engineering design process. Implementation of mathematics learning with STEM approach makes graduates trained in using of mathematics knowledge that they have to create innovative products that are able to solve the problems that exist in society.

  16. Assessing Senior Secondary School Students' Mathematical Proficiency as Related to Gender and Performance in Mathematics in Nigeria

    ERIC Educational Resources Information Center

    Awofala, Adeneye O. A.

    2017-01-01

    The study investigated mathematical proficiency as related to gender and performance in mathematics among 400 Nigerian senior secondary school students from 10 elitist senior secondary schools in Lagos State using the quantitative research method within the blueprint of descriptive survey design. Data collected were analysed using the descriptive…

  17. Assessing Preservice Teachers' Mathematics Cognitive Failures as Related to Mathematics Anxiety and Performance in Undergraduate Calculus

    ERIC Educational Resources Information Center

    Awofala, Adeneye O. A.; Odogwu, Helen N.

    2017-01-01

    The study investigated mathematics cognitive failures as related to mathematics anxiety, gender and performance in calculus among 450 preservice teachers from four public universities in the South West geo-political zone of Nigeria using the quantitative research method within the blueprint of the descriptive survey design. Data collected were…

  18. Neuroscience from a mathematical perspective: key concepts, scales and scaling hypothesis, universality.

    PubMed

    van Hemmen, J Leo

    2014-10-01

    This article analyzes the question of whether neuroscience allows for mathematical descriptions and whether an interaction between experimental and theoretical neuroscience can be expected to benefit both of them. It is argued that a mathematization of natural phenomena never happens by itself. First, appropriate key concepts must be found that are intimately connected with the phenomena one wishes to describe and explain mathematically. Second, the scale on, and not beyond, which a specific description can hold must be specified. Different scales allow for different conceptual and mathematical descriptions. This is the scaling hypothesis. Third, can a mathematical description be universally valid and, if so, how? Here we put forth the argument that universals also exist in theoretical neuroscience, that evolution proves the rule, and that theoretical neuroscience is a domain with still lots of space for new developments initiated by an intensive interaction with experiment. Finally, major insight is provided by a careful analysis of the way in which particular brain structures respond to perceptual input and in so doing induce action in an animal's surroundings.

  19. Relating Difficulty in School Mathematics to Nature of Mathematics: Perception of High School Students from Kerala

    ERIC Educational Resources Information Center

    Gafoor, Kunnathodi Abdul; Sarabi, M. K.

    2015-01-01

    This study relates factors in nature of Mathematics and its teaching learning to student difficulties for diverse mathematics tasks. Descriptive survey was done on a sample of 300 high school students in Kerala with a questionnaire on difficulties in learning. Student perception of difficulty on 26 types of tasks, under five heads that students…

  20. The Definition of Mathematics: Philosophical and Pedagogical Aspects

    ERIC Educational Resources Information Center

    Khait, Alexander

    2005-01-01

    There is a strange fact that many works written with the purpose to explain what is mathematics, somehow avoid the issue. This paper is aimed at filling this gap. After discussing various descriptions of mathematics as they appear in literature, it is suggested that mathematics is an essentially linguistic activity characterized by association of…

  1. Computer-Game-Based Tutoring of Mathematics

    ERIC Educational Resources Information Center

    Ke, Fengfeng

    2013-01-01

    This in-situ, descriptive case study examined the potential of implementing computer mathematics games as an anchor for tutoring of mathematics. Data were collected from middle school students at a rural pueblo school and an urban Hispanic-serving school, through in-field observation, content analysis of game-based tutoring-learning interactions,…

  2. Secondary School Mathematics Curriculum Improvement Study.

    ERIC Educational Resources Information Center

    Secondary School Mathematics Curriculum Improvement Study, New York, NY.

    This bulletin contains: (1) a summary and conclusions of a study of mathematics curricula in Europe and Japan, and (2) a description of beginning efforts to evaluate the Secondary School Mathematics Curriculum Improvement Study (SSMCIS) project. Some of the conclusions of the European and Japanese study are: (1) the study of Euclidean synthetic…

  3. Science and Mathematics

    ERIC Educational Resources Information Center

    Redlich, Otto

    1972-01-01

    The foundation of science, and of thermodynamics in particular, can be developed cogently and without arbitrariness. The goal of science, description of nature, is externally given; it requires a set of basic concepts as indispensable tools. Mathematics has no similar externally given goal. (Author/TS)

  4. A Cognitive Analysis of Students’ Mathematical Communication Ability on Geometry

    NASA Astrophysics Data System (ADS)

    Sari, D. S.; Kusnandi, K.; Suhendra, S.

    2017-09-01

    This study aims to analyze the difficulties of mathematical communication ability of students in one of secondary school on “three-dimensional space” topic. This research conducted by using quantitative approach with descriptive method. The population in this research was all students of that school and the sample was thirty students that was chosen by purposive sampling technique. Data of mathematical communication were collected through essay test. Furthermore, the data were analyzed with a descriptive way. The results of this study indicate that the percentage of achievement of student mathematical communication indicators as follows 1) Stating a situation, ideas, and mathematic correlation into images, graphics, or algebraic expressions is 35%; 2) Stating daily experience into a mathematic language / symbol, or a mathematic model is 35%; and 3) Associating images or diagrams into mathematical ideas is 53.3%. Based on the percentage of achievement on each indicator, it can be concluded that the level of achievement of students’ mathematical communication ability is still low. It can be caused the students were not used to convey or write their mathematical ideas systematically. Therefore students’ mathematical communication ability need to be improved.

  5. The Effect of German and Turkish Mathematics Teachers' Teaching Experience on Mathematics Education Values: A Cross-Comparative Study

    ERIC Educational Resources Information Center

    Dede, Yuksel

    2013-01-01

    This study reported the specific findings of a larger comparative study concerning Turkish and German mathematics teachers' values. The main focus was on the teaching experience of the mathematics teachers. Interactions related to nationality were also of interest. The research methodology employed in this study was a descriptive study. The…

  6. Applied mathematical problems in modern electromagnetics

    NASA Astrophysics Data System (ADS)

    Kriegsman, Gregory

    1994-05-01

    We have primarily investigated two classes of electromagnetic problems. The first contains the quantitative description of microwave heating of dispersive and conductive materials. Such problems arise, for example, when biological tissue are exposed, accidentally or purposefully, to microwave radiation. Other instances occur in ceramic processing, such as sintering and microwave assisted chemical vapor infiltration and other industrial drying processes, such as the curing of paints and concrete. The second class characterizes the scattering of microwaves by complex targets which possess two or more disparate length and/or time scales. Spatially complex scatterers arise in a variety of applications, such as large gratings and slowly changing guiding structures. The former are useful in developing microstrip energy couplers while the later can be used to model anatomical subsystems (e.g., the open guiding structure composed of two legs and the adjoining lower torso). Temporally complex targets occur in applications involving dispersive media whose relaxation times differ by orders of magnitude from thermal and/or electromagnetic time scales. For both cases the mathematical description of the problems gives rise to complicated ill-conditioned boundary value problems, whose accurate solutions require a blend of both asymptotic techniques, such as multiscale methods and matched asymptotic expansions, and numerical methods incorporating radiation boundary conditions, such as finite differences and finite elements.

  7. Social media enhances languages differentiation: a mathematical description.

    PubMed

    Vidal-Franco, Ignacio; Guiu-Souto, Jacobo; Muñuzuri, Alberto P

    2017-05-01

    Understanding and predicting the evolution of competing languages is a topic of high interest in a world with more than 6000 languages competing in a highly connected environment. We consider a reasonable mathematical model describing a situation of competition between two languages and analyse the effect of the speakers' connectivity (i.e. social networks). Surprisingly, instead of homogenizing the system, a high degree of connectivity helps to introduce differentiation for the appropriate parameters.

  8. Mathematical model of rolling an elastic wheel over deformable support base

    NASA Astrophysics Data System (ADS)

    Volskaia, V. N.; Zhileykin, M. M.; Zakharov, A. Y.

    2018-02-01

    to provide the most accurate description of the interaction process of a wheeled propulsion devices and the ground, also this method allows to define tension in the ground, deformation of the ground and the tire and ground’s compression. However, the high laboriousness of computations is essential shortcoming of that method therefore it’s hard to use these models as part of the general motion model of multi-axis wheeled vehicles. The purpose of this research is the elaboration of mathematical model of elastic wheel rolling over deformable rough support base taking into account the contact patch deformation. The mathematical model of rectilinear rolling an elastic wheel over rough deformable support base, taking into account variation of contact patch area and variation in the direction of the radial and tangential reactions also load bearing capacity of the ground, is developed. The efficiency of developed mathematical model of rectilinear rolling an elastic wheel over rough deformable support base is proved by the simulation methods.

  9. On the Role of Mathematics in Physics

    ERIC Educational Resources Information Center

    Quale, Andreas

    2011-01-01

    I examine the association between the observable physical world and the mathematical models of theoretical physics. These models will exhibit many entities that have no counterpart in the physical world, but which are still necessary for the mathematical description of physical systems. Moreover, when the model is applied to the analysis of a…

  10. A domain-knowledge-inspired mathematical framework for the description and classification of H&E stained histopathology images.

    PubMed

    Massar, Melody L; Bhagavatula, Ramamurthy; Ozolek, John A; Castro, Carlos A; Fickus, Matthew; Kovačević, Jelena

    2011-10-19

    We present the current state of our work on a mathematical framework for identification and delineation of histopathology images-local histograms and occlusion models. Local histograms are histograms computed over defined spatial neighborhoods whose purpose is to characterize an image locally. This unit of description is augmented by our occlusion models that describe a methodology for image formation. In the context of this image formation model, the power of local histograms with respect to appropriate families of images will be shown through various proved statements about expected performance. We conclude by presenting a preliminary study to demonstrate the power of the framework in the context of histopathology image classification tasks that, while differing greatly in application, both originate from what is considered an appropriate class of images for this framework.

  11. Mathematical Rigor vs. Conceptual Change: Some Early Results

    NASA Astrophysics Data System (ADS)

    Alexander, W. R.

    2003-05-01

    Results from two different pedagogical approaches to teaching introductory astronomy at the college level will be presented. The first of these approaches is a descriptive, conceptually based approach that emphasizes conceptual change. This descriptive class is typically an elective for non-science majors. The other approach is a mathematically rigorous treatment that emphasizes problem solving and is designed to prepare students for further study in astronomy. The mathematically rigorous class is typically taken by science majors. It also fulfills an elective science requirement for these science majors. The Astronomy Diagnostic Test version 2 (ADT 2.0) was used as an assessment instrument since the validity and reliability have been investigated by previous researchers. The ADT 2.0 was administered as both a pre-test and post-test to both groups. Initial results show no significant difference between the two groups in the post-test. However, there is a slightly greater improvement for the descriptive class between the pre and post testing compared to the mathematically rigorous course. There was great care to account for variables. These variables included: selection of text, class format as well as instructor differences. Results indicate that the mathematically rigorous model, doesn't improve conceptual understanding any better than the conceptual change model. Additional results indicate that there is a similar gender bias in favor of males that has been measured by previous investigators. This research has been funded by the College of Science and Mathematics at James Madison University.

  12. Humanize Your Classroom with the History of Mathematics.

    ERIC Educational Resources Information Center

    Bidwell, James K.

    1993-01-01

    History humanizes mathematics and explains the "whys" by showing its logical development. Communicating, connecting, and valuing of mathematics can be effected by interjecting historical moments, reading biographies, creating displays for the classroom, and tracing historically accurate developments of topics in class. (Contains 26…

  13. Mathematics Education and the Objectivist Programme in HPS

    ERIC Educational Resources Information Center

    Glas, Eduard

    2013-01-01

    Using history of mathematics for studying concepts, methods, problems and other internal features of the discipline may give rise to a certain tension between descriptive adequacy and educational demands. Other than historians, educators are concerned with mathematics as a "normatively defined" discipline. Teaching cannot but be based on a…

  14. On accurate determination of contact angle

    NASA Technical Reports Server (NTRS)

    Concus, P.; Finn, R.

    1992-01-01

    Methods are proposed that exploit a microgravity environment to obtain highly accurate measurement of contact angle. These methods, which are based on our earlier mathematical results, do not require detailed measurement of a liquid free-surface, as they incorporate discontinuous or nearly-discontinuous behavior of the liquid bulk in certain container geometries. Physical testing is planned in the forthcoming IML-2 space flight and in related preparatory ground-based experiments.

  15. Science modelling in pre-calculus: how to make mathematics problems contextually meaningful

    NASA Astrophysics Data System (ADS)

    Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

    2011-04-01

    of computer-based science simulations. Although there are several exceptional computer-based science simulations designed for mathematics classes (see, e.g. Kinetic Book (http://www.kineticbooks.com/) or Gizmos (http://www.explorelearning.com/)), we concentrate mainly on the PhET Interactive Simulations developed at the University of Colorado at Boulder (http://phet.colorado.edu/) in generating our argument that computer simulations more accurately represent the contextual characteristics of scientific phenomena than their textual descriptions.

  16. Towards a more accurate microscopic description of the moving contact line problem - incorporating nonlocal effects through a statistical mechanics framework

    NASA Astrophysics Data System (ADS)

    Nold, Andreas; Goddard, Ben; Sibley, David; Kalliadasis, Serafim

    2014-03-01

    Multiscale effects play a predominant role in wetting phenomena such as the moving contact line. An accurate description is of paramount interest for a wide range of industrial applications, yet it is a matter of ongoing research, due to the difficulty of incorporating different physical effects in one model. Important small-scale phenomena are corrections to the attractive fluid-fluid and wall-fluid forces in inhomogeneous density distributions, which often previously have been accounted for by the disjoining pressure in an ad-hoc manner. We systematically derive a novel model for the description of a single-component liquid-vapor multiphase system which inherently incorporates these nonlocal effects. This derivation, which is inspired by statistical mechanics in the framework of colloidal density functional theory, is critically discussed with respect to its assumptions and restrictions. The model is then employed numerically to study a moving contact line of a liquid fluid displacing its vapor phase. We show how nonlocal physical effects are inherently incorporated by the model and describe how classical macroscopic results for the contact line motion are retrieved. We acknowledge financial support from ERC Advanced Grant No. 247031 and Imperial College through a DTG International Studentship.

  17. Mathematics and academic diversity in Japan.

    PubMed

    Woodward, John; Ono, Yumiko

    2004-01-01

    Japanese education has been the subject of considerable research and educational commentary in the United States over the last 20 years. Since the early 1990s, there has been increased interest in Japanese methods for teaching mathematics, and the Third International Mathematics and Science Study has accelerated American interest in Japanese methods. Observational studies, teacher and student surveys, and analyses of classroom videotapes have provided a rich picture of how the Japanese teach the whole class. However, little has been written about how academically low-achieving math students fare in Japanese schools. This article briefly summarizes Japanese methods for teaching mathematics and describes how the educational system addresses academic diversity. It concludes with a description of a method for teaching mathematics that some Japanese mathematics educators feel has promise for students with learning disabilities.

  18. Tools for Accurate and Efficient Analysis of Complex Evolutionary Mechanisms in Microbial Genomes. Final Report

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Nakhleh, Luay

    I proposed to develop computationally efficient tools for accurate detection and reconstruction of microbes' complex evolutionary mechanisms, thus enabling rapid and accurate annotation, analysis and understanding of their genomes. To achieve this goal, I proposed to address three aspects. (1) Mathematical modeling. A major challenge facing the accurate detection of HGT is that of distinguishing between these two events on the one hand and other events that have similar "effects." I proposed to develop a novel mathematical approach for distinguishing among these events. Further, I proposed to develop a set of novel optimization criteria for the evolutionary analysis of microbialmore » genomes in the presence of these complex evolutionary events. (2) Algorithm design. In this aspect of the project, I proposed to develop an array of e cient and accurate algorithms for analyzing microbial genomes based on the formulated optimization criteria. Further, I proposed to test the viability of the criteria and the accuracy of the algorithms in an experimental setting using both synthetic as well as biological data. (3) Software development. I proposed the nal outcome to be a suite of software tools which implements the mathematical models as well as the algorithms developed.« less

  19. Profile of Metacognition of Mathematics and Mathematics Education Students in Understanding the Concept of Integral Calculus

    NASA Astrophysics Data System (ADS)

    Misu, La; Ketut Budayasa, I.; Lukito, Agung

    2018-03-01

    This study describes the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. The metacognition profile is a natural and intact description of a person’s cognition that involves his own thinking in terms of using his knowledge, planning and monitoring his thinking process, and evaluating his thinking results when understanding a concept. The purpose of this study was to produce the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. This research method is explorative method with the qualitative approach. The subjects of this study are mathematics and mathematics education students who have studied integral calculus. The results of this study are as follows: (1) the summarizing category, the mathematics and mathematics education students can use metacognition knowledge and metacognition skills in understanding the concept of indefinite integrals. While the definite integrals, only mathematics education students use metacognition skills; and (2) the explaining category, mathematics students can use knowledge and metacognition skills in understanding the concept of indefinite integrals, while the definite integrals only use metacognition skills. In addition, mathematics education students can use knowledge and metacognition skills in understanding the concept of both indefinite and definite integrals.

  20. Improving accessibility to mathematical formulas: the Wikipedia Math Accessor

    NASA Astrophysics Data System (ADS)

    Fuentes Sepúlveda, J.; Ferres, L.

    2012-09-01

    Mathematics accessibility is an important topic for inclusive education. In this paper, we make Wikipedia's repository of mathematical formulas accessible by providing a natural language description of its more than 420,000 formulas using a well-researched sub-language. We also contribute by targeting Spanish speakers, for whom assistive technologies, particularly domain-specific technologies like the one described here, are scarce. Our focus on the semantics of formulas (rather than their visual appearance) allowed us to generate verbalizations with a precision of approximately 80% of understandable descriptions, as shown in an evaluation with sighted users.

  1. Learning to Solve Story Problems--Supporting Transitions between Reality and Mathematics

    ERIC Educational Resources Information Center

    Große, Cornelia S.

    2014-01-01

    Applying mathematics to real problems is increasingly emphasized in school education; however, it is often complained that many students are not able to solve mathematical problems embedded in contexts. In order to solve story problems, a transition from a textual description to a mathematical notation has to be found, intra-mathematical…

  2. Assessment Mathematics Teacher's Competencies

    ERIC Educational Resources Information Center

    Alnoor, A. G.; Yuanxiang, Guo; Abudhuim, F. S.

    2007-01-01

    This paper aimed to identifying the professional efficiencies for the intermediate schools mathematics teachers and tries to know at what level the math teachers experience those competencies. The researcher used a descriptive research approach, the study data collected from specialist educators and teacher's experts and previous studies to…

  3. Indicators that influence prospective mathematics teachers representational and reasoning abilities

    NASA Astrophysics Data System (ADS)

    Darta; Saputra, J.

    2018-01-01

    Representational and mathematical reasoning ability are very important ability as basic in mathematics learning process. The 2013 curriculum suggests that the use of a scientific approach emphasizes higher order thinking skills. Therefore, a scientific approach is required in mathematics learning to improve ability of representation and mathematical reasoning. The objectives of this research are: (1) to analyze representational and reasoning abilities, (2) to analyze indicators affecting the ability of representation and mathematical reasoning, (3) to analyze scientific approaches that can improve the ability of representation and mathematical reasoning. The subject of this research is the students of mathematics prospective teachers in the first semester at Private Higher Education of Bandung City. The research method of this research was descriptive analysis. The research data were collected using reasoning and representation tests on sixty-one students. Data processing was done by descriptive analysis specified based on the indicators of representation ability and mathematical reasoning that influenced it. The results of this first-year study showed that students still had many weaknesses in reasoning and mathematical representation that were influenced by the ability to understand the indicators of both capabilities. After observing the results of the first-year research, then in the second and third year, the development of teaching materials with a scientific approach in accordance with the needs of prospective students was planned.

  4. The reasonable effectiveness of mathematics in the natural sciences

    NASA Astrophysics Data System (ADS)

    Harvey, Alex

    2011-12-01

    Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism—mathematics exists and is discovered; Logicism—all mathematics may be deduced through pure logic; Formalism—mathematics is just the manipulation of formulas and rules invented for the purpose; Intuitionism—mathematics comprises mental constructs governed by self evident rules. The debate among the several schools has major importance in understanding what Eugene Wigner called, The Unreasonable Effectiveness of Mathematics in the Natural Sciences. In return, this `Unreasonable Effectiveness' suggests a possible resolution of the debate in favor of Realism. The crucial element is the extraordinary predictive capacity of mathematical structures descriptive of physical theories.

  5. Three-dimensional description and mathematical characterization of the parasellar internal carotid artery in human infants

    PubMed Central

    Meng, Stefan; da F Costa, Luciano; Geyer, Stefan H; Viana, Matheus P; Reiter, Christian; Müller, Gerd B; Weninger, Wolfgang J

    2008-01-01

    Inside the ‘cavernous sinus’ or ‘parasellar region’ the human internal carotid artery takes the shape of a siphon that is twisted and torqued in three dimensions and surrounded by a network of veins. The parasellar section of the internal carotid artery is of broad biological and medical interest, as its peculiar shape is associated with temperature regulation in the brain and correlated with the occurrence of vascular pathologies. The present study aims to provide anatomical descriptions and objective mathematical characterizations of the shape of the parasellar section of the internal carotid artery in human infants and its modifications during ontogeny. Three-dimensional (3D) computer models of the parasellar section of the internal carotid artery of infants were generated with a state-of-the-art 3D reconstruction method and analysed using both traditional morphometric methods and novel mathematical algorithms. We show that four constant, demarcated bends can be described along the infant parasellar section of the internal carotid artery, and we provide measurements of their angles. We further provide calculations of the curvature and torsion energy, and the total complexity of the 3D skeleton of the parasellar section of the internal carotid artery, and compare the complexity of this in infants and adults. Finally, we examine the relationship between shape parameters of the parasellar section of the internal carotid artery in infants, and the occurrence of intima cushions, and evaluate the reliability of subjective angle measurements for characterizing the complexity of the parasellar section of the internal carotid artery in infants. The results can serve as objective reference data for comparative studies and for medical imaging diagnostics. They also form the basis for a new hypothesis that explains the mechanisms responsible for the ontogenetic transformation in the shape of the parasellar section of the internal carotid artery. PMID:18397239

  6. DMPy: a Python package for automated mathematical model construction of large-scale metabolic systems.

    PubMed

    Smith, Robert W; van Rosmalen, Rik P; Martins Dos Santos, Vitor A P; Fleck, Christian

    2018-06-19

    Models of metabolism are often used in biotechnology and pharmaceutical research to identify drug targets or increase the direct production of valuable compounds. Due to the complexity of large metabolic systems, a number of conclusions have been drawn using mathematical methods with simplifying assumptions. For example, constraint-based models describe changes of internal concentrations that occur much quicker than alterations in cell physiology. Thus, metabolite concentrations and reaction fluxes are fixed to constant values. This greatly reduces the mathematical complexity, while providing a reasonably good description of the system in steady state. However, without a large number of constraints, many different flux sets can describe the optimal model and we obtain no information on how metabolite levels dynamically change. Thus, to accurately determine what is taking place within the cell, finer quality data and more detailed models need to be constructed. In this paper we present a computational framework, DMPy, that uses a network scheme as input to automatically search for kinetic rates and produce a mathematical model that describes temporal changes of metabolite fluxes. The parameter search utilises several online databases to find measured reaction parameters. From this, we take advantage of previous modelling efforts, such as Parameter Balancing, to produce an initial mathematical model of a metabolic pathway. We analyse the effect of parameter uncertainty on model dynamics and test how recent flux-based model reduction techniques alter system properties. To our knowledge this is the first time such analysis has been performed on large models of metabolism. Our results highlight that good estimates of at least 80% of the reaction rates are required to accurately model metabolic systems. Furthermore, reducing the size of the model by grouping reactions together based on fluxes alters the resulting system dynamics. The presented pipeline automates the

  7. Sequentially Simulated Outcomes: Kind Experience versus Nontransparent Description

    ERIC Educational Resources Information Center

    Hogarth, Robin M.; Soyer, Emre

    2011-01-01

    Recently, researchers have investigated differences in decision making based on description and experience. We address the issue of when experience-based judgments of probability are more accurate than are those based on description. If description is well understood ("transparent") and experience is misleading ("wicked"), it…

  8. SKYMAP system description: Star catalog data base generation and utilization

    NASA Technical Reports Server (NTRS)

    Gottlieb, D. M.

    1979-01-01

    The specifications, design, software description, and use of the SKYMAP star catalog system are detailed. The SKYMAP system was developed to provide an accurate and complete catalog of all stars with blue or visual magnitudes brighter than 9.0 for use by attitude determination programs. Because of the large number of stars which are brighter than 9.0 magnitude, efficient techniques of manipulating and accessing the data were required. These techniques of staged distillation of data from a Master Catalog to a Core Catalog, and direct access of overlapping zone catalogs, form the basis of the SKYMAP system. The collection and tranformation of data required to produce the Master Catalog data base is described. The data flow through the main programs and levels of star catalogs is detailed. The mathematical and logical techniques for each program and the format of all catalogs are documented.

  9. Soft Biometrics; Human Identification Using Comparative Descriptions.

    PubMed

    Reid, Daniel A; Nixon, Mark S; Stevenage, Sarah V

    2014-06-01

    Soft biometrics are a new form of biometric identification which use physical or behavioral traits that can be naturally described by humans. Unlike other biometric approaches, this allows identification based solely on verbal descriptions, bridging the semantic gap between biometrics and human description. To permit soft biometric identification the description must be accurate, yet conventional human descriptions comprising of absolute labels and estimations are often unreliable. A novel method of obtaining human descriptions will be introduced which utilizes comparative categorical labels to describe differences between subjects. This innovative approach has been shown to address many problems associated with absolute categorical labels-most critically, the descriptions contain more objective information and have increased discriminatory capabilities. Relative measurements of the subjects' traits can be inferred from comparative human descriptions using the Elo rating system. The resulting soft biometric signatures have been demonstrated to be robust and allow accurate recognition of subjects. Relative measurements can also be obtained from other forms of human representation. This is demonstrated using a support vector machine to determine relative measurements from gait biometric signatures-allowing retrieval of subjects from video footage by using human comparisons, bridging the semantic gap.

  10. Exploring Rural High School Learners' Experience of Mathematics Anxiety in Academic Settings

    ERIC Educational Resources Information Center

    Hlalele, Dipane

    2012-01-01

    The purpose of the study was to explore rural high school learners' experience of mathematics anxiety in academic settings. Mathematics anxiety has been found to have an adverse effect on confidence, motivation and achievement. This quantitative study is exploratory and descriptive in nature. The participants were 403 learners doing mathematics in…

  11. Teaching Mathematics in Seven Countries: Results from the TIMSS 1999 Video Study.

    ERIC Educational Resources Information Center

    Hiebert, James; Gallimore, Ronald; Garnier, Helen; Givvin, Karen Bogard; Hollingsworth, Hilary; Jacobs, Jennifer; Chui, Angel Miu-Ying; Wearne, Diana; Smith, Margaret; Kersting, Nicole; Manaster, Alfred; Tseng, Ellen; Etterbeek, Wallace; Manaster, Carl; Gonzales, Patrick; Stigler, James

    This book reports teaching practices in mathematics in seven countries from the Third International Mathematics and Science Study (TIMSS) 1999 video study. A detailed description of the methods in the mathematics portion of the study is presented in an accompanying technical report from an international perspective. Contexts of the lessons, the…

  12. Can Raters with Reduced Job Descriptive Information Provide Accurate Position Analysis Questionnaire (PAQ) Ratings?

    ERIC Educational Resources Information Center

    Friedman, Lee; Harvey, Robert J.

    1986-01-01

    Job-naive raters provided with job descriptive information made Position Analysis Questionnaire (PAQ) ratings which were validated against ratings of job analysts who were also job content experts. None of the reduced job descriptive information conditions enabled job-naive raters to obtain either acceptable levels of convergent validity with…

  13. Learning to Assess and Assessing to Learn: A Descriptive Study of a District-Wide Mathematics Assessment Implementation

    ERIC Educational Resources Information Center

    Ringer, Catharina W.

    2013-01-01

    In today's mathematics education, there is an increasing emphasis on students' understanding of the mathematics set forth in standards documents such as the "Principles and Standards for School Mathematics" (National Council of Teachers of Mathematics, 2000) and, most recently, the "Common Core State Standards for Mathematics"…

  14. Factors involved in making post-performance judgments in mathematics problem-solving.

    PubMed

    García Fernández, Trinidad; Kroesbergen, Evelyn; Rodríguez Pérez, Celestino; González-Castro, Paloma; González-Pienda, Julio A

    2015-01-01

    This study examines the impact of executive functions, affective-motivational variables related to mathematics, mathematics achievement and task characteristics on fifth and sixth graders’ calibration accuracy after completing two mathematical problems. A sample of 188 students took part in the study. They were divided into two groups as function of their judgment accuracy after completing the two tasks (accurate= 79, inaccurate= 109). Differences between these groups were examined. The discriminative value of these variables to predict group membership was analyzed, as well as the effect of age, gender, and grade level. The results indicated that accurate students showed better levels of executive functioning, and more positive feelings, beliefs, and motivation related to mathematics. They also spent more time on the tasks. Mathematics achievement, perceived usefulness of mathematics, and time spent on Task 1 significantly predicted group membership, classifying 71.3% of the sample correctly. These results support the relationship between academic achievement and calibration accuracy, suggesting the need to consider a wide range of factors when explaining performance judgments.

  15. Fostering Creativity Through Mathematics.

    ERIC Educational Resources Information Center

    Lichtenberg, Betty K., Ed.; Troutman, Andria P., Ed.

    The 26 activities described in this volume deal with a wide variety of mathematical ideas. Most of the activities are appropriate for grades 6-9; many could be used with older or younger groups as well. All activities are described in detail; some descriptions include sample worksheets, and several provide suggestions for followup activities. The…

  16. The mathematical formula of the intravaginal ejaculation latency time (IELT) distribution of lifelong premature ejaculation differs from the IELT distribution formula of men in the general male population

    PubMed Central

    Janssen, Paddy K.C.

    2016-01-01

    Purpose To find the most accurate mathematical description of the intravaginal ejaculation latency time (IELT) distribution in the general male population. Materials and Methods We compared the fitness of various well-known mathematical distributions with the IELT distribution of two previously published stopwatch studies of the Caucasian general male population and a stopwatch study of Dutch Caucasian men with lifelong premature ejaculation (PE). The accuracy of fitness is expressed by the Goodness of Fit (GOF). The smaller the GOF, the more accurate is the fitness. Results The 3 IELT distributions are gamma distributions, but the IELT distribution of lifelong PE is another gamma distribution than the IELT distribution of men in the general male population. The Lognormal distribution of the gamma distributions most accurately fits the IELT distribution of 965 men in the general population, with a GOF of 0.057. The Gumbel Max distribution most accurately fits the IELT distribution of 110 men with lifelong PE with a GOF of 0.179. There are more men with lifelong PE ejaculating within 30 and 60 seconds than can be extrapolated from the probability density curve of the Lognormal IELT distribution of men in the general population. Conclusions Men with lifelong PE have a distinct IELT distribution, e.g., a Gumbel Max IELT distribution, that can only be retrieved from the general male population Lognormal IELT distribution when thousands of men would participate in a IELT stopwatch study. The mathematical formula of the Lognormal IELT distribution is useful for epidemiological research of the IELT. PMID:26981594

  17. The Mathematical Formatting of Climate Change: Critical Mathematics Education and Post-Normal Science

    ERIC Educational Resources Information Center

    Barwell, Richard

    2013-01-01

    Climate change is one of the most pressing issues of the 21st Century. Mathematics is involved at every level of understanding climate change, including the description, prediction and communication of climate change. As a highly complex issue, climate change is an example of "post-normal" science -- it is urgent, complex and involves a…

  18. Mathematical ability of first year undergraduate paramedic students-A before and after study.

    PubMed

    Eastwood, Kathryn; Boyle, Malcolm; Kim, Visal; Stam, Nathan; Williams, Brett

    2015-11-01

    An ability to accurately perform drug calculations unassisted is an essential skill for all health professionals, with various occupational-specific stressors exacerbating mathematical deficiencies. The objective of this study was to determine the unaided mathematic ability of first year undergraduate paramedic students before and after mathematical and drug calculation tutorials. Students were administered a questionnaire containing demographic, drug calculation and arithmetic questions during week one of the semester before the tutorials. During the semester students participated in three 2-hour tutorials which included both mathematical and drug calculation questions without assistance of computational devices. At the end of semester was a summative drug calculation examination of which five key questions were compared to similar questions from the first questionnaire. Descriptive statistics describe the demographic data with a paired t-test comparing the questionnaire and exam results. Drug calculation and mathematical ability was markedly improved following the tutorials, mean score of correct answers before 1.74 (SD 1.4) and after 4.14 (SD 0.93), p<0001. When comparing the correct results for the same question type, there were statistically significant differences in four of five different drug calculations: volume of drug drawn up 10 v 57 p<0.0001, infusion rate 29 v 31 p=0.717, drip rate 16 v 54 p<0.0001, volume from a syringe 30 v 59 p<0.0001, and drug dose 42 v 62 p<0.0001. Total errors reduced from 188 to 45. First year undergraduate paramedic students initially demonstrated a poor ability to complete mathematical and drug calculations without the assistance of computational devices. This improved significantly following appropriate education and practice. Further research is required to determine the retention of this ability over time. Copyright © 2015 Elsevier Ltd. All rights reserved.

  19. The Definition of Mathematics: Philosophical and Pedagogical Aspects

    NASA Astrophysics Data System (ADS)

    Khait, Alexander

    There is a strange fact that many works written with the purpose to explain what is mathematics, somehow avoid the issue. This paper is aimed at filling this gap. After discussing various descriptions of mathematics as they appear in literature, it is suggested that mathematics is an essentially linguistic activity characterized by association of words with precise meanings. Educational implications of this idea are considered in the light of(1) a strong tendency of most humans to the fuzzy way of thought as described by the dual-process theory developed by researchers of human reasoning;

  20. Contributions from specific and general factors to unique deficits: two cases of mathematics learning difficulties

    PubMed Central

    Haase, Vitor G.; Júlio-Costa, Annelise; Lopes-Silva, Júlia B.; Starling-Alves, Isabella; Antunes, Andressa M.; Pinheiro-Chagas, Pedro; Wood, Guilherme

    2014-01-01

    Mathematics learning difficulties are a highly comorbid and heterogeneous set of disorders linked to several dissociable mechanisms and endophenotypes. Two of these endophenotypes consist of primary deficits in number sense and verbal numerical representations. However, currently acknowledged endophenotypes are underspecified regarding the role of automatic vs. controlled information processing, and their description should be complemented. Two children with specific deficits in number sense and verbal numerical representations and normal or above-normal intelligence and preserved visuospatial cognition illustrate this point. Child H.V. exhibited deficits in number sense and fact retrieval. Child G.A. presented severe deficits in orally presented problems and transcoding tasks. A partial confirmation of the two endophenotypes that relate to the number sense and verbal processing was obtained, but a much more clear differentiation between the deficits presented by H.V. and G.A. can be reached by looking at differential impairments in modes of processing. H.V. is notably competent in the use of controlled processing but has problems with more automatic processes, such as nonsymbolic magnitude processing, speeded counting and fact retrieval. In contrast, G.A. can retrieve facts and process nonsymbolic magnitudes but exhibits severe impairment in recruiting executive functions and the concentration that is necessary to accomplish transcoding tasks and word problem solving. These results indicate that typical endophenotypes might be insufficient to describe accurately the deficits that are observed in children with mathematics learning abilities. However, by incorporating domain-specificity and modes of processing into the assessment of the endophenotypes, individual deficit profiles can be much more accurately described. This process calls for further specification of the endophenotypes in mathematics learning difficulties. PMID:24592243

  1. [Cambridge Conference on School Mathematics Feasibility Studies 9-13.

    ERIC Educational Resources Information Center

    Cambridge Conference on School Mathematics, Newton, MA.

    These materials are a part of a series of studies sponsored by the Cambridge Conference on School Mathematics which reflects the ideas of CCSM regarding the goals and objectives for school mathematics K-12. Feasibility Studies 9-13 contain a wide range of topics. The following are the titles and brief descriptions of these studies. Number…

  2. Profile of mathematics anxiety of 7th graders

    NASA Astrophysics Data System (ADS)

    Udil, Patrisius Afrisno; Kusmayadi, Tri Atmojo; Riyadi

    2017-08-01

    Mathematics anxiety is one of the important factors affect students mathematics achievement. This present research investigates profile of students' mathematics anxiety. This research focuses on analysis and description of students' mathematics anxiety level generally and its dominant domain and aspect. Qualitative research with case study strategy was used in this research. Subject in this research involved 15 students of 7th grade chosen with purposive sampling. Data in this research were students' mathematics anxiety scale result, interview record, and observation result during both mathematics learning activity and test. They were asked to complete mathematics anxiety scale before interviewed and observed. The results show that generally students' mathematics anxiety was identified in the moderate level. In addition, students' mathematics anxiety during mathematics test was identified in the high level, but it was in the moderate level during mathematics learning process. Based on the anxiety domain, students have a high mathematics anxiety on cognitive domain, while it was in the moderate level for psychological and physiological domains. On the other hand, it was identified in low level for psychological domain during mathematics learning process. Therefore, it can be concluded that students have serious and high anxiety regarding mathematics on the cognitive domain and mathematics test aspect.

  3. An accurate analytic description of neutrino oscillations in matter

    NASA Astrophysics Data System (ADS)

    Akhmedov, E. Kh.; Niro, Viviana

    2008-12-01

    A simple closed-form analytic expression for the probability of two-flavour neutrino oscillations in a matter with an arbitrary density profile is derived. Our formula is based on a perturbative expansion and allows an easy calculation of higher order corrections. The expansion parameter is small when the density changes relatively slowly along the neutrino path and/or neutrino energy is not very close to the Mikheyev-Smirnov-Wolfenstein (MSW) resonance energy. Our approximation is not equivalent to the adiabatic approximation and actually goes beyond it. We demonstrate the validity of our results using a few model density profiles, including the PREM density profile of the Earth. It is shown that by combining the results obtained from the expansions valid below and above the MSW resonance one can obtain a very good description of neutrino oscillations in matter in the entire energy range, including the resonance region.

  4. Mathematical modeling of forest fire initiation in three dimensional setting

    Treesearch

    Valeriy Perminov

    2007-01-01

    In this study, the assignment and theoretical investigations of the problems of forest fire initiation were carried out, including development of a mathematical model for description of heat and mass transfer processes in overterrestrial layer of atmosphere at crown forest fire initiation, taking into account their mutual influence. Mathematical model of forest fire...

  5. Student Teachers' Views about Assessment and Evaluation Methods in Mathematics

    ERIC Educational Resources Information Center

    Dogan, Mustafa

    2011-01-01

    This study aimed to find out assessment and evaluation approaches in a Mathematics Teacher Training Department based on the views and experiences of student teachers. The study used a descriptive survey method, with the research sample consisting of 150 third- and fourth-year Primary Mathematics student teachers. Data were collected using a…

  6. Accurate color synthesis of three-dimensional objects in an image

    NASA Astrophysics Data System (ADS)

    Xin, John H.; Shen, Hui-Liang

    2004-05-01

    Our study deals with color synthesis of a three-dimensional object in an image; i.e., given a single image, a target color can be accurately mapped onto the object such that the color appearance of the synthesized object closely resembles that of the actual one. As it is almost impossible to acquire the complete geometric description of the surfaces of an object in an image, this study attempted to recover the implicit description of geometry for the color synthesis. The description was obtained from either a series of spectral reflectances or the RGB signals at different surface positions on the basis of the dichromatic reflection model. The experimental results showed that this implicit image-based representation is related to the object geometry and is sufficient for accurate color synthesis of three-dimensional objects in an image. The method established is applicable to the color synthesis of both rigid and deformable objects and should contribute to color fidelity in virtual design, manufacturing, and retailing.

  7. Mathematics learning on geometry for children with autism

    NASA Astrophysics Data System (ADS)

    Widayati, F. E.; Usodo, B.; Pamudya, I.

    2017-12-01

    The purpose of this research is to describe: (1) the mathematics learning process in an inclusion class and (2) the obstacle during the process of mathematics learning in the inclusion class. This research is a descriptive qualitative research. The subjects were a mathematics teacher, children with autism, and a teacher assistant. Method of collecting data was observation and interview. Data validation technique is triangulation technique. The results of this research are : (1) There is a modification of lesson plan for children with autism. This modification such as the indicator of success, material, time, and assessment. Lesson plan for children with autism is arranged by mathematics teacher and teacher assistant. There is no special media for children with autism used by mathematics teacher. (2) The obstacle of children with autism is that they are difficult to understand mathematics concept. Besides, children with autism are easy to lose their focus.

  8. Comparing South African Female and Male Pre-Service Teachers' Beliefs about the Nature of Mathematics

    ERIC Educational Resources Information Center

    Spangenberg, Erica Dorethea; Myburgh, Chris

    2017-01-01

    Girls performing well in mathematics at school do not necessarily enrol for mathematics courses at South African universities. Teachers could be transferring beliefs about the nature of mathematics favouring boys. This paper compared male and female pre-service teachers' beliefs about the nature of mathematics. A quantitative, descriptive research…

  9. Motivational Classroom Climate for Learning Mathematics: A Reversal Theory Perspective

    ERIC Educational Resources Information Center

    Lewis, Gareth

    2015-01-01

    In this article, a case is made that affect is central in determining students' experience of learning or not learning mathematics. I show how reversal theory (Apter, 2001), and particularly its taxonomy of motivations and emotions, provides a basis for a thick description of students' experiences of learning in a mathematics classroom. Using data…

  10. Qualitative and quantitative descriptions of glenohumeral motion.

    PubMed

    Hill, A M; Bull, A M J; Wallace, A L; Johnson, G R

    2008-02-01

    Joint modelling plays an important role in qualitative and quantitative descriptions of both normal and abnormal joints, as well as predicting outcomes of alterations to joints in orthopaedic practice and research. Contemporary efforts in modelling have focussed upon the major articulations of the lower limb. Well-constrained arthrokinematics can form the basis of manageable kinetic and dynamic mathematical predictions. In order to contain computation of shoulder complex modelling, glenohumeral joint representations in both limited and complete shoulder girdle models have undergone a generic simplification. As such, glenohumeral joint models are often based upon kinematic descriptions of inadequate degrees of freedom (DOF) for clinical purposes and applications. Qualitative descriptions of glenohumeral motion range from the parody of a hinge joint to the complex realism of a spatial joint. In developing a model, a clear idea of intention is required in order to achieve a required application. Clinical applicability of a model requires both descriptive and predictive output potentials, and as such, a high level of validation is required. Without sufficient appreciation of the clinical intention of the arthrokinematic foundation to a model, error is all too easily introduced. Mathematical description of joint motion serves to quantify all relevant clinical parameters. Commonly, both the Euler angle and helical (screw) axis methods have been applied to the glenohumeral joint, although concordance between these methods and classical anatomical appreciation of joint motion is limited, resulting in miscommunication between clinician and engineer. Compounding these inconsistencies in motion quantification is gimbal lock and sequence dependency.

  11. Experimenting with Impacts in a Conceptual Physics or Descriptive Astronomy Laboratory

    ERIC Educational Resources Information Center

    LoPresto, Michael C.

    2016-01-01

    What follows is a description of the procedure for and results of a simple experiment on the formation of impact craters designed for the laboratory portions of lower mathematical-level general education science courses such as conceptual physics or descriptive astronomy. The experiment provides necessary experience with data collection and…

  12. Unpacking Teachers' Moves in the Classroom: Navigating Micro- and Macro-Levels of Mathematical Complexity

    ERIC Educational Resources Information Center

    Wasserman, Nicholas H.

    2015-01-01

    The work that mathematics teachers do is frequently mathematical in nature and different from other professions. Understanding and describing common ways that teachers draw upon their content knowledge in the practice of teaching is important. Building on the descriptions by McCrory et al. ("Journal for Research in Mathematics Education"…

  13. Compact and Hybrid Feature Description for Building Extraction

    NASA Astrophysics Data System (ADS)

    Li, Z.; Liu, Y.; Hu, Y.; Li, P.; Ding, Y.

    2017-05-01

    Building extraction in aerial orthophotos is crucial for various applications. Currently, deep learning has been shown to be successful in addressing building extraction with high accuracy and high robustness. However, quite a large number of samples is required in training a classifier when using deep learning model. In order to realize accurate and semi-interactive labelling, the performance of feature description is crucial, as it has significant effect on the accuracy of classification. In this paper, we bring forward a compact and hybrid feature description method, in order to guarantees desirable classification accuracy of the corners on the building roof contours. The proposed descriptor is a hybrid description of an image patch constructed from 4 sets of binary intensity tests. Experiments show that benefiting from binary description and making full use of color channels, this descriptor is not only computationally frugal, but also accurate than SURF for building extraction.

  14. Teachers' Beliefs and Technology: Calculator Use in Mathematics Instruction in Junior Secondary Schools in Botswana

    ERIC Educational Resources Information Center

    Salani, End

    2013-01-01

    Lesson starts are transitional events which may cause management problems for teachers. This study sought junior secondary school mathematics teachers' beliefs about calculator use in mathematics instruction in Botswana and was descriptive in nature adopting a survey design. The sample of seventeen (17) mathematics teachers from four (4) junior…

  15. Mathematical calculation skills required for drug administration in undergraduate nursing students to ensure patient safety: A descriptive study: Drug calculation skills in nursing students.

    PubMed

    Bagnasco, Annamaria; Galaverna, Lucia; Aleo, Giuseppe; Grugnetti, Anna Maria; Rosa, Francesca; Sasso, Loredana

    2016-01-01

    In the literature we found many studies that confirmed our concerns about nursing students' poor maths skills that directly impact on their ability to correctly calculate drug dosages with very serious consequences for patient safety. The aim of our study was to explore where students had most difficulty and identify appropriate educational interventions to bridge their mathematical knowledge gaps. This was a quali-quantitative descriptive study that included a sample of 726 undergraduate nursing students. We identified exactly where students had most difficulty and identified appropriate educational interventions to bridge their mathematical knowledge gaps. We found that the undergraduate nursing students mainly had difficulty with basic maths principles. Specific learning interventions are needed to improve their basic maths skills and their dosage calculation skills. For this purpose, we identified safeMedicate and eDose (Authentic World Ltd.), only that they are only available in English. In the near future we hope to set up a partnership to work together on the Italian version of these tools. Copyright © 2015 Elsevier Ltd. All rights reserved.

  16. A Multifaceted Mathematical Approach for Complex Systems

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Alexander, F.; Anitescu, M.; Bell, J.

    2012-03-07

    Applied mathematics has an important role to play in developing the tools needed for the analysis, simulation, and optimization of complex problems. These efforts require the development of the mathematical foundations for scientific discovery, engineering design, and risk analysis based on a sound integrated approach for the understanding of complex systems. However, maximizing the impact of applied mathematics on these challenges requires a novel perspective on approaching the mathematical enterprise. Previous reports that have surveyed the DOE's research needs in applied mathematics have played a key role in defining research directions with the community. Although these reports have had significantmore » impact, accurately assessing current research needs requires an evaluation of today's challenges against the backdrop of recent advances in applied mathematics and computing. To address these needs, the DOE Applied Mathematics Program sponsored a Workshop for Mathematics for the Analysis, Simulation and Optimization of Complex Systems on September 13-14, 2011. The workshop had approximately 50 participants from both the national labs and academia. The goal of the workshop was to identify new research areas in applied mathematics that will complement and enhance the existing DOE ASCR Applied Mathematics Program efforts that are needed to address problems associated with complex systems. This report describes recommendations from the workshop and subsequent analysis of the workshop findings by the organizing committee.« less

  17. Assessment in the Context of Mathematics Instruction Reform: The Design of Assessment in the QUASAR Project.

    ERIC Educational Resources Information Center

    Silver, Edward A.; Lane, Suzanne

    Recent reports on mathematics education reform have focused the attention of educational practitioners and policymakers on new goals for mathematics education and new descriptions of mathematical proficiency. QUASAR is a national project (Quantitative Understanding: Amplifying Student Achievement and Reasoning) designed to improve the mathematics…

  18. Mathematical models of cell motility.

    PubMed

    Flaherty, Brendan; McGarry, J P; McHugh, P E

    2007-01-01

    Cell motility is an essential biological action in the creation, operation and maintenance of our bodies. Developing mathematical models elucidating cell motility will greatly advance our understanding of this fundamental biological process. With accurate models it is possible to explore many permutations of the same event and concisely investigate their outcome. While great advancements have been made in experimental studies of cell motility, it now has somewhat fallen on mathematical models to taking a leading role in future developments. The obvious reason for this is the complexity of cell motility. Employing the processing power of today's computers will give researches the ability to run complex biophysical and biochemical scenarios, without the inherent difficulty and time associated with in vitro investigations. Before any great advancement can be made, the basics of cell motility will have to be well-defined. Without this, complicated mathematical models will be hindered by their inherent conjecture. This review will look at current mathematical investigations of cell motility, explore the reasoning behind such work and conclude with how best to advance this interesting and challenging research area.

  19. The Influence of Mathematics Professional Development, School-Level, and Teacher-Level Variables on Primary Students' Mathematics Achievement

    ERIC Educational Resources Information Center

    Polly, Drew; Wang, Chuang; Martin, Christie; Lambert, Richard; Pugalee, David; Middleton, Catherina

    2018-01-01

    This study examined the influence of a professional development project about an internet-based mathematics formative assessment tool and related pedagogies on primary teachers' instruction and student achievement. Teachers participated in 72 h of professional development during the year. Descriptive statistics and multivariate analyses of…

  20. Mathematical and Statistical Software Index. Final Report.

    ERIC Educational Resources Information Center

    Black, Doris E., Comp.

    Brief descriptions are provided of general-purpose mathematical and statistical software, including 27 "stand-alone" programs, three subroutine systems, and two nationally recognized statistical packages, which are available in the Air Force Human Resources Laboratory (AFHRL) software library. This index was created to enable researchers…

  1. Dissociations in mathematical knowledge: case studies in Down's syndrome and Williams syndrome.

    PubMed

    Robinson, Sally J; Temple, Christine M

    2013-02-01

    A study is reported of mathematical vocabulary and factual mathematical knowledge in PQ, a 22 year old with Down's syndrome (DS) who has a verbal mental age (MA) of 9 years 2 months and ST, a 15 year old with Williams syndrome (WS) who has a verbal MA of 9 years 6 months, matched to typically developing controls. The number of mathematical words contained within PQ's lexical stores was significantly reduced as reflected by performance on lexical decision. PQ was also impaired at both naming from descriptions and describing mathematical words. These results contrast with normal lexical decision and item descriptions for concrete words reported recently for PQ (Robinson and Temple, 2010). PQ's recall of mathematical facts was also impaired, whilst his recall of general knowledge facts was normal. This performance in DS indicates a deficit in both lexical representation and semantic knowledge for mathematical words and mathematical facts. In contrast, ST, the teenager with WS had good accuracy on lexical decision, naming and generating definitions for mathematical words. This contrasted with the atypical performance with concrete words recently reported for ST (Robinson and Temple, 2009). Knowledge of addition facts and general knowledge facts was also unimpaired for ST, though knowledge of multiplication facts was weak. Together the cases form a double dissociation and provide support for the distinct representation of mathematical and concrete items within the lexical-semantic system during development. The dissociations between mathematical and general factual knowledge also indicate that different types of factual knowledge may be selectively impaired during development. There is further support for a modular structure within which mathematical vocabulary and mathematical knowledge have distinct representations. This supports the case for the independent representation of factual and language-based knowledge within the semantic system during development. Copyright

  2. On Possible Uses of Traditional Angolan Sand Drawings in the Mathematics Classroom.

    ERIC Educational Resources Information Center

    Gerdes, Paulus

    1988-01-01

    Both industrialized and Third World countries see the need to "multi-culturalize" their mathematics curricula. Following a brief description of the drawing tradition of the Tchokwe people (Angola), some possible uses of their pictograms in the mathematics classroom are suggested. Examples given in this paper include the study of arithmetical…

  3. Managing Your Mathematics Program: A Total System. A Guide to the U-SAIL Basic Mathematics System.

    ERIC Educational Resources Information Center

    Hales, Carma M.; Jones, Maurine E.

    The Utah System Approach to Individual Learning (U-SAIL) Mathematics System was developed to make it possible for teachers to provide excellence in arithmetic instruction. It is based on the premise that in order to teach arithmetic well, teachers must accurately assess, teach directly, provide students with focused practice, corrective feedback,…

  4. ASTP ranging system mathematical model

    NASA Technical Reports Server (NTRS)

    Ellis, M. R.; Robinson, L. H.

    1973-01-01

    A mathematical model is presented of the VHF ranging system to analyze the performance of the Apollo-Soyuz test project (ASTP). The system was adapted for use in the ASTP. The ranging system mathematical model is presented in block diagram form, and a brief description of the overall model is also included. A procedure for implementing the math model is presented along with a discussion of the validation of the math model and the overall summary and conclusions of the study effort. Detailed appendices of the five study tasks are presented: early late gate model development, unlock probability development, system error model development, probability of acquisition and model development, and math model validation testing.

  5. Development of a Mathematical Ability Test: A Validity and Reliability Study

    ERIC Educational Resources Information Center

    Dündar, Sefa; Temel, Hasan; Gündüz, Nazan

    2016-01-01

    The identification of talented students accurately at an early age and the adaptation of the education provided to the students depending on their abilities are of great importance for the future of the countries. In this regard, this study aims to develop a mathematical ability test for the identification of the mathematical abilities of students…

  6. Mathematical Representation by Students in Building Relational Understanding on Concepts of Area and Perimeter of Rectangle

    ERIC Educational Resources Information Center

    Anwar, Rahmad Bustanul; Yuwono, Ipung; As'ari, Abdur Rahman; Sisworo; Dwi, Rahmawati

    2016-01-01

    Representation is an important aspect of learners in building a relational understanding of mathematical concepts. But the ability of a mathematical representation of students in building relational understanding is still very limited. The purpose of this research is to description of mathematical representation of students who appear in building…

  7. Accurately tracking single-cell movement trajectories in microfluidic cell sorting devices.

    PubMed

    Jeong, Jenny; Frohberg, Nicholas J; Zhou, Enlu; Sulchek, Todd; Qiu, Peng

    2018-01-01

    Microfluidics are routinely used to study cellular properties, including the efficient quantification of single-cell biomechanics and label-free cell sorting based on the biomechanical properties, such as elasticity, viscosity, stiffness, and adhesion. Both quantification and sorting applications require optimal design of the microfluidic devices and mathematical modeling of the interactions between cells, fluid, and the channel of the device. As a first step toward building such a mathematical model, we collected video recordings of cells moving through a ridged microfluidic channel designed to compress and redirect cells according to cell biomechanics. We developed an efficient algorithm that automatically and accurately tracked the cell trajectories in the recordings. We tested the algorithm on recordings of cells with different stiffness, and showed the correlation between cell stiffness and the tracked trajectories. Moreover, the tracking algorithm successfully picked up subtle differences of cell motion when passing through consecutive ridges. The algorithm for accurately tracking cell trajectories paves the way for future efforts of modeling the flow, forces, and dynamics of cell properties in microfluidics applications.

  8. Creating Constructivist Environments and Constructing Creative Mathematics.

    ERIC Educational Resources Information Center

    Pirie, Susan; Kieren, Thomas

    1992-01-01

    Proposes and describes four teachers' beliefs necessary in creating constructivist classroom environments. Presents the background, description, and analysis of seven teaching episodes that examine the mathematical understanding actions of pupils in classrooms in which teachers exhibit these beliefs in an effort to verify the necessity of the…

  9. Models in biology: ‘accurate descriptions of our pathetic thinking’

    PubMed Central

    2014-01-01

    In this essay I will sketch some ideas for how to think about models in biology. I will begin by trying to dispel the myth that quantitative modeling is somehow foreign to biology. I will then point out the distinction between forward and reverse modeling and focus thereafter on the former. Instead of going into mathematical technicalities about different varieties of models, I will focus on their logical structure, in terms of assumptions and conclusions. A model is a logical machine for deducing the latter from the former. If the model is correct, then, if you believe its assumptions, you must, as a matter of logic, also believe its conclusions. This leads to consideration of the assumptions underlying models. If these are based on fundamental physical laws, then it may be reasonable to treat the model as ‘predictive’, in the sense that it is not subject to falsification and we can rely on its conclusions. However, at the molecular level, models are more often derived from phenomenology and guesswork. In this case, the model is a test of its assumptions and must be falsifiable. I will discuss three models from this perspective, each of which yields biological insights, and this will lead to some guidelines for prospective model builders. PMID:24886484

  10. The relationship between mathematics and language: academic implications for children with specific language impairment and English language learners.

    PubMed

    Alt, Mary; Arizmendi, Genesis D; Beal, Carole R

    2014-07-01

    The present study examined the relationship between mathematics and language to better understand the nature of the deficit and the academic implications associated with specific language impairment (SLI) and academic implications for English language learners (ELLs). School-age children (N = 61; 20 SLI, 20 ELL, 21 native monolingual English [NE]) were assessed using a norm-referenced mathematics instrument and 3 experimental computer-based mathematics games that varied in language demands. Group means were compared with analyses of variance. The ELL group was less accurate than the NE group only when tasks were language heavy. In contrast, the group with SLI was less accurate than the groups with NE and ELLs on language-heavy tasks and some language-light tasks. Specifically, the group with SLI was less accurate on tasks that involved comparing numerical symbols and using visual working memory for patterns. However, there were no group differences between children with SLI and peers without SLI on language-light mathematics tasks that involved visual working memory for numerical symbols. Mathematical difficulties of children who are ELLs appear to be related to the language demands of mathematics tasks. In contrast, children with SLI appear to have difficulty with mathematics tasks because of linguistic as well as nonlinguistic processing constraints.

  11. Explicating mathematical thinking in differential equations using a computer algebra system

    NASA Astrophysics Data System (ADS)

    Zeynivandnezhad, Fereshteh; Bates, Rachel

    2018-07-01

    The importance of developing students' mathematical thinking is frequently highlighted in literature regarding the teaching and learning of mathematics. Despite this importance, most curricula and instructional activities for undergraduate mathematics fail to bring the learner beyond the mathematics. The purpose of this study was to enhance students' mathematical thinking by implementing a computer algebra system and active learning pedagogical approaches. students' mathematical thinking processes were analyzed while completing specific differential equations tasks based on posed prompts and questions and Instrumental Genesis. Data were collected from 37 engineering students in a public Malaysian university. This study used the descriptive and interpretive qualitative research design to investigate the students' perspectives of emerging mathematical understanding and approaches to learning mathematics in an undergraduate differential equations course. Results of this study concluded that students used a variety of mathematical thinking processes in a non-sequential manner. Additionally, the outcomes provide justification for continued use of technologies such as computer algebra systems in undergraduate mathematics courses and the need for further studies to uncover the various processes students utilize to complete specific mathematical tasks.

  12. Mathematics of Information Processing and the Internet

    ERIC Educational Resources Information Center

    Hart, Eric W.

    2010-01-01

    The mathematics of information processing and the Internet can be organized around four fundamental themes: (1) access (finding information easily); (2) security (keeping information confidential); (3) accuracy (ensuring accurate information); and (4) efficiency (data compression). In this article, the author discusses each theme with reference to…

  13. A Cognitive Analysis of Students’ Mathematical Problem Solving Ability on Geometry

    NASA Astrophysics Data System (ADS)

    Rusyda, N. A.; Kusnandi, K.; Suhendra, S.

    2017-09-01

    The purpose of this research is to analyze of mathematical problem solving ability of students in one of secondary school on geometry. This research was conducted by using quantitative approach with descriptive method. Population in this research was all students of that school and the sample was twenty five students that was chosen by purposive sampling technique. Data of mathematical problem solving were collected through essay test. The results showed the percentage of achievement of mathematical problem solving indicators of students were: 1) solve closed mathematical problems with context in math was 50%; 2) solve the closed mathematical problems with the context beyond mathematics was 24%; 3) solving open mathematical problems with contexts in mathematics was 35%; And 4) solving open mathematical problems with contexts outside mathematics was 44%. Based on the percentage, it can be concluded that the level of achievement of mathematical problem solving ability in geometry still low. This is because students are not used to solving problems that measure mathematical problem solving ability, weaknesses remember previous knowledge, and lack of problem solving framework. So the students’ ability of mathematical problems solving need to be improved with implement appropriate learning strategy.

  14. A Descriptive Study Examining the Impact of Digital Writing Environments on Communication and Mathematical Reasoning for Students with Learning Disabilities

    ERIC Educational Resources Information Center

    Huscroft-D'Angelo, Jacqueline; Higgins, Kristina N.; Crawford, Lindy L.

    2014-01-01

    Proficiency in mathematics, including mathematical reasoning skills, requires students to communicate their mathematical thinking. Mathematical reasoning involves making sense of mathematical concepts in a logical way to form conclusions or judgments, and is often underdeveloped in students with learning disabilities. Technology-based environments…

  15. Cross-national Retrospective Studies of Mathematics Olympians.

    ERIC Educational Resources Information Center

    Campbell, James Reed, Ed.

    1996-01-01

    The eight chapters of this theme issue use quantitative and qualitative methods to explore the nature and nurture of young participants in the mathematics Olympiad from five countries. Parallel studies are presented of winners from China, Taiwan, and the United States, along with descriptions of programs in Japan and Russia. (SLD)

  16. 37 CFR 1.58 - Chemical and mathematical formulae and tables.

    Code of Federal Regulations, 2014 CFR

    2014-07-01

    ..., including the claims, may contain chemical and mathematical formulae, but shall not contain drawings or flow diagrams. The description portion of the specification may contain tables, but the same tables should not...

  17. In-Situ Assays Using a New Advanced Mathematical Algorithm - 12400

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Oginni, B.M.; Bronson, F.L.; Field, M.B.

    2012-07-01

    Current mathematical efficiency modeling software for in-situ counting, such as the commercially available In-Situ Object Calibration Software (ISOCS), typically allows the description of measurement geometries via a list of well-defined templates which describe regular objects, such as boxes, cylinder, or spheres. While for many situations, these regular objects are sufficient to describe the measurement conditions, there are occasions in which a more detailed model is desired. We have developed a new all-purpose geometry template that can extend the flexibility of current ISOCS templates. This new template still utilizes the same advanced mathematical algorithms as current templates, but allows the extensionmore » to a multitude of shapes and objects that can be placed at any location and even combined. In addition, detectors can be placed anywhere and aimed at any location within the measurement scene. Several applications of this algorithm to in-situ waste assay measurements, as well as, validations of this template using Monte Carlo calculations and experimental measurements are studied. Presented in this paper is a new template of the mathematical algorithms for evaluating efficiencies. This new template combines all the advantages of the ISOCS and it allows the use of very complex geometries, it also allows stacking of geometries on one another in the same measurement scene and it allows the detector to be placed anywhere in the measurement scene and pointing in any direction. We have shown that the template compares well with the previous ISOCS software within the limit of convergence of the code, and also compare well with the MCNPX and measured data within the joint uncertainties for the code and the data. The new template agrees with ISOCS to within 1.5% at all energies. It agrees with the MCNPX to within 10% at all energies and it agrees with most geometries within 5%. It finally agrees with measured data to within 10%. This mathematical algorithm can

  18. Teacher-Directed Student Use of Technology and Mathematics Achievement: Examining Trends in International Patterns

    ERIC Educational Resources Information Center

    Wang, Yang; O'Dwyer, Laura

    2011-01-01

    Using data from the Trends in International Mathematics and Science Study (TIMSS) 2003 and 2007 administrations, this study examines international trends in technology use and explores the international patterns in how teacher-directed, student-use of technology is related to eighth grade mathematics achievement. Descriptive patterns in…

  19. Compact, accurate description of diagnostic neutral beam propagation and attenuation in a high temperature plasma for charge exchange recombination spectroscopy analysis.

    PubMed

    Bespamyatnov, Igor O; Rowan, William L; Granetz, Robert S

    2008-10-01

    Charge exchange recombination spectroscopy on Alcator C-Mod relies on the use of the diagnostic neutral beam injector as a source of neutral particles which penetrate deep into the plasma. It employs the emission resulting from the interaction of the beam atoms with fully ionized impurity ions. To interpret the emission from a given point in the plasma as the density of emitting impurity ions, the density of beam atoms must be known. Here, an analysis of beam propagation is described which yields the beam density profile throughout the beam trajectory from the neutral beam injector to the core of the plasma. The analysis includes the effects of beam formation, attenuation in the neutral gas surrounding the plasma, and attenuation in the plasma. In the course of this work, a numerical simulation and an analytical approximation for beam divergence are developed. The description is made sufficiently compact to yield accurate results in a time consistent with between-shot analysis.

  20. 37 CFR 1.58 - Chemical and mathematical formulae and tables.

    Code of Federal Regulations, 2011 CFR

    2011-07-01

    ..., including the claims, may contain chemical and mathematical formulae, but shall not contain drawings or flow diagrams. The description portion of the specification may contain tables, but the same tables may only be...

  1. 37 CFR 1.58 - Chemical and mathematical formulae and tables.

    Code of Federal Regulations, 2013 CFR

    2013-07-01

    ..., including the claims, may contain chemical and mathematical formulae, but shall not contain drawings or flow diagrams. The description portion of the specification may contain tables, but the same tables may only be...

  2. Year 12 Students' Mathematical Performance on the 1980 and 1981 External Examinations. Mathematics Education Centre Report No. 25.

    ERIC Educational Resources Information Center

    Clarkson, P. C.

    Descriptions of Papua New Guinea's national high schools, grade 12 major/minor mathematics courses, and an analysis of the 1980 and 1981 major/minor course examination results are presented. The analysis is intended for use by post year 12 lecturers/instructors planning their courses. Findings indicate that topic scores were far too low for these…

  3. Single-gender mathematics and science classes and the effects on urban middle school boys and girls

    NASA Astrophysics Data System (ADS)

    Sudler, Dawn M.

    This study compared the differences in the Criterion-Referenced Competency Test (CRCT) mathematics and science achievement scores of boys and girls in Grade 7 at two urban middle schools. The data allowed the researcher to determine to what degree boys and girls in Grade 7 differ in their mathematics and science achievements within a single-gender environment versus a coeducational learning environment. The study compared any differences between boys and girls in Grade 7 within a single-gender environment in the subjects of mathematics and science, as measured by the CRCT assessments. The study also compared differences between boys and girls in Grade 7 within a coeducational environment in the subjects of mathematics and science, as measured by the CRCT assessments. Two middle schools were used within the study. One middle school was identified as a single-gender school (Middle School A); the other was identified as a coeducational school (Middle School B). This quantitative study applied the use of a descriptive research design. In addition, CRCT scores for the subjects of mathematics and science were taken during the spring of 2008 from both middle schools. Data were measured using descriptive statistics and independent t test calculations. The frequency statistics proceeded to compare each sample performance levels. The data were described in means, standard deviations, standard error means, frequency, and percentages. This method provided an excellent description of a sample scored on the spring 2008 CRCT mathematics and science assessments.

  4. Relationship between mathematical abstraction in learning parallel coordinates concept and performance in learning analytic geometry of pre-service mathematics teachers: an investigation

    NASA Astrophysics Data System (ADS)

    Nurhasanah, F.; Kusumah, Y. S.; Sabandar, J.; Suryadi, D.

    2018-05-01

    As one of the non-conventional mathematics concepts, Parallel Coordinates is potential to be learned by pre-service mathematics teachers in order to give them experiences in constructing richer schemes and doing abstraction process. Unfortunately, the study related to this issue is still limited. This study wants to answer a research question “to what extent the abstraction process of pre-service mathematics teachers in learning concept of Parallel Coordinates could indicate their performance in learning Analytic Geometry”. This is a case study that part of a larger study in examining mathematical abstraction of pre-service mathematics teachers in learning non-conventional mathematics concept. Descriptive statistics method is used in this study to analyze the scores from three different tests: Cartesian Coordinate, Parallel Coordinates, and Analytic Geometry. The participants in this study consist of 45 pre-service mathematics teachers. The result shows that there is a linear association between the score on Cartesian Coordinate and Parallel Coordinates. There also found that the higher levels of the abstraction process in learning Parallel Coordinates are linearly associated with higher student achievement in Analytic Geometry. The result of this study shows that the concept of Parallel Coordinates has a significant role for pre-service mathematics teachers in learning Analytic Geometry.

  5. Values taught, values learned, attitude and performance in mathematics

    NASA Astrophysics Data System (ADS)

    Limbaco, K. S. A.

    2015-03-01

    The purpose of the study was to identify, describe and find the relationship among values taught, values learned, attitude and performance in mathematics. The researcher used descriptive-correlational method of research to gather information and to describe the nature of situation. The following instruments were used in this study: Math Attitude Inventory, Inventory of Values Taught and Learned which were content validated by experts in the field of Mathematics, Values and Education. Generally, most of the values were taught by the teachers. All of the values were learned by the students. The following got the highest mean ratings for values taught: moral strength, sharing, charity, valuing life, love of God, truth and honesty, reason, alternativism and articulation. The following got highest mean ratings for values learned: patience/tolerance, sharing, charity, valuing life, faith, love of God, truth and honesty, analogical thinking, confidence and individual liberty. Majority of the respondents have moderately positive attitude towards mathematics. Positive statements in the Mathematics Attitude Inventory are "Generally true" while negative statements are "Neutral." In conclusion, values were taught by mathematics teacher, thus, learned by the students. Therefore, mathematics is very much related to life. Values can be learned and strengthened through mathematics; there is a significant relationship between values taught by the teachers and values learned by the students and attitude towards mathematics and performance in mathematics; values taught does not affect attitude towards mathematics and performance in mathematics. A student may have a positive attitude towards mathematics or have an exemplary performance in mathematics even if the mathematics teacher did not teach values; values learned does not affect attitude towards mathematics and performance in mathematics. A student may have a positive attitude towards mathematics or have an exemplary performance

  6. The relation between learning mathematics and students' competencies in undesrtanding texts

    NASA Astrophysics Data System (ADS)

    Hapipi, Azmi, Syahrul; Sripatmi, Amrullah

    2017-08-01

    This study was a descriptive study that aimed to gain an overview on the relation between learning mathematics and students' competencies in understanding texts. This research was classified as an ex post facto study due in part to the variable studied is the variable that was already happening. While the technique of taking the sample using stratified proportional sampling techniques. These techniques have been selected for the condition of the population, in the context of learning mathematics, diverse and also tiered. The results of this study indicate that there is a relationship between learning mathematics and students' competencies in understanding texts.

  7. Mathematics creative thinking levels based on interpersonal intelligence

    NASA Astrophysics Data System (ADS)

    Kuncorowati, R. H.; Mardiyana; Saputro, D. R. S.

    2017-12-01

    Creative thinking ability was one of student’s ability to determine various alternative solutions toward mathematics problem. One of indicators related to creative thinking ability was interpersonal intelligence. Student’s interpersonal intelligence would influence to student’s creativity. This research aimed to analyze creative thinking ability level of junior high school students in Karanganyar using descriptive method. Data was collected by test, questionnaire, interview, and documentation. The result showed that students with high interpersonal intelligence achieved third and fourth level in creative thinking ability. Students with moderate interpersonal intelligence achieved second level in creative thinking ability and students with low interpersonal intelligence achieved first and zero level in creative thinking ability. Hence, students with high, moderate, and low interpersonal intelligence could solve mathematics problem based on their mathematics creative thinking ability.

  8. Methods to achieve accurate projection of regional and global raster databases

    USGS Publications Warehouse

    Usery, E. Lynn; Seong, Jeong Chang; Steinwand, Dan

    2002-01-01

    Modeling regional and global activities of climatic and human-induced change requires accurate geographic data from which we can develop mathematical and statistical tabulations of attributes and properties of the environment. Many of these models depend on data formatted as raster cells or matrices of pixel values. Recently, it has been demonstrated that regional and global raster datasets are subject to significant error from mathematical projection and that these errors are of such magnitude that model results may be jeopardized (Steinwand, et al., 1995; Yang, et al., 1996; Usery and Seong, 2001; Seong and Usery, 2001). There is a need to develop methods of projection that maintain the accuracy of these datasets to support regional and global analyses and modeling

  9. Basic research and data analysis for the earth and ocean physics applications program and for the National Geodetic Satellite Program

    NASA Technical Reports Server (NTRS)

    1976-01-01

    Data analysis and supporting research in connection with the following objectives are discussed: (1) provide a precise and accurate geometric description of the earth's surface, (2) provide a precise and accurate mathematical description of the earth's gravitational field, and (3) determine time variations of the geometry of the ocean surface, the solid earth, the gravity field and other geophysical parameters.

  10. Adapting Technological Pedagogical Content Knowledge Framework to Teach Mathematics

    ERIC Educational Resources Information Center

    Getenet, Seyum Tekeher

    2017-01-01

    The technological pedagogical content knowledge framework is increasingly in use by educational technology researcher as a generic description of the knowledge requirements for teachers using technology in all subjects. This study describes the development of a mathematics specific variety of the technological pedagogical content knowledge…

  11. A History of the Description of the Three-Dimensional Finite Rotation

    NASA Astrophysics Data System (ADS)

    Fraiture, Luc

    2009-01-01

    A history of the description of a three-dimensional finite rotation is given starting with Cardano in the middle of the sixteenth century and ending with Bryan in the beginning of the past century. Description means both a textual description and/or a mathematical representation. To appreciate the historical context of the milestones reached over the centuries, the background and personality of the main players in this history are given. At the end, a short critical discussion is added, reviewing the present names of rotation parameters in use related to the scientists which have been considered here.

  12. Developing calculus textbook model that supported with GeoGebra to enhancing students’ mathematical problem solving and mathematical representation

    NASA Astrophysics Data System (ADS)

    Dewi, N. R.; Arini, F. Y.

    2018-03-01

    The main purpose of this research is developing and produces a Calculus textbook model that supported with GeoGebra. This book was designed to enhancing students’ mathematical problem solving and mathematical representation. There were three stages in this research i.e. define, design, and develop. The textbooks consisted of 6 chapters which each chapter contains introduction, core materials and include examples and exercises. The textbook developed phase begins with the early stages of designed the book (draft 1) which then validated by experts. Revision of draft 1 produced draft 2. The data were analyzed with descriptive statistics. The analysis showed that the Calculus textbook model that supported with GeoGebra, valid and fill up the criteria of practicality.

  13. On canonical cylinder sections for accurate determination of contact angle in microgravity

    NASA Technical Reports Server (NTRS)

    Concus, Paul; Finn, Robert; Zabihi, Farhad

    1992-01-01

    Large shifts of liquid arising from small changes in certain container shapes in zero gravity can be used as a basis for accurately determining contact angle. Canonical geometries for this purpose, recently developed mathematically, are investigated here computationally. It is found that the desired nearly-discontinuous behavior can be obtained and that the shifts of liquid have sufficient volume to be readily observed.

  14. Students’ Representation in Mathematical Word Problem-Solving: Exploring Students’ Self-efficacy

    NASA Astrophysics Data System (ADS)

    Sahendra, A.; Budiarto, M. T.; Fuad, Y.

    2018-01-01

    This descriptive qualitative research aims at investigating student represented in mathematical word problem solving based on self-efficacy. The research subjects are two eighth graders at a school in Surabaya with equal mathematical ability consisting of two female students with high and low self-efficacy. The subjects were chosen based on the results of test of mathematical ability, documentation of the result of middle test in even semester of 2016/2017 academic year, and results of questionnaire of mathematics word problem in terms of self-efficacy scale. The selected students were asked to do mathematical word problem solving and be interviewed. The result of this study shows that students with high self-efficacy tend to use multiple representations of sketches and mathematical models, whereas students with low self-efficacy tend to use single representation of sketches or mathematical models only in mathematical word problem-solving. This study emphasizes that teachers should pay attention of student’s representation as a consideration of designing innovative learning in order to increase the self-efficacy of each student to achieve maximum mathematical achievement although it still requires adjustment to the school situation and condition.

  15. Using Mathematics, Mathematical Applications, Mathematical Modelling, and Mathematical Literacy: A Theoretical Study

    ERIC Educational Resources Information Center

    Mumcu, Hayal Yavuz

    2016-01-01

    The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…

  16. Basic Phage Mathematics.

    PubMed

    Abedon, Stephen T; Katsaounis, Tena I

    2018-01-01

    Basic mathematical descriptions are useful in phage ecology, applied phage ecology such as in the course of phage therapy, and also toward keeping track of expected phage-bacterial interactions as seen during laboratory manipulation of phages. The most basic mathematical descriptor of phages is their titer, that is, their concentration within stocks, experimental vessels, or other environments. Various phenomena can serve to modify phage titers, and indeed phage titers can vary as a function of how they are measured. An important aspect of how changes in titers can occur results from phage interactions with bacteria. These changes tend to vary in degree as a function of bacterial densities within environments, and particularly densities of those bacteria that are susceptible to or at least adsorbable by a given phage type. Using simple mathematical models one can describe phage-bacterial interactions that give rise particularly to phage adsorption events. With elaboration one can consider changes in both phage and bacterial densities as a function of both time and these interactions. In addition, phages along with their impact on bacteria can be considered as spatially constrained processes. In this chapter we consider the simpler of these concepts, providing in particular detailed verbal explanations toward facile mathematical insight. The primary goal is to stimulate a more informed use and manipulation of phages and phage populations within the laboratory as well as toward more effective phage application outside of the laboratory, such as during phage therapy. More generally, numerous issues and approaches to the quantification of phages are considered along with the quantification of individual, ecological, and applied properties of phages.

  17. Recognising `good at mathematics': using a performative lens for identity

    NASA Astrophysics Data System (ADS)

    Darragh, Lisa

    2015-03-01

    Many students do not recognise in themselves positive learner identities in mathematics and thus exclude themselves from further mathematics education, limiting their life opportunities. In this study, I use a performance metaphor for identity, drawing on G.H. Mead, Erving Goffman and Judith Butler to analyse interviews with students, taken at four time points as they make the transition from primary to secondary school. The question I focus on is `How do you recognise someone who is "good at mathematics"?' The students' responses reveal that there is a wide variety of scripts available when enacting the role of `good at mathematics', and these include getting high marks, knowing the answer quickly, helping others and demonstrating the confidence to put up their hand to answer questions. Despite the variety of ways in which to demonstrate `good at mathematics', most of the students did not recognise themselves in their own descriptions. This goes some way towards explaining why students may opt out of further study in mathematics, despite high achievement in this subject.

  18. The Force-Frequency Relationship: Insights from Mathematical Modeling

    ERIC Educational Resources Information Center

    Puglisi, Jose L.; Negroni, Jorge A.; Chen-Izu, Ye; Bers, Donald M.

    2013-01-01

    The force-frequency relationship has intrigued researchers since its discovery by Bowditch in 1871. Many attempts have been made to construct mathematical descriptions of this phenomenon, beginning with the simple formulation of Koch-Wesser and Blinks in 1963 to the most sophisticated ones of today. This property of cardiac muscle is amplified by…

  19. Teaching undergraduate mathematics in interactive groups: how does it fit with students' learning?

    NASA Astrophysics Data System (ADS)

    Sheryn, Louise; Ell, Fiona

    2014-08-01

    Debates about how undergraduate mathematics should be taught are informed by different views of what it is to learn and to do mathematics. In this qualitative study 10 students enrolled in an advanced undergraduate course in mathematics shared their views about how they best learn mathematics. After participating in a semester-long course in combinatorics, taught using a non-traditional, formal group work approach, the 10 students shared their views about how such an approach fitted in with their experience of learning mathematics. A descriptive thematic analysis of the students' responses revealed that despite being very comfortable with the traditional approach to learning new mathematics, most students were open to a formal group work approach and could see benefits from it after their participation. The students' prior conceptions of the goal of undergraduate mathematics learning and their view of themselves as 'mathematicians' framed their experience of learning mathematics in a non-traditional class.

  20. Pre-service mathematics teachers’ ability in solving well-structured problem

    NASA Astrophysics Data System (ADS)

    Paradesa, R.

    2018-01-01

    This study aimed to describe the mathematical problem-solving ability of undergraduate students of mathematics education in solving the well-structured problem. The type of this study was qualitative descriptive. The subjects in this study were 100 undergraduate students of Mathematics Education at one of the private universities in Palembang city. The data in this study was collected through two test items with essay form. The results of this study showed that, from the first problem, only 8% students can solve it, but do not check back again to validate the process. Based on a scoring rubric that follows Polya strategy, their answer satisfied 2 4 2 0 patterns. But, from the second problem, 45% students satisfied it. This is because the second problem imitated from the example that was given in learning process. The average score of undergraduate students mathematical problem-solving ability in solving well-structured problems showed 56.00 with standard deviation was 13.22. It means that, from 0 - 100 scale, undergraduate students mathematical problem-solving ability can be categorized low. From this result, the conclusion was undergraduate students of mathematics education in Palembang still have a problem in solving mathematics well-structured problem.

  1. Pattern of mathematic representation ability in magnetic electricity problem

    NASA Astrophysics Data System (ADS)

    Hau, R. R. H.; Marwoto, P.; Putra, N. M. D.

    2018-03-01

    The mathematic representation ability in solving magnetic electricity problem gives information about the way students understand magnetic electricity. Students have varied mathematic representation pattern ability in solving magnetic electricity problem. This study aims to determine the pattern of students' mathematic representation ability in solving magnet electrical problems.The research method used is qualitative. The subject of this study is the fourth semester students of UNNES Physics Education Study Program. The data collection is done by giving a description test that refers to the test of mathematical representation ability and interview about field line topic and Gauss law. The result of data analysis of student's mathematical representation ability in solving magnet electric problem is categorized into high, medium and low category. The ability of mathematical representations in the high category tends to use a pattern of making known and asked symbols, writing equations, using quantities of physics, substituting quantities into equations, performing calculations and final answers. The ability of mathematical representation in the medium category tends to use several patterns of writing the known symbols, writing equations, using quantities of physics, substituting quantities into equations, performing calculations and final answers. The ability of mathematical representations in the low category tends to use several patterns of making known symbols, writing equations, substituting quantities into equations, performing calculations and final answer.

  2. The "Emerging" and "Emergent" Present: A View on the Indeterminate Nature of Mathematics Lessons

    ERIC Educational Resources Information Center

    Roth, Wolff-Michael; Maheux, Jean-François

    2014-01-01

    The notion of emergence has considerable currency in mathematics education. However, the notion tends to be used in a descriptive way rather than being theorized and developed as a phenomenon sui generis. The purpose of this article is to contribute to building a theory of "emergence." After providing an exemplifying description and…

  3. Applying Problem Solving to Statistics and Consumer Mathematics.

    ERIC Educational Resources Information Center

    Hawaii Univ., Honolulu. Curriculum Research and Development Group.

    This text is an example of a Selected Mathematics Applications (Level A) course, developed for the Hawaii State Department of Education. There are two basic parts to this document. Section one discusses the approach used to develop this course, and provides a brief description of current alternative materials and resources. No materials were found…

  4. Engaging Students in Mathematical Modeling through Service-Learning

    ERIC Educational Resources Information Center

    Carducci, Olivia M.

    2014-01-01

    I have included a service-learning project in my mathematical modeling course for the last 6 years. This article describes my experience with service-learning in this course. The article includes a description of the course and the service-learning projects. There is a discussion of how to connect with community partners and identify…

  5. Towards an accurate description of perovskite ferroelectrics: exchange and correlation effects

    DOE PAGES

    Yuk, Simuck F.; Pitike, Krishna Chaitanya; Nakhmanson, Serge M.; ...

    2017-03-03

    Using the van der Waals density functional with C09 exchange (vdW-DF-C09), which has been applied to describing a wide range of dispersion-bound systems, we explore the physical properties of prototypical ABO 3 bulk ferroelectric oxides. Surprisingly, vdW-DF-C09 provides a superior description of experimental values for lattice constants, polarization and bulk moduli, exhibiting similar accuracy to the modified Perdew-Burke-Erzenhoff functional which was designed specifically for bulk solids (PBEsol). The relative performance of vdW-DF-C09 is strongly linked to the form of the exchange enhancement factor which, like PBEsol, tends to behave like the gradient expansion approximation for small reduced gradients. These resultsmore » suggest the general-purpose nature of the class of vdW-DF functionals, with particular consequences for predicting material functionality across dense and sparse matter regimes.« less

  6. Towards an accurate description of perovskite ferroelectrics: exchange and correlation effects

    PubMed Central

    Yuk, Simuck F.; Pitike, Krishna Chaitanya; Nakhmanson, Serge M.; Eisenbach, Markus; Li, Ying Wai; Cooper, Valentino R.

    2017-01-01

    Using the van der Waals density functional with C09 exchange (vdW-DF-C09), which has been applied to describing a wide range of dispersion-bound systems, we explore the physical properties of prototypical ABO3 bulk ferroelectric oxides. Surprisingly, vdW-DF-C09 provides a superior description of experimental values for lattice constants, polarization and bulk moduli, exhibiting similar accuracy to the modified Perdew-Burke-Erzenhoff functional which was designed specifically for bulk solids (PBEsol). The relative performance of vdW-DF-C09 is strongly linked to the form of the exchange enhancement factor which, like PBEsol, tends to behave like the gradient expansion approximation for small reduced gradients. These results suggest the general-purpose nature of the class of vdW-DF functionals, with particular consequences for predicting material functionality across dense and sparse matter regimes. PMID:28256544

  7. Experiences Teaching a Software Aided Mathematics Course for a General University Audience.

    ERIC Educational Resources Information Center

    McGivney, Raymond J., Jr.

    1990-01-01

    Described is a nonmajor mathematics course taught using computers and lab experiments. Included are the challenge, solution, description of the first class, problems, successes, the syllabus, student comments, and the conclusion. (KR)

  8. Inquiry based learning: a student centered learning to develop mathematical habits of mind

    NASA Astrophysics Data System (ADS)

    Handayani, A. D.; Herman, T.; Fatimah, S.; Setyowidodo, I.; Katminingsih, Y.

    2018-05-01

    Inquiry based learning is learning that based on understanding constructivist mathematics learning. Learning based on constructivism is the Student centered learning. In constructivism, students are trained and guided to be able to construct their own knowledge on the basis of the initial knowledge that they have before. This paper explained that inquiry based learning can be used to developing student’s Mathematical habits of mind. There are sixteen criteria Mathematical Habits of mind, among which are diligent, able to manage time well, have metacognition ability, meticulous, etc. This research method is qualitative descriptive. The result of this research is that the instruments that have been developed to measure mathematical habits of mind are validated by the expert. The conclusion is the instrument of mathematical habits of mind are valid and it can be used to measure student’s mathematical habits of mind.

  9. DigitalHuman (DH): An Integrative Mathematical Model ofHuman Physiology

    NASA Technical Reports Server (NTRS)

    Hester, Robert L.; Summers, Richard L.; lIescu, Radu; Esters, Joyee; Coleman, Thomas G.

    2010-01-01

    Mathematical models and simulation are important tools in discovering the key causal relationships governing physiological processes and improving medical intervention when physiological complexity is a central issue. We have developed a model of integrative human physiology called DigitalHuman (DH) consisting of -5000 variables modeling human physiology describing cardiovascular, renal, respiratory, endocrine, neural and metabolic physiology. Users can view time-dependent solutions and interactively introduce perturbations by altering numerical parameters to investigate new hypotheses. The variables, parameters and quantitative relationships as well as all other model details are described in XML text files. All aspects of the model, including the mathematical equations describing the physiological processes are written in XML open source, text-readable files. Model structure is based upon empirical data of physiological responses documented within the peer-reviewed literature. The model can be used to understand proposed physiological mechanisms and physiological interactions that may not be otherwise intUitively evident. Some of the current uses of this model include the analyses of renal control of blood pressure, the central role of the liver in creating and maintaining insulin resistance, and the mechanisms causing orthostatic hypotension in astronauts. Additionally the open source aspect of the modeling environment allows any investigator to add detailed descriptions of human physiology to test new concepts. The model accurately predicts both qualitative and more importantly quantitative changes in clinically and experimentally observed responses. DigitalHuman provides scientists a modeling environment to understand the complex interactions of integrative physiology. This research was supported by.NIH HL 51971, NSF EPSCoR, and NASA

  10. More than Meets the Eye: Patterns and Shifts in Middle School Mathematics Teachers' Descriptions of Models

    ERIC Educational Resources Information Center

    Wilkerson, Michelle H.; Bautista, Alfredo; Tobin, Roger G.; Brizuela, Bárbara M.; Cao, Ying

    2018-01-01

    Modeling is a major topic of interest in mathematics education. However, the field's definition of models is diverse. Less is known about what teachers identify as mathematical models, even though it is teachers who ultimately enact modeling activities in the classroom. In this study, we asked nine middle school teachers with a variety of academic…

  11. The Math Gap: a description of the mathematics performance of preschool-aged deaf/hard-of-hearing children.

    PubMed

    Pagliaro, Claudia M; Kritzer, Karen L

    2013-04-01

    Over decades and across grade levels, deaf/hard-of-hearing (d/hh) student performance in mathematics has shown a gap in achievement. It is unclear, however, exactly when this gap begins to emerge and in what areas. This study describes preschool d/hh children's knowledge of early mathematics concepts. Both standardized and nonstandardized measures were used to assess understanding in number, geometry, measurement, problem solving, and patterns, reasoning and algebra. Results present strong evidence that d/hh students' difficulty in mathematics may begin prior to the start of formal schooling. Findings also show areas of strength (geometry) and weakness (problem solving and measurement) for these children. Evidence of poor foundational performance may relate to later academic achievement.

  12. A novel approach to teach the generation of bioelectrical potentials from a descriptive and quantitative perspective.

    PubMed

    Rodriguez-Falces, Javier

    2013-12-01

    In electrophysiology studies, it is becoming increasingly common to explain experimental observations using both descriptive methods and quantitative approaches. However, some electrophysiological phenomena, such as the generation of extracellular potentials that results from the propagation of the excitation source along the muscle fiber, are difficult to describe and conceptualize. In addition, most traditional approaches aimed at describing extracellular potentials consist of complex mathematical machinery that gives no chance for physical interpretation. The aim of the present study is to present a new method to teach the formation of extracellular potentials around a muscle fiber from both a descriptive and quantitative perspective. The implementation of this method was tested through a written exam and a satisfaction survey. The new method enhanced the ability of students to visualize the generation of bioelectrical potentials. In addition, the new approach improved students' understanding of how changes in the fiber-to-electrode distance and in the shape of the excitation source are translated into changes in the extracellular potential. The survey results show that combining general principles of electrical fields with accurate graphic imagery gives students an intuitive, yet quantitative, feel for electrophysiological signals and enhances their motivation to continue their studies in the biomedical engineering field.

  13. Student’s social interaction in mathematics learning

    NASA Astrophysics Data System (ADS)

    Apriliyanto, B.; Saputro, D. R. S.; Riyadi

    2018-03-01

    Mathematics learning achievement is influenced by the internal and external factor of the students. One of the influencing external factors is social interaction with friends in learning activities. In modern learning, the learning is student-centered, so the student interaction is needed to learn about certain basic competence. Potential and motivation of students in learning are expected to develop with good social interaction in order to get maximum results. Social interaction is an important aspect of learning Mathematics because students get the opportunity to express their own thoughts in order to encourage a reflection on the knowledge they have. This research uses the correlational descriptive method involving 36 students for the tenth grade, eleventh grade, and twelfth grade of SMA Negeri 1 Wuryantoro and data collecting technique using questionnaire for social interaction and documentation for learning outcome. The result of this research shows that learning achievement and social interaction of students are not good. Based on the result of data analysis, it is shown that the social interaction and Mathematics learning achievement are still in the low level. This research concludes that students’ social interaction influences student learning achievement in Mathematics subjects.

  14. Cognitive Predictors of Achievement Growth in Mathematics: A Five Year Longitudinal Study

    PubMed Central

    Geary, David C.

    2011-01-01

    The study's goal was to identify the beginning of first grade quantitative competencies that predict mathematics achievement start point and growth through fifth grade. Measures of number, counting, and arithmetic competencies were administered in early first grade and used to predict mathematics achievement through fifth (n = 177), while controlling for intelligence, working memory, and processing speed. Multilevel models revealed intelligence, processing speed, and the central executive component of working memory predicted achievement or achievement growth in mathematics and, as a contrast domain, word reading. The phonological loop was uniquely predictive of word reading and the visuospatial sketch pad of mathematics. Early fluency in processing and manipulating numerical set size and Arabic numerals, accurate use of sophisticated counting procedures for solving addition problems, and accuracy in making placements on a mathematical number line were uniquely predictive of mathematics achievement. Use of memory-based processes to solve addition problems predicted mathematics and reading achievement but in different ways. The results identify the early quantitative competencies that uniquely contribute to mathematics learning. PMID:21942667

  15. Use of a Mathematics Word Problem Strategy to Improve Achievement for Students with Mild Disabilities

    ERIC Educational Resources Information Center

    Taber, Mary R.

    2013-01-01

    Mathematics can be a difficult topic both to teach and to learn. Word problems specifically can be difficult for students with disabilities because they have to conceptualize what the problem is asking for, and they must perform the correct operation accurately. Current trends in mathematics instruction stem from the National Council of Teachers…

  16. Workplace Mathematics Research: Reflections on Personal Practical Experiences

    ERIC Educational Resources Information Center

    Naresh, Nirmala; Chahine, Iman

    2013-01-01

    This article describes our transitions through three phases of a reflective cycle as a journey from the past to the future. In the descriptive phase, we delve into our past research experiences and address questions such as: What is the role of mathematics at work? In doing so, we uncovered additional venues for exploration that called for a new…

  17. Mathematics anxiety and mathematics achievement

    NASA Astrophysics Data System (ADS)

    Sherman, Brian F.; Wither (Post.), David P.

    2003-09-01

    This paper is a distillation of the major result from the 1998 Ph.D. thesis of the late David Wither. It details a longitudinal study over five years of the relationship between mathematics anxiety and mathematics achievement. It starts from the already well documented negative correlation between the two, and seeks to establish one of the three hypotheses—that mathematics anxiety causes an impairment of mathematics achievement; that lack of mathematics achievement causes mathematics anxiety; or that there is a third underlying cause of the two.

  18. Explicating the Role of Mathematical Tasks in Conceptual Learning: An Elaboration of the Hypothetical Learning Trajectory

    ERIC Educational Resources Information Center

    Simon, Martin A.; Tzur, Ron

    2004-01-01

    Simon's (1995) development of the construct of hypothetical learning trajectory (HLT) offered a description of key aspects of planning mathematics lessons. An HLT consists of the goal for the students' learning, the mathematical tasks that will be used to promote student learning, and hypotheses about the process of the students' learning.…

  19. Workshop in Al Kalfus: History of Mathematics, Problem Solving, Enrichment. Dissemination Packet--Summer 1989: Booklet #7.

    ERIC Educational Resources Information Center

    Barbera, Janet; And Others

    This booklet is the seventh in a series of nine from the Teacher Training Institute at Hofstra University (New York) and synthesizes the contribution of the late mathematics educator, Alfred Kalfus, to the institute as adviser, guest lecturer, and instructor. Descriptions of the enrichment topics for secondary school mathematics included in his…

  20. An analysis of primary school students’ representational ability in mathematics based on gender perspective

    NASA Astrophysics Data System (ADS)

    Kowiyah; Mulyawati, I.

    2018-01-01

    Mathematic representation is one of the basic mathematic skills that allows students to communicate their mathematic ideas through visual realities such as pictures, tables, mathematic expressions and mathematic equities. The present research aims at: 1) analysing students’ mathematic representation ability in solving mathematic problems and 2) examining the difference of students’ mathematic ability based on their gender. A total of sixty primary school students participated in this study comprising of thirty males and thirty females. Data required in this study were collected through mathematic representation tests, interviews and test evaluation rubric. Findings of this study showed that students’ mathematic representation of visual realities (image and tables) was reported higher at 62.3% than at in the form of description (or statement) at 8.6%. From gender perspective, male students performed better than the females at action planning stage. The percentage of males was reported at 68% (the highest), 33% (medium) and 21.3% (the lowest) while the females were at 36% (the highest), 37.7% (medium) and 32.6% (the lowest).

  1. Mathematizing Process of Junior High School Students to Improve Mathematics Literacy Refers PISA on RCP Learning

    NASA Astrophysics Data System (ADS)

    Wardono; Mariani, S.; Hendikawati, P.; Ikayani

    2017-04-01

    Mathematizing process (MP) is the process of modeling a phenomenon mathematically or establish the concept of a phenomenon. There are two mathematizing that is Mathematizing Horizontal (MH) and Mathematizing Vertical (MV). MH as events changes contextual problems into mathematical problems, while MV is the process of formulation of the problem into a variety of settlement mathematics by using some appropriate rules. Mathematics Literacy (ML) is the ability to formulate, implement and interpret mathematics in various contexts, including the capacity to perform reasoning mathematically and using the concepts, procedures, and facts to describe, explain or predict phenomena incident. If junior high school students are conditioned continuously to conduct mathematizing activities on RCP (RME-Card Problem) learning, it will be able to improve ML that refers PISA. The purpose of this research is to know the capability of the MP grade VIII on ML content shape and space with the matter of the cube and beams with RCP learning better than the scientific learning, upgrade MP grade VIII in the issue of the cube and beams with RCP learning better than the scientific learning in terms of cognitive styles reflective and impulsive the MP grade VIII with the approach of the RCP learning in terms of cognitive styles reflective and impulsive This research is the mixed methods model concurrent embedded. The population in this study, i.e., class VIII SMPN 1 Batang with sample two class. Data were taken with the observation, interviews, and tests and analyzed with a different test average of one party the right qualitative and descriptive. The results of this study demonstrate the capability of the MP student with RCP learning better than the scientific learning, upgrade MP with RCP learning better compare with scientific learning in term cognitive style of reflective and impulsive. The subject of the reflective group top, middle, and bottom can meet all the process of MH indicators are

  2. Preferences of Teaching Methods and Techniques in Mathematics with Reasons

    ERIC Educational Resources Information Center

    Ünal, Menderes

    2017-01-01

    In this descriptive study, the goal was to determine teachers' preferred pedagogical methods and techniques in mathematics. Qualitative research methods were employed, primarily case studies. 40 teachers were randomly chosen from various secondary schools in Kirsehir during the 2015-2016 educational terms, and data were gathered via…

  3. Merging Mathematics and English: One Approach to Bridging the Disciplines.

    ERIC Educational Resources Information Center

    Hansbarger, J. Clark; Stewart, Eric Lane

    1996-01-01

    Discusses two six-week projects for high school students involving qualitative and quantitative research methods to integrate mathematics and English. Students use descriptive statistics and prose to present findings about (1) their school space and (2) daily life for American troops in the Gulf War. (KMC)

  4. Chapter I Mathematics Program, 1983-84. Report of Evaluation.

    ERIC Educational Resources Information Center

    Tompkins, John F.

    This report provides an evaluation of the Chapter I mathematics program for 1,020 first through eighth grade students in the Des Moines Independent Community School District. Included is a description of the program, information on program budget and expenditures, and narrative accounts of the attainment of 17 performance and process objectives.…

  5. The Role of Self-Assessment in Foundation of Mathematics Learning

    NASA Astrophysics Data System (ADS)

    Masriyah

    2018-01-01

    This research is motivated by the low performance of students who took Foundations of Mathematics course. This study was aimed to describe (1) the learning outcomes of students who learned Mathematics Foundation after learning axiomatic applying self-assessment; (2) the difficulty of students and the alternative solutions; and (3) the response of students toward Foundation of Mathematics learning taught by applying self-assessment. This research was a descriptive research. The subjects were 25 mathematics students who studied Foundation of Mathematics in odd semester of the 2015/2016 academic year. Data collection was done using questionnaires, and testing methods. Based on the results of data analysis, it can be concluded that the learning outcomes of students were categorized as “good.” Student responses were positive; the difficulties lied in the sub material: Classification of Axiom Systems and the requirements, Theorem and how the formation, and finite geometry. The alternatives deal with these difficulties are to give emphasis and explanation as needed on these materials, as well as provide some more exercises to reinforce their understanding.

  6. Mathematics Education and the Objectivist Programme in HPS

    NASA Astrophysics Data System (ADS)

    Glas, Eduard

    2013-06-01

    Using history of mathematics for studying concepts, methods, problems and other internal features of the discipline may give rise to a certain tension between descriptive adequacy and educational demands. Other than historians, educators are concerned with mathematics as a normatively defined discipline. Teaching cannot but be based on a pre-understanding of what mathematics `is' or, in other words, on a normative (methodological, philosophical) view of the identity or nature of the discipline. Educators are primarily concerned with developments at the level of objective mathematical knowledge, that is: with the relations between successive theories, problems and proposed solutions—relations which are independent of whatever has been the role of personal or collective beliefs, convictions, traditions and other historical circumstances. Though not exactly `historical' in the usual sense, I contend that this `objectivist' approach does represent one among other entirely legitimate and valuable approaches to the historical development of mathematics. Its retrospective importance to current practitioners and students is illustrated by a reconstruction of the development of Eudoxus's theory of proportionality in response to the problem of irrationality, and the way in which Dedekind some two millennia later almost literally used this ancient theory for the rigorous introduction of irrational numbers and hence of the real number continuum.

  7. Basic research and data analysis for the National Geodetic Satellite Program and for the Earth and Ocean Physics Application Program

    NASA Technical Reports Server (NTRS)

    1974-01-01

    Accomplishments in the continuing programs are reported. The data were obtained in support of the following broad objectives: (1) to provide a precise and accurate geometric description of the earth's surface; (2) to provide a precise and accurate mathematical description of the earth's gravitational field; and (3) to determine time variations of the geometry of the ocean surface, the solid earth, the gravity field, and other geophysical parameters.

  8. Student Achievement in Turkey, According to Question Types Used in PISA 2003-2012 Mathematic Literacy Tests

    ERIC Educational Resources Information Center

    Özkan, Yesim Özer; Özaslan, Nesrin

    2018-01-01

    The aim of this study is to determine the level of achievement of students participating in Programme for International Student Assessment (PISA) 2003 and PISA 2012 tests in Turkey according to questions in the mathematical literacy test. This study is a descriptive survey. Within the scope of the study, the mathematical literacy test items were…

  9. Mathematical Description Development of Reactions of Metallic Gallium Using Kinetic Block Diagram

    NASA Astrophysics Data System (ADS)

    Yakovleva, A. A.; Soboleva, V. G.; Filatova, E. G.

    2018-05-01

    A kinetic block diagram based on a logical sequence of actions in the mathematical processing of a kinetic data is used. A type of reactions of metallic gallium in hydrochloric acid solutions is determined. It has been established that the reactions of the formation of gallium oxide and its salts proceed independently and in the absence of the diffusion resistance. Kinetic models connecting the constants of the reaction rate with the activation energy and describing the evolution of the process are obtained.

  10. Prospects of a mathematical theory of human behavior in complex man-machine systems tasks. [time sharing computer analogy of automobile driving

    NASA Technical Reports Server (NTRS)

    Johannsen, G.; Rouse, W. B.

    1978-01-01

    A hierarchy of human activities is derived by analyzing automobile driving in general terms. A structural description leads to a block diagram and a time-sharing computer analogy. The range of applicability of existing mathematical models is considered with respect to the hierarchy of human activities in actual complex tasks. Other mathematical tools so far not often applied to man machine systems are also discussed. The mathematical descriptions at least briefly considered here include utility, estimation, control, queueing, and fuzzy set theory as well as artificial intelligence techniques. Some thoughts are given as to how these methods might be integrated and how further work might be pursued.

  11. Elementary School Mathematics: What Parents Should Know About... Estimation.

    ERIC Educational Resources Information Center

    Reys, Barbara

    Parents have many opportunities every day to develop, nurture, and refine their children's mathematics skills. This pamphlet was designed to help parents become aware of these opportunities and to encourage them to participate in their children's learning process. Estimation is the skill of making a reasonably accurate guess and is prominently…

  12. The mathematical research for the Kuramoto model of the describing neuronal synchrony in the brain

    NASA Astrophysics Data System (ADS)

    Lin, Chang; Lin, Mai-mai

    2009-08-01

    The Kuramoto model of the describing neuronal synchrony is mathematically investigated in the brain. A general analytical solutions (the most sententious description) for the Kuramoto model, incorporating the inclusion of a Ki,j (t) term to represent time-varying coupling strengths, have been obtained by using the precise mathematical approach. We derive an exact analytical expression, opening out the connotative and latent linear relation, for the mathematical character of the phase configurations in the Kuramoto model of the describing neuronal synchrony in the brain.

  13. The description of a method for accurately estimating creatinine clearance in acute kidney injury.

    PubMed

    Mellas, John

    2016-05-01

    Acute kidney injury (AKI) is a common and serious condition encountered in hospitalized patients. The severity of kidney injury is defined by the RIFLE, AKIN, and KDIGO criteria which attempt to establish the degree of renal impairment. The KDIGO guidelines state that the creatinine clearance should be measured whenever possible in AKI and that the serum creatinine concentration and creatinine clearance remain the best clinical indicators of renal function. Neither the RIFLE, AKIN, nor KDIGO criteria estimate actual creatinine clearance. Furthermore there are no accepted methods for accurately estimating creatinine clearance (K) in AKI. The present study describes a unique method for estimating K in AKI using urine creatinine excretion over an established time interval (E), an estimate of creatinine production over the same time interval (P), and the estimated static glomerular filtration rate (sGFR), at time zero, utilizing the CKD-EPI formula. Using these variables estimated creatinine clearance (Ke)=E/P * sGFR. The method was tested for validity using simulated patients where actual creatinine clearance (Ka) was compared to Ke in several patients, both male and female, and of various ages, body weights, and degrees of renal impairment. These measurements were made at several serum creatinine concentrations in an attempt to determine the accuracy of this method in the non-steady state. In addition E/P and Ke was calculated in hospitalized patients, with AKI, and seen in nephrology consultation by the author. In these patients the accuracy of the method was determined by looking at the following metrics; E/P>1, E/P<1, E=P in an attempt to predict progressive azotemia, recovering azotemia, or stabilization in the level of azotemia respectively. In addition it was determined whether Ke<10 ml/min agreed with Ka and whether patients with AKI on renal replacement therapy could safely terminate dialysis if Ke was greater than 5 ml/min. In the simulated patients there

  14. Mathematical challenges from theoretical/computational chemistry

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    NONE

    1995-12-31

    The committee believes that this report has relevance and potentially valuable suggestions for a wide range of readers. Target audiences include: graduate departments in the mathematical and chemical sciences; federal and private agencies that fund research in the mathematical and chemical sciences; selected industrial and government research and development laboratories; developers of software and hardware for computational chemistry; and selected individual researchers. Chapter 2 of this report covers some history of computational chemistry for the nonspecialist, while Chapter 3 illustrates the fruits of some past successful cross-fertilization between mathematical scientists and computational/theoretical chemists. In Chapter 4 the committee has assembledmore » a representative, but not exhaustive, survey of research opportunities. Most of these are descriptions of important open problems in computational/theoretical chemistry that could gain much from the efforts of innovative mathematical scientists, written so as to be accessible introductions to the nonspecialist. Chapter 5 is an assessment, necessarily subjective, of cultural differences that must be overcome if collaborative work is to be encouraged between the mathematical and the chemical communities. Finally, the report ends with a brief list of conclusions and recommendations that, if followed, could promote accelerated progress at this interface. Recognizing that bothersome language issues can inhibit prospects for collaborative research at the interface between distinctive disciplines, the committee has attempted throughout to maintain an accessible style, in part by using illustrative boxes, and has included at the end of the report a glossary of technical terms that may be familiar to only a subset of the target audiences listed above.« less

  15. Redundancy management of electrohydraulic servoactuators by mathematical model referencing

    NASA Technical Reports Server (NTRS)

    Campbell, R. A.

    1971-01-01

    A description of a mathematical model reference system is presented which provides redundancy management for an electrohydraulic servoactuator. The mathematical model includes a compensation network that calculates reference parameter perturbations induced by external disturbance forces. This is accomplished by using the measured pressure differential data taken from the physical system. This technique was experimentally verified by tests performed using the H-1 engine thrust vector control system for Saturn IB. The results of these tests are included in this report. It was concluded that this technique improves the tracking accuracy of the model reference system to the extent that redundancy management of electrohydraulic servosystems may be performed using this method.

  16. Math Description Engine Software Development Kit

    NASA Technical Reports Server (NTRS)

    Shelton, Robert O.; Smith, Stephanie L.; Dexter, Dan E.; Hodgson, Terry R.

    2010-01-01

    The Math Description Engine Software Development Kit (MDE SDK) can be used by software developers to make computer-rendered graphs more accessible to blind and visually-impaired users. The MDE SDK generates alternative graph descriptions in two forms: textual descriptions and non-verbal sound renderings, or sonification. It also enables display of an animated trace of a graph sonification on a visual graph component, with color and line-thickness options for users having low vision or color-related impairments. A set of accessible graphical user interface widgets is provided for operation by end users and for control of accessible graph displays. Version 1.0 of the MDE SDK generates text descriptions for 2D graphs commonly seen in math and science curriculum (and practice). The mathematically rich text descriptions can also serve as a virtual math and science assistant for blind and sighted users, making graphs more accessible for everyone. The MDE SDK has a simple application programming interface (API) that makes it easy for programmers and Web-site developers to make graphs accessible with just a few lines of code. The source code is written in Java for cross-platform compatibility and to take advantage of Java s built-in support for building accessible software application interfaces. Compiled-library and NASA Open Source versions are available with API documentation and Programmer s Guide at http:/ / prim e.jsc.n asa. gov.

  17. Early identification and interventions for students with mathematics difficulties.

    PubMed

    Gersten, Russell; Jordan, Nancy C; Flojo, Jonathan R

    2005-01-01

    This article highlights key findings from the small body of research on mathematics difficulties (MD) relevant to early identification and early intervention. The research demonstrates that (a) for many children, mathematics difficulties are not stable over time; (b) the presence of reading difficulties seems related to slower progress in many aspects of mathematics; (c) almost all students with MD demonstrate problems with accurate and automatic retrieval of basic arithmetic combinations, such as 6 + 3. The following measures appear to be valid and reliable indicators of potential MD in kindergartners: (a) magnitude comparison (i.e., knowing which digit in a pair is larger), (b) sophistication of counting strategies, (c) fluent identification of numbers, and (d) working memory (as evidenced by reverse digit span). These are discussed in terms of the components of number sense. Implications for early intervention strategies are explored.

  18. Methodology and Results of Mathematical Modelling of Complex Technological Processes

    NASA Astrophysics Data System (ADS)

    Mokrova, Nataliya V.

    2018-03-01

    The methodology of system analysis allows us to draw a mathematical model of the complex technological process. The mathematical description of the plasma-chemical process was proposed. The importance the quenching rate and initial temperature decrease time was confirmed for producing the maximum amount of the target product. The results of numerical integration of the system of differential equations can be used to describe reagent concentrations, plasma jet rate and temperature in order to achieve optimal mode of hardening. Such models are applicable both for solving control problems and predicting future states of sophisticated technological systems.

  19. The Applied Mathematics for Power Systems (AMPS)

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Chertkov, Michael

    2012-07-24

    Increased deployment of new technologies, e.g., renewable generation and electric vehicles, is rapidly transforming electrical power networks by crossing previously distinct spatiotemporal scales and invalidating many traditional approaches for designing, analyzing, and operating power grids. This trend is expected to accelerate over the coming years, bringing the disruptive challenge of complexity, but also opportunities to deliver unprecedented efficiency and reliability. Our Applied Mathematics for Power Systems (AMPS) Center will discover, enable, and solve emerging mathematics challenges arising in power systems and, more generally, in complex engineered networks. We will develop foundational applied mathematics resulting in rigorous algorithms and simulation toolboxesmore » for modern and future engineered networks. The AMPS Center deconstruction/reconstruction approach 'deconstructs' complex networks into sub-problems within non-separable spatiotemporal scales, a missing step in 20th century modeling of engineered networks. These sub-problems are addressed within the appropriate AMPS foundational pillar - complex systems, control theory, and optimization theory - and merged or 'reconstructed' at their boundaries into more general mathematical descriptions of complex engineered networks where important new questions are formulated and attacked. These two steps, iterated multiple times, will bridge the growing chasm between the legacy power grid and its future as a complex engineered network.« less

  20. Natural Systems: MINNEMAST Coordinated Mathematics - Science Series, Unit 29.

    ERIC Educational Resources Information Center

    Bakke, Jeannette; And Others

    This volume is the last in a series of 29 coordinated MINNEMAST units in mathematics and science for kindergarten and the primary grades. Intended for use by third-grade teachers, this unit guide provides a summary and overview of the unit, a list of materials needed, and descriptions of three groups of lessons. The purposes and procedures for…

  1. Brain Hemisphericity and Mathematics Achievement of High School Students

    ERIC Educational Resources Information Center

    Fernandez, Sanny F.

    2011-01-01

    This study aimed to find out the brain hemisphericity and mathematics achievement of high school students. The respondents of the study were the 168 first year high school students of Colegio de San Jose, during school year 2010-2011 who were chosen through stratified random sampling. The descriptive and interview methods of research were used in…

  2. The relationship among mathematics anxiety, beliefs about mathematics, mathematics self-efficacy, and mathematics performance in associate degree nursing students.

    PubMed

    Walsh, Kathleen A

    2008-01-01

    This research explored nursing students' mathematics anxiety, beliefs about mathematics, and mathematics self-efficacy in relation to performance on a medication mathematics test. Results revealed that the participants experienced some mathematics anxiety and had positive beliefs about mathematics and mathematics self-efficacy. Qualitative responses indicated that participants worried about the consequences of failing the medication mathematics test and that practice helped reduce this anxiety. In addition, participants acknowledged the importance of correct dosage calculations for nursing practice. Implications for nursing education are discussed.

  3. A Weibull statistics-based lignocellulose saccharification model and a built-in parameter accurately predict lignocellulose hydrolysis performance.

    PubMed

    Wang, Mingyu; Han, Lijuan; Liu, Shasha; Zhao, Xuebing; Yang, Jinghua; Loh, Soh Kheang; Sun, Xiaomin; Zhang, Chenxi; Fang, Xu

    2015-09-01

    Renewable energy from lignocellulosic biomass has been deemed an alternative to depleting fossil fuels. In order to improve this technology, we aim to develop robust mathematical models for the enzymatic lignocellulose degradation process. By analyzing 96 groups of previously published and newly obtained lignocellulose saccharification results and fitting them to Weibull distribution, we discovered Weibull statistics can accurately predict lignocellulose saccharification data, regardless of the type of substrates, enzymes and saccharification conditions. A mathematical model for enzymatic lignocellulose degradation was subsequently constructed based on Weibull statistics. Further analysis of the mathematical structure of the model and experimental saccharification data showed the significance of the two parameters in this model. In particular, the λ value, defined the characteristic time, represents the overall performance of the saccharification system. This suggestion was further supported by statistical analysis of experimental saccharification data and analysis of the glucose production levels when λ and n values change. In conclusion, the constructed Weibull statistics-based model can accurately predict lignocellulose hydrolysis behavior and we can use the λ parameter to assess the overall performance of enzymatic lignocellulose degradation. Advantages and potential applications of the model and the λ value in saccharification performance assessment were discussed. Copyright © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  4. Predicting Relationships between Mathematics Anxiety, Mathematics Teaching Anxiety, Self-Efficacy Beliefs towards Mathematics and Mathematics Teaching

    ERIC Educational Resources Information Center

    Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent

    2017-01-01

    The purpose of the research is to investigate the relationships between self-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacy beliefs toward mathematics teaching, mathematics teaching anxiety variables and testing the relationships between these variables with structural equation model. The sample of the research, which…

  5. Application of mathematical modeling in sustained release delivery systems.

    PubMed

    Grassi, Mario; Grassi, Gabriele

    2014-08-01

    This review, presenting as starting point the concept of the mathematical modeling, is aimed at the physical and mathematical description of the most important mechanisms regulating drug delivery from matrix systems. The precise knowledge of the delivery mechanisms allows us to set up powerful mathematical models which, in turn, are essential for the design and optimization of appropriate drug delivery systems. The fundamental mechanisms for drug delivery from matrices are represented by drug diffusion, matrix swelling, matrix erosion, drug dissolution with possible recrystallization (e.g., as in the case of amorphous and nanocrystalline drugs), initial drug distribution inside the matrix, matrix geometry, matrix size distribution (in the case of spherical matrices of different diameter) and osmotic pressure. Depending on matrix characteristics, the above-reported variables may play a different role in drug delivery; thus the mathematical model needs to be built solely on the most relevant mechanisms of the particular matrix considered. Despite the somewhat diffident behavior of the industrial world, in the light of the most recent findings, we believe that mathematical modeling may have a tremendous potential impact in the pharmaceutical field. We do believe that mathematical modeling will be more and more important in the future especially in the light of the rapid advent of personalized medicine, a novel therapeutic approach intended to treat each single patient instead of the 'average' patient.

  6. [Mathematical calculation of strength of the vertebral column in surgical treatment of unstable fractures of the spine].

    PubMed

    Orlov, S V; Kanykin, A Iu; Moskalev, V P; Shchedrenok, V V; Sedov, R L

    2009-01-01

    A mathematical model of a three-vertebra complex was developed in order to make an exact calculation of loss of supporting ability of the vertebral column in trauma. Mathematical description of the dynamic processes was based on Lagrange differential equation of the second order. The degree of compression and instability of the three-vertebra complex, established using mathematical modeling, determines the decision on the surgical treatment and might be considered as a prognostic criterion of the course of the compression trauma of the spine. The method of mathematical modeling of supporting ability of the vertebral column was used in 72 patients.

  7. HIDDEN DISPARITIES: HOW COURSES AND CURRICULA SHAPE OPPORTUNITIES IN MATHEMATICS DURING HIGH SCHOOL1

    PubMed Central

    Schiller, Kathryn S.; Schmidt, William H.; Muller, Chandra; Houang, Richard

    2011-01-01

    Efforts to promote academic achievement by increasing access to courses, especially in mathematics, may mask educational disparities if variations in curriculum are not also monitored. A multi-dimensional description of students’ mathematics curricula during high school was obtained from analyses of surveys, transcripts, and textbooks collected for a nationally representative study of adolescents during the mid-1990s. Few gaps in the number of years or credits in mathematics coursework were found. However, the quantity and cognitive challenge of instructional materials in textbooks adopted for those courses differed significantly both across and within mathematics tracks. Differences in the quality of curriculum accumulating during high school were also related to parents’ education level. Reducing such gaps in learning opportunities would require teachers to supplement adopted instructional materials to ensure that all students receive a high quality mathematics curriculum. PMID:23554547

  8. The Effect of Mathematics Research on Mathematics Majors' Mathematical Beliefs

    ERIC Educational Resources Information Center

    Goodson, Joshua E.

    2012-01-01

    This is a dissertation about the beliefs that mathematics majors have about mathematics and how their beliefs are affected by the introduction of mathematics research. The mathematics research presented to the students dealt with counting regular orbits of an action. Research has shown that the beliefs that teachers hold about mathematics…

  9. Electrooculography: Connecting Mind, Brain, and Behavior in Mathematics Education Research

    ERIC Educational Resources Information Center

    Shipulina, Olga V.; Campbell, Stephen R.; Cimen, Arda O.

    2009-01-01

    This paper reports on the potential roles and importance of electrooculography (EOG) for mathematics educational neuroscience research. EOG enables accurate measurements of eye-related behavior (i.e., blinks & movements) by recording changes in voltage potentials generated by eye-related behavior. We identify and discuss three main uses of EOG.…

  10. The use of cognitive task analysis to improve instructional descriptions of procedures.

    PubMed

    Clark, Richard E; Pugh, Carla M; Yates, Kenneth A; Inaba, Kenji; Green, Donald J; Sullivan, Maura E

    2012-03-01

    Surgical training relies heavily on the ability of expert surgeons to provide complete and accurate descriptions of a complex procedure. However, research from a variety of domains suggests that experts often omit critical information about the judgments, analysis, and decisions they make when solving a difficult problem or performing a complex task. In this study, we compared three methods for capturing surgeons' descriptions of how to perform the procedure for inserting a femoral artery shunt (unaided free-recall, unaided free-recall with simulation, and cognitive task analysis methods) to determine which method produced more accurate and complete results. Cognitive task analysis was approximately 70% more complete and accurate than free-recall and or free-recall during a simulation of the procedure. Ten expert trauma surgeons at a major urban trauma center were interviewed separately and asked to describe how to perform an emergency shunt procedure. Four surgeons provided an unaided free-recall description of the shunt procedure, five surgeons provided an unaided free-recall description of the procedure using visual aids and surgical instruments (simulation), and one (chosen randomly) was interviewed using cognitive task analysis (CTA) methods. An 11th vascular surgeon approved the final CTA protocol. The CTA interview with only one expert surgeon resulted in significantly greater accuracy and completeness of the descriptions compared with the unaided free-recall interviews with multiple expert surgeons. Surgeons in the unaided group omitted nearly 70% of necessary decision steps. In the free-recall group, heavy use of simulation improved surgeons' completeness when describing the steps of the procedure. CTA significantly increases the completeness and accuracy of surgeons' instructional descriptions of surgical procedures. In addition, simulation during unaided free-recall interviews may improve the completeness of interview data. Copyright © 2012 Elsevier Inc

  11. Accurate atomistic first-principles calculations of electronic stopping

    DOE PAGES

    Schleife, André; Kanai, Yosuke; Correa, Alfredo A.

    2015-01-20

    In this paper, we show that atomistic first-principles calculations based on real-time propagation within time-dependent density functional theory are capable of accurately describing electronic stopping of light projectile atoms in metal hosts over a wide range of projectile velocities. In particular, we employ a plane-wave pseudopotential scheme to solve time-dependent Kohn-Sham equations for representative systems of H and He projectiles in crystalline aluminum. This approach to simulate nonadiabatic electron-ion interaction provides an accurate framework that allows for quantitative comparison with experiment without introducing ad hoc parameters such as effective charges, or assumptions about the dielectric function. Finally, our work clearlymore » shows that this atomistic first-principles description of electronic stopping is able to disentangle contributions due to tightly bound semicore electrons and geometric aspects of the stopping geometry (channeling versus off-channeling) in a wide range of projectile velocities.« less

  12. Multilevel model of polycrystalline materials: grain boundary sliding description

    NASA Astrophysics Data System (ADS)

    Sharifullina, E.; Shveykin, A.; Trusov, P.

    2017-12-01

    Material behavior description in a wide range of thermomechanical effects is one of the topical areas in mathematical modeling. Inclusion of grain boundary sliding as an important mechanism of polycrystalline material deformation at elevated temperatures and predominant deformation mechanism of metals and alloys in structural superplasticity allows to simulate various deformation regimes and their transitions (including superplasticity regime with switch-on and switch-off regimes). The paper is devoted to description of grain boundary sliding in structure of two-level model, based on crystal plasticity, and relations for determination the contribution of this mechanism to inelastic deformation. Some results are presented concerning computational experiments of polycrystalline representative volume deformation using developed model.

  13. Descriptive Geometry in Educational Process of Technical University in Russia Today

    ERIC Educational Resources Information Center

    Voronina, Marianna V.; Tretyakova, Zlata O.; Moroz, Olga N.; Folomkin, Andrey I.

    2016-01-01

    The relevance of the investigated problem is caused by the need for monitoring the impact of the Unified State Examination (USE) on the level of mathematical culture and the level of geometric literacy of applicants and students of modern engineering universities of Russia. The need to determine the position of Descriptive Geometry in the…

  14. Computational Fluency Performance Profile of High School Students with Mathematics Disabilities

    ERIC Educational Resources Information Center

    Calhoon, Mary Beth; Emerson, Robert Wall; Flores, Margaret; Houchins, David E.

    2007-01-01

    The purpose of this descriptive study was to develop a computational fluency performance profile of 224 high school (Grades 9-12) students with mathematics disabilities (MD). Computational fluency performance was examined by grade-level expectancy (Grades 2-6) and skill area (whole numbers: addition, subtraction, multiplication, division;…

  15. Teachers' Mathematics as Mathematics-at-Work

    ERIC Educational Resources Information Center

    Bednarz, Nadine; Proulx, Jérôme

    2017-01-01

    Through recognising mathematics teachers as professionals who use mathematics in their workplace, this article traces a parallel between the mathematics enacted by teachers in their practice and the mathematics used in workplaces found in studies of professionals (e.g. nurses, engineers, bankers). This parallel is developed through the five…

  16. Accurate thermoelastic tensor and acoustic velocities of NaCl

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Marcondes, Michel L., E-mail: michel@if.usp.br; Chemical Engineering and Material Science, University of Minnesota, Minneapolis, 55455; Shukla, Gaurav, E-mail: shukla@physics.umn.edu

    Despite the importance of thermoelastic properties of minerals in geology and geophysics, their measurement at high pressures and temperatures are still challenging. Thus, ab initio calculations are an essential tool for predicting these properties at extreme conditions. Owing to the approximate description of the exchange-correlation energy, approximations used in calculations of vibrational effects, and numerical/methodological approximations, these methods produce systematic deviations. Hybrid schemes combining experimental data and theoretical results have emerged as a way to reconcile available information and offer more reliable predictions at experimentally inaccessible thermodynamics conditions. Here we introduce a method to improve the calculated thermoelastic tensor bymore » using highly accurate thermal equation of state (EoS). The corrective scheme is general, applicable to crystalline solids with any symmetry, and can produce accurate results at conditions where experimental data may not exist. We apply it to rock-salt-type NaCl, a material whose structural properties have been challenging to describe accurately by standard ab initio methods and whose acoustic/seismic properties are important for the gas and oil industry.« less

  17. Analysis of Prospective Mathematics Teachers’ Basic Teaching Skills (a Study of Mathematics Education Departement Students’ Field Experience Program at STKIP Garut)

    NASA Astrophysics Data System (ADS)

    Rahayu, D. V.

    2017-02-01

    This study was intended to figure out basic teaching skills of Mathematics Department Students of STKIP Garut at Field Experience Program in academic year 2014/2015. This study was qualitative research with analysis descriptive technique. Instrument used in this study was observation sheet to measure basic teaching mathematics skills. The result showed that ability of content mastery and explaining skill were in average category. Questioning skill, conducting variations skill and conducting assessment skill were in good category. Managing classroom skill and giving motivation skill were in poor category. Based on the result, it can be concluded that the students’ basic teaching skills weren’t optimal. It is recommended for the collegians to get lesson with appropriate strategy so that they can optimize their basic teaching skills.

  18. Formal logic rewrite system bachelor in teaching mathematical informatics

    NASA Astrophysics Data System (ADS)

    Habiballa, Hashim; Jendryscik, Radek

    2017-07-01

    The article presents capabilities of the formal rewrite logic system - Bachelor - for teaching theoretical computer science (mathematical informatics). The system Bachelor enables constructivist approach to teaching and therefore it may enhance the learning process in hard informatics essential disciplines. It brings not only detailed description of formal rewrite process but also it can demonstrate algorithmical principles for logic formulae manipulations.

  19. Iterative channel decoding of FEC-based multiple-description codes.

    PubMed

    Chang, Seok-Ho; Cosman, Pamela C; Milstein, Laurence B

    2012-03-01

    Multiple description coding has been receiving attention as a robust transmission framework for multimedia services. This paper studies the iterative decoding of FEC-based multiple description codes. The proposed decoding algorithms take advantage of the error detection capability of Reed-Solomon (RS) erasure codes. The information of correctly decoded RS codewords is exploited to enhance the error correction capability of the Viterbi algorithm at the next iteration of decoding. In the proposed algorithm, an intradescription interleaver is synergistically combined with the iterative decoder. The interleaver does not affect the performance of noniterative decoding but greatly enhances the performance when the system is iteratively decoded. We also address the optimal allocation of RS parity symbols for unequal error protection. For the optimal allocation in iterative decoding, we derive mathematical equations from which the probability distributions of description erasures can be generated in a simple way. The performance of the algorithm is evaluated over an orthogonal frequency-division multiplexing system. The results show that the performance of the multiple description codes is significantly enhanced.

  20. Examining Fourth-Grade Mathematics Writing: Features of Organization, Mathematics Vocabulary, and Mathematical Representations

    ERIC Educational Resources Information Center

    Hebert, Michael A.; Powell, Sarah R.

    2016-01-01

    Increasingly, students are expected to write about mathematics. Mathematics writing may be informal (e.g., journals, exit slips) or formal (e.g., writing prompts on high-stakes mathematics assessments). In order to develop an effective mathematics-writing intervention, research needs to be conducted on how students organize mathematics writing and…

  1. Accurate expansion of cylindrical paraxial waves for its straightforward implementation in electromagnetic scattering

    NASA Astrophysics Data System (ADS)

    Naserpour, Mahin; Zapata-Rodríguez, Carlos J.

    2018-01-01

    The evaluation of vector wave fields can be accurately performed by means of diffraction integrals, differential equations and also series expansions. In this paper, a Bessel series expansion which basis relies on the exact solution of the Helmholtz equation in cylindrical coordinates is theoretically developed for the straightforward yet accurate description of low-numerical-aperture focal waves. The validity of this approach is confirmed by explicit application to Gaussian beams and apertured focused fields in the paraxial regime. Finally we discuss how our procedure can be favorably implemented in scattering problems.

  2. Refractive Thinking Profile In Solving Mathematical Problem Reviewed from Students Math Capability

    NASA Astrophysics Data System (ADS)

    Maslukha, M.; Lukito, A.; Ekawati, R.

    2018-01-01

    Refraction is a mental activity experienced by a person to make a decision through reflective thinking and critical thinking. Differences in mathematical capability have an influence on the difference of student’s refractive thinking processes in solving math problems. This descriptive research aims to generate a picture of refractive thinking of students in solving mathematical problems in terms of students’ math skill. Subjects in this study consisted of three students, namely students with high, medium, and low math skills based on mathematics capability test. Data collection methods used are test-based methods and interviews. After collected data is analyzed through three stages that are, condensing and displaying data, data display, and drawing and verifying conclusion. Results showed refractive thinking profiles of three subjects is different. This difference occurs at the planning and execution stage of the problem. This difference is influenced by mathematical capability and experience of each subject.

  3. Teaching Mathematical Modeling in Mathematics Education

    ERIC Educational Resources Information Center

    Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant

    2016-01-01

    Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…

  4. Mathematical Modeling and Pure Mathematics

    ERIC Educational Resources Information Center

    Usiskin, Zalman

    2015-01-01

    Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…

  5. The Harmony of Physics, Mathematics, and Music: A discovery in mathematical music theory is found to apply in physics

    NASA Astrophysics Data System (ADS)

    Krantz, Richard; Douthett, Jack

    2009-05-01

    Although it is common practice to borrow tools from mathematics to apply to physics or music, it is unusual to use tools developed in music theory to mathematically describe physical phenomena. So called ``Maximally Even Set'' theory fits this unusual case. In this poster, we summarize, by example, the theory of Maximally Even (ME) sets and show how this formalism leads to the distribution of black and white keys on the piano keyboard. We then show how ME sets lead to a generalization of the well-known ``Cycle-of-Fifths'' in music theory. Subsequently, we describe ordering in one-dimensional spin-1/2 anti-ferromagnets using ME sets showing that this description leads to a fractal ``Devil's Staircase'' magnetic phase diagram. Finally, we examine an extension of ME sets, ``Iterated Maximally Even Sets'' that describes chord structure in music.

  6. The Harmony of Physics, Mathematics, and Music: A discovery in mathematical music theory is found to apply in physics

    NASA Astrophysics Data System (ADS)

    Krantz, Richard; Douthett, Jack

    2009-10-01

    Although it is common practice to borrow tools from mathematics to apply to physics or music, it is unusual to use tools developed in music theory to mathematically describe physical phenomena. So called ``Maximally Even Set'' theory fits this unusual case. In this poster, we summarize, by example, the theory of Maximally Even (ME) sets and show how this formalism leads to the distribution of black and white keys on the piano keyboard. We then show how ME sets lead to a generalization of the well-known ``Cycle-of-Fifths'' in music theory. Subsequently, we describe ordering in one-dimensional spin-1/2 anti-ferromagnets using ME sets showing that this description leads to a fractal ``Devil's Staircase'' magnetic phase diagram. Finally, we examine an extension of ME sets, ``Iterated Maximally Even'' sets that describes chord structure in music.

  7. A Spectrum of Pedagogical Awareness for Undergraduate Mathematics: From "Tricks" to "Techniques"

    ERIC Educational Resources Information Center

    Nardi, Elena; Jaworski, Barbara; Hegedus, Stephen

    2005-01-01

    We describe a four-level spectrum of pedagogical awareness (SPA) that emerged from the analysis of six undergraduate mathematics tutors' (1) conceptualizations of their first-year students' difficulties; (2) descriptive accounts of their strategies for facilitating the overcoming of these difficulties; and (3) self-reflective accounts regarding…

  8. Accuracy and Calibration of High Explosive Thermodynamic Equations of State

    NASA Astrophysics Data System (ADS)

    Baker, Ernest L.; Capellos, Christos; Stiel, Leonard I.; Pincay, Jack

    2010-10-01

    The Jones-Wilkins-Lee-Baker (JWLB) equation of state (EOS) was developed to more accurately describe overdriven detonation while maintaining an accurate description of high explosive products expansion work output. The increased mathematical complexity of the JWLB high explosive equations of state provides increased accuracy for practical problems of interest. Increased numbers of parameters are often justified based on improved physics descriptions but can also mean increased calibration complexity. A generalized extent of aluminum reaction Jones-Wilkins-Lee (JWL)-based EOS was developed in order to more accurately describe the observed behavior of aluminized explosives detonation products expansion. A calibration method was developed to describe the unreacted, partially reacted, and completely reacted explosive using nonlinear optimization. A reasonable calibration of a generalized extent of aluminum reaction JWLB EOS as a function of aluminum reaction fraction has not yet been achieved due to the increased mathematical complexity of the JWLB form.

  9. Linking Preservice Teachers' Mathematics Self-Efficacy and Mathematics Teaching Efficacy to Their Mathematical Performance

    ERIC Educational Resources Information Center

    Bates, Alan B.; Latham, Nancy; Kim, Jin-ah

    2011-01-01

    This study examined preservice teachers' mathematics self-efficacy and mathematics teaching efficacy and compared them to their mathematical performance. Participants included 89 early childhood preservice teachers at a Midwestern university. Instruments included the Mathematics Self-Efficacy Scale (MSES), Mathematics Teaching Efficacy Beliefs…

  10. Early Career Teachers' Ability to Focus on Typical Students Errors in Relation to the Complexity of a Mathematical Topic

    ERIC Educational Resources Information Center

    Pankow, Lena; Kaiser, Gabriele; Busse, Andreas; König, Johannes; Blömeke, Sigrid; Hoth, Jessica; Döhrmann, Martina

    2016-01-01

    The paper presents results from a computer-based assessment in which 171 early career mathematics teachers from Germany were asked to anticipate typical student errors on a given mathematical topic and identify them under time constraints. Fast and accurate perception and knowledge-based judgments are widely accepted characteristics of teacher…

  11. On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process.

    PubMed

    Flegg, Jennifer A; Menon, Shakti N; Maini, Philip K; McElwain, D L Sean

    2015-01-01

    Over the last 30 years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical models of the interlinked processes that underlie the healing mechanism has yielded considerable insight into aspects of this critical phenomenon that remain difficult to investigate empirically. In particular, the mathematical modeling of angiogenesis, i.e., capillary sprout growth, has offered new paradigms for the understanding of this highly complex and crucial step in the healing pathway. With the recent advances in imaging and cell tracking, the time is now ripe for an appraisal of the utility and importance of mathematical modeling in wound healing angiogenesis research. The purpose of this review is to pedagogically elucidate the conceptual principles that have underpinned the development of mathematical descriptions of wound healing angiogenesis, specifically those that have utilized a continuum reaction-transport framework, and highlight the contribution that such models have made toward the advancement of research in this field. We aim to draw attention to the common assumptions made when developing models of this nature, thereby bringing into focus the advantages and limitations of this approach. A deeper integration of mathematical modeling techniques into the practice of wound healing angiogenesis research promises new perspectives for advancing our knowledge in this area. To this end we detail several open problems related to the understanding of wound healing angiogenesis, and outline how these issues could be addressed through closer cross-disciplinary collaboration.

  12. On the mathematical modeling of wound healing angiogenesis in skin as a reaction-transport process

    PubMed Central

    Flegg, Jennifer A.; Menon, Shakti N.; Maini, Philip K.; McElwain, D. L. Sean

    2015-01-01

    Over the last 30 years, numerous research groups have attempted to provide mathematical descriptions of the skin wound healing process. The development of theoretical models of the interlinked processes that underlie the healing mechanism has yielded considerable insight into aspects of this critical phenomenon that remain difficult to investigate empirically. In particular, the mathematical modeling of angiogenesis, i.e., capillary sprout growth, has offered new paradigms for the understanding of this highly complex and crucial step in the healing pathway. With the recent advances in imaging and cell tracking, the time is now ripe for an appraisal of the utility and importance of mathematical modeling in wound healing angiogenesis research. The purpose of this review is to pedagogically elucidate the conceptual principles that have underpinned the development of mathematical descriptions of wound healing angiogenesis, specifically those that have utilized a continuum reaction-transport framework, and highlight the contribution that such models have made toward the advancement of research in this field. We aim to draw attention to the common assumptions made when developing models of this nature, thereby bringing into focus the advantages and limitations of this approach. A deeper integration of mathematical modeling techniques into the practice of wound healing angiogenesis research promises new perspectives for advancing our knowledge in this area. To this end we detail several open problems related to the understanding of wound healing angiogenesis, and outline how these issues could be addressed through closer cross-disciplinary collaboration. PMID:26483695

  13. pp ii Brain, behaviour and mathematics: Are we using the right approaches? [review article

    NASA Astrophysics Data System (ADS)

    Perez Velazquez, Jose Luis

    2005-12-01

    Mathematics are used in biological sciences mostly as a quantifying tool, for it is the science of numbers after all. There is a long-standing interest in the application of mathematical methods and concepts to neuroscience in attempts to decipher brain activity. While there has been a very wide use of mathematical/physical methodologies, less effort has been made to formulate a comprehensive and integrative theory of brain function. This review concentrates on recent developments, uses and abuses of mathematical formalisms and techniques that are being applied in brain research, particularly the current trend of using dynamical system theory to unravel the global, collective dynamics of brain activity. It is worth emphasising that the theoretician-neuroscientist, eager to apply mathematical analysis to neuronal recordings, has to consider carefully some crucial anatomo-physiological assumptions, that may not be as accurate as the specific methods require. On the other hand, the experimentalist neuro-physicist, with an inclination to implement mathematical thoughts in brain science, has to make an effort to comprehend the bases of the theoretical concepts that can be used as frameworks or as analysis methods of brain electrophysiological recordings, and to critically inspect the accuracy of the interpretations of the results based on the neurophysiological ground. It is hoped that this brief overview of anatomical and physiological presumptions and their relation to theoretical paradigms will help clarify some particular points of interest in current trends in brain science, and may provoke further reflections on how certain or uncertain it is to conceptualise brain function based on these theoretical frameworks, if the physiological and experimental constraints are not as accurate as the models prescribe.

  14. Mathematical description of drug-target interactions: application to biologics that bind to targets with two binding sites.

    PubMed

    Gibiansky, Leonid; Gibiansky, Ekaterina

    2018-02-01

    The emerging discipline of mathematical pharmacology occupies the space between advanced pharmacometrics and systems biology. A characteristic feature of the approach is application of advance mathematical methods to study the behavior of biological systems as described by mathematical (most often differential) equations. One of the early application of mathematical pharmacology (that was not called this name at the time) was formulation and investigation of the target-mediated drug disposition (TMDD) model and its approximations. The model was shown to be remarkably successful, not only in describing the observed data for drug-target interactions, but also in advancing the qualitative and quantitative understanding of those interactions and their role in pharmacokinetic and pharmacodynamic properties of biologics. The TMDD model in its original formulation describes the interaction of the drug that has one binding site with the target that also has only one binding site. Following the framework developed earlier for drugs with one-to-one binding, this work aims to describe a rigorous approach for working with similar systems and to apply it to drugs that bind to targets with two binding sites. The quasi-steady-state, quasi-equilibrium, irreversible binding, and Michaelis-Menten approximations of the model are also derived. These equations can be used, in particular, to predict concentrations of the partially bound target (RC). This could be clinically important if RC remains active and has slow internalization rate. In this case, introduction of the drug aimed to suppress target activity may lead to the opposite effect due to RC accumulation.

  15. Mathematics as a Conduit for Translational Research in Post-Traumatic Osteoarthritis

    PubMed Central

    Ayati, Bruce P.; Kapitanov, Georgi I.; Coleman, Mitchell C.; Anderson, Donald D.; Martin, James A.

    2016-01-01

    Biomathematical models offer a powerful method of clarifying complex temporal interactions and the relationships among multiple variables in a system. We present a coupled in silico biomathematical model of articular cartilage degeneration in response to impact and/or aberrant loading such as would be associated with injury to an articular joint. The model incorporates fundamental biological and mechanical information obtained from explant and small animal studies to predict post-traumatic osteoarthritis (PTOA) progression, with an eye toward eventual application in human patients. In this sense, we refer to the mathematics as a “conduit of translation”. The new in silico framework presented in this paper involves a biomathematical model for the cellular and biochemical response to strains computed using finite element analysis. The model predicts qualitative responses presently, utilizing system parameter values largely taken from the literature. To contribute to accurate predictions, models need to be accurately parameterized with values that are based on solid science. We discuss a parameter identification protocol that will enable us to make increasingly accurate predictions of PTOA progression using additional data from smaller scale explant and small animal assays as they become available. By distilling the data from the explant and animal assays into parameters for biomathematical models, mathematics can translate experimental data to clinically relevant knowledge. PMID:27653021

  16. Antioxidant Capacity: Experimental Determination by EPR Spectroscopy and Mathematical Modeling.

    PubMed

    Polak, Justyna; Bartoszek, Mariola; Chorążewski, Mirosław

    2015-07-22

    A new method of determining antioxidant capacity based on a mathematical model is presented in this paper. The model was fitted to 1000 data points of electron paramagnetic resonance (EPR) spectroscopy measurements of various food product samples such as tea, wine, juice, and herbs with Trolox equivalent antioxidant capacity (TEAC) values from 20 to 2000 μmol TE/100 mL. The proposed mathematical equation allows for a determination of TEAC of food products based on a single EPR spectroscopy measurement. The model was tested on the basis of 80 EPR spectroscopy measurements of herbs, tea, coffee, and juice samples. The proposed model works for both strong and weak antioxidants (TEAC values from 21 to 2347 μmol TE/100 mL). The determination coefficient between TEAC values obtained experimentally and TEAC values calculated with proposed mathematical equation was found to be R(2) = 0.98. Therefore, the proposed new method of TEAC determination based on a mathematical model is a good alternative to the standard EPR method due to its being fast, accurate, inexpensive, and simple to perform.

  17. Contrasts in Mathematical Challenges in A-Level Mathematics and Further Mathematics, and Undergraduate Mathematics Examinations

    ERIC Educational Resources Information Center

    Darlington, Ellie

    2014-01-01

    This article describes part of a study which investigated the role of questions in students' approaches to learning mathematics at the secondary-tertiary interface, focussing on the enculturation of students at the University of Oxford. Use of the Mathematical Assessment Task Hierarchy taxonomy revealed A-level Mathematics and Further Mathematics…

  18. Combinatorial neural codes from a mathematical coding theory perspective.

    PubMed

    Curto, Carina; Itskov, Vladimir; Morrison, Katherine; Roth, Zachary; Walker, Judy L

    2013-07-01

    Shannon's seminal 1948 work gave rise to two distinct areas of research: information theory and mathematical coding theory. While information theory has had a strong influence on theoretical neuroscience, ideas from mathematical coding theory have received considerably less attention. Here we take a new look at combinatorial neural codes from a mathematical coding theory perspective, examining the error correction capabilities of familiar receptive field codes (RF codes). We find, perhaps surprisingly, that the high levels of redundancy present in these codes do not support accurate error correction, although the error-correcting performance of receptive field codes catches up to that of random comparison codes when a small tolerance to error is introduced. However, receptive field codes are good at reflecting distances between represented stimuli, while the random comparison codes are not. We suggest that a compromise in error-correcting capability may be a necessary price to pay for a neural code whose structure serves not only error correction, but must also reflect relationships between stimuli.

  19. Evaluation of Limb Load Asymmetry Using Two New Mathematical Models

    PubMed Central

    Kumar, Senthil NS; Omar, Baharudin; Joseph, Leonard H.; Htwe, Ohnmar; Jagannathan, K.; Hamdan, Nor M Y; Rajalakshmi, D.

    2015-01-01

    Quantitative measurement of limb loading is important in orthopedic and neurological rehabilitation. In current practice, mathematical models such as Symmetry index (SI), Symmetry ratio (SR), and Symmetry angle (SA) are used to quantify limb loading asymmetry. Literatures have identified certain limitations with the above mathematical models. Hence this study presents two new mathematical models Modified symmetry index (MSI) and Limb loading error (LLE) that would address these limitations. Furthermore, the current mathematical models were compared against the new model with the goal of achieving a better model. This study uses hypothetical data to simulate an algorithmic preliminary computational measure to perform with all numerical possibilities of even and uneven limb loading that can occur in human legs. Descriptive statistics are used to interpret the limb loading patterns: symmetry, asymmetry and maximum asymmetry. The five mathematical models were similar in analyzing symmetry between limbs. However, for asymmetry and maximum asymmetry data, the SA and SR values do not give any meaningful interpretation, and SI gives an inflated value. The MSI and LLE are direct, easy to interpret and identify the loading patterns with the side of asymmetry. The new models are notable as they quantify the amount and side of asymmetry under different loading patterns. PMID:25716372

  20. Quantitative Methods in Library and Information Science Literature: Descriptive vs. Inferential Statistics.

    ERIC Educational Resources Information Center

    Brattin, Barbara C.

    Content analysis was performed on the top six core journals for 1990 in library and information science to determine the extent of research in the field. Articles (n=186) were examined for descriptive or inferential statistics and separately for the presence of mathematical models. Results show a marked (14%) increase in research for 1990,…

  1. High School Mathematics Curricula, University Mathematics Placement Recommendations, and Student University Mathematics Performance

    ERIC Educational Resources Information Center

    Norman, Ke Wu; Medhanie, Amanuel G.; Harwell, Michael R.; Anderson, Edwin; Post, Thomas R.

    2011-01-01

    Recent "math wars" have drawn attention to how well various high school mathematics curricula prepare students for college-level mathematics. The purpose of this study was to investigate the relationship between the high school mathematics curricula and students' post-secondary mathematics placement recommendation, specifically how…

  2. Using Mathematics Literature with Prospective Secondary Mathematics Teachers

    ERIC Educational Resources Information Center

    Jett, Christopher C.

    2014-01-01

    Literature in mathematics has been found to foster positive improvements in mathematics learning. This manuscript reports on a mathematics teacher educator's use of literature via literature circles with 11 prospective secondary mathematics teachers in a mathematics content course. Using survey and reflection data, the author found that…

  3. Mathematical Language Skills of Mathematics Prospective Teachers

    ERIC Educational Resources Information Center

    Gürefe, Nejla

    2018-01-01

    Effective mathematics teaching can be actualized only with correct use of the mathematical content language which comprises mathematical rules, concepts, symbols and terms. In this research, it was aimed to examine the mathematics prospective teachers' content language skills in some basic geometric concepts which are ray, angle, polygon,…

  4. The SEM description of interaction of a transient electromagnetic wave with an object

    NASA Technical Reports Server (NTRS)

    Pearson, L. W.; Wilton, D. R.

    1980-01-01

    The singularity expansion method (SEM), proposed as a means for determining and representing the transient surface current density induced on a scatterer by a transient electromagnetic wave is described. The resulting mathematical description of the transient surface current on the object is discussed. The data required to represent the electromagnetic scattering properties of a given object are examined. Experimental methods which were developed for the determination of the SEM description are discussed. The feasibility of characterizing the surface current induced on aircraft flying in proximity to a lightning stroke by way of SEM is examined.

  5. Quantum descriptions of singularities leading to pair creation. [of gravitons

    NASA Technical Reports Server (NTRS)

    Misner, C. W.

    1974-01-01

    A class of cosmological models is analyzed which provide a mathematically convenient (but idealized) description of a cosmological singularity that develops into a pair creation epoch and terminates in an adiabatic expansion with redshifting particle energies. This class of models was obtained by Gowdy (1971, 1974) as a set of exact solutions of the classical empty space Einstein equations describing inhomogeneous universes populated only by gravitational waves. It is shown that these models can be used to exhibit simplified models of quantized gravitational fields, and that a quantum description can be given arbitrarily near a cosmological singularity. Graviton pair creation occurs, and can be seen to convert anisotropic expansion rates into the energy of graviton pairs.

  6. Parsimonious description for predicting high-dimensional dynamics

    PubMed Central

    Hirata, Yoshito; Takeuchi, Tomoya; Horai, Shunsuke; Suzuki, Hideyuki; Aihara, Kazuyuki

    2015-01-01

    When we observe a system, we often cannot observe all its variables and may have some of its limited measurements. Under such a circumstance, delay coordinates, vectors made of successive measurements, are useful to reconstruct the states of the whole system. Although the method of delay coordinates is theoretically supported for high-dimensional dynamical systems, practically there is a limitation because the calculation for higher-dimensional delay coordinates becomes more expensive. Here, we propose a parsimonious description of virtually infinite-dimensional delay coordinates by evaluating their distances with exponentially decaying weights. This description enables us to predict the future values of the measurements faster because we can reuse the calculated distances, and more accurately because the description naturally reduces the bias of the classical delay coordinates toward the stable directions. We demonstrate the proposed method with toy models of the atmosphere and real datasets related to renewable energy. PMID:26510518

  7. Doing Mathematics with Purpose: Mathematical Text Types

    ERIC Educational Resources Information Center

    Dostal, Hannah M.; Robinson, Richard

    2018-01-01

    Mathematical literacy includes learning to read and write different types of mathematical texts as part of purposeful mathematical meaning making. Thus in this article, we describe how learning to read and write mathematical texts (proof text, algorithmic text, algebraic/symbolic text, and visual text) supports the development of students'…

  8. Rigorous mathematical modelling for a Fast Corrector Power Supply in TPS

    NASA Astrophysics Data System (ADS)

    Liu, K.-B.; Liu, C.-Y.; Chien, Y.-C.; Wang, B.-S.; Wong, Y. S.

    2017-04-01

    To enhance the stability of beam orbit, a Fast Orbit Feedback System (FOFB) eliminating undesired disturbances was installed and tested in the 3rd generation synchrotron light source of Taiwan Photon Source (TPS) of National Synchrotron Radiation Research Center (NSRRC). The effectiveness of the FOFB greatly depends on the output performance of Fast Corrector Power Supply (FCPS); therefore, the design and implementation of an accurate FCPS is essential. A rigorous mathematical modelling is very useful to shorten design time and improve design performance of a FCPS. A rigorous mathematical modelling derived by the state-space averaging method for a FCPS in the FOFB of TPS composed of a full-bridge topology is therefore proposed in this paper. The MATLAB/SIMULINK software is used to construct the proposed mathematical modelling and to conduct the simulations of the FCPS. Simulations for the effects of the different resolutions of ADC on the output accuracy of the FCPS are investigated. A FCPS prototype is realized to demonstrate the effectiveness of the proposed rigorous mathematical modelling for the FCPS. Simulation and experimental results show that the proposed mathematical modelling is helpful for selecting the appropriate components to meet the accuracy requirements of a FCPS.

  9. Accurate and efficient calculation of response times for groundwater flow

    NASA Astrophysics Data System (ADS)

    Carr, Elliot J.; Simpson, Matthew J.

    2018-03-01

    We study measures of the amount of time required for transient flow in heterogeneous porous media to effectively reach steady state, also known as the response time. Here, we develop a new approach that extends the concept of mean action time. Previous applications of the theory of mean action time to estimate the response time use the first two central moments of the probability density function associated with the transition from the initial condition, at t = 0, to the steady state condition that arises in the long time limit, as t → ∞ . This previous approach leads to a computationally convenient estimation of the response time, but the accuracy can be poor. Here, we outline a powerful extension using the first k raw moments, showing how to produce an extremely accurate estimate by making use of asymptotic properties of the cumulative distribution function. Results are validated using an existing laboratory-scale data set describing flow in a homogeneous porous medium. In addition, we demonstrate how the results also apply to flow in heterogeneous porous media. Overall, the new method is: (i) extremely accurate; and (ii) computationally inexpensive. In fact, the computational cost of the new method is orders of magnitude less than the computational effort required to study the response time by solving the transient flow equation. Furthermore, the approach provides a rigorous mathematical connection with the heuristic argument that the response time for flow in a homogeneous porous medium is proportional to L2 / D , where L is a relevant length scale, and D is the aquifer diffusivity. Here, we extend such heuristic arguments by providing a clear mathematical definition of the proportionality constant.

  10. Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics

    ERIC Educational Resources Information Center

    Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.

    2016-01-01

    Mathematical modeling plays an increasingly important role both in real-life applications--in engineering, business, the social sciences, climate study, advanced design, and more--and within mathematics education itself. This 2016 volume of "Annual Perspectives in Mathematics Education" ("APME") focuses on this key topic from a…

  11. History of Mathematics: Illuminating Understanding of School Mathematics Concepts for Prospective Mathematics Teachers

    ERIC Educational Resources Information Center

    Clark, Kathleen Michelle

    2012-01-01

    The use of the history of mathematics in teaching has long been considered a tool for enriching students' mathematical learning. However, in the USA few, if any, research efforts have investigated how the study of history of mathematics contributes to a person's mathematical knowledge for teaching. In this article, I present the results of…

  12. Mathematics for Life: Sustainable Mathematics Education

    ERIC Educational Resources Information Center

    Renert, Moshe

    2011-01-01

    Ecological sustainability has not been a major focus of mathematics education research, even though it has attracted considerable attention in other areas of educational research in the past decade. The connections between mathematics education and ecological sustainability are not readily apparent. This paper explores how mathematics educators…

  13. Introductory life science mathematics and quantitative neuroscience courses.

    PubMed

    Duffus, Dwight; Olifer, Andrei

    2010-01-01

    We describe two sets of courses designed to enhance the mathematical, statistical, and computational training of life science undergraduates at Emory College. The first course is an introductory sequence in differential and integral calculus, modeling with differential equations, probability, and inferential statistics. The second is an upper-division course in computational neuroscience. We provide a description of each course, detailed syllabi, examples of content, and a brief discussion of the main issues encountered in developing and offering the courses.

  14. Experimental Mathematics and Mathematical Physics

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David

    2009-06-26

    One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.

  15. Evaluate E-loyalty of sales website: a Fuzzy mathematics method

    NASA Astrophysics Data System (ADS)

    Yi, Ying; Liu, Zhen-Yu; Xiong, Ying-Zi

    The study about online consumer loyalty is limited, but how to evaluate the customers' E-loyalty to a sales website is always a noticeable question. By using some methods of fuzzy mathematics, we provide a more accurate way to evaluate E-loyalty of sales website. Moreover, this method can differentiate level and degree of each factor that influences E-loyalty.

  16. Mathematics Literacy of Secondary Students in Solving Simultanenous Linear Equations

    NASA Astrophysics Data System (ADS)

    Sitompul, R. S. I.; Budayasa, I. K.; Masriyah

    2018-01-01

    This study examines the profile of secondary students’ mathematical literacy in solving simultanenous linear equations problems in terms of cognitive style of visualizer and verbalizer. This research is a descriptive research with qualitative approach. The subjects in this research consist of one student with cognitive style of visualizer and one student with cognitive style of verbalizer. The main instrument in this research is the researcher herself and supporting instruments are cognitive style tests, mathematics skills tests, problem-solving tests and interview guidelines. Research was begun by determining the cognitive style test and mathematics skill test. The subjects chosen were given problem-solving test about simultaneous linear equations and continued with interview. To ensure the validity of the data, the researcher conducted data triangulation; the steps of data reduction, data presentation, data interpretation, and conclusion drawing. The results show that there is a similarity of visualizer and verbalizer-cognitive style in identifying and understanding the mathematical structure in the process of formulating. There are differences in how to represent problems in the process of implementing, there are differences in designing strategies and in the process of interpreting, and there are differences in explaining the logical reasons.

  17. EDAC Test Collection Catalogue: A Description of Tests for Use in Bilingual Education Programs.

    ERIC Educational Resources Information Center

    Wolfsfeld, Lynn

    The descriptions of 200 tests for a variety of language groups are designed for use with the test file maintained by the Evaluation, Dissemination, and Assessment Center for Bilingual Education (EDAC). The content areas covered include reading, mathematics, self-concept, language dominance, language proficiency, and intelligence. Tests are…

  18. Abstraction in Mathematics and Mathematics Learning

    ERIC Educational Resources Information Center

    Mitchelmore, Michael; White, Paul

    2004-01-01

    It is claimed that, since mathematics is essentially a self-contained system, mathematical objects may best be described as "abstract-apart." On the other hand, fundamental mathematical ideas are closely related to the real world and their learning involves empirical concepts. These concepts may be called "abstract-general" because they embody…

  19. Anxiety (Low Ago Strength) And Intelligence Among Students Of High School Mathematics

    NASA Astrophysics Data System (ADS)

    Naderi, Habibollah

    2008-01-01

    The aim of this study was to investigate the relationship between anxiety (low ago strength) and intelligence among student's mathematics. All the effects of anxiety were studied within the sample of 112 subjects (boys). 56 of them were regular of students (RS) and 56 were intelligent of students (IS) of high schools. Mean age was (17.1 years), SD (.454) and range age was 16-18 years in 3 classes of regular of high school mathematics was for regular students. For the IS, mean age was (16.75 years), SD (.436) and range age was l6-17 years in 4 classes of students exceptional talent for high school mathematics. The sampling method in this study was the simple randomization method. In this studied, for analysis of method used both descriptive and inference of research, which for description of analysis used Average and analysis of covariance and Variance, also for inference of analysis, used with t-test between two the groups of students. The Cattell of Anxiety Test (1958) (CTAT) has been used in a number of studies for measurement trait anxiety in Iran. In general, the findings were found not statistical significant between the RS and the IS of students in that factorial of low of ago strength (C-). Further research is needed to investigate whether the current findings hold for student populations by others anxiety tests.

  20. Tensor Arithmetic, Geometric and Mathematic Principles of Fluid Mechanics in Implementation of Direct Computational Experiments

    NASA Astrophysics Data System (ADS)

    Bogdanov, Alexander; Khramushin, Vasily

    2016-02-01

    The architecture of a digital computing system determines the technical foundation of a unified mathematical language for exact arithmetic-logical description of phenomena and laws of continuum mechanics for applications in fluid mechanics and theoretical physics. The deep parallelization of the computing processes results in functional programming at a new technological level, providing traceability of the computing processes with automatic application of multiscale hybrid circuits and adaptive mathematical models for the true reproduction of the fundamental laws of physics and continuum mechanics.

  1. The use of mathematical models to inform influenza pandemic preparedness and response

    PubMed Central

    Wu, Joseph T; Cowling, Benjamin J

    2011-01-01

    Summary Influenza pandemics have occurred throughout history and were associated with substantial excess mortality and morbidity. Mathematical models of infectious diseases permit quantitative description of epidemic processes based on the underlying biological mechanisms. Mathematical models have been widely used in the past decade to aid pandemic planning by allowing detailed predictions of the speed of spread of an influenza pandemic and the likely effectiveness of alternative control strategies. During the initial waves of the 2009 influenza pandemic, mathematical models were used to track the spread of the virus, predict the time course of the pandemic and assess the likely impact of large-scale vaccination. While mathematical modeling has made substantial contributions to influenza pandemic preparedness, its use as a real-time tool for pandemic control is currently limited by the lack of essential surveillance information such as serologic data. Mathematical modeling provided a useful framework for analyzing and interpreting surveillance data during the 2009 influenza pandemic, for highlighting limitations in existing pandemic surveillance systems, and for guiding how these systems should be strengthened in order to cope with future epidemics of influenza or other emerging infectious diseases. PMID:21727183

  2. Mathematical Modelling Approach in Mathematics Education

    ERIC Educational Resources Information Center

    Arseven, Ayla

    2015-01-01

    The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…

  3. Mathematics Underground

    ERIC Educational Resources Information Center

    Luther, Kenneth H.

    2012-01-01

    Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…

  4. Eleventh-Grade High School Students' Accounts of Mathematical Metacognitive Knowledge: Explicitness and Systematicity

    ERIC Educational Resources Information Center

    van Velzen, Joke H.

    2016-01-01

    Theoretically, it has been argued that a conscious understanding of metacognitive knowledge requires that this knowledge is explicit and systematic. The purpose of this descriptive study was to obtain a better understanding of explicitness and systematicity in knowledge of the mathematical problem-solving process. Eighteen 11th-grade…

  5. Beginning Teachers' Perspectives on Attributes for Teaching Secondary Mathematics: Reflections on Teacher Education

    ERIC Educational Resources Information Center

    Wasserman, Nicholas H.; Ham, Edward

    2013-01-01

    The aim of this collaborative study was to understand what factors beginning secondary mathematics teachers attribute their success to in the classroom, regardless of their preparation program. Further description of how and when beginning teachers reported acquiring important teaching attributes provides a perspective on how they make the…

  6. Exploring mathematics anxiety and attitude: Mathematics students' experiences

    NASA Astrophysics Data System (ADS)

    Sahri, Nurul Ashikin; Kamaruzaman, Wan Nur Farahdalila Wan; Jamil, Jastini Mohd.; Shaharanee, Izwan Nizal Mohd.

    2017-11-01

    A quantitative and correlational, survey methods were used to investigate the relationships among mathematical anxiety and attitude toward student's mathematics performance. Participants were 100 students volunteer to enroll in undergraduate Industrial Statistics, Decision Sciences and Business Mathematics at one of northern university in Malaysia. Survey data consisted of demographic items and Likert scale items. The collected data was analyzed by using the idea of correlation and regression analysis. The results indicated that there was a significant positive relationship between students' attitude and mathematics anxiety. Results also indicated that a substantial positive effect of students' attitude and mathematics anxiety in students' achievement. Further study can be conducted on how mathematical anxiety and attitude toward mathematics affects can be used to predict the students' performance in the class.

  7. Computer programs: Operational and mathematical, a compilation

    NASA Technical Reports Server (NTRS)

    1973-01-01

    Several computer programs which are available through the NASA Technology Utilization Program are outlined. Presented are: (1) Computer operational programs which can be applied to resolve procedural problems swiftly and accurately. (2) Mathematical applications for the resolution of problems encountered in numerous industries. Although the functions which these programs perform are not new and similar programs are available in many large computer center libraries, this collection may be of use to centers with limited systems libraries and for instructional purposes for new computer operators.

  8. Development of a Star Tracker-Based Reference System for Accurate Attitude Determination of a Simulated Spacecraft

    DTIC Science & Technology

    2012-03-01

    the mathematical pretext for quaternions, which summarizes as: In three- dimensional space , any displacement of a rigid body such that a ...for the patch board was selected, with a uniform 8 mm spacing between LED centers. Figure 33 is schematic of the patch board layout, and Fig. 34 shows...attitude determination since the dawn of the space age. Without accurate attitude determination, a “Lost- in-

  9. A Capstone Mathematics Course for Prospective Secondary Mathematics Teachers

    ERIC Educational Resources Information Center

    Artzt, Alice F.; Sultan, Alan; Curcio, Frances R.; Gurl, Theresa

    2012-01-01

    This article describes an innovative capstone mathematics course that links college mathematics with school mathematics and pedagogy. It describes how college juniors in a secondary mathematics teacher preparation program engage in leadership experiences that enable them to learn mathematics for teaching while developing student-centered…

  10. Error analysis of mathematical problems on TIMSS: A case of Indonesian secondary students

    NASA Astrophysics Data System (ADS)

    Priyani, H. A.; Ekawati, R.

    2018-01-01

    Indonesian students’ competence in solving mathematical problems is still considered as weak. It was pointed out by the results of international assessment such as TIMSS. This might be caused by various types of errors made. Hence, this study aimed at identifying students’ errors in solving mathematical problems in TIMSS in the topic of numbers that considered as the fundamental concept in Mathematics. This study applied descriptive qualitative analysis. The subject was three students with most errors in the test indicators who were taken from 34 students of 8th graders. Data was obtained through paper and pencil test and student’s’ interview. The error analysis indicated that in solving Applying level problem, the type of error that students made was operational errors. In addition, for reasoning level problem, there are three types of errors made such as conceptual errors, operational errors and principal errors. Meanwhile, analysis of the causes of students’ errors showed that students did not comprehend the mathematical problems given.

  11. Emotional and cognitive effects of peer tutoring among secondary school mathematics students

    NASA Astrophysics Data System (ADS)

    Alegre Ansuategui, Francisco José; Moliner Miravet, Lidón

    2017-11-01

    This paper describes an experience of same-age peer tutoring conducted with 19 eighth-grade mathematics students in a secondary school in Castellon de la Plana (Spain). Three constructs were analysed before and after launching the program: academic performance, mathematics self-concept and attitude of solidarity. Students' perceptions of the method were also analysed. The quantitative data was gathered by means of a mathematics self-concept questionnaire, an attitude of solidarity questionnaire and the students' numerical ratings. A statistical analysis was performed using Student's t-test. The qualitative information was gathered by means of discussion groups and a field diary. This information was analysed using descriptive analysis and by categorizing the information. Results show statistically significant improvements in all the variables and the positive assessment of the experience and the interactions that took place between the students.

  12. Toward Precision Healthcare: Context and Mathematical Challenges

    PubMed Central

    Colijn, Caroline; Jones, Nick; Johnston, Iain G.; Yaliraki, Sophia; Barahona, Mauricio

    2017-01-01

    Precision medicine refers to the idea of delivering the right treatment to the right patient at the right time, usually with a focus on a data-centered approach to this task. In this perspective piece, we use the term “precision healthcare” to describe the development of precision approaches that bridge from the individual to the population, taking advantage of individual-level data, but also taking the social context into account. These problems give rise to a broad spectrum of technical, scientific, policy, ethical and social challenges, and new mathematical techniques will be required to meet them. To ensure that the science underpinning “precision” is robust, interpretable and well-suited to meet the policy, ethical and social questions that such approaches raise, the mathematical methods for data analysis should be transparent, robust, and able to adapt to errors and uncertainties. In particular, precision methodologies should capture the complexity of data, yet produce tractable descriptions at the relevant resolution while preserving intelligibility and traceability, so that they can be used by practitioners to aid decision-making. Through several case studies in this domain of precision healthcare, we argue that this vision requires the development of new mathematical frameworks, both in modeling and in data analysis and interpretation. PMID:28377724

  13. Using a Cognitive-Scientific Inflected Anthropological Approach to Researching the Teaching and Learning of Elementary School Mathematics: An Instance of the Use of Aggregates

    ERIC Educational Resources Information Center

    Davis, Zain

    2016-01-01

    Anthropological approaches to studying the contextual specificity of mathematical thought and practice in schools can productively inform descriptions and analyses of mathematical practices within and across different teaching and learning contexts. In this paper I argue for an anthropological methodological orientation that takes into…

  14. Hands-On Mathematics: Two Cases from Ancient Chinese Mathematics

    ERIC Educational Resources Information Center

    Wang, Youjun

    2009-01-01

    In modern mathematical teaching, it has become increasingly emphasized that mathematical knowledge should be taught by problem-solving, hands-on activities, and interactive learning experiences. Comparing the ideas of modern mathematical education with the development of ancient Chinese mathematics, we find that the history of mathematics in…

  15. On Mathematical Understanding: Perspectives of Experienced Chinese Mathematics Teachers

    ERIC Educational Resources Information Center

    Cai, Jinfa; Ding, Meixia

    2017-01-01

    Researchers have long debated the meaning of mathematical understanding and ways to achieve mathematical understanding. This study investigated experienced Chinese mathematics teachers' views about mathematical understanding. It was found that these mathematics teachers embrace the view that understanding is a web of connections, which is a result…

  16. Theoretical Mathematics

    NASA Astrophysics Data System (ADS)

    Stöltzner, Michael

    Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a `theoretical' mathematics (alongside `theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's axiomatic method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.

  17. Exploring Differential Effects of Mathematics Courses on Mathematics Achievement

    ERIC Educational Resources Information Center

    Ma, Xin; McIntyre, Laureen J.

    2005-01-01

    Using data from the Longitudinal Study of Mathematics Participation (N = 1,518 students from 34 schools), we investigated the effects of pure and applied mathematics courses on mathematics achievement, controlling for prior mathematics achievement. Results of multilevel modelling showed that the effects of pure mathematics were significant after…

  18. Funnel metadynamics as accurate binding free-energy method

    PubMed Central

    Limongelli, Vittorio; Bonomi, Massimiliano; Parrinello, Michele

    2013-01-01

    A detailed description of the events ruling ligand/protein interaction and an accurate estimation of the drug affinity to its target is of great help in speeding drug discovery strategies. We have developed a metadynamics-based approach, named funnel metadynamics, that allows the ligand to enhance the sampling of the target binding sites and its solvated states. This method leads to an efficient characterization of the binding free-energy surface and an accurate calculation of the absolute protein–ligand binding free energy. We illustrate our protocol in two systems, benzamidine/trypsin and SC-558/cyclooxygenase 2. In both cases, the X-ray conformation has been found as the lowest free-energy pose, and the computed protein–ligand binding free energy in good agreement with experiments. Furthermore, funnel metadynamics unveils important information about the binding process, such as the presence of alternative binding modes and the role of waters. The results achieved at an affordable computational cost make funnel metadynamics a valuable method for drug discovery and for dealing with a variety of problems in chemistry, physics, and material science. PMID:23553839

  19. Introductory Life Science Mathematics and Quantitative Neuroscience Courses

    PubMed Central

    Olifer, Andrei

    2010-01-01

    We describe two sets of courses designed to enhance the mathematical, statistical, and computational training of life science undergraduates at Emory College. The first course is an introductory sequence in differential and integral calculus, modeling with differential equations, probability, and inferential statistics. The second is an upper-division course in computational neuroscience. We provide a description of each course, detailed syllabi, examples of content, and a brief discussion of the main issues encountered in developing and offering the courses. PMID:20810971

  20. Pre-service Mathematics Teachers' Knowledge of History of Mathematics and Their Attitudes and Beliefs Towards Using History of Mathematics in Mathematics Education

    NASA Astrophysics Data System (ADS)

    Alpaslan, Mustafa; Işıksal, Mine; Haser, Çiğdem

    2014-01-01

    This study examined pre-service mathematics teachers' knowledge of history of mathematics and their attitudes and beliefs towards using history of mathematics in mathematics education based on year level in teacher education program and gender. The sample included 1,593 freshman, sophomore, junior, and senior pre-service middle school (grades 4-8) mathematics teachers from nine universities in Turkey. Data were collected through Knowledge of History of Mathematics Test and Attitudes and Beliefs towards the Use of History of Mathematics in Mathematics Education Questionnaire. Results indicate that pre-service teachers have moderate knowledge of history of mathematics and positive attitudes and beliefs towards using history of mathematics. Their knowledge scores increase as the year level in teacher education program advanced. Males' knowledge scores are significantly higher than females' scores in the first 2 years. This situation reverses in the last 2 years, but it is not statistically significant. Pre-service teachers have more positive attitudes and availing beliefs towards using history of mathematics as they progress in their teacher education program. Females have greater attitudes and beliefs mean scores than males in each of the years. The results indicate that the teacher education program may have enhanced the pre-service teachers' knowledge of history of mathematics by related courses. However, the moderate knowledge scores indicate that there is a need for revision of these courses. The pre-service teachers' positive attitudes and beliefs towards using history of mathematics stress the importance of teacher education program in order to prepare them for implementing this alternative strategy in the future.

  1. Mathematics, the Computer, and the Impact on Mathematics Education.

    ERIC Educational Resources Information Center

    Tooke, D. James

    2001-01-01

    Discusses the connection between mathematics and the computer; mathematics curriculum; mathematics instruction, including teachers learning to use computers; and the impact of the computer on learning mathematics. (LRW)

  2. Finite Mathematics and Discrete Mathematics: Is There a Difference?

    ERIC Educational Resources Information Center

    Johnson, Marvin L.

    Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…

  3. Differences in students' mathematics engagement between gender and between rural and urban schools

    NASA Astrophysics Data System (ADS)

    Ayub, Ahmad Fauzi Mohd; Yunus, Aida Suraya Md.; Mahmud, Rosnaini; Salim, Nur Raidah; Sulaiman, Tajularipin

    2017-01-01

    The purpose of this study was to explore secondary school students' mathematics engagement focusing on the cognitive, affective and behavioural engagement domains. A total of 387 students (186 male and 201 female) from the urban and rural secondary schools in Pahang, Malaysia, were randomly selected. There were 158 students from the urban schools and 229 students from the rural schools. Descriptive analyses for mathematics engagement domains revealed behavioural engagement had the highest mean (M = 3.74, SD = .63), followed by cognitive engagement (M = 3.56, SD = .43) and affective engagement (M = 3.48, SD = .47). The mean for students' overall mathematics engagement was 3.56 (SD = .46). Further analyses showed there were significant differences in each of the engagement domains in mathematics learning (affective, cognitive and behavioural), where students in the urban schools showed significantly better in the mean scores for affective, cognitive, behavioural domains and the overall mathematics engagement as compared to the students in the rural schools. Similar findings also showed there were significant differences in the overall mathematics engagement mean between the genders. The findings indicated girls were significantly better than boys in all (affective, cognitive and behavioural) of the engagement domains in mathematics learning. It was also shown girls had higher overall mathematics engagement mean as compared to boys. However, the study also indicated the overall students' mathematics engagement was at a moderate level. Besides, the rural school students did not show high mathematics engagement as compared to the urban school students. Further analyses showed girls significantly had better mathematics engagement as compared to boys. Hence, it is recommended that in order to optimize students' mathematics engagement, they should be actively engaged in more participative learning activities in mathematics classrooms. Focus should be given to rural schools

  4. Mathematical Intelligence and Mathematical Creativity: A Causal Relationship

    ERIC Educational Resources Information Center

    Tyagi, Tarun Kumar

    2017-01-01

    This study investigated the causal relationship between mathematical creativity and mathematical intelligence. Four hundred thirty-nine 8th-grade students, age ranged from 11 to 14 years, were included in the sample of this study by random cluster technique on which mathematical creativity and Hindi adaptation of mathematical intelligence test…

  5. A new algebraic turbulence model for accurate description of airfoil flows

    NASA Astrophysics Data System (ADS)

    Xiao, Meng-Juan; She, Zhen-Su

    2017-11-01

    We report a new algebraic turbulence model (SED-SL) based on the SED theory, a symmetry-based approach to quantifying wall turbulence. The model specifies a multi-layer profile of a stress length (SL) function in both the streamwise and wall-normal directions, which thus define the eddy viscosity in the RANS equation (e.g. a zero-equation model). After a successful simulation of flat plate flow (APS meeting, 2016), we report here further applications of the model to the flow around airfoil, with significant improvement of the prediction accuracy of the lift (CL) and drag (CD) coefficients compared to other popular models (e.g. BL, SA, etc.). Two airfoils, namely RAE2822 airfoil and NACA0012 airfoil, are computed for over 50 cases. The results are compared to experimental data from AGARD report, which shows deviations of CL bounded within 2%, and CD within 2 counts (10-4) for RAE2822 and 6 counts for NACA0012 respectively (under a systematic adjustment of the flow conditions). In all these calculations, only one parameter (proportional to the Karmen constant) shows slight variation with Mach number. The most remarkable outcome is, for the first time, the accurate prediction of the drag coefficient. The other interesting outcome is the physical interpretation of the multi-layer parameters: they specify the corresponding multi-layer structure of turbulent boundary layer; when used together with simulation data, the SED-SL enables one to extract physical information from empirical data, and to understand the variation of the turbulent boundary layer.

  6. Low- and High-Achieving Sixth-Grade Students' Access to Participation during Mathematics Discourse

    ERIC Educational Resources Information Center

    Lack, Brian; Swars, Susan Lee; Meyers, Barbara

    2014-01-01

    A descriptive, holistic, multiple-case methodology was applied to examine the nature of participation in discourse of two low- and two high-achieving grade 6 students while solving mathematical tasks in a standards-based classroom. Data collected via classroom observations and student interviews were analyzed through a multiple-cycle coding…

  7. Predominant Teaching Strategies in Schools: Implications for Curriculum Implementation in Mathematics, Science and Technology

    ERIC Educational Resources Information Center

    Achuonye, Keziah Akuoma

    2015-01-01

    This descriptive survey is hinged on predominant teaching strategies in schools, implications for curriculum implementation in Mathematics, Science and Technology. Target population consisted of teachers in primary, secondary and tertiary schools. However, purposive sample of 900 respondents was drawn from the six BRACED states namely Bayelsa,…

  8. Designing and Using Research Instruments to Describe the Beliefs and Practices of Mathematics Teachers

    ERIC Educational Resources Information Center

    Swan, Malcolm

    2006-01-01

    This article describes research instruments that facilitate the description of teachers' beliefs and practices and their use with further education (FE) mathematics teachers. They consist of linked questionnaires aimed at both teachers and students, validated by cross-referencing with more open questionnaires and with classroom observation. They…

  9. "Geomat.dk": Historical Instruments of Navigation--Used as Educational Tools in Mathematics

    ERIC Educational Resources Information Center

    Jakobsen, Ivan Tafteberg; Matthiasen, Jesper

    2016-01-01

    This paper gives a short description of the scope and content of an educational project. The approach is to use historical navigational devices, such as sextants and cross staffs, to teach mathematics in secondary schools. By making collections of these devices available to teachers and bringing them into the class room a new approach to combine…

  10. Promoting middle school students’ mathematical creative thinking ability using scientific approach

    NASA Astrophysics Data System (ADS)

    Istiqomah, A.; Perbowo, K. S.; Purwanto, S. E.

    2018-01-01

    This research aims to identify the strength of scientific approach in order to develop mathematical creative thinking in junior high school. Descriptive qualitative method is used in this research. 34 students in 7th grade are chosen using purposive sampling. For collecting data, this research uses test, observation, and interview. The test consists of 6 items which have been tested for their validity and reliability and used in pre-test and post-test. The pre-test shows that students average score in mathematical creative thinking is 43 (low), while in post-test it is 69 (middle). The N-gain in mathematical creative thinking point is 0.461, which is classified in the middle grade. Furthermore, the N-gain for each indicator, they score 0.438 for fluency; 0.568 for flexibility; and 0.382 for novelty. The N-gain for those indicators falls under middle grade. The research shows that scientific approach develops more flexibility, and, on the other hand, it develops less novelty.

  11. Learning Mathematics for Teaching Mathematics: Non-Specialist Teachers' Mathematics Teacher Identity

    ERIC Educational Resources Information Center

    Crisan, Cosette; Rodd, Melissa

    2017-01-01

    A non-specialist teacher of mathematics is a school teacher who qualified to teach in a subject other than mathematics yet teaches mathematics to students in secondary school. There is an emerging interest internationally in this population, a brief report of which is given in the paper. Because of concerns about the quality of non-specialists'…

  12. Mathematization Competencies of Pre-Service Elementary Mathematics Teachers in the Mathematical Modelling Process

    ERIC Educational Resources Information Center

    Yilmaz, Suha; Tekin-Dede, Ayse

    2016-01-01

    Mathematization competency is considered in the field as the focus of modelling process. Considering the various definitions, the components of the mathematization competency are determined as identifying assumptions, identifying variables based on the assumptions and constructing mathematical model/s based on the relations among identified…

  13. The Impact of Critical Thinking and Logico-Mathematical Intelligence on Algorithmic Design Skills

    ERIC Educational Resources Information Center

    Korkmaz, Ozgen

    2012-01-01

    The present study aims to reveal the impact of students' critical thinking and logico-mathematical intelligence levels of students on their algorithm design skills. This research was a descriptive study and carried out by survey methods. The sample consisted of 45 first-year educational faculty undergraduate students. The data was collected by…

  14. Crossroads in the History of Mathematics and Mathematics Education. The Montana Mathematics Enthusiast: Monograph Series in Mathematics Education

    ERIC Educational Resources Information Center

    Sriraman, Bharath, Ed.

    2012-01-01

    The interaction of the history of mathematics and mathematics education has long been construed as an esoteric area of inquiry. Much of the research done in this realm has been under the auspices of the history and pedagogy of mathematics group. However there is little systematization or consolidation of the existing literature aimed at…

  15. Rocket injector anomalies study. Volume 1: Description of the mathematical model and solution procedure

    NASA Technical Reports Server (NTRS)

    Przekwas, A. J.; Singhal, A. K.; Tam, L. T.

    1984-01-01

    The capability of simulating three dimensional two phase reactive flows with combustion in the liquid fuelled rocket engines is demonstrated. This was accomplished by modifying an existing three dimensional computer program (REFLAN3D) with Eulerian Lagrangian approach to simulate two phase spray flow, evaporation and combustion. The modified code is referred as REFLAN3D-SPRAY. The mathematical formulation of the fluid flow, heat transfer, combustion and two phase flow interaction of the numerical solution procedure, boundary conditions and their treatment are described.

  16. The slow-scale linear noise approximation: an accurate, reduced stochastic description of biochemical networks under timescale separation conditions

    PubMed Central

    2012-01-01

    Background It is well known that the deterministic dynamics of biochemical reaction networks can be more easily studied if timescale separation conditions are invoked (the quasi-steady-state assumption). In this case the deterministic dynamics of a large network of elementary reactions are well described by the dynamics of a smaller network of effective reactions. Each of the latter represents a group of elementary reactions in the large network and has associated with it an effective macroscopic rate law. A popular method to achieve model reduction in the presence of intrinsic noise consists of using the effective macroscopic rate laws to heuristically deduce effective probabilities for the effective reactions which then enables simulation via the stochastic simulation algorithm (SSA). The validity of this heuristic SSA method is a priori doubtful because the reaction probabilities for the SSA have only been rigorously derived from microscopic physics arguments for elementary reactions. Results We here obtain, by rigorous means and in closed-form, a reduced linear Langevin equation description of the stochastic dynamics of monostable biochemical networks in conditions characterized by small intrinsic noise and timescale separation. The slow-scale linear noise approximation (ssLNA), as the new method is called, is used to calculate the intrinsic noise statistics of enzyme and gene networks. The results agree very well with SSA simulations of the non-reduced network of elementary reactions. In contrast the conventional heuristic SSA is shown to overestimate the size of noise for Michaelis-Menten kinetics, considerably under-estimate the size of noise for Hill-type kinetics and in some cases even miss the prediction of noise-induced oscillations. Conclusions A new general method, the ssLNA, is derived and shown to correctly describe the statistics of intrinsic noise about the macroscopic concentrations under timescale separation conditions. The ssLNA provides a

  17. The Relationship of Mathematics Anxiety and Mathematical Knowledge to the Learning of Mathematical Pedagogy by Preservice Elementary Teachers.

    ERIC Educational Resources Information Center

    Battista, Michael T.

    1986-01-01

    Examined how preservice elementary teachers' (N=38) mathematical knowledge and mathematics anxiety affect their success in a mathematics methods course. Also examined the hypothesis that a mathematics methods course can reduce the mathematics anxiety of these teachers. One finding is that mathematics anxiety does not inhibit their learning of…

  18. How to build a course in mathematical-biological modeling: content and processes for knowledge and skill.

    PubMed

    Hoskinson, Anne-Marie

    2010-01-01

    Biological problems in the twenty-first century are complex and require mathematical insight, often resulting in mathematical models of biological systems. Building mathematical-biological models requires cooperation among biologists and mathematicians, and mastery of building models. A new course in mathematical modeling presented the opportunity to build both content and process learning of mathematical models, the modeling process, and the cooperative process. There was little guidance from the literature on how to build such a course. Here, I describe the iterative process of developing such a course, beginning with objectives and choosing content and process competencies to fulfill the objectives. I include some inductive heuristics for instructors seeking guidance in planning and developing their own courses, and I illustrate with a description of one instructional model cycle. Students completing this class reported gains in learning of modeling content, the modeling process, and cooperative skills. Student content and process mastery increased, as assessed on several objective-driven metrics in many types of assessments.

  19. The Relationships among Mathematics Teaching Efficacy, Mathematics Self-Efficacy, and Mathematical Beliefs for Elementary Pre-Service Teachers

    ERIC Educational Resources Information Center

    Briley, Jason S.

    2012-01-01

    Ninety-five elementary pre-service teachers enrolled in a mathematics content course for elementary school teachers completed 3 surveys to measure mathematics teaching efficacy, mathematics self-efficacy, and mathematical beliefs. The pre-service teachers who reported stronger beliefs in their capabilities to teach mathematics effectively were…

  20. Constructing Mathematical Knowledge: Epistemology and Mathematics Education. Studies in Mathematics Education Series: 4.

    ERIC Educational Resources Information Center

    Ernest, Paul, Ed.

    This book illustrates the breadth of theoretical and philosophical perspectives that can be brought to bear on mathematics and education. Part 1, "Constructivism and the Learning of Mathematics," contains the following chapters: (1) "A Radical Constructivist View of Basic Mathematical Concepts" (E. von Glasersfeld); (2) "Interaction and Children's…

  1. Family Child Care Learning Environments: Caregiver Knowledge and Practices Related to Early Literacy and Mathematics

    ERIC Educational Resources Information Center

    Phillips, Beth M.; Morse, Erika E.

    2011-01-01

    This paper presents findings from a stratified-random survey of family child care providers' backgrounds, caregiving environments, practices, attitudes, and knowledge related to language, literacy, and mathematics development for preschool children. Descriptive results are consistent with prior studies suggesting that home-based providers are…

  2. Analysis of Mathematics Critical Thinking Students in Junior High School Based on Cognitive Style

    NASA Astrophysics Data System (ADS)

    Agoestanto, A.; Sukestiyarno, YL; Rochmad

    2017-04-01

    The purpose of this research was to determine the critical thinking ability of mathematics from junior high school students based on FI and FD cognitive style. Data of this research were taken from students grade VIII at SMPN 2 Ambarawa. The research method used a descriptive qualitative approach. Data was taken with a testing method; the critical thinking was measured with WGCTA which is modified with mathematical problems, the cognitive style was measured with GEFT. The student’s test result was analysed, then four students were selected, the two of them are FI cognitive style, and the others are FD cognitive style, for qualitative analysis. The result showed that the ability of mathematics critical thinking students with FI cognitive style is better than FD cognitive style on the ability of inference, assumption, deduction, and interpretation. While on the aspect of argument evaluation, mathematics critical thinking ability of students with FD cognitive style is a little better than students with FI cognitive style.

  3. Universal gestational age effects on cognitive and basic mathematic processing: 2 cohorts in 2 countries.

    PubMed

    Wolke, Dieter; Strauss, Vicky Yu-Chun; Johnson, Samantha; Gilmore, Camilla; Marlow, Neil; Jaekel, Julia

    2015-06-01

    To determine whether general cognitive ability, basic mathematic processing, and mathematic attainment are universally affected by gestation at birth, as well as whether mathematic attainment is more strongly associated with cohort-specific factors such as schooling than basic cognitive and mathematical abilities. The Bavarian Longitudinal Study (BLS, 1289 children, 27-41 weeks gestational age [GA]) was used to estimate effects of GA on IQ, basic mathematic processing, and mathematic attainment. These estimations were used to predict IQ, mathematic processing, and mathematic attainment in the EPICure Study (171 children <26 weeks GA). For children born <34 weeks GA, each lower week decreased IQ and mathematic attainment scores by 2.34 (95% CI: -2.99, -1.70) and 2.76 (95% CI: -3.40, -2.11) points, respectively. There were no differences among children born 34-41 weeks GA. Similarly, for children born <36 weeks GA, mathematic processing scores decreased by 1.77 (95% CI: -2.20, -1.34) points with each lower GA week. The prediction function generated using BLS data accurately predicted the effect of GA on IQ and mathematic processing among EPICure children. However, these children had better attainment than predicted by BLS. Prematurity has adverse effects on basic mathematic processing following birth at all gestations <36 weeks and on IQ and mathematic attainment <34 weeks GA. The ability to predict IQ and mathematic processing scores from one cohort to another among children cared for in different eras and countries suggests that universal neurodevelopmental factors may explain the effects of gestation at birth. In contrast, mathematic attainment may be improved by schooling. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

  4. Recent Advances of Malaria Parasites Detection Systems Based on Mathematical Morphology

    PubMed Central

    Di Ruberto, Cecilia; Kocher, Michel

    2018-01-01

    Malaria is an epidemic health disease and a rapid, accurate diagnosis is necessary for proper intervention. Generally, pathologists visually examine blood stained slides for malaria diagnosis. Nevertheless, this kind of visual inspection is subjective, error-prone and time-consuming. In order to overcome the issues, numerous methods of automatic malaria diagnosis have been proposed so far. In particular, many researchers have used mathematical morphology as a powerful tool for computer aided malaria detection and classification. Mathematical morphology is not only a theory for the analysis of spatial structures, but also a very powerful technique widely used for image processing purposes and employed successfully in biomedical image analysis, especially in preprocessing and segmentation tasks. Microscopic image analysis and particularly malaria detection and classification can greatly benefit from the use of morphological operators. The aim of this paper is to present a review of recent mathematical morphology based methods for malaria parasite detection and identification in stained blood smears images. PMID:29419781

  5. Recent Advances of Malaria Parasites Detection Systems Based on Mathematical Morphology.

    PubMed

    Loddo, Andrea; Di Ruberto, Cecilia; Kocher, Michel

    2018-02-08

    Malaria is an epidemic health disease and a rapid, accurate diagnosis is necessary for proper intervention. Generally, pathologists visually examine blood stained slides for malaria diagnosis. Nevertheless, this kind of visual inspection is subjective, error-prone and time-consuming. In order to overcome the issues, numerous methods of automatic malaria diagnosis have been proposed so far. In particular, many researchers have used mathematical morphology as a powerful tool for computer aided malaria detection and classification. Mathematical morphology is not only a theory for the analysis of spatial structures, but also a very powerful technique widely used for image processing purposes and employed successfully in biomedical image analysis, especially in preprocessing and segmentation tasks. Microscopic image analysis and particularly malaria detection and classification can greatly benefit from the use of morphological operators. The aim of this paper is to present a review of recent mathematical morphology based methods for malaria parasite detection and identification in stained blood smears images.

  6. Mathematical model for gyroscope effects

    NASA Astrophysics Data System (ADS)

    Usubamatov, Ryspek

    2015-05-01

    Gyroscope effects are used in many engineering calculations of rotating parts, and a gyroscope is the basic unit of numerous devices and instruments used in aviation, space, marine and other industries. The primary attribute of a gyroscope is a spinning rotor that persists in maintaining its plane of rotation, creating gyroscope effects. Numerous publications represent the gyroscope theory using mathematical models based on the law of kinetic energy conservation and the rate of change in angular momentum of a spinning rotor. Gyroscope theory still attracts many researchers who continue to discover new properties of gyroscopic devices. In reality, gyroscope effects are more complex and known mathematical models do not accurately reflect the actual motions. Analysis of forces acting on a gyroscope shows that four dynamic components act simultaneously: the centrifugal, inertial and Coriolis forces and the rate of change in angular momentum of the spinning rotor. The spinning rotor generates a rotating plane of centrifugal and Coriols forces that resist the twisting of the spinning rotor with external torque applied. The forced inclination of the spinning rotor generates inertial forces, resulting in precession torque of a gyroscope. The rate of change of the angular momentum creates resisting and precession torques which are not primary one in gyroscope effects. The new mathematical model for the gyroscope motions under the action of the external torque applied can be as base for new gyroscope theory. At the request of the author of the paper, this corrigendum was issued on 24 May 2016 to correct an incomplete Table 1 and errors in Eq. (47) and Eq. (48).

  7. Discrete Mathematics and the Secondary Mathematics Curriculum.

    ERIC Educational Resources Information Center

    Dossey, John

    Discrete mathematics, the mathematics of decision making for finite settings, is a topic of great interest in mathematics education at all levels. Attention is being focused on resolving the diversity of opinion concerning the exact nature of the subject, what content the curriculum should contain, who should study that material, and how that…

  8. Mathematics Self-Efficacy and Flow in Developmental Mathematics Students

    ERIC Educational Resources Information Center

    Golnabi, Laura

    2017-01-01

    This study examined mathematics self-efficacy and the characteristics of flow in the context of performing mathematical tasks. In particular, it explored the subjective experiences of 113 undergraduate students enrolled in a developmental mathematics course while they were independently solving certain mathematical problems. This study…

  9. The Relationship between State High School Exit Exams and Mathematical Proficiency: Analyses of the Complexity, Content, and Format of Items and Assessment Protocols

    ERIC Educational Resources Information Center

    Regan, Blake B.

    2012-01-01

    This study examined the relationship between high school exit exams and mathematical proficiency. With the No Child Left Behind (NCLB) Act requiring all students to be proficient in mathematics by 2014, it is imperative that high-stakes assessments accurately evaluate all aspects of student achievement, appropriately set the yardstick by which…

  10. Analysis of Undergraduate Students’ Mathematical Understanding Ability of the Limit of Function Based on APOS Theory Perspective

    NASA Astrophysics Data System (ADS)

    Afgani, M. W.; Suryadi, D.; Dahlan, J. A.

    2017-09-01

    The aim of this study was to know the level of undergraduate students’ mathematical understanding ability based on APOS theory perspective. The APOS theory provides an evaluation framework to describe the level of students’ understanding and mental structure about their conception to a mathematics concept. The levels of understanding in APOS theory are action, process, object, and schema conception. The subjects were 59 students of mathematics education whom had attended a class of the limit of function at a university in Palembang. The method was qualitative descriptive with 4 test items. The result showed that most of students were still at the level of action conception. They could calculate and use procedure precisely to the mathematics objects that was given, but could not reach the higher conception yet.

  11. Impact of Student Calculator Use on the 2013 NAEP Twelfth-Grade Mathematics Assessment

    ERIC Educational Resources Information Center

    Klecker, Beverly M.; Klecker, Richard L.

    2014-01-01

    This descriptive research study examined 2013 NAEP 12th-grade mathematics scores by students' use of graphing calculators in math classes and the kind of calculator students used during NAEP assessment. NAEP Data Explorer analysis included two questions from Student Factors: How often do you use these different kinds of calculators in math class?…

  12. A Descriptive, Survey Research Study of the Student Characteristics Influencing the Four Theoretical Sources of Mathematical Self-Efficacy of College Freshmen

    ERIC Educational Resources Information Center

    Locklear, Tonja Motley

    2012-01-01

    The Sources of Middle School Mathematics Self-Efficacy Scale (Usher & Pajares, 2009) was adapted for use in this study investigating the impact that gender, race, sexual orientation, hometown location (rural, suburban, or urban), high school GPA, college GPA and letter grade of a mathematics course in the previous semester had on the four…

  13. Mathematics as a conduit for translational research in post-traumatic osteoarthritis.

    PubMed

    Ayati, Bruce P; Kapitanov, Georgi I; Coleman, Mitchell C; Anderson, Donald D; Martin, James A

    2017-03-01

    Biomathematical models offer a powerful method of clarifying complex temporal interactions and the relationships among multiple variables in a system. We present a coupled in silico biomathematical model of articular cartilage degeneration in response to impact and/or aberrant loading such as would be associated with injury to an articular joint. The model incorporates fundamental biological and mechanical information obtained from explant and small animal studies to predict post-traumatic osteoarthritis (PTOA) progression, with an eye toward eventual application in human patients. In this sense, we refer to the mathematics as a "conduit of translation." The new in silico framework presented in this paper involves a biomathematical model for the cellular and biochemical response to strains computed using finite element analysis. The model predicts qualitative responses presently, utilizing system parameter values largely taken from the literature. To contribute to accurate predictions, models need to be accurately parameterized with values that are based on solid science. We discuss a parameter identification protocol that will enable us to make increasingly accurate predictions of PTOA progression using additional data from smaller scale explant and small animal assays as they become available. By distilling the data from the explant and animal assays into parameters for biomathematical models, mathematics can translate experimental data to clinically relevant knowledge. © 2016 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:566-572, 2017. © 2016 Orthopaedic Research Society. Published by Wiley Periodicals, Inc.

  14. On the Helix Propensity in Generalized Born Solvent Descriptions of Modeling the Dark Proteome

    DTIC Science & Technology

    2017-01-10

    benchmarks of conformational sampling methods and their all-atom force fields plus solvent descriptions to accurately model structural transitions on a...atom simulations of proteins is the replacement of explicit water interactions with a continuum description of treating implicitly the bulk physical... structure was reported by Amarasinghe and coworkers (Leung et al., 2015) of the Ebola nucleoprotein NP in complex with a 28-residue peptide extracted

  15. Latina girls of Puerto Rican origin who are successful in science and mathematics high school courses

    NASA Astrophysics Data System (ADS)

    Oquendo-Rodriguez, Aida L.

    Professions and careers related to science and mathematics lack representation of minorities. Within these underrepresented minority populations there is no other group more affected than Latina women and girls. Women in general, are still underrepresented in many areas of our society. While women's roles are changing in today's society, most changes encourage the participation of more White/Anglo women in traditionally male roles. Latina women are still more disadvantaged than White women. There is no doubt that education is significant in increasing the participation of minorities in the fields of science and mathematics, especially for minority girls (Oakes, 1990; Rodriguez, 1993). This study explored the interests, life experiences, characteristics and motivations of Latina girls of Puerto Rican origin who are successful in science and mathematics high school courses. The study identifies factors that can influence the interest of Latina girls of Puerto Rican origin in science and mathematics career choices. This research is significant and relevant to educators and policy makers, especially to science and mathematics educators. The research is primarily descriptive and exploratory. It explores the social characteristics of Latina girls and professional women who have been successful in science and mathematics high school courses. The research offers the reader a visit to the participants' homes with descriptions and the opportunity to explore the thoughts and life experiences of Latina girls, their mothers and young Latina professionals of Puerto Rican origin. This research reveals the common characteristics of successful students found in the Latina girls of Puerto Rican origin who where interviewed. Creating a portrait of Latina girls of Puerto Rican origin who are successful in science and mathematics high school courses in one of the school districts of western Massachusetts. The research findings reveal that teacher relationships, family expectations

  16. Accurate measurement of junctional conductance between electrically coupled cells with dual whole-cell voltage-clamp under conditions of high series resistance.

    PubMed

    Hartveit, Espen; Veruki, Margaret Lin

    2010-03-15

    Accurate measurement of the junctional conductance (G(j)) between electrically coupled cells can provide important information about the functional properties of coupling. With the development of tight-seal, whole-cell recording, it became possible to use dual, single-electrode voltage-clamp recording from pairs of small cells to measure G(j). Experiments that require reduced perturbation of the intracellular environment can be performed with high-resistance pipettes or the perforated-patch technique, but an accompanying increase in series resistance (R(s)) compromises voltage-clamp control and reduces the accuracy of G(j) measurements. Here, we present a detailed analysis of methodologies available for accurate determination of steady-state G(j) and related parameters under conditions of high R(s), using continuous or discontinuous single-electrode voltage-clamp (CSEVC or DSEVC) amplifiers to quantify the parameters of different equivalent electrical circuit model cells. Both types of amplifiers can provide accurate measurements of G(j), with errors less than 5% for a wide range of R(s) and G(j) values. However, CSEVC amplifiers need to be combined with R(s)-compensation or mathematical correction for the effects of nonzero R(s) and finite membrane resistance (R(m)). R(s)-compensation is difficult for higher values of R(s) and leads to instability that can damage the recorded cells. Mathematical correction for R(s) and R(m) yields highly accurate results, but depends on accurate estimates of R(s) throughout an experiment. DSEVC amplifiers display very accurate measurements over a larger range of R(s) values than CSEVC amplifiers and have the advantage that knowledge of R(s) is unnecessary, suggesting that they are preferable for long-duration experiments and/or recordings with high R(s). Copyright (c) 2009 Elsevier B.V. All rights reserved.

  17. Analysis of Mathematical Modelling on Potentiometric Biosensors

    PubMed Central

    Mehala, N.; Rajendran, L.

    2014-01-01

    A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories. PMID:25969765

  18. Analysis of mathematical modelling on potentiometric biosensors.

    PubMed

    Mehala, N; Rajendran, L

    2014-01-01

    A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories.

  19. Transient Mathematical Modeling for Liquid Rocket Engine Systems: Methods, Capabilities, and Experience

    NASA Technical Reports Server (NTRS)

    Seymour, David C.; Martin, Michael A.; Nguyen, Huy H.; Greene, William D.

    2005-01-01

    The subject of mathematical modeling of the transient operation of liquid rocket engines is presented in overview form from the perspective of engineers working at the NASA Marshall Space Flight Center. The necessity of creating and utilizing accurate mathematical models as part of liquid rocket engine development process has become well established and is likely to increase in importance in the future. The issues of design considerations for transient operation, development testing, and failure scenario simulation are discussed. An overview of the derivation of the basic governing equations is presented along with a discussion of computational and numerical issues associated with the implementation of these equations in computer codes. Also, work in the field of generating usable fluid property tables is presented along with an overview of efforts to be undertaken in the future to improve the tools use for the mathematical modeling process.

  20. Transient Mathematical Modeling for Liquid Rocket Engine Systems: Methods, Capabilities, and Experience

    NASA Technical Reports Server (NTRS)

    Martin, Michael A.; Nguyen, Huy H.; Greene, William D.; Seymout, David C.

    2003-01-01

    The subject of mathematical modeling of the transient operation of liquid rocket engines is presented in overview form from the perspective of engineers working at the NASA Marshall Space Flight Center. The necessity of creating and utilizing accurate mathematical models as part of liquid rocket engine development process has become well established and is likely to increase in importance in the future. The issues of design considerations for transient operation, development testing, and failure scenario simulation are discussed. An overview of the derivation of the basic governing equations is presented along with a discussion of computational and numerical issues associated with the implementation of these equations in computer codes. Also, work in the field of generating usable fluid property tables is presented along with an overview of efforts to be undertaken in the future to improve the tools use for the mathematical modeling process.

  1. Discrete Mathematical Models [and] Spreadsheets in the Classroom. Dissemination Packet--Summer 1989: Booklet #8.

    ERIC Educational Resources Information Center

    Knee, David; And Others

    This booklet is the eighth in a series of nine from the Teacher Training Institute at Hofstra University (New York) and contains descriptive information about two courses included in the institute's program. The first course, by David Knee, William McKeough, and Robert Silverstone, is "Discrete Mathematical Models," which deals with…

  2. A Phenomenological Study of Middle Grade Female and Male Students' Single-Sex Mathematical Experiences

    ERIC Educational Resources Information Center

    Simpson, Amber; Che, S. Megan

    2016-01-01

    Utilizing a descriptive phenomenological design, this study examines the lived experiences of seven middle grade students, four females and three males, enrolled in a single-sex mathematics classroom within a coeducational school setting. The intent of the study is to understand, from students themselves, about the experience of single-sex…

  3. Contextualising Mathematics Self-Efficacy and Performance among Rural High School Students in the Philippines

    ERIC Educational Resources Information Center

    Causapin, Mark

    2016-01-01

    This paper expands the scope of typical quantitative studies on mathematics self-efficacy by including a short ethnography of the students' daily classroom experiences. It attempts to provide a "thicker description" and a context in which these beliefs could be interpreted. Using both qualitative and quantitative sets of data, it is…

  4. A study of students' learning styles and mathematics anxiety amongst form four students in Kerian Perak

    NASA Astrophysics Data System (ADS)

    Esa, Suraya; Mohamed, Nurul Akmal

    2017-05-01

    This study aims to identify the relationship between students' learning styles and mathematics anxiety amongst Form Four students in Kerian, Perak. The study involves 175 Form Four students as respondents. The instrument which is used to assess the students' learning styles and mathematic anxiety is adapted from the Grasha's Learning Styles Inventory and the Mathematics Anxiety Scale (MAS) respectively. The types of learning styles used are independent, avoidant, collaborative, dependent, competitive and participant. The collected data is processed by SPSS (Statistical Packages for Social Sciences 16.0). The data is analysed by using descriptive statistics and inferential statistics that include t-test and Pearson correlation. The results show that majority of the students adopt collaborative learning style and the students have moderate level of mathematics anxiety. Moreover, it is found that there is significant difference between learning style avoidant, collaborative, dependent and participant based on gender. Amongst all students' learning style, there exists a weak but significant correlation between avoidant, independent and participant learning style and mathematics anxiety. It is very important for the teachers need to be concerned about the effects of learning styles on mathematics anxiety. Therefore, the teachers should understand mathematics anxiety and implement suitable learning strategies in order for the students to overcome their mathematics anxiety.

  5. Mathematics, Anyone?

    ERIC Educational Resources Information Center

    Reys, Robert; Reys, Rustin

    2011-01-01

    In their dual roles as mathematics teachers and tennis coaches, the authors have worked with tennis players who have never thought about how a knowledge of mathematics might help them become "better" tennis players. They have also worked with many mathematics students who have never considered how much mathematics is associated with tennis. This…

  6. Mathematical Selfies: Students' Real-World Mathematics

    ERIC Educational Resources Information Center

    Jaqua, Kathy M. C.

    2017-01-01

    The activity of snapping photographs to document all parts of daily life and sharing them with friends is the norm for many students. What if we could make mathematics as natural a part of daily life through "mathematical selfies"? The author's goal is to use students' love of selfies to help them see that mathematics is already part of…

  7. Knowledge Growth of Mathematics Teachers during Professional Activity Based on the Task of Lesson Explaining

    ERIC Educational Resources Information Center

    Peng, Aihui

    2007-01-01

    "Lesson explaining" has been developed in China from an evaluative resource to an effective form of teacher professional development with the value of emphasizing teacher reflective practice. This paper begins with a general description of lesson explaining. Then an example of "explaining" a mathematics lesson for teaching…

  8. Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties.

    PubMed

    Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun

    2015-01-01

    Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil's Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children's LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions.

  9. Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties

    PubMed Central

    Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun

    2015-01-01

    Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil’s Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children’s LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions. PMID:26090806

  10. International note: Are Emirati parents' attitudes toward mathematics linked to their adolescent children's attitudes toward mathematics and mathematics achievement?

    PubMed

    Areepattamannil, Shaljan; Khine, Myint Swe; Melkonian, Michael; Welch, Anita G; Al Nuaimi, Samira Ahmed; Rashad, Fatimah F

    2015-10-01

    Drawing on data from the 2012 Program for International Student Assessment (PISA) and employing multilevel modeling as an analytic strategy, this study examined the relations of adolescent children's perceptions of their parents' attitudes towards mathematics to their own attitudes towards mathematics and mathematics achievement among a sample of 5116 adolescents from 384 schools in the United Arab Emirates. The results of this cross-sectional study revealed that adolescents who perceived that their parents liked mathematics and considered mathematics was important for their children not only to study but also for their career tended to report higher levels of intrinsic and instrumental motivation to learn mathematics, mathematics self-concept and self-efficacy, and mathematics work ethic. Moreover, adolescents who perceived that their parents liked mathematics and considered mathematics was important for their children's career tended to report positive intentions and behaviors toward mathematics. However, adolescents who perceived that their parents considered mathematics was important for their children's career tended to report higher levels of mathematics anxiety. Finally, adolescents who perceived that their parents considered mathematics was important for their children to study performed significantly better on the mathematics assessment than did their peers whose parents disregarded the importance of learning mathematics. Copyright © 2015 The Foundation for Professionals in Services for Adolescents. Published by Elsevier Ltd. All rights reserved.

  11. The Relationships among Pre-Service Mathematics Teachers' Beliefs about Mathematics, Mathematics Teaching, and Use of Technology in China

    ERIC Educational Resources Information Center

    Yang, Xinrong; Leung, Frederick K. S.

    2015-01-01

    This paper investigated pre-service mathematics teachers' mathematics beliefs, beliefs about information and communication technology (ICT), and their relationships. 787 pre-service mathematics teachers in China completed a survey questionnaire measuring their beliefs about the nature of mathematics, beliefs about mathematics learning and…

  12. The analysis of mathematics literacy on PMRI learning with media schoology of junior high school students

    NASA Astrophysics Data System (ADS)

    Wardono; Mariani, S.

    2018-03-01

    Indonesia as a developing country in the future will have high competitiveness if its students have high mathematics literacy ability. The current reality from year to year rankings of PISA mathematics literacy Indonesian students are still not good. This research is motivated by the importance and low ability of the mathematics literacy. The purpose of this study is to: (1) analyze the effectiveness of PMRI learning with media Schoology, (2) describe the ability of students' mathematics literacy on PMRI learning with media Schoology which is reviewed based on seven components of mathematics literacy, namely communication, mathematizing, representation, reasoning, devising strategies, using symbols, and using mathematics tool. The method used in this research is the method of sequential design method mix. Techniques of data collection using observation, interviews, tests, and documentation. Data analysis techniques use proportion test, appellate test, and use descriptive analysis. Based on the data analysis, it can be concluded; (1) PMRI learning with media Schoology effectively improve the ability of mathematics literacy because of the achievement of classical completeness, students' mathematics literacy ability in PMRI learning with media Schoology is higher than expository learning, and there is increasing ability of mathematics literacy in PMRI learning with media Schoology of 30%. (2) Highly capable students attain excellent mathematics literacy skills, can work using broad thinking with appropriate resolution strategies. Students who are capable of achieving good mathematics literacy skills can summarize information, present problem-solving processes, and interpret solutions. low-ability students have reached the level of ability of mathematics literacy good enough that can solve the problem in a simple way.

  13. The application of brain-based learning principles aided by GeoGebra to improve mathematical representation ability

    NASA Astrophysics Data System (ADS)

    Priatna, Nanang

    2017-08-01

    The use of Information and Communication Technology (ICT) in mathematics instruction will help students in building conceptual understanding. One of the software products used in mathematics instruction is GeoGebra. The program enables simple visualization of complex geometric concepts and helps improve students' understanding of geometric concepts. Instruction applying brain-based learning principles is one oriented at the efforts of naturally empowering the brain potentials which enable students to build their own knowledge. One of the goals of mathematics instruction in school is to develop mathematical communication ability. Mathematical representation is regarded as a part of mathematical communication. It is a description, expression, symbolization, or modeling of mathematical ideas/concepts as an attempt of clarifying meanings or seeking for solutions to the problems encountered by students. The research aims to develop a learning model and teaching materials by applying the principles of brain-based learning aided by GeoGebra to improve junior high school students' mathematical representation ability. It adopted a quasi-experimental method with the non-randomized control group pretest-posttest design and the 2x3 factorial model. Based on analysis of the data, it is found that the increase in the mathematical representation ability of students who were treated with mathematics instruction applying the brain-based learning principles aided by GeoGebra was greater than the increase of the students given conventional instruction, both as a whole and based on the categories of students' initial mathematical ability.

  14. Prospective Mathematics Teachers' Attitudes Towards Learning Mathematics with Technology

    ERIC Educational Resources Information Center

    Ipek, A. Sabri; Berigel, Muhammed; Albayrak, Mustafa

    2007-01-01

    Role of technology which is an important tool for new approaches in learning mathematics is rapidly increasing at focus point of learning mathematics with new designs. One of the biggest factors at learning and instructing technology based mathematic education is attitudes of mathematics teachers towards technology. At this study, attitudes of…

  15. Pre-Service Teachers' Mathematics Self-Efficacy and Mathematics Teaching Self-Efficacy

    ERIC Educational Resources Information Center

    Zuya, Habila Elisha; Kwalat, Simon Kevin; Attah, Bala Galle

    2016-01-01

    Pre-service mathematics teachers' mathematics self-efficacy and mathematics teaching self-efficacy were investigated in this study. The purpose was to determine the confidence levels of their self-efficacy in mathematics and mathematics teaching. Also, the study was aimed at finding whether their mathematics self-efficacy and teaching…

  16. An adaptive maneuvering logic computer program for the simulation of one-to-one air-to-air combat. Volume 2: Program description

    NASA Technical Reports Server (NTRS)

    Burgin, G. H.; Owens, A. J.

    1975-01-01

    A detailed description is presented of the computer programs in order to provide an understanding of the mathematical and geometrical relationships as implemented in the programs. The individual sbbroutines and their underlying mathematical relationships are described, and the required input data and the output provided by the program are explained. The relationship of the adaptive maneuvering logic program with the program to drive the differential maneuvering simulator is discussed.

  17. Mathematics Teachers' Perceptions of Their Students' Mathematical Competence: Relations to Mathematics Achievement, Affect, and Engagement in Singapore and Australia

    ERIC Educational Resources Information Center

    Areepattamannil, Shaljan; Kaur, Berinderjeet

    2013-01-01

    This study, drawing on data from the Trends in International Mathematics and Science Study (TIMSS) 2011, examined whether mathematics teachers' perceptions of their students' mathematical competence were related to mathematics achievement, affect toward mathematics, and engagement in mathematics lessons among Grade 8 students in Singapore and…

  18. Physical and mathematical modeling of antimicrobial photodynamic therapy

    NASA Astrophysics Data System (ADS)

    Bürgermeister, Lisa; López, Fernando Romero; Schulz, Wolfgang

    2014-07-01

    Antimicrobial photodynamic therapy (aPDT) is a promising method to treat local bacterial infections. The therapy is painless and does not cause bacterial resistances. However, there are gaps in understanding the dynamics of the processes, especially in periodontal treatment. This work describes the advances in fundamental physical and mathematical modeling of aPDT used for interpretation of experimental evidence. The result is a two-dimensional model of aPDT in a dental pocket phantom model. In this model, the propagation of laser light and the kinetics of the chemical reactions are described as coupled processes. The laser light induces the chemical processes depending on its intensity. As a consequence of the chemical processes, the local optical properties and distribution of laser light change as well as the reaction rates. The mathematical description of these coupled processes will help to develop treatment protocols and is the first step toward an inline feedback system for aPDT users.

  19. Dynamic Boolean Mathematics

    ERIC Educational Resources Information Center

    Bossé, Michael J.; Adu-Gyamfi, Kwaku; Chandler, Kayla; Lynch-Davis, Kathleen

    2016-01-01

    Dynamic mathematical environments allow users to reify mathematical concepts through multiple representations, transform mathematical relations and organically explore mathematical properties, investigate integrated mathematics, and develop conceptual understanding. Herein, we integrate Boolean algebra, the functionalities of a dynamic…

  20. Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

    ERIC Educational Resources Information Center

    Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem

    2014-01-01

    Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…

  1. Profile of male-field dependent (FD) prospective teacher's reflective thinking in solving contextual mathematical problem

    NASA Astrophysics Data System (ADS)

    Agustan, S.; Juniati, Dwi; Siswono, Tatag Yuli Eko

    2017-08-01

    Reflective thinking is an important component in the world of education, especially in professional education of teachers. In learning mathematics, reflective thinking is one way to solve mathematical problem because it can improve student's curiosity when student faces a mathematical problem. Reflective thinking is also a future competence that should be taught to students to face the challenges and to respond of demands of the 21st century. There are many factors which give impact toward the student's reflective thinking when student solves mathematical problem. One of them is cognitive style. For this reason, reflective thinking and cognitive style are important things in solving contextual mathematical problem. This research paper describes aspect of reflective thinking in solving contextual mathematical problem involved solution by using some mathematical concept, namely linear program, algebra arithmetic operation, and linear equations of two variables. The participant, in this research paper, is a male-prospective teacher who has Field Dependent. The purpose of this paper is to describe aspect of prospective teachers' reflective thinking in solving contextual mathematical problem. This research paper is a descriptive by using qualitative approach. To analyze the data, the researchers focus in four main categories which describe prospective teacher's activities using reflective thinking, namely; (a) formulation and synthesis of experience, (b) orderliness of experience, (c) evaluating the experience and (d) testing the selected solution based on the experience.

  2. Mathematical Creative Process Wallas Model in Students Problem Posing with Lesson Study Approach

    ERIC Educational Resources Information Center

    Nuha, Muhammad 'Azmi; Waluya, S. B.; Junaedi, Iwan

    2018-01-01

    Creative thinking is very important in the modern era so that it should be improved by doing efforts such as making a lesson that train students to pose their own problems. The purposes of this research are (1) to give an initial description of students about mathematical creative thinking level in Problem Posing Model with Lesson Study approach…

  3. Using Mathematics in Science: Working with Your Mathematics Department

    ERIC Educational Resources Information Center

    Lyon, Steve

    2014-01-01

    Changes to the mathematics and science curriculums are designed to increase rigour in mathematics, and place greater emphasis on mathematical content in science subjects at key stages 3, 4 and 5 (ages 11-18). One way to meet the growing challenge of providing increased emphasis on mathematics in the science curriculum is greater collaboration…

  4. Creating Body Shapes From Verbal Descriptions by Linking Similarity Spaces.

    PubMed

    Hill, Matthew Q; Streuber, Stephan; Hahn, Carina A; Black, Michael J; O'Toole, Alice J

    2016-11-01

    Brief verbal descriptions of people's bodies (e.g., "curvy," "long-legged") can elicit vivid mental images. The ease with which these mental images are created belies the complexity of three-dimensional body shapes. We explored the relationship between body shapes and body descriptions and showed that a small number of words can be used to generate categorically accurate representations of three-dimensional bodies. The dimensions of body-shape variation that emerged in a language-based similarity space were related to major dimensions of variation computed directly from three-dimensional laser scans of 2,094 bodies. This relationship allowed us to generate three-dimensional models of people in the shape space using only their coordinates on analogous dimensions in the language-based description space. Human descriptions of photographed bodies and their corresponding models matched closely. The natural mapping between the spaces illustrates the role of language as a concise code for body shape that captures perceptually salient global and local body features. © The Author(s) 2016.

  5. Mathematical-Artificial Neural Network Hybrid Model to Predict Roll Force during Hot Rolling of Steel

    NASA Astrophysics Data System (ADS)

    Rath, S.; Sengupta, P. P.; Singh, A. P.; Marik, A. K.; Talukdar, P.

    2013-07-01

    Accurate prediction of roll force during hot strip rolling is essential for model based operation of hot strip mills. Traditionally, mathematical models based on theory of plastic deformation have been used for prediction of roll force. In the last decade, data driven models like artificial neural network have been tried for prediction of roll force. Pure mathematical models have accuracy limitations whereas data driven models have difficulty in convergence when applied to industrial conditions. Hybrid models by integrating the traditional mathematical formulations and data driven methods are being developed in different parts of world. This paper discusses the methodology of development of an innovative hybrid mathematical-artificial neural network model. In mathematical model, the most important factor influencing accuracy is flow stress of steel. Coefficients of standard flow stress equation, calculated by parameter estimation technique, have been used in the model. The hybrid model has been trained and validated with input and output data collected from finishing stands of Hot Strip Mill, Bokaro Steel Plant, India. It has been found that the model accuracy has been improved with use of hybrid model, over the traditional mathematical model.

  6. Universal Gestational Age Effects on Cognitive and Basic Mathematic Processing: 2 Cohorts in 2 Countries

    PubMed Central

    Wolke, Dieter; Strauss, Vicky Yu-Chun; Johnson, Samantha; Gilmore, Camilla; Marlow, Neil; Jaekel, Julia

    2015-01-01

    Objective To determine whether general cognitive ability, basic mathematic processing, and mathematic attainment are universally affected by gestation at birth, as well as whether mathematic attainment is more strongly associated with cohort-specific factors such as schooling than basic cognitive and mathematical abilities. Study design The Bavarian Longitudinal Study (BLS, 1289 children, 27-41 weeks gestational age [GA]) was used to estimate effects of GA on IQ, basic mathematic processing, and mathematic attainment. These estimations were used to predict IQ, mathematic processing, and mathematic attainment in the EPICure Study (171 children <26 weeks GA). Results For children born <34 weeks GA, each lower week decreased IQ and mathematic attainment scores by 2.34 (95% CI: −2.99, −1.70) and 2.76 (95% CI: −3.40, −2.11) points, respectively. There were no differences among children born 34-41 weeks GA. Similarly, for children born <36 weeks GA, mathematic processing scores decreased by 1.77 (95% CI: −2.20, −1.34) points with each lower GA week. The prediction function generated using BLS data accurately predicted the effect of GA on IQ and mathematic processing among EPICure children. However, these children had better attainment than predicted by BLS. Conclusions Prematurity has adverse effects on basic mathematic processing following birth at all gestations <36 weeks and on IQ and mathematic attainment <34 weeks GA. The ability to predict IQ and mathematic processing scores from one cohort to another among children cared for in different eras and countries suggests that universal neurodevelopmental factors may explain the effects of gestation at birth. In contrast, mathematic attainment may be improved by schooling. PMID:25842966

  7. High precision analytical description of the allowed β spectrum shape

    NASA Astrophysics Data System (ADS)

    Hayen, Leendert; Severijns, Nathal; Bodek, Kazimierz; Rozpedzik, Dagmara; Mougeot, Xavier

    2018-01-01

    A fully analytical description of the allowed β spectrum shape is given in view of ongoing and planned measurements. Its study forms an invaluable tool in the search for physics beyond the standard electroweak model and the weak magnetism recoil term. Contributions stemming from finite size corrections, mass effects, and radiative corrections are reviewed. Particular focus is placed on atomic and chemical effects, where the existing description is extended and analytically provided. The effects of QCD-induced recoil terms are discussed, and cross-checks were performed for different theoretical formalisms. Special attention was given to a comparison of the treatment of nuclear structure effects in different formalisms. Corrections were derived for both Fermi and Gamow-Teller transitions, and methods of analytical evaluation thoroughly discussed. In its integrated form, calculated f values were in agreement with the most precise numerical results within the aimed for precision. The need for an accurate evaluation of weak magnetism contributions was stressed, and the possible significance of the oft-neglected induced pseudoscalar interaction was noted. Together with improved atomic corrections, an analytical description was presented of the allowed β spectrum shape accurate to a few parts in 10-4 down to 1 keV for low to medium Z nuclei, thereby extending the work by previous authors by nearly an order of magnitude.

  8. On the Reasonable and Unreasonable Effectiveness of Mathematics in Classical and Quantum Physics

    NASA Astrophysics Data System (ADS)

    Plotnitsky, Arkady

    2011-03-01

    The point of departure for this article is Werner Heisenberg's remark, made in 1929: "It is not surprising that our language [or conceptuality] should be incapable of describing processes occurring within atoms, for … it was invented to describe the experiences of daily life, and these consist only of processes involving exceedingly large numbers of atoms. … Fortunately, mathematics is not subject to this limitation, and it has been possible to invent a mathematical scheme—the quantum theory [quantum mechanics]—which seems entirely adequate for the treatment of atomic processes." The cost of this discovery, at least in Heisenberg's and related interpretations of quantum mechanics (such as that of Niels Bohr), is that, in contrast to classical mechanics, the mathematical scheme in question no longer offers a description, even an idealized one, of quantum objects and processes. This scheme only enables predictions, in general, probabilistic in character, of the outcomes of quantum experiments. As a result, a new type of the relationships between mathematics and physics is established, which, in the language of Eugene Wigner adopted in my title, indeed makes the effectiveness of mathematics unreasonable in quantum but, as I shall explain, not in classical physics. The article discusses these new relationships between mathematics and physics in quantum theory and their implications for theoretical physics—past, present, and future.

  9. Mathematics, Thermodynamics, and Modeling to Address Ten Common Misconceptions about Protein Structure, Folding, and Stability

    ERIC Educational Resources Information Center

    Robic, Srebrenka

    2010-01-01

    To fully understand the roles proteins play in cellular processes, students need to grasp complex ideas about protein structure, folding, and stability. Our current understanding of these topics is based on mathematical models and experimental data. However, protein structure, folding, and stability are often introduced as descriptive, qualitative…

  10. Promoting Mathematical Argumentation

    ERIC Educational Resources Information Center

    Rumsey, Chepina; Langrall, Cynthia W.

    2016-01-01

    The Standards for Mathematical Practice (SMP) in the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) highlight the mathematical habits that educators should be fostering in mathematics classrooms throughout K-grade 12 education. That argumentation and discourse are important components of developing mathematically proficient…

  11. [Treatment of surface burns with proteolytic enzymes: mathematic description of lysis kinetics].

    PubMed

    Domogatskaia, A S; Domogatskiĭ, S P; Ruuge, E K

    2003-01-01

    The lysis of necrotic tissue by a proteolytic enzyme applied to the surface of a burn wound was studied. A mathematical model was proposed, which describes changes in the thickness of necrotic tissue as a function of the proteolytic activity of the enzyme. The model takes into account the inward-directed diffusion of the enzyme, the counterflow of interstitial fluid (exudates) containing specific inhibitors, and the extracellular matrix proteolysis. It was shown in terms of the quasi-stationary approach that the thickness of the necrotic tissue layer decreases exponentially with time; i.e., the lysis slows down as the thickness of the necrotic tissue layer decreases. The dependence of the characteristic time of this decrease on enzyme concentration was obtained. It was shown that, at high enzyme concentrations (more than 5 mg/ml), the entire time of lysis (after the establishment of quasi-stationary equilibrium) is inversely proportional to the concentration of the enzyme.

  12. Description of Student’s Metacognitive Ability in Understanding and Solving Mathematics Problem

    NASA Astrophysics Data System (ADS)

    Ahmad, Herlina; Febryanti, Fatimah; Febryanti, Fatimah; Muthmainnah

    2018-01-01

    This research was conducted qualitative which was aim to describe metacognitive ability to understand and solve the problems of mathematics. The subject of the research was the first year students at computer and networking department of SMK Mega Link Majene. The sample was taken by purposive sampling technique. The data obtained used the research instrument based on the form of students achievements were collected by using test of student’s achievement and interview guidance. The technique of collecting data researcher had observation to ascertain the model that used by teacher was teaching model of developing metacognitive. The technique of data analysis in this research was reduction data, presentation and conclusion. Based on the whole findings in this study it was shown that student’s metacognitive ability generally not develops optimally. It was because of limited scope of the materials, and cognitive teaching strategy handled by verbal presentation and trained continuously in facing cognitive tasks, such as understanding and solving problem.

  13. A new sensor system for accurate and precise determination of sediment dynamics and position.

    NASA Astrophysics Data System (ADS)

    Maniatis, Georgios; Hoey, Trevor; Sventek, Joseph; Hodge, Rebecca

    2014-05-01

    Sediment transport processes control many significant geomorphological changes. Consequently, sediment transport dynamics are studied across a wide range of scales leading to application of a variety of conceptually different mathematical descriptions (models) and data acquisition techniques (sensing). For river sediment transport processes both Eulerian and Lagrangian formulations are used. Data are gathered using a very wide range of sensing techniques that are not always compatible with the conceptual formulation applied. We are concerned with small to medium sediment grain-scale motion in gravel-bed rivers, and other coarse-grained environments, and: a) are developing a customised environmental sensor capable of providing coherent data that reliably record the motion; and, b) provide a mathematical framework in which these data can be analysed and interpreted, this being compatible with current stochastic approaches to sediment transport theory. Here we present results from three different aspects of the above developmental process. Firstly, we present a requirement analysis for the sensor based on the state of the art of the existing technologies. We focus on the factors that enhance data coherence and representativeness, extending the common practice for optimization which is based exclusively on electronics/computing related criteria. This analysis leads to formalization of a method that permits accurate control on the physical properties of the sensor using contemporary rapid prototyping techniques [Maniatis et al. 2013]. Secondly the first results are presented from a series of entrainment experiments in a 5 x 0.8 m flume in which a prototype sensor was deployed to monitor entrainment dynamics under increasing flow conditions (0.037 m3.s-1). The sensor was enclosed in an idealized spherical case (111 mm diameter) and placed on a constructed bed of hemispheres of the same diameter. We measured 3-axial inertial acceleration (as a measure of flow stress

  14. Student’s rigorous mathematical thinking based on cognitive style

    NASA Astrophysics Data System (ADS)

    Fitriyani, H.; Khasanah, U.

    2017-12-01

    The purpose of this research was to determine the rigorous mathematical thinking (RMT) of mathematics education students in solving math problems in terms of reflective and impulsive cognitive styles. The research used descriptive qualitative approach. Subjects in this research were 4 students of the reflective and impulsive cognitive style which was each consisting male and female subjects. Data collection techniques used problem-solving test and interview. Analysis of research data used Miles and Huberman model that was reduction of data, presentation of data, and conclusion. The results showed that impulsive male subjects used three levels of the cognitive function required for RMT that were qualitative thinking, quantitative thinking with precision, and relational thinking completely while the other three subjects were only able to use cognitive function at qualitative thinking level of RMT. Therefore the subject of impulsive male has a better RMT ability than the other three research subjects.

  15. Effect of Using Mathematics Laboratory in Teaching Mathematics on the Achievement of Mathematics Students

    ERIC Educational Resources Information Center

    Okigbo, Ebele C.; Osuafor, Abigail M.

    2008-01-01

    The study investigated the effect of using mathematics laboratory in teaching on students' achievement in Junior Secondary School Mathematics. A total of 100 JS 3 Mathematics students were involved in the study. The study is a quasi-experimental research. Results were analyzed using mean, standard deviation and analysis of covariance (ANCOVA).…

  16. Teaching Mathematics to Non-Mathematics Majors through Applications

    ERIC Educational Resources Information Center

    Abramovich, Sergei; Grinshpan, Arcadii Z.

    2008-01-01

    This article focuses on the important role of applications in teaching mathematics to students with career paths other than mathematics. These include the fields as diverse as education, engineering, business, and life sciences. Particular attention is given to instructional computing as a means for concept development in mathematics education…

  17. An Approach for a Mathematical Description of Human Root Canals by Means of Elementary Parameters.

    PubMed

    Dannemann, Martin; Kucher, Michael; Kirsch, Jasmin; Binkowski, Alexander; Modler, Niels; Hannig, Christian; Weber, Marie-Theres

    2017-04-01

    Root canal geometry is an important factor for instrumentation and preparation of the canals. Curvature, length, shape, and ramifications need to be evaluated in advance to enhance the success of the treatment. Therefore, the present study aimed to design and realize a method for analyzing the geometric characteristics of human root canals. Two extracted human lower molars were radiographed in the occlusal direction using micro-computed tomographic imaging. The 3-dimensional geometry of the root canals, calculated by a self-implemented image evaluation algorithm, was described by 3 different mathematical models: the elliptical model, the 1-circle model, and the 3-circle model. The different applied mathematical models obtained similar geometric properties depending on the parametric model used. Considering more complex root canals, the differences of the results increase because of the different adaptability and the better approximation of the geometry. With the presented approach, it is possible to estimate and compare the geometry of natural root canals. Therefore, the deviation of the canal can be assessed, which is important for the choice of taper of root canal instruments. Root canals with a nearly elliptical cross section are reasonably approximated by the elliptical model, whereas the 3-circle model obtains a good agreement for curved shapes. Copyright © 2017 American Association of Endodontists. Published by Elsevier Inc. All rights reserved.

  18. Pedagogical Factors Affecting Integration of Computers in Mathematics Instruction in Secondary Schools in Kenya

    ERIC Educational Resources Information Center

    Wanjala, Martin M. S.; Aurah, Catherine M.; Symon, Koros C.

    2015-01-01

    The paper reports findings of a study which sought to examine the pedagogical factors that affect the integration of computers in mathematics instruction as perceived by teachers in secondary schools in Kenya. This study was based on the Technology Acceptance Model (TAM). A descriptive survey design was used for this study. Stratified and simple…

  19. Mathematical values in the processing of Chinese numeral classifiers and measure words.

    PubMed

    Her, One-Soon; Chen, Ying-Chun; Yen, Nai-Shing

    2017-01-01

    A numeral classifier is required between a numeral and a noun in Chinese, which comes in two varieties, sortal classifer (C) and measural classifier (M), also known as 'classifier' and 'measure word', respectively. Cs categorize objects based on semantic attributes and Cs and Ms both denote quantity in terms of mathematical values. The aim of this study was to conduct a psycholinguistic experiment to examine whether participants process C/Ms based on their mathematical values with a semantic distance comparison task, where participants judged which of the two C/M phrases was semantically closer to the target C/M. Results showed that participants performed more accurately and faster for C/Ms with fixed values than the ones with variable values. These results demonstrated that mathematical values do play an important role in the processing of C/Ms. This study may thus shed light on the influence of the linguistic system of C/Ms on magnitude cognition.

  20. Segmentation of vessel-like patterns using mathematical morphology and curvature evaluation.

    PubMed

    Zana, F; Klein, J C

    2001-01-01

    This paper presents an algorithm based on mathematical morphology and curvature evaluation for the detection of vessel-like patterns in a noisy environment. Such patterns are very common in medical images. Vessel detection is interesting for the computation of parameters related to blood flow. Its tree-like geometry makes it a usable feature for registration between images that can be of a different nature. In order to define vessel-like patterns, segmentation is performed with respect to a precise model. We define a vessel as a bright pattern, piece-wise connected, and locally linear, mathematical morphology is very well adapted to this description, however other patterns fit such a morphological description. In order to differentiate vessels from analogous background patterns, a cross-curvature evaluation is performed. They are separated out as they have a specific Gaussian-like profile whose curvature varies smoothly along the vessel. The detection algorithm that derives directly from this modeling is based on four steps: (1) noise reduction; (2) linear pattern with Gaussian-like profile improvement; (3) cross-curvature evaluation; (4) linear filtering. We present its theoretical background and illustrate it on real images of various natures, then evaluate its robustness and its accuracy with respect to noise.

  1. Interest in mathematics and science among students having high mathematics aptitude

    NASA Astrophysics Data System (ADS)

    Ely, Jane Alice

    The study investigates why men and women differ in their interest in mathematics and science and in the pursuit of careers in mathematics and science. The most persistent gender differential in educational standard testing is the scores in mathematics achievement. The mean Scholastic Aptitude Test (Mathematics) scores for women are consistently below that of men by about 40 points. One result of this gender differential in mathematics is that few women entertain a career requiring a robust knowledge of higher mathematics (i.e. engineering, computing, or the physical sciences). A large body of literature has been written attempting to explain why this is happening. Biological, cultural, structural and psychological explanations have been suggested and empirically examined. Controlling for mathematical ability is one method of sorting out these explanations. Eliminating mathematical ability as a factor, this dissertation reports the results of a study of men and women college students who all had high mathematics ability. Thus, any differences we found among them would have to be a result of other variables. Using a Mathematics Placement Exam and the SAT-M, forty-two students (12 males and 30 females) with high scores in both were interviewed. Student were asked about their experiences in high school and college mathematics, their career choices, and their attitudes toward mathematics. The findings, that there were no gender differences in the course selection, attitudes towards mathematics, and career choice, differed from my initial expectations. This negative finding suggests that women with high ability in mathematics are just as likely as men to pursue interests in mathematics and related courses in college and in selecting careers.

  2. Mathematical thinking styles of undergraduate students and their achievement in mathematics

    NASA Astrophysics Data System (ADS)

    Risnanosanti

    2017-08-01

    The main purpose of this study is to analyze the role of mathematical thinking styles in students' achievement in mathematics. On the basis of this study, it is also to generate recommendation for classroom instruction. The two specific aims are; first to observe students' mathematical thinking styles during problem solving, the second to asses students' achievement in mathematics. The data were collected by using Mathematical Thinking Styles questionnaires and test of students' achievement in mathematics. The subject in this study was 35 students from third year at mathematics study program of Muhammadiyah University of Bengkulu in academic year 2016/2017. The result of this study was that the students have three mathematical thinking styles (analytic, visual, and integrated), and the students who have analytic styles have better achievement than those who have visual styles in mathematics.

  3. Quotable Quotes in Mathematics

    ERIC Educational Resources Information Center

    Lo, Bruce W. N.

    1983-01-01

    As a way to dispel negative feelings toward mathematics, a variety of quotations are given. They are categorized by: what mathematics is, mathematicians, mathematics and other disciplines, different areas of mathematics, mathematics and humor, applications of mathematics, and pure versus applied mathematics. (MNS)

  4. Faculty Provisions of Accommodations for Students with Disabilities in Higher Education: An Analysis of Community College Faculty in the Traditional, Hybrid, and Online Mathematics Course Teaching Environments

    ERIC Educational Resources Information Center

    Mongiovi, Kelly Anne

    2012-01-01

    The purpose of this exploratory descriptive study was to examine the mathematics faculty provisions of accommodations for students with disabilities within a Florida Community College. Both developmental and college level mathematics courses were included in this study. This study examined courses taught in the traditional, hybrid, and online…

  5. Elementary Mathematics Teachers' Perceptions and Lived Experiences on Mathematical Communication

    ERIC Educational Resources Information Center

    Kaya, Defne; Aydin, Hasan

    2016-01-01

    Mathematical thinking skills and meaningful mathematical understanding are among the goals of current mathematics education. There is a wide consensus among scholars about the purpose of developing mathematical understanding and higher order thinking skills in students. However, how to develop those skills in classroom settings is an area that…

  6. History of Modern Applied Mathematics in Mathematics Education

    ERIC Educational Resources Information Center

    Jankvist, Uffe Thomas

    2009-01-01

    This article discusses the integration of history of modern applied mathematics in mathematics education as well as the possible teaching and learning benefits of introducing a newer history of mathematics over an old(er) one--something that seems to be done most often when integrating history. Three cases of the history of modern applied…

  7. The kinds of questions asked by novice teachers in learning mathematics

    NASA Astrophysics Data System (ADS)

    Zahra, L.; Kusmayadi, T. A.; Usodo, B.

    2018-05-01

    This study describes the kinds of questions asked by novice teachers during mathematics learning process in senior high school. This study used descriptive analysis. The subjects of this study were two novice teachers who teach mathematics in 10th grade. The result showed that the frequently asked questions by novice teachers based on the objective were compliance questions, rethorical questions and sometimes prompting questions and probing questions. The frequently questions asked by novice teacher based on the cognitive process dimension of Revised Bloom’s Taxonomy were questions of remembering, questions of understanding, questions of applying, questions of analyzing and questions of evaluating. The novice teachers asked the routine questions which had same thinking level. The question with the highest level of thinking did not asked by the novice teachers.

  8. Comparison of student's learning achievement through realistic mathematics education (RME) approach and problem solving approach on grade VII

    NASA Astrophysics Data System (ADS)

    Ilyas, Muhammad; Salwah

    2017-02-01

    The type of this research was experiment. The purpose of this study was to determine the difference and the quality of student's learning achievement between students who obtained learning through Realistic Mathematics Education (RME) approach and students who obtained learning through problem solving approach. This study was a quasi-experimental research with non-equivalent experiment group design. The population of this study was all students of grade VII in one of junior high school in Palopo, in the second semester of academic year 2015/2016. Two classes were selected purposively as sample of research that was: year VII-5 as many as 28 students were selected as experiment group I and VII-6 as many as 23 students were selected as experiment group II. Treatment that used in the experiment group I was learning by RME Approach, whereas in the experiment group II by problem solving approach. Technique of data collection in this study gave pretest and posttest to students. The analysis used in this research was an analysis of descriptive statistics and analysis of inferential statistics using t-test. Based on the analysis of descriptive statistics, it can be concluded that the average score of students' mathematics learning after taught using problem solving approach was similar to the average results of students' mathematics learning after taught using realistic mathematics education (RME) approach, which are both at the high category. In addition, It can also be concluded that; (1) there was no difference in the results of students' mathematics learning taught using realistic mathematics education (RME) approach and students who taught using problem solving approach, (2) quality of learning achievement of students who received RME approach and problem solving approach learning was same, which was at the high category.

  9. Advanced Mathematical Thinking and Students' Mathematical Learning: Reflection from Students' Problem-Solving in Mathematics Classroom

    ERIC Educational Resources Information Center

    Sangpom, Wasukree; Suthisung, Nisara; Kongthip, Yanin; Inprasitha, Maitree

    2016-01-01

    Mathematical teaching in Thai tertiary education still employs traditional methods of explanation and the use of rules, formulae, and theories in order for students to memorize and apply to their mathematical learning. This results in students' inability to concretely learn, fully comprehend and understand mathematical concepts and practice. In…

  10. Developing Instructional Design to Improve Mathematical Higher Order Thinking Skills of Students

    NASA Astrophysics Data System (ADS)

    Apino, E.; Retnawati, H.

    2017-02-01

    This study aimed to describe the instructional design to improve the Higher Order Thinking Skills (HOTS) of students in learning mathematics. This research is design research involving teachers and students of class X MIPA 1 MAN Yigyakarta III, Special Region of Yogyakarta, Indonesia. Data collected through focus group discussions and tests. Data analyzed by quantitative descriptive. The results showed that the instructional design developed is effective to improving students’ HOTS in learning mathematics. Instructional design developed generally include three main components: (1) involve students in the activities non-routine problem solving; (2) facilitating students to develop the ability to analyze and evaluate (critical thinking) and the ability to create (creative thinking); and (3) encourage students to construct their own knowledge.

  11. Elementary Pre-Service Teachers' Mathematics Anxiety and Mathematics Teaching Anxiety

    ERIC Educational Resources Information Center

    Haciomeroglu, Guney

    2014-01-01

    The present study examined the structure of elementary pre-service teachers' mathematics anxiety and mathematics teaching anxiety by asking whether the two systems of anxiety are related. The Turkish Mathematics Anxiety Rating Scale Short Version and the Mathematics Teaching Anxiety Scale were administered to 260 elementary pre-service teachers.…

  12. Studies in Mathematics, Volume XVI. Some Uses of Mathematics: A Source Book for Teachers and Students of School Mathematics.

    ERIC Educational Resources Information Center

    Bell, Max S., Ed.

    This is a collection of articles dealing with mathematical applications for use by high school teachers and students. The articles are intended to illustrate several themes: (1) how mathematics is applied via construction of mathematical models; (2) the various types of activities in applied mathematics; (3) the role of pure mathematics in applied…

  13. Validation of a multi-phase plant-wide model for the description of the aeration process in a WWTP.

    PubMed

    Lizarralde, I; Fernández-Arévalo, T; Beltrán, S; Ayesa, E; Grau, P

    2018-02-01

    This paper introduces a new mathematical model built under the PC-PWM methodology to describe the aeration process in a full-scale WWTP. This methodology enables a systematic and rigorous incorporation of chemical and physico-chemical transformations into biochemical process models, particularly for the description of liquid-gas transfer to describe the aeration process. The mathematical model constructed is able to reproduce biological COD and nitrogen removal, liquid-gas transfer and chemical reactions. The capability of the model to describe the liquid-gas mass transfer has been tested by comparing simulated and experimental results in a full-scale WWTP. Finally, an exploration by simulation has been undertaken to show the potential of the mathematical model. Copyright © 2017 Elsevier Ltd. All rights reserved.

  14. Basic and Advanced Numerical Performances Relate to Mathematical Expertise but Are Fully Mediated by Visuospatial Skills

    PubMed Central

    2016-01-01

    Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. PMID:26913930

  15. Mathematical psychology.

    PubMed

    Batchelder, William H

    2010-09-01

    Mathematical psychology is a sub-field of psychology that started in the 1950s and has continued to grow as an important contributor to formal psychological theory, especially in the cognitive areas of psychology such as learning, memory, classification, choice response time, decision making, attention, and problem solving. In addition, there are several scientific sub-areas that were originated by mathematical psychologists such as the foundations of measurement, stochastic memory models, and psychologically motivated reformulations of expected utility theory. Mathematical psychology does not include all uses of mathematics and statistics in psychology, and indeed there is a long history of such uses especially in the areas of perception and psychometrics. What is most unique about mathematical psychology is its approach to theory construction. While accepting the behaviorist dictum that the data in psychology must be observable and replicable, mathematical models are specified in terms of unobservable formal constructs that can predict detailed aspects of data across multiple experimental and natural settings. By now almost all the substantive areas of cognitive and experimental psychology have formal mathematical models and theories, and many of these are due to researchers that identify with mathematical psychology. Copyright © 2010 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website. Copyright © 2010 John Wiley & Sons, Ltd.

  16. Mathematical marriages: intercourse between mathematics and Semiotic choice.

    PubMed

    Wagner, Roy

    2009-04-01

    This paper examines the interaction between Semiotic choices and the presentation and solution of a family of contemporary mathematical problems centred around the so-called 'stable marriage problem'. I investigate how a socially restrictive choice of signs impacts mathematical production both in terms of problem formation and of solutions. I further note how the choice of gendered language ends up constructing a reality, which duplicates the very structural framework that it imported into mathematical analysis in the first place. I go on to point out some semiotic lines of flight from this interlocking grip of mathematics and gendered language.

  17. Students’ Algebraic Reasonsing In Solving Mathematical Problems With Adversity Quotient

    NASA Astrophysics Data System (ADS)

    Aryani, F.; Amin, S. M.; Sulaiman, R.

    2018-01-01

    Algebraic reasoning is a process in which students generalize mathematical ideas from a set of particular instances and express them in increasingly formal and age-appropriate ways. Using problem solving approach to develop algebraic reasoning of mathematics may enhace the long-term learning trajectory of the majority students. The purpose of this research was to describe the algebraic reasoning of quitter, camper, and climber junior high school students in solving mathematical problems. This research used qualitative descriptive method. Subjects were determined by purposive sampling. The technique of collecting data was done by task-based interviews.The results showed that the algebraic reasoning of three students in the process of pattern seeking by identifying the things that are known and asked in a similar way. But three students found the elements of pattern recognition in different ways or method. So, they are generalize the problem of pattern formation with different ways. The study of algebraic reasoning and problem solving can be a learning paradigm in the improve students’ knowledge and skills in algebra work. The goal is to help students’ improve academic competence, develop algebraic reasoning in problem solving.

  18. Multiple Intelligences Patterns of Students at King Saud University and Its Relationship with Mathematics' Achievement

    ERIC Educational Resources Information Center

    Kandeel, Refat A. A.

    2016-01-01

    The purpose of this study was to determine the multiple intelligences patterns of students at King Saud University and its relationship with academic achievement for the courses of Mathematics. The study sample consisted of 917 students were selected a stratified random manner, the descriptive analysis method and Pearson correlation were used, the…

  19. Structural Equation Model to Validate: Mathematics-Computer Interaction, Computer Confidence, Mathematics Commitment, Mathematics Motivation and Mathematics Confidence

    ERIC Educational Resources Information Center

    Garcia-Santillán, Arturo; Moreno-Garcia, Elena; Escalera-Chávez, Milka E.; Rojas-Kramer, Carlos A.; Pozos-Texon, Felipe

    2016-01-01

    Most mathematics students show a definite tendency toward an attitudinal deficiency, which can be primarily understood as intolerance to the matter, affecting their scholar performance adversely. In addition, information and communication technologies have been gradually included within the process of teaching mathematics. Such adoption of…

  20. Attitudes towards Computer and Computer Self-Efficacy as Predictors of Preservice Mathematics Teachers' Computer Anxiety

    ERIC Educational Resources Information Center

    Awofala, Adeneye O. A.; Akinoso, Sabainah O.; Fatade, Alfred O.

    2017-01-01

    The study investigated attitudes towards computer and computer self-efficacy as predictors of computer anxiety among 310 preservice mathematics teachers from five higher institutions of learning in Lagos and Ogun States of Nigeria using the quantitative research method within the blueprint of the descriptive survey design. Data collected were…

  1. Opportunities and Challenges: Integration of ICT in Teaching and Learning Mathematics in Secondary Schools, Nairobi, Kenya

    ERIC Educational Resources Information Center

    Amuko, Sheila; Miheso, Marguerite; Ndeuthi, Sophie

    2015-01-01

    This presentation is based on a larger study whose purpose was to explore the various opportunities and challenges influencing integration of ICT in teaching and learning Mathematics in secondary schools in Nairobi County. The study, adopted a descriptive survey design. Three instruments questionnaires', a structured interview schedule and an…

  2. Investigating Instructional Practices of an African American Male Mathematics Teacher with Underachieving African American Male Students

    ERIC Educational Resources Information Center

    Muhammad, Rhonda K.

    2012-01-01

    This qualitative study examined the instructional practices of an experienced African American mathematics teacher to determine his perceived capabilities in augmenting academic proficiency for his African American male students. Provided in this descriptive case study are the lived experiences of an African American male teacher working to move…

  3. Between the Academic Mathematics and the Mathematics Education Worlds.

    ERIC Educational Resources Information Center

    Moreira, Candida Queiroz

    1997-01-01

    Investigated stresses confronted by Portuguese secondary mathematics teachers during the first semester in a master's course, Perspectives on Mathematics Education, noting how they negatively affected teachers' self-confidence and morale and discussing fundamental issues teachers addressed in bridging the academic mathematics and mathematics…

  4. The materiality of mathematics: presenting mathematics at the blackboard.

    PubMed

    Greiffenhagen, Christian

    2014-09-01

    Sociology has been accused of neglecting the importance of material things in human life and the material aspects of social practices. Efforts to correct this have recently been made, with a growing concern to demonstrate the materiality of social organization, not least through attention to objects and the body. As a result, there have been a plethora of studies reporting the social construction and effects of a variety of material objects as well as studies that have explored the material dimensions of a diversity of practices. In different ways these studies have questioned the Cartesian dualism of a strict separation of 'mind' and 'body'. However, it could be argued that the idea of the mind as immaterial has not been entirely banished and lingers when it comes to discussing abstract thinking and reasoning. The aim of this article is to extend the material turn to abstract thought, using mathematics as a paradigmatic example. This paper explores how writing mathematics (on paper, blackboards, or even in the air) is indispensable for doing and thinking mathematics. The paper is based on video recordings of lectures in formal logic and investigates how mathematics is presented at the blackboard. The paper discusses the iconic character of blackboards in mathematics and describes in detail a number of inscription practices of presenting mathematics at the blackboard (such as the use of lines and boxes, the designation of particular regions for specific mathematical purposes, as well as creating an 'architecture' visualizing the overall structure of the proof). The paper argues that doing mathematics really is 'thinking with eyes and hands' (Latour 1986). Thinking in mathematics is inextricably interwoven with writing mathematics. © London School of Economics and Political Science 2014.

  5. Descriptive Drinking Norms: For Whom Does Reference Group Matter?*

    PubMed Central

    Larimer, Mary E.; Neighbors, Clayton; LaBrie, Joseph W.; Atkins, David C.; Lewis, Melissa A.; Lee, Christine M.; Kilmer, Jason R.; Kaysen, Debra L.; Pedersen, Eric r.; Montoya, Heidi; Hodge, Kimberley; Desai, Sruti; Hummer, Justin F.; Walter, Theresa

    2011-01-01

    Objective: Perceived descriptive drinking norms often differ from actual norms and are positively related to personal consumption. However, it is not clear how normative perceptions vary with specificity of the reference group. Are drinking norms more accurate and more closely related to drinking behavior as reference group specificity increases? Do these relationships vary as a function of participant demographics? The present study examined the relationship between perceived descriptive norms and drinking behavior by ethnicity (Asian or White), sex, and fraternity/sorority status. Method: Participants were 2,699 (58% female) White (75%) or Asian (25%) undergraduates from two universities who reported their own alcohol use and perceived descriptive norms for eight reference groups: "typical student"; same sex, ethnicity, or fraternity/sorority status; and all combinations of these three factors. Results: Participants generally reported the highest perceived norms for the most distal reference group (typical student), with perceptions becoming more accurate as individuals' similarity to the reference group increased. Despite increased accuracy, participants perceived that all reference groups drank more than was actually the case. Across specific subgroups (fraternity/sorority members and men) different patterns emerged. Fraternity/sorority members reliably reported higher estimates of drinking for reference groups that included fraternity/ sorority status, and, to a lesser extent, men reported higher estimates for reference groups that included men. Conclusions: The results suggest that interventions targeting normative misperceptions may need to provide feedback based on participant demography or group membership. Although reference group-specific feedback may be important for some subgroups, typical student feedback provides the largest normative discrepancy for the majority of students. PMID:21906510

  6. Contextual approach using VBA learning media to improve students’ mathematical displacement and disposition ability

    NASA Astrophysics Data System (ADS)

    Chotimah, Siti; Bernard, M.; Wulandari, S. M.

    2018-01-01

    The main problems of the research were the lack of reasoning ability and mathematical disposition of students to the learning of mathematics in high school students in Cimahi - West Java. The lack of mathematical reasoning ability in students was caused by the process of learning. The teachers did not train the students to do the problems of reasoning ability. The students still depended on each other. Sometimes, one of patience teacher was still guiding his students. In addition, the basic ability aspects of students also affected the ability the mathematics skill. Furthermore, the learning process with contextual approach aided by VBA Learning Media (Visual Basic Application for Excel) gave the positive influence to the students’ mathematical disposition. The students are directly involved in learning process. The population of the study was all of the high school students in Cimahi. The samples were the students of SMA Negeri 4 Cimahi class XIA and XIB. There were both of tested and non-tested instruments. The test instrument was a description test of mathematical reasoning ability. The non-test instruments were questionnaire-scale attitudes about students’ mathematical dispositions. This instrument was used to obtain data about students’ mathematical reasoning and disposition of mathematics learning with contextual approach supported by VBA (Visual Basic Application for Excel) and by conventional learning. The data processed in this study was from the post-test score. These scores appeared from both of the experimental class group and the control class group. Then, performing data was processed by using SPSS 22 and Microsoft Excel. The data was analyzed using t-test statistic. The final result of this study concluded the achievement and improvement of reasoning ability and mathematical disposition of students whose learning with contextual approach supported by learning media of VBA (Visual Basic Application for Excel) was better than students who got

  7. Rainforest Mathematics

    ERIC Educational Resources Information Center

    Kilpatrick, Jeremy

    2014-01-01

    This paper addresses the contested way that ethnomathematics has sometimes been received by mathematicians and others and what that disagreement might suggest about issues in mathematics education; namely, (a) the relation of ethnomathematics to academic mathematics; (b) recent efforts to reform secondary school mathematics so that it prepares…

  8. Accurate polarimeter with multicapture fitting for plastic lens evaluation

    NASA Astrophysics Data System (ADS)

    Domínguez, Noemí; Mayershofer, Daniel; Garcia, Cristina; Arasa, Josep

    2016-02-01

    Due to their manufacturing process, plastic injection molded lenses do not achieve a constant density throughout their volume. This change of density introduces tensions in the material, inducing local birefringence, which in turn is translated into a variation of the ordinary and extraordinary refractive indices that can be expressed as a retardation phase plane using the Jones matrix notation. The detection and measurement of the value of the retardation of the phase plane are therefore very useful ways to evaluate the quality of plastic lenses. We introduce a polariscopic device to obtain two-dimensional maps of the tension distribution in the bulk of a lens, based on detection of the local birefringence. In addition to a description of the device and the mathematical approach used, a set of initial measurements is presented that confirms the validity of the developed system for the testing of the uniformity of plastic lenses.

  9. Formative questioning in computer learning environments: a course for pre-service mathematics teachers

    NASA Astrophysics Data System (ADS)

    Akkoç, Hatice

    2015-11-01

    This paper focuses on a specific aspect of formative assessment, namely questioning. Given that computers have gained widespread use in learning and teaching, specific attention should be made when organizing formative assessment in computer learning environments (CLEs). A course including various workshops was designed to develop knowledge and skills of questioning in CLEs. This study investigates how pre-service mathematics teachers used formative questioning with technological tools such as Geogebra and Graphic Calculus software. Participants are 35 pre-service mathematics teachers. To analyse formative questioning, two types of questions are investigated: mathematical questions and technical questions. Data were collected through lesson plans, teaching notes, interviews and observations. Descriptive statistics of the number of questions in the lesson plans before and after the workshops are presented. Examples of two types of questions are discussed using the theoretical framework. One pre-service teacher was selected and a deeper analysis of the way he used questioning during his three lessons was also investigated. The findings indicated an improvement in using technical questions for formative purposes and that the course provided a guideline in planning and using mathematical and technical questions in CLEs.

  10. Mathematical treatment of isotopologue and isotopomer speciation and fractionation in biochemical kinetics

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Maggi, F.M.; Riley, W.J.

    2009-11-01

    We present a mathematical treatment of the kinetic equations that describe isotopologue and isotopomer speciation and fractionation during enzyme-catalyzed biochemical reactions. These equations, presented here with the name GEBIK (general equations for biochemical isotope kinetics) and GEBIF (general equations for biochemical isotope fractionation), take into account microbial biomass and enzyme dynamics, reaction stoichiometry, isotope substitution number, and isotope location within each isotopologue and isotopomer. In addition to solving the complete GEBIK and GEBIF, we also present and discuss two approximations to the full solutions under the assumption of biomass-free and enzyme steady-state, and under the quasi-steady-state assumption as applied tomore » the complexation rate. The complete and approximate approaches are applied to observations of biological denitrification in soils. Our analysis highlights that the full GEBIK and GEBIF provide a more accurate description of concentrations and isotopic compositions of substrates and products throughout the reaction than do the approximate forms. We demonstrate that the isotopic effects of a biochemical reaction depend, in the most general case, on substrate and complex concentrations and, therefore, the fractionation factor is a function of time. We also demonstrate that inverse isotopic effects can occur for values of the fractionation factor smaller than 1, and that reactions that do not discriminate isotopes do not necessarily imply a fractionation factor equal to 1.« less

  11. Army Sustainability Modelling Analysis and Reporting Tool (A-SMART) Prototype: Model Description and Algorithms

    DTIC Science & Technology

    2012-12-01

    states.2 The research activities in this area are focused on the mathematical description of the dynamic behaviour within the hierarchy of organisations...Aviation, Infantry, Medical, Catering, Armoured , Artillery, Transport, Signals, and Ordnance). The corps structure essentially maps to that of the training...calculation of the casualty levels for personnel from a hypothetical force composed of infantry and armour . Table 2: Calculated Monthly Casualty Rates for

  12. Exploring Mathematical Capital: An Essential Construct for Mathematical Success?

    ERIC Educational Resources Information Center

    Baber, Marla Ann Lasswell

    2017-01-01

    In the United States students have traditionally struggled with mathematics. Many students leave the educational system with limited mathematical literacy that can adversely affect their success as a college student, a consumer and citizen. In turn, lack of mathematical literacy affects their socioeconomic status. Through improving their…

  13. From Mathematical Reading to Mathematical Literacy

    ERIC Educational Resources Information Center

    Beaudine, Gregory

    2018-01-01

    If teachers have a deeper comprehension of their students' reading ability, it may lead to students' improved literacy and understanding of the subject. The account presented in this article of the author's growing interest in mathematical literacy specifically involves mathematical reading. This shift in interest began with a six-week…

  14. Gender Equality in Public Higher Education Institutions of Ethiopia: The Case of Science, Technology, Engineering, and Mathematics

    ERIC Educational Resources Information Center

    Egne, Robsan Margo

    2014-01-01

    Ensuring gender equality in higher education system is high on the agenda worldwide particularly in science disciplines. This study explores the problems and prospects of gender equality in public higher education institutions of Ethiopia, especially in science, technology, engineering, and mathematics. Descriptive survey and analytical research…

  15. Exploration of Mathematics Problem Solving Process Based on the Thinking Level of Students in Junior High School

    ERIC Educational Resources Information Center

    Rahman, Abdul; Ahmar, Ansari Saleh

    2016-01-01

    Several studies suggest that most students are not in the same level of development (Slavin, 2008). From concrete operation level to formal operation level, students experience lateness in the transition phase. Consequently, students feel difficulty in solving mathematics problems. Method research is a qualitatively descriptive-explorative…

  16. Accurate description of charged excitations in molecular solids from embedded many-body perturbation theory

    NASA Astrophysics Data System (ADS)

    Li, Jing; D'Avino, Gabriele; Duchemin, Ivan; Beljonne, David; Blase, Xavier

    2018-01-01

    We present a novel hybrid quantum/classical approach to the calculation of charged excitations in molecular solids based on the many-body Green's function G W formalism. Molecules described at the G W level are embedded into the crystalline environment modeled with an accurate classical polarizable scheme. This allows the calculation of electron addition and removal energies in the bulk and at crystal surfaces where charged excitations are probed in photoelectron experiments. By considering the paradigmatic case of pentacene and perfluoropentacene crystals, we discuss the different contributions from intermolecular interactions to electronic energy levels, distinguishing between polarization, which is accounted for combining quantum and classical polarizabilities, and crystal field effects, that can impact energy levels by up to ±0.6 eV. After introducing band dispersion, we achieve quantitative agreement (within 0.2 eV) on the ionization potential and electron affinity measured at pentacene and perfluoropentacene crystal surfaces characterized by standing molecules.

  17. Mathematical Modeling: Challenging the Figured Worlds of Elementary Mathematics

    ERIC Educational Resources Information Center

    Wickstrom, Megan H.

    2017-01-01

    This article is a report on a teacher study group that focused on three elementary teachers' perceptions of mathematical modeling in contrast to typical mathematics instruction. Through the theoretical lens of figured worlds, I discuss how mathematics instruction was conceptualized across the classrooms in terms of artifacts, discourse, and…

  18. Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape

    ERIC Educational Resources Information Center

    Bautista, Alfredo; Wilkerson-Jerde, Michelle H.; Tobin, Roger G.; Brizuela, Bárbara M.

    2014-01-01

    This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers' ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers' written responses to three open-ended…

  19. Enhancing Core Mathematics Courses

    ERIC Educational Resources Information Center

    Billings, Esther; Schlicker, Steven; Novotny, Karen; Tefera, Akalu

    2004-01-01

    The Departments of Mathematics and Statistics at Grand Valley State University are engaged in a project to address the mathematical preparation of all its majors, including prospective elementary and secondary mathematics teachers. In this article, we describe how the mathematics and mathematics education faculty in our mathematics department…

  20. Mathematics and engineering in real life through mathematical competitions

    NASA Astrophysics Data System (ADS)

    More, M.

    2018-02-01

    We bring out an experience of organizing mathematical competitions that can be used as a medium to motivate the student and teacher minds in new directions of thinking. This can contribute to fostering research, innovation and provide a hands-on experience of mathematical concepts with the real world. Mathematical competitions can be used to build curiosity and give an understanding of mathematical applications in real life. Participation in the competition has been classified under four broad categories. Student can showcase their findings in various forms of expression like model, poster, soft presentation, animation, live performance, art and poetry. The basic focus of the competition is on using open source computation tools and modern technology, to emphasize the relationship of mathematical concepts with engineering applications in real life.

  1. The relative importance of two different mathematical abilities to mathematical achievement.

    PubMed

    Nunes, Terezinha; Bryant, Peter; Barros, Rossana; Sylva, Kathy

    2012-03-01

    Two distinct abilities, mathematical reasoning and arithmetic skill, might make separate and specific contributions to mathematical achievement. However, there is little evidence to inform theory and educational practice on this matter. The aims of this study were (1) to assess whether mathematical reasoning and arithmetic make independent contributions to the longitudinal prediction of mathematical achievement over 5 years and (2) to test the specificity of this prediction. Data from Avon Longitudinal Study of Parents and Children (ALSPAC) were available on 2,579 participants for analyses of KS2 achievement and on 1,680 for the analyses of KS3 achievement. Hierarchical regression analyses were used to assess the independence and specificity of the contribution of mathematical reasoning and arithmetic skill to the prediction of achievement in KS2 and KS3 mathematics, science, and English. Age, intelligence, and working memory (WM) were controls in these analyses. Mathematical reasoning and arithmetic did make independent contributions to the prediction of mathematical achievement; mathematical reasoning was by far the stronger predictor of the two. These predictions were specific in so far as these measures were more strongly related to mathematics than to science or English. Intelligence and WM were non-specific predictors; intelligence contributed more to the prediction of science than of maths, and WM predicted maths and English equally well. There is clear justification for making a distinction between mathematical reasoning and arithmetic skills. The implication is that schools must plan explicitly to improve mathematical reasoning as well as arithmetic skills. ©2011 The British Psychological Society.

  2. Mathematical misconception in calculus 1: Identification and gender difference

    NASA Astrophysics Data System (ADS)

    Nassir, Asyura Abd; Abdullah, Nur Hidayah Masni; Ahmad, Salimah; Tarmuji, Nor Habibah; Idris, Aminatul Solehah

    2017-08-01

    A few years of experience of teaching mathematics make us notice that the same types of mistakes are done repeatedly by students. This paper presents an insight into categories of mistakes, how male and female students differ in terms of mistakes that are commonly done and the ability of the students to identify the mistakes. Sample of mistakes were taken from Calculus 1 final exam answer scripts, then it was listed and analyzed. Data analysis revealed that students' misconceptions fall into four categories. The first category is misunderstanding the meaning of brackets, followed by misconception of basic mathematics rules, misconception in notation and misconception in properties of trigonometry. A mistake identification test which consists of ten false mathematical statements was designed based on the mistake done by the previous batch of students that covered topics algebra, trigonometry, index, limit, differentiation and integration. Then, the test was given to students who enrolled in Calculus I course. Respondents of this study were randomly selected among two hundreds engineering students. Data obtained were analyzed using basic descriptive analysis and Chi Square test to capture gender differences in the mistake done for each category. Findings indicate that thirty five percent of the students have the ability to identify the mistakes and make a proper correction for at most two statements. Thirty one percent of the students are able to identify the mistakes but unable to make proper correction. Twenty five percent of the students failed to identify the mistakes in six out of ten false statements. Female students' misconception is more likely in basic mathematics rules compared to male. The findings of this study could serve as baseline information to be stressed in improving teaching and learning mathematics.

  3. Mathematics for Language, Language for Mathematics

    ERIC Educational Resources Information Center

    Prochazkova, Lenka Tejkalova

    2013-01-01

    The author discusses the balance and mutual influence of the language of instruction and mathematics in the context of CLIL, Content and Language Integrated Learning. Different aspects of the relationship of language and Mathematics teaching and learning are discussed: the benefits of using a foreign language of instruction, as well as the…

  4. Sex and mathematical background as predictors of anxiety and self-efficacy in mathematics.

    PubMed

    Lussier, G

    1996-12-01

    Anxiety and self-efficacy in mathematics as a function of sex and mathematical background were investigated. This study employed an ex post facto 2 x 2 factorial design in which sex and mathematical background were classification variables. It was predicted that men would report lower anxiety scores and higher self-efficacy scores than women and that students with a high mathematical background would report lower anxiety scores and higher self-efficacy scores than those with a low background in mathematics. An interaction between sex and mathematical background was also predicted. 51 subjects were given the revised Mathematics Anxiety Scale and the Mathematics Self-efficacy Scale. Results supported the hypotheses with respect to background in mathematics for anxiety in mathematics, and all of the hypotheses were supported for self-efficacy in mathematics.

  5. Effects of Modern Educational Game Play on Attitudes towards Mathematics, Mathematics Self-Efficacy, and Mathematics Achievement

    ERIC Educational Resources Information Center

    Ritzhaupt, Albert; Higgins, Heidi; Allred, Beth

    2011-01-01

    This study investigated the effects of modern educational game playing on middle school students' attitudes towards mathematics, mathematics self-efficacy, and mathematics achievement. Two hundred twenty-five middle school students from four different Title 1 schools in two different counties in the southeastern United States were recruited.…

  6. Proceedings of the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (11th, New Brunswick, New Jersey, September 20-23, 1989), Volume 2: Plenary Lectures and Symposia.

    ERIC Educational Resources Information Center

    Maher, Carolyn A., Ed.; Goldin, Gerald A., Ed.; Davis, Robert B., Ed.

    This document reports on the 11th annual conference of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA). Plenary and response lectures and speakers include: "The Description and Analysis of Mathematical Processes" (Nicolas Herscovics); "To Know Mathematics is to Go Beyond Thinking That…

  7. Mathematics Anxiety in Young Children: Concurrent and Longitudinal Associations with Mathematical Performance

    ERIC Educational Resources Information Center

    Vukovic, Rose K.; Kieffer, Michael J.; Bailey, Sean P.; Harari, Rachel R.

    2013-01-01

    This study explored mathematics anxiety in a longitudinal sample of 113 children followed from second to third grade. We examined how mathematics anxiety related to different types of mathematical performance concurrently and longitudinally and whether the relations between mathematics anxiety and mathematical performance differed as a function of…

  8. It all adds up …. Or does it? Numbers, mathematics and purpose.

    PubMed

    Conway Morris, Simon

    2016-08-01

    No chimpanzee knows what a square root is, let alone a complex number. Yet not only our closest ape cousins but even some invertebrates, possess a capacity for numerosity, that is the ability to assess relative numerical magnitudes and distances. That numerosity should confer adaptive advantages, such as social species that choose shoal size, is obvious. Moreover, it is widely assumed that numerosity and mathematics are seamlessly linked, as would be consistent with Darwinian notions of descent and modification. Animal numerosity, however, involves sensory processes (usually vision, but other modalities such as olfaction can be as effective) that follow psychophysical principles, notable the Weber-Fechner law. In contrast, mathematics may require sensory mediation but is an abstract process. The supposed connection between these processes is described as supramodality but the mechanisms that allow humans, but not animals, to engage in even simple mathematics are opaque. Here, I argue that any resolution will depend on proper explanations for not only mathematics, but language and by implication consciousness. In this light, concepts of purpose are not intellectual mirages but legitimate descriptions of the worlds in which we are embedded. These are both visible (and tangible) and invisible (and although intangible, equally real). Copyright © 2015 Elsevier Ltd. All rights reserved.

  9. Accurate Identification of MCI Patients via Enriched White-Matter Connectivity Network

    NASA Astrophysics Data System (ADS)

    Wee, Chong-Yaw; Yap, Pew-Thian; Brownyke, Jeffery N.; Potter, Guy G.; Steffens, David C.; Welsh-Bohmer, Kathleen; Wang, Lihong; Shen, Dinggang

    Mild cognitive impairment (MCI), often a prodromal phase of Alzheimer's disease (AD), is frequently considered to be a good target for early diagnosis and therapeutic interventions of AD. Recent emergence of reliable network characterization techniques have made understanding neurological disorders at a whole brain connectivity level possible. Accordingly, we propose a network-based multivariate classification algorithm, using a collection of measures derived from white-matter (WM) connectivity networks, to accurately identify MCI patients from normal controls. An enriched description of WM connections, utilizing six physiological parameters, i.e., fiber penetration count, fractional anisotropy (FA), mean diffusivity (MD), and principal diffusivities (λ 1, λ 2, λ 3), results in six connectivity networks for each subject to account for the connection topology and the biophysical properties of the connections. Upon parcellating the brain into 90 regions-of-interest (ROIs), the average statistics of each ROI in relation to the remaining ROIs are extracted as features for classification. These features are then sieved to select the most discriminant subset of features for building an MCI classifier via support vector machines (SVMs). Cross-validation results indicate better diagnostic power of the proposed enriched WM connection description than simple description with any single physiological parameter.

  10. Mathematics Lessons without ...

    ERIC Educational Resources Information Center

    Cross, Kath; Hibbs, John

    2006-01-01

    In the Association of Teachers of Mathematics (ATM) Easter conference, 2006, the authors presented a list of important aspects of mathematics lessons, recommended for students to have a positive attitude to mathematics and for teachers to acquire effective teaching. The following are discussed in detail: (1) Mathematics lessons without good…

  11. Mathematical Modelling in the Junior Secondary Years: An Approach Incorporating Mathematical Technology

    ERIC Educational Resources Information Center

    Lowe, James; Carter, Merilyn; Cooper, Tom

    2018-01-01

    Mathematical models are conceptual processes that use mathematics to describe, explain, and/or predict the behaviour of complex systems. This article is written for teachers of mathematics in the junior secondary years (including out-of-field teachers of mathematics) who may be unfamiliar with mathematical modelling, to explain the steps involved…

  12. Accurate radiation temperature and chemical potential from quantitative photoluminescence analysis of hot carrier populations.

    PubMed

    Gibelli, François; Lombez, Laurent; Guillemoles, Jean-François

    2017-02-15

    In order to characterize hot carrier populations in semiconductors, photoluminescence measurement is a convenient tool, enabling us to probe the carrier thermodynamical properties in a contactless way. However, the analysis of the photoluminescence spectra is based on some assumptions which will be discussed in this work. We especially emphasize the importance of the variation of the material absorptivity that should be considered to access accurate thermodynamical properties of the carriers, especially by varying the excitation power. The proposed method enables us to obtain more accurate results of thermodynamical properties by taking into account a rigorous physical description and finds direct application in investigating hot carrier solar cells, which are an adequate concept for achieving high conversion efficiencies with a relatively simple device architecture.

  13. Dilemma in Teaching Mathematics

    ERIC Educational Resources Information Center

    Md Kamaruddin, Nafisah Kamariah; Md Amin, Zulkarnain

    2012-01-01

    The challenge in mathematics education is finding the best way to teach mathematics. When students learn the reasoning and proving in mathematics, they will be proficient in mathematics. Students must know mathematics before they can apply it. Symbolism and logic is the key to both the learning of mathematics and its effective application to…

  14. Exploring the Associations Among Nutrition, Science, and Mathematics Knowledge for an Integrative, Food-Based Curriculum.

    PubMed

    Stage, Virginia C; Kolasa, Kathryn M; Díaz, Sebastián R; Duffrin, Melani W

    2018-01-01

    Explore associations between nutrition, science, and mathematics knowledge to provide evidence that integrating food/nutrition education in the fourth-grade curriculum may support gains in academic knowledge. Secondary analysis of a quasi-experimental study. Sample included 438 students in 34 fourth-grade classrooms across North Carolina and Ohio; mean age 10 years old; gender (I = 53.2% female; C = 51.6% female). Dependent variable = post-test-nutrition knowledge; independent variables = baseline-nutrition knowledge, and post-test science and mathematics knowledge. Analyses included descriptive statistics and multiple linear regression. The hypothesized model predicted post-nutrition knowledge (F(437) = 149.4, p < .001; Adjusted R = .51). All independent variables were significant predictors with positive association. Science and mathematics knowledge were predictive of nutrition knowledge indicating use of an integrative science and mathematics curriculum to improve academic knowledge may also simultaneously improve nutrition knowledge among fourth-grade students. Teachers can benefit from integration by meeting multiple academic standards, efficiently using limited classroom time, and increasing nutrition education provided in the classroom. © 2018, American School Health Association.

  15. Mathematics Teacher Candidates' Metaphors about the Concept of "Mathematics"

    ERIC Educational Resources Information Center

    Erdogan, Ahmet; Yazlik, Derya Ozlem; Erdik, Cengiz

    2014-01-01

    The main purpose of this study was to research mathematics teacher candidates' perceptions about the concept of "mathematics" through the use of metaphors. The research is conducted during 2012-2013 academic year, on a group of 111 mathematics teacher candidates at the Education Faculty of a University in Turkey. To collect the research…

  16. Influences of Self-Perceived Competence in Mathematics and Positive Affect toward Mathematics on Mathematics Achievement of Adolescents in Singapore

    ERIC Educational Resources Information Center

    Areepattamannil, Shaljan; Kaur, Berinderjeet

    2012-01-01

    This study, drawing on data from the Trends in International Mathematics and Science Study (TIMSS) 2007, examined the influences of self-perceived competence in mathematics and positive affect toward mathematics on mathematics achievement of adolescents in Singapore. Ordinary least squares (OLS) regression analyses revealed the positive influences…

  17. Measuring and factors influencing mathematics teachers' technological pedagogical and content knowledge (TPACK) in three southernmost provinces, Thailand

    NASA Astrophysics Data System (ADS)

    Adulyasas, Lilla

    2017-08-01

    Technology becomes an important role in teaching and learning mathematics nowadays. Integrating technology in the classroom helps students have better understanding in many of mathematics concepts. One of the major framework for assessing the knowledge of integrating technology with the pedagogy and content in the classroom is Technological Pedagogical and Content Knowledge (TPACK) framework. This study aimed to measure mathematics teachers' TPACK in three southernmost provinces, Thailand and to study on factors influencing their TPACK. A quantitative study was carried out with 210 secondary level mathematics teachers in the three southernmost provinces, Thailand which were random by two stage sampling technique. Data were collected by using a questionnaire to identify the level of mathematics teachers' TPACK and the factors influencing their TPACK. Descriptive statistics, Pearson product moment correlation and multiple regression analysis were used for analysing data. Findings reveal that the mean score of mathematics teachers' TPACK is 3.33 which is in the medium level and the three factors which have positive correlation at .05 level of significant with the level of TPACK are teaching experience factor, individual specialization factor and personal & organization factor. However, there are only two factors influencing mathematics teachers' TPACK. The two factors are individual specialization factor and personal & organization factors. These give better understanding on mathematics teachers' knowledge in integrating technology with the pedagogy and content which will be the important information for improving mathematics teachers' TPACK.

  18. Profile of Secondary School Students with High Mathematics Ability in Solving Shape and Space Problem

    ERIC Educational Resources Information Center

    Putra, Mulia; Novita, Rita

    2015-01-01

    This study aimed to describe the profile of secondary school students with high mathematics ability in solving shape and space problem in PISA (Program for International Student Assessment). It is a descriptive research with a qualitative approach, in which the subjects in this study were students of class VIII SMP N 1 Banda Aceh. The results show…

  19. Functioning Mathematically: 1

    ERIC Educational Resources Information Center

    Cain, David

    2007-01-01

    This article presents the first part of the closing address given by the author to the 2007 Association of Teachers of Mathematics (ATM) Easter conference at Loughborough. In his closing address, the author focuses on functioning mathematically as opposed to functional mathematics. His view of functional mathematics is that the focus is on someone…

  20. A Phenomenological Research Study of the Experience of Teachers in the Virgin Islands Teacher Enhancement in Mathematics and Science Project

    NASA Astrophysics Data System (ADS)

    Thurland, Karen C.

    The purpose of conducting this study was to describe the experience of elementary teachers in a mathematics and science staff development project in the U.S. Virgin Islands. The focus of this study was to describe the meaning teachers attribute to their experience in this three year project, in which many of the national mathematics and science reform efforts were implemented. A phenomenological approach was used in order to develop a complete picture of the teachers' experiences. Data collection consisted of interviews with seven elementary teachers. The data were subjective descriptions of the teachers pertaining to the initial summer institute, the follow-up sessions, and the new innovative methods. The transcendental phenomenological model was used. The textural and structural themes included enhanced learning and changes in teaching practice, and interactions with colleagues. From these themes, individual and composite textual descriptions of the experience of the teacher participants were developed. The synthesis of those descriptions illuminated the meanings and essence of their lived experience. The findings indicate that the essence of the experience was the development of a positive attitude towards the teaching of math and science. The teachers gained confidence in their ability to motivate students with the inquiry method and taught more math and science. The implications for the Virgin Islands Department of Education include establishing a partnership with the local university to offer staff development training in mathematics and science and to conduct evaluations of its training efforts.

  1. Application of the Rangeland Hydrology and Erosion Model to Ecological Site Descriptions and Management

    USDA-ARS?s Scientific Manuscript database

    The utility of Ecological Site Descriptions (ESDs) and State-and-Transition Models (STMs) concepts in guiding rangeland management hinges on their ability to accurately describe and predict community dynamics and the associated consequences. For many rangeland ecosystems, plant community dynamics ar...

  2. Mathematics and Engineering in Real Life through Mathematical Competitions

    ERIC Educational Resources Information Center

    More, M.

    2018-01-01

    We bring out an experience of organizing mathematical competitions that can be used as a medium to motivate the student and teacher minds in new directions of thinking. This can contribute to fostering research, innovation and provide a hands-on experience of mathematical concepts with the real world. Mathematical competitions can be used to build…

  3. Mathematical Fiction: Its Place in Secondary-School Mathematics Learning

    ERIC Educational Resources Information Center

    Padula, Janice

    2005-01-01

    This article contains a small selection of mathematical fiction chosen with the teaching of mathematics in secondary school in mind. However, an attempt is made to classify the works and provide a few ideas about how these items may be used by mathematics teachers, sometimes, but not necessarily, in collaboration with science and humanities…

  4. The effect of team accelerated instruction on students’ mathematics achievement and learning motivation

    NASA Astrophysics Data System (ADS)

    Sri Purnami, Agustina; Adi Widodo, Sri; Charitas Indra Prahmana, Rully

    2018-01-01

    This study aimed to know the improvement of achievement and motivation of learning mathematics by using Team Accelerated Instruction. The research method used was the experiment with descriptive pre-test post-test experiment. The population in this study was all students of class VIII junior high school in Jogjakarta. The sample was taken using cluster random sampling technique. The instrument used in this research was questionnaire and test. Data analysis technique used was Wilcoxon test. It concluded that there was an increase in motivation and student achievement of class VII on linear equation system material by using the learning model of Team Accelerated Instruction. Based on the results of the learning model Team Accelerated Instruction can be used as a variation model in learning mathematics.

  5. Peirce's Philosophy of Mathematical Education: Fostering Reasoning Abilities for Mathematical Inquiry

    ERIC Educational Resources Information Center

    Campos, Daniel G.

    2010-01-01

    I articulate Charles S. Peirce's philosophy of mathematical education as related to his conception of mathematics, the nature of its method of inquiry, and especially, the reasoning abilities required for mathematical inquiry. The main thesis is that Peirce's philosophy of mathematical education primarily aims at fostering the development of the…

  6. An Investigation of Mathematical Modeling with Pre-Service Secondary Mathematics Teachers

    ERIC Educational Resources Information Center

    Thrasher, Emily Plunkett

    2016-01-01

    The goal of this thesis was to investigate and enhance our understanding of what occurs while pre-service mathematics teachers engage in a mathematical modeling unit that is broadly based upon mathematical modeling as defined by the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices & Council…

  7. A Conceptual Model of Mathematical Reasoning for School Mathematics

    ERIC Educational Resources Information Center

    Jeannotte, Doris; Kieran, Carolyn

    2017-01-01

    The development of students' mathematical reasoning (MR) is a goal of several curricula and an essential element of the culture of the mathematics education research community. But what mathematical reasoning consists of is not always clear; it is generally assumed that everyone has a sense of what it is. Wanting to clarify the elements of MR,…

  8. Analysis instrument test on mathematical power the material geometry of space flat side for grade 8

    NASA Astrophysics Data System (ADS)

    Kusmaryono, Imam; Suyitno, Hardi; Dwijanto, Karomah, Nur

    2017-08-01

    The main problem of research to determine the quality of test items on the material side of flat geometry to assess students' mathematical power. The method used is quantitative descriptive. The subjects were students of class 8 as many as 20 students. The object of research is the quality of test items in terms of the power of mathematics: validity, reliability, level of difficulty and power differentiator. Instrument mathematical power ratings are tested include: written tests and questionnaires about the disposition of mathematical power. Data were obtained from the field, in the form of test data on the material geometry of space flat side and questionnaires. The results of the test instrument to the reliability of the test item is influenced by many factors. Factors affecting the reliability of the instrument is the number of items, homogeneity test questions, the time required, the uniformity of conditions of the test taker, the homogeneity of the group, the variability problem, and motivation of the individual (person taking the test). Overall, the evaluation results of this study stated that the test instrument can be used as a tool to measure students' mathematical power.

  9. Electrostatics of proteins in dielectric solvent continua. I. An accurate and efficient reaction field description

    NASA Astrophysics Data System (ADS)

    Bauer, Sebastian; Mathias, Gerald; Tavan, Paul

    2014-03-01

    We present a reaction field (RF) method which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of an electrostatics calculation with polarizable molecular mechanics (MM) force fields. The method combines an approach originally suggested by Egwolf and Tavan [J. Chem. Phys. 118, 2039 (2003)] with concepts generalizing the Born solution [Z. Phys. 1, 45 (1920)] for a solvated ion. First, we derive an exact representation according to which the sources of the RF potential and energy are inducible atomic anti-polarization densities and atomic shielding charge distributions. Modeling these atomic densities by Gaussians leads to an approximate representation. Here, the strengths of the Gaussian shielding charge distributions are directly given in terms of the static partial charges as defined, e.g., by standard MM force fields for the various atom types, whereas the strengths of the Gaussian anti-polarization densities are calculated by a self-consistency iteration. The atomic volumes are also described by Gaussians. To account for covalently overlapping atoms, their effective volumes are calculated by another self-consistency procedure, which guarantees that the dielectric function ɛ(r) is close to one everywhere inside the protein. The Gaussian widths σi of the atoms i are parameters of the RF approximation. The remarkable accuracy of the method is demonstrated by comparison with Kirkwood's analytical solution for a spherical protein [J. Chem. Phys. 2, 351 (1934)] and with computationally expensive grid-based numerical solutions for simple model systems in dielectric continua including a di-peptide (Ac-Ala-NHMe) as modeled by a standard MM force field. The latter example shows how weakly the RF conformational free energy landscape depends on the parameters σi. A summarizing discussion highlights the achievements of the new theory and of its approximate solution particularly by

  10. Electrostatics of proteins in dielectric solvent continua. I. An accurate and efficient reaction field description.

    PubMed

    Bauer, Sebastian; Mathias, Gerald; Tavan, Paul

    2014-03-14

    We present a reaction field (RF) method which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of an electrostatics calculation with polarizable molecular mechanics (MM) force fields. The method combines an approach originally suggested by Egwolf and Tavan [J. Chem. Phys. 118, 2039 (2003)] with concepts generalizing the Born solution [Z. Phys. 1, 45 (1920)] for a solvated ion. First, we derive an exact representation according to which the sources of the RF potential and energy are inducible atomic anti-polarization densities and atomic shielding charge distributions. Modeling these atomic densities by Gaussians leads to an approximate representation. Here, the strengths of the Gaussian shielding charge distributions are directly given in terms of the static partial charges as defined, e.g., by standard MM force fields for the various atom types, whereas the strengths of the Gaussian anti-polarization densities are calculated by a self-consistency iteration. The atomic volumes are also described by Gaussians. To account for covalently overlapping atoms, their effective volumes are calculated by another self-consistency procedure, which guarantees that the dielectric function ε(r) is close to one everywhere inside the protein. The Gaussian widths σ(i) of the atoms i are parameters of the RF approximation. The remarkable accuracy of the method is demonstrated by comparison with Kirkwood's analytical solution for a spherical protein [J. Chem. Phys. 2, 351 (1934)] and with computationally expensive grid-based numerical solutions for simple model systems in dielectric continua including a di-peptide (Ac-Ala-NHMe) as modeled by a standard MM force field. The latter example shows how weakly the RF conformational free energy landscape depends on the parameters σ(i). A summarizing discussion highlights the achievements of the new theory and of its approximate solution particularly by

  11. Grounded Blends and Mathematical Gesture Spaces: Developing Mathematical Understandings via Gestures

    ERIC Educational Resources Information Center

    Yoon, Caroline; Thomas, Michael O. J.; Dreyfus, Tommy

    2011-01-01

    This paper examines how a person's gesture space can become endowed with mathematical meaning associated with mathematical spaces and how the resulting mathematical gesture space can be used to communicate and interpret mathematical features of gestures. We use the theory of grounded blends to analyse a case study of two teachers who used gestures…

  12. The Use of Open-Ended Questions with Giving Feedback (OEQGF) for Effective Mathematic Learning

    NASA Astrophysics Data System (ADS)

    Sabilah, I.; Manoy, J. T.

    2018-01-01

    Feedback deals with giving information to students related to their task which is done through score of their achievement, reaction, and comments. Considering its hierarchy, task difficulty level consists of low, middle and high levels. The difficulty level of open-ended questions is middle to high. Open-ended question is a good way to train students’ knowledge. This research is a descriptive research which aims at describing teacher’s learning management, students’ activities, students’ learning achievement, and students’ responses in mathematic learning using OEQGF. The subject was a teacher of mathematics who teaches eighth graders, and students themselves. The research design used is one shot case study. The result shows that: management learning has been very well implemented by the teacher; every students’ activity has been carried out by students; the students’ learning achievement have reached the criteria of completeness, and the students’ responses can be considered as positive. Therefore, it can be concluded that mathematic learning using OEQGF is effective.

  13. Some unsolved problems in discrete mathematics and mathematical cybernetics

    NASA Astrophysics Data System (ADS)

    Korshunov, Aleksei D.

    2009-10-01

    There are many unsolved problems in discrete mathematics and mathematical cybernetics. Writing a comprehensive survey of such problems involves great difficulties. First, such problems are rather numerous and varied. Second, they greatly differ from each other in degree of completeness of their solution. Therefore, even a comprehensive survey should not attempt to cover the whole variety of such problems; only the most important and significant problems should be reviewed. An impersonal choice of problems to include is quite hard. This paper includes 13 unsolved problems related to combinatorial mathematics and computational complexity theory. The problems selected give an indication of the author's studies for 50 years; for this reason, the choice of the problems reviewed here is, to some extent, subjective. At the same time, these problems are very difficult and quite important for discrete mathematics and mathematical cybernetics. Bibliography: 74 items.

  14. Basic and advanced numerical performances relate to mathematical expertise but are fully mediated by visuospatial skills.

    PubMed

    Sella, Francesco; Sader, Elie; Lolliot, Simon; Cohen Kadosh, Roi

    2016-09-01

    Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

  15. Taxonomy of Macromotettixoides with the description of a new species (Tetrigidae, Metrodorinae)

    PubMed Central

    Zha, Ling-Sheng; Yu, Feng-Ming; Boonmee, Saranyaphat; Eungwanichayapant, Prapassorn D.; Wen, Ting-Chi

    2017-01-01

    Abstract Descriptions of the flying organs and generic characteristics of the genus Macromotettixoides Zheng, Wei & Jiang are currently imprecise. Macromotettixoides is reviewed and compared with allied genera. A re-description is undertaken and a determination key is provided to Macromotettixoides. Macromotettixoides parvula Zha & Wen, sp. n. from the Guizhou Karst Region, China, is described and illustrated with photographs. Observations on the ecology and habits of the new species are recorded. Four current species of Hyboella Hancock are transferred to Macromotettixoides. Variations of the flying organs and tegminal sinus in the Tetrigidae are discussed, which will help to describe them accurately. PMID:28228664

  16. Reflections on the Notion of Culture in the History of Mathematics: The Example of "Geometrical Equations".

    PubMed

    Lê, François

    2016-09-01

    Argument This paper challenges the use of the notion of "culture" to describe a particular organization of mathematical knowledge, shared by a few mathematicians over a short period of time in the second half of the nineteenth century. This knowledge relates to "geometrical equations," objects that proved crucial for the mechanisms of encounters between equation theory, substitution theory, and geometry at that time, although they were not well-defined mathematical objects. The description of the mathematical collective activities linked to "geometrical equations," and especially the technical aspects of these activities, is made on the basis of a sociological definition of "culture." More precisely, after an examination of the social organization of the group of mathematicians, I argue that these activities form an intricate system of patterns, symbols, and values, for which I suggest a characterization as a "cultural system."

  17. Licensure tests for special education teachers: how well they assess knowledge of reading instruction and mathematics.

    PubMed

    Stotsky, Sandra

    2009-01-01

    To determine the extent to which knowledge of evidence-based reading instruction and mathematics is assessed on licensure tests for prospective special education teachers, this study drew on information provided by Educational Testing Service (ETS), the American Board for Certification of Teacher Excellence, and National Evaluation Systems (now Evaluation Systems group of Pearson). It estimated the percentage of test items on phonemic awareness, phonics, and vocabulary knowledge and on mathematics content. It also analyzed descriptions of ETS's tests of "principles of teaching and learning." Findings imply that prospective special education teachers should be required to take both a dedicated test of evidence-based reading instructional knowledge, as in California, Massachusetts, and Virginia, and a test of mathematical knowledge, as in Massachusetts. States must design their own tests of teaching principles to assess knowledge of evidence-based educational theories.

  18. Accurate approximation of in-ecliptic trajectories for E-sail with constant pitch angle

    NASA Astrophysics Data System (ADS)

    Huo, Mingying; Mengali, Giovanni; Quarta, Alessandro A.

    2018-05-01

    Propellantless continuous-thrust propulsion systems, such as electric solar wind sails, may be successfully used for new space missions, especially those requiring high-energy orbit transfers. When the mass-to-thrust ratio is sufficiently large, the spacecraft trajectory is characterized by long flight times with a number of revolutions around the Sun. The corresponding mission analysis, especially when addressed within an optimal context, requires a significant amount of simulation effort. Analytical trajectories are therefore useful aids in a preliminary phase of mission design, even though exact solution are very difficult to obtain. The aim of this paper is to present an accurate, analytical, approximation of the spacecraft trajectory generated by an electric solar wind sail with a constant pitch angle, using the latest mathematical model of the thrust vector. Assuming a heliocentric circular parking orbit and a two-dimensional scenario, the simulation results show that the proposed equations are able to accurately describe the actual spacecraft trajectory for a long time interval when the propulsive acceleration magnitude is sufficiently small.

  19. Mathematics and Sports. Mathematical World. Volume 3.

    ERIC Educational Resources Information Center

    Sadovskii, L. E.; Sadovskii, A. L.

    This volume contains some examples of mathematical applications in sports. Sports discussed include tennis, figure skating, gymnastics, track and field, soccer, skiing, hockey, and swimming. Problems and situations are posed and answers with thorough explanations are provided. Chapters include: (1) Mathematics and Sports; (2) What Is Applied…

  20. Predicting Academic Success of Junior Secondary School Students in Mathematics through Cognitive Style and Problem Solving Technique

    ERIC Educational Resources Information Center

    Badru, Ademola K.

    2015-01-01

    This study examined the prediction of academic success of Junior secondary school mathematics students using their cognitive style and problem solving technique. A descriptive survey of correlation type was adopted for this study. A purposive sampling procedure was used to select five Public Junior secondary schools in Ijebu-Ode local government…

  1. Stereotactically Standard Areas: Applied Mathematics in the Service of Brain Targeting in Deep Brain Stimulation.

    PubMed

    Mavridis, Ioannis N

    2017-12-11

    The concept of stereotactically standard areas (SSAs) within human brain nuclei belongs to the knowledge of the modern field of stereotactic brain microanatomy. These are areas resisting the individual variability of the nuclear location in stereotactic space. This paper summarizes the current knowledge regarding SSAs. A mathematical formula of SSAs was recently invented, allowing for their robust, reproducible, and accurate application to laboratory studies and clinical practice. Thus, SSAs open new doors for the application of stereotactic microanatomy to highly accurate brain targeting, which is mainly useful for minimally invasive neurosurgical procedures, such as deep brain stimulation.

  2. Investigation of High School Students' Attitude and Anxiety Levels towards Mathematics in Terms of Some Variables

    ERIC Educational Resources Information Center

    Dursun, Semsettin

    2015-01-01

    The purpose of this study was to investigate Turkish high school students' attitude and anxiety levels towards mathematics. For this purpose, the methodology employed in this study was a descriptive study. The participants of the study consisted of 361 high school students from three different high school types from a province in Turkey during…

  3. A Fuzzy mathematical model to estimate the effects of global warming on the vitality of Laelia purpurata orchids.

    PubMed

    Putti, Fernando Ferrari; Filho, Luis Roberto Almeida Gabriel; Gabriel, Camila Pires Cremasco; Neto, Alfredo Bonini; Bonini, Carolina Dos Santos Batista; Rodrigues Dos Reis, André

    2017-06-01

    This study aimed to develop a fuzzy mathematical model to estimate the impacts of global warming on the vitality of Laelia purpurata growing in different Brazilian environmental conditions. In order to develop the mathematical model was considered as intrinsic factors the parameters: temperature, humidity and shade conditions to determine the vitality of plants. Fuzzy model results could accurately predict the optimal conditions for cultivation of Laelia purpurata in several sites of Brazil. Based on fuzzy model results, we found that higher temperatures and lacking of properly shading can reduce the vitality of orchids. Fuzzy mathematical model could precisely detect the effect of higher temperatures causing damages on vitality of plants as a consequence of global warming. Copyright © 2017 Elsevier Inc. All rights reserved.

  4. Mathematical Creativity and Mathematical Aptitude: A Cross-Lagged Panel Analysis

    ERIC Educational Resources Information Center

    Tyagi, Tarun Kumar

    2016-01-01

    Cross-lagged panel correlation (CLPC) analysis has been used to identify causal relationships between mathematical creativity and mathematical aptitude. For this study, 480 8th standard students were selected through a random cluster technique from 9 intermediate and high schools of Varanasi, India. Mathematical creativity and mathematical…

  5. Mathematical Models of Elementary Mathematics Learning and Performance. Final Report.

    ERIC Educational Resources Information Center

    Suppes, Patrick

    This project was concerned with the development of mathematical models of elementary mathematics learning and performance. Probabilistic finite automata and register machines with a finite number of registers were developed as models and extensively tested with data arising from the elementary-mathematics strand curriculum developed by the…

  6. Adults' Use of Mathematics and Its Influence on Mathematical Competence

    ERIC Educational Resources Information Center

    Duchhardt, Christoph; Jordan, Anne-Katrin; Ehmke, Timo

    2017-01-01

    The Programme for the International Assessment of Adult Competencies (PIAAC) has recently drawn additional attention to "mathematical literacy" as an important influential factor for individuals' life chances. High levels of mathematical literacy have thereby been linked to using mathematics in daily and working life frequently. In this…

  7. Mathematics Coursework Regulates Growth in Mathematics Achievement

    ERIC Educational Resources Information Center

    Ma, Xin; Wilkins, Jesse L. M.

    2007-01-01

    Using data from the Longitudinal Study of American Youth (LSAY), we examined the extent to which students' mathematics coursework regulates (influences) the rate of growth in mathematics achievement during middle and high school. Graphical analysis showed that students who started middle school with higher achievement took individual mathematics…

  8. The Mathematics and Mathematical Thinking of Seamstresses.

    ERIC Educational Resources Information Center

    Hancock, Sabrina J. C.

    This study documents the mathematics practiced by four women in the context of sewing. The study describes the mathematics recognized in the skills, thinking and strategies used by the seamstresses. Through their work, the seamstresses exhibited an understanding of the concepts of angles, direction, parallel, reflection, symmetry, proportion,…

  9. A synthesis of mathematical and cognitive performances of students with mathematics learning disabilities.

    PubMed

    Shin, Mikyung; Bryant, Diane Pedrotty

    2015-01-01

    The purpose of this study was to synthesize the findings from 23 articles that compared the mathematical and cognitive performances of students with mathematics learning disabilities (LD) to (a) students with LD in mathematics and reading, (b) age- or grade-matched students with no LD, and (c) mathematical-ability-matched younger students with no LD. Overall results revealed that students with mathematics LD exhibited higher word problem-solving abilities and no significant group differences on working memory, long-term memory, and metacognition measures compared to students with LD in mathematics and reading. Findings also revealed students with mathematics LD demonstrated significantly lower performance compared to age- or grade-matched students with no LD on both mathematical and cognitive measures. Comparison between students with mathematics LD and younger students with no LD revealed mixed outcomes on mathematical measures and generally no significant group differences on cognitive measures. © Hammill Institute on Disabilities 2013.

  10. Modeling Simple Telescope Optics in Secondary Mathematics Classrooms

    NASA Astrophysics Data System (ADS)

    Siegel, Lauren; Dickinson, G.; Hooper, E. J.; Daniels, M.

    2007-12-01

    This presentation describes the results of collaboration between instructors in the UTeach teacher preparation program at the University of Texas at Austin, and an astronomer teaching at the university as part of a National Science Foundation Astronomy and Astrophysics Postdoctoral Fellowship. The astronomer provided training to give pre-service teachers an authentic understanding of the principles of telescope optics. This made it possible for the preservice teachers to include real design constraints and optical properties into lessons developed as part of a collaborative field experience to teach astronomical telescope design and construction to high school Algebra II students. One result is a sequence of investigations designed to explore how and why the physical and mathematical properties of parabolic mirrors both enable and constrain our ability to build and use telescopes to focus light from distant objects. Various approaches, including generating and exploring computer models, traditional proofs, even making paper models, are all woven together into a coherent set of eleven investigations for use in mathematics and science classrooms. The presentation will include a description of the suite of investigations, as well as a discussion of the collaborative process which generated the work and resulted in an article submission to a preeminent teaching journal. Teaching Algebra and Geometry Concepts by Modeling Telescope Optics, 2008, Mathematics Teacher is currently in press. Many thanks to the University of Texas UTeach Program for sponsorship of this submission.

  11. North American Chapter of the International Group for the Psychology of Mathematics Education, Proceedings of the Annual Meeting (13th, Blacksburg, Virginia, October 16-19, 1991). Volumes 1 and 2.

    ERIC Educational Resources Information Center

    Underhill, Robert G., Ed.

    This document, presented in two volumes, reports on a psychology of mathematics education conference, the theme of which was "Theoretical and Conceptual Frameworks in Mathematics Education." The two volumes include 58 papers, descriptions of 4 poster and 2 video presentations, and reports of and reactions to 2 plenary sessions presented…

  12. Mathematical modeling and numerical simulation of the mitotic spindle orientation system.

    PubMed

    Ibrahim, Bashar

    2018-05-21

    The mitotic spindle orientation and position is crucial for the fidelity of chromosome segregation during asymmetric cell division to generate daughter cells with different sizes or fates. This mechanism is best understood in the budding yeast Saccharomyces cerevisiae, named the spindle position checkpoint (SPOC). The SPOC inhibits cells from exiting mitosis until the mitotic spindle is properly oriented along the mother-daughter polarity axis. Despite many experimental studies, the mechanisms underlying SPOC regulation remains elusive and unexplored theoretically. Here, a minimal mathematical is developed to describe SPOC activation and silencing having autocatalytic feedback-loop. Numerical simulations of the nonlinear ordinary differential equations (ODEs) model accurately reproduce the phenotype of SPOC mechanism. Bifurcation analysis of the nonlinear ODEs reveals the orientation dependency on spindle pole bodies, and how this dependence is altered by parameter values. These results provide for systems understanding on the molecular organization of spindle orientation system via mathematical modeling. The presented mathematical model is easy to understand and, within the above mentioned context, can be used as a base for further development of quantitative models in asymmetric cell-division. Copyright © 2018. Published by Elsevier Inc.

  13. Thermodynamically accurate modeling of the catalytic cycle of photosynthetic oxygen evolution: a mathematical solution to asymmetric Markov chains.

    PubMed

    Vinyard, David J; Zachary, Chase E; Ananyev, Gennady; Dismukes, G Charles

    2013-07-01

    Forty-three years ago, Kok and coworkers introduced a phenomenological model describing period-four oscillations in O2 flash yields during photosynthetic water oxidation (WOC), which had been first reported by Joliot and coworkers. The original two-parameter Kok model was subsequently extended in its level of complexity to better simulate diverse data sets, including intact cells and isolated PSII-WOCs, but at the expense of introducing physically unrealistic assumptions necessary to enable numerical solutions. To date, analytical solutions have been found only for symmetric Kok models (inefficiencies are equally probable for all intermediates, called "S-states"). However, it is widely accepted that S-state reaction steps are not identical and some are not reversible (by thermodynamic restraints) thereby causing asymmetric cycles. We have developed a mathematically more rigorous foundation that eliminates unphysical assumptions known to be in conflict with experiments and adopts a new experimental constraint on solutions. This new algorithm termed STEAMM for S-state Transition Eigenvalues of Asymmetric Markov Models enables solutions to models having fewer adjustable parameters and uses automated fitting to experimental data sets, yielding higher accuracy and precision than the classic Kok or extended Kok models. This new tool provides a general mathematical framework for analyzing damped oscillations arising from any cycle period using any appropriate Markov model, regardless of symmetry. We illustrate applications of STEAMM that better describe the intrinsic inefficiencies for photon-to-charge conversion within PSII-WOCs that are responsible for damped period-four and period-two oscillations of flash O2 yields across diverse species, while using simpler Markov models free from unrealistic assumptions. Copyright © 2013 Elsevier B.V. All rights reserved.

  14. Causal Connections between Mathematical Language and Mathematical Knowledge: A Dialogic Reading Intervention

    ERIC Educational Resources Information Center

    Purpura, David J.; Napoli, Amy R.; Wehrspann, Elizabeth A.; Gold, Zachary S.

    2017-01-01

    The acquisition of early mathematical knowledge is critical for successful long-term academic development. Mathematical language is one of the strongest predictors of children's early mathematical success. Findings from previous studies have provided correlational evidence supporting the importance of mathematical language to the development of…

  15. The Mathematics Education Debates: Preparing Students to Become Professionally Active Mathematics Teachers

    ERIC Educational Resources Information Center

    Munakata, Mika

    2010-01-01

    The Mathematics Education Debate is an assignment designed for and implemented in an undergraduate mathematics methods course for prospective secondary school mathematics teachers. For the assignment, students read and analyze current research and policy reports related to mathematics education, prepare and present their positions, offer…

  16. Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving

    ERIC Educational Resources Information Center

    Ayllón, María F.; Gómez, Isabel A.; Ballesta-Claver, Julio

    2016-01-01

    This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas), flexibility (range of ideas),…

  17. Mathematical Writing Errors in Expository Writings of College Mathematics Students

    ERIC Educational Resources Information Center

    Guce, Ivee K.

    2017-01-01

    Despite the efforts to confirm the effectiveness of writing in learning mathematics, analysis on common errors in mathematical writings has not received sufficient attention. This study aimed to provide an account of the students' procedural explanations in terms of their commonly committed errors in mathematical writing. Nine errors in…

  18. "Mathematics Is Like a Lion": Elementary Students' Beliefs about Mathematics

    ERIC Educational Resources Information Center

    Markovits, Zvia; Forgasz, Helen

    2017-01-01

    The aim of this study was to explore the beliefs of elementary school students about mathematics and about themselves as mathematics learners. The participants, Israeli grade 4 and grade 6 students, completed questionnaires. Using an "animal metaphor" to tap beliefs, some students perceived mathematics as difficult and complicated, while…

  19. Authenticity of Mathematical Modeling

    ERIC Educational Resources Information Center

    Tran, Dung; Dougherty, Barbara J.

    2014-01-01

    Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…

  20. Evaluation of the Thermodynamic Consistency of Closure Approximations in Several Models Proposed for the Description of Liquid Crystalline Dynamics

    NASA Astrophysics Data System (ADS)

    Edwards, Brian J.

    2002-05-01

    Given the premise that a set of dynamical equations must possess a definite, underlying mathematical structure to ensure local and global thermodynamic stability, as has been well documented, several different models for describing liquid crystalline dynamics are examined with respect to said structure. These models, each derived during the past several years using a specific closure approximation for the fourth moment of the distribution function in Doi's rigid rod theory, are all shown to be inconsistent with this basic mathematical structure. The source of this inconsistency lies in Doi's expressions for the extra stress tensor and temporal evolution of the order parameter, which are rederived herein using a transformation that allows for internal compatibility with the underlying mathematical structure that is present on the distribution function level of description.

  1. Ninth and Tenth Grade Students' Mathematics Self-Efficacy Beliefs: The Sources and Relationships to Teacher Classroom Interpersonal Behaviors

    ERIC Educational Resources Information Center

    White, Amanda Garrett

    2009-01-01

    The purpose of the mix-methods action research study was to seek how the changes in students' perceptions about teacher classroom interpersonal behaviors, the four efficacy sources and mathematics self-efficacy beliefs were related. The methods used to accomplish this were: descriptive statistics, t-test, Pearson correlation coefficient…

  2. Elementary Core Curriculum Standards: Levels K-3: Arts, Information Technology, Science, Language Arts, Mathematics, Social Studies, Health, Lifestyles.

    ERIC Educational Resources Information Center

    Utah State Office of Education, Salt Lake City.

    Utah's 1987 minimum course description standards for students in kindergarten through third grade are provided in the required core curriculum areas of arts, information technology, science, language arts, mathematics, social studies, and healthy lifestyles. For each curricular area a rationale is given, followed by a brief course description…

  3. Pre-Service Secondary Mathematics Teachers' Reflections on Good and Bad Mathematics Teaching

    ERIC Educational Resources Information Center

    Dayal, Hem Chand

    2013-01-01

    Researchers suggest that teachers' beliefs about teaching are strongly influenced by their personal experiences with mathematics. This study aimed to explore Pacific Island pre-service secondary mathematics teachers' perceptions about good and bad mathematics teachers. Thirty pre-service teachers, enrolled in a mathematics teaching methods course…

  4. HGVS Recommendations for the Description of Sequence Variants: 2016 Update.

    PubMed

    den Dunnen, Johan T; Dalgleish, Raymond; Maglott, Donna R; Hart, Reece K; Greenblatt, Marc S; McGowan-Jordan, Jean; Roux, Anne-Francoise; Smith, Timothy; Antonarakis, Stylianos E; Taschner, Peter E M

    2016-06-01

    The consistent and unambiguous description of sequence variants is essential to report and exchange information on the analysis of a genome. In particular, DNA diagnostics critically depends on accurate and standardized description and sharing of the variants detected. The sequence variant nomenclature system proposed in 2000 by the Human Genome Variation Society has been widely adopted and has developed into an internationally accepted standard. The recommendations are currently commissioned through a Sequence Variant Description Working Group (SVD-WG) operating under the auspices of three international organizations: the Human Genome Variation Society (HGVS), the Human Variome Project (HVP), and the Human Genome Organization (HUGO). Requests for modifications and extensions go through the SVD-WG following a standard procedure including a community consultation step. Version numbers are assigned to the nomenclature system to allow users to specify the version used in their variant descriptions. Here, we present the current recommendations, HGVS version 15.11, and briefly summarize the changes that were made since the 2000 publication. Most focus has been on removing inconsistencies and tightening definitions allowing automatic data processing. An extensive version of the recommendations is available online, at http://www.HGVS.org/varnomen. © 2016 WILEY PERIODICALS, INC.

  5. Exploring Teachers' Descriptions of 'Ways of Working with the Curriculum' in Teaching Mathematics and Statistics

    ERIC Educational Resources Information Center

    Umugiraneza, Odette; Bansilal, Sarah; North, Delia

    2018-01-01

    What teachers teach, how they teach it and when they teach it should be guided by the curriculum. This paper focuses on teachers' reports about how they integrate the curriculum documentation in teaching mathematics and statistics concepts. Questionnaires containing both Likert scale and closed and open-ended questions were administered to 75…

  6. Racial Differences in Mathematics Test Scores for Advanced Mathematics Students

    ERIC Educational Resources Information Center

    Minor, Elizabeth Covay

    2016-01-01

    Research on achievement gaps has found that achievement gaps are larger for students who take advanced mathematics courses compared to students who do not. Focusing on the advanced mathematics student achievement gap, this study found that African American advanced mathematics students have significantly lower test scores and are less likely to be…

  7. Primary School Pre-Service Mathematics Teachers' Views on Mathematical Modeling

    ERIC Educational Resources Information Center

    Karali, Diren; Durmus, Soner

    2015-01-01

    The current study aimed to identify the views of pre-service teachers, who attended a primary school mathematics teaching department but did not take mathematical modeling courses. The mathematical modeling activity used by the pre-service teachers was developed with regards to the modeling activities utilized by Lesh and Doerr (2003) in their…

  8. A pairwise maximum entropy model accurately describes resting-state human brain networks

    PubMed Central

    Watanabe, Takamitsu; Hirose, Satoshi; Wada, Hiroyuki; Imai, Yoshio; Machida, Toru; Shirouzu, Ichiro; Konishi, Seiki; Miyashita, Yasushi; Masuda, Naoki

    2013-01-01

    The resting-state human brain networks underlie fundamental cognitive functions and consist of complex interactions among brain regions. However, the level of complexity of the resting-state networks has not been quantified, which has prevented comprehensive descriptions of the brain activity as an integrative system. Here, we address this issue by demonstrating that a pairwise maximum entropy model, which takes into account region-specific activity rates and pairwise interactions, can be robustly and accurately fitted to resting-state human brain activities obtained by functional magnetic resonance imaging. Furthermore, to validate the approximation of the resting-state networks by the pairwise maximum entropy model, we show that the functional interactions estimated by the pairwise maximum entropy model reflect anatomical connexions more accurately than the conventional functional connectivity method. These findings indicate that a relatively simple statistical model not only captures the structure of the resting-state networks but also provides a possible method to derive physiological information about various large-scale brain networks. PMID:23340410

  9. Why do early mathematics skills predict later reading? The role of mathematical language.

    PubMed

    Purpura, David J; Logan, Jessica A R; Hassinger-Das, Brenna; Napoli, Amy R

    2017-09-01

    A growing body of evidence indicates that the development of mathematics and literacy skills is highly related. The importance of literacy skills-specifically language-for mathematics development has been well rationalized. However, despite several prominent studies indicating that mathematics skills are highly predictive of literacy development, the reason for this relation is not well understood. The purpose of this study was to identify how and why early mathematics is predictive of early literacy development. Participants included 125 preschool children 3-5 years old (M = 4 years 3 months). Participants were assessed on mathematics, literacy, and cognitive measures in both the fall and spring of their preschool year. Mediation analyses indicated that the relation between early mathematics and literacy skills is mediated by children's mathematical language skills. These findings suggest that, in prior research identifying mathematical performance as a significant predictor of later literacy skills, mathematical performance may have acted only as a proxy measure for more complex language skills such as those assessed on a mathematical language measure. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

  10. The Mathematical Event: Mapping the Axiomatic and the Problematic in School Mathematics

    ERIC Educational Resources Information Center

    de Freitas, Elizabeth

    2013-01-01

    Traditional philosophy of mathematics has been concerned with the nature of mathematical objects rather than events. This traditional focus on reified objects is reflected in dominant theories of learning mathematics whereby the learner is meant to acquire familiarity with ideal mathematical objects, such as number, polygon, or tangent. I argue…

  11. A Comparative Study of the FET Phase Mathematical Literacy and Mathematics Curriculum

    ERIC Educational Resources Information Center

    Mhakure, Duncan; Mokoena, Mamolahluwa Amelia

    2011-01-01

    This article is based on a study that compared the FET (further education and training) phase mathematics literacy curriculum and mathematics curriculum. The study looked into how the conceptualization of a mathematical literacy curriculum enhanced the acquisition of mathematical concepts among the learners. In order to carry out this comparison…

  12. Mathematical Geology.

    ERIC Educational Resources Information Center

    Jones, Thomas A.

    1983-01-01

    Mathematical techniques used to solve geological problems are briefly discussed (including comments on use of geostatistics). Highlights of conferences/meetings and conference papers in mathematical geology are also provided. (JN)

  13. Mathematical Formulation used by MATLAB Code to Convert FTIR Interferograms to Calibrated Spectra

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Armstrong, Derek Elswick

    This report discusses the mathematical procedures used to convert raw interferograms from Fourier transform infrared (FTIR) sensors to calibrated spectra. The work discussed in this report was completed as part of the Helios project at Los Alamos National Laboratory. MATLAB code was developed to convert the raw interferograms to calibrated spectra. The report summarizes the developed MATLAB scripts and functions, along with a description of the mathematical methods used by the code. The first step in working with raw interferograms is to convert them to uncalibrated spectra by applying an apodization function to the raw data and then by performingmore » a Fourier transform. The developed MATLAB code also addresses phase error correction by applying the Mertz method. This report provides documentation for the MATLAB scripts.« less

  14. Equations for description of nonlinear standing waves in constant-cross-sectioned resonators.

    PubMed

    Bednarik, Michal; Cervenka, Milan

    2014-03-01

    This work is focused on investigation of applicability of two widely used model equations for description of nonlinear standing waves in constant-cross-sectioned resonators. The investigation is based on the comparison of numerical solutions of these model equations with solutions of more accurate model equations whose validity has been verified experimentally in a number of published papers.

  15. Secondary Teachers’ Mathematics-related Beliefs and Knowledge about Mathematical Problem-solving

    NASA Astrophysics Data System (ADS)

    E Siswono, T. Y.; Kohar, A. W.; Hartono, S.

    2017-02-01

    This study investigates secondary teachers’ belief about the three mathematics-related beliefs, i.e. nature of mathematics, teaching mathematics, learning mathematics, and knowledge about mathematical problem solving. Data were gathered through a set of task-based semi-structured interviews of three selected teachers with different philosophical views of teaching mathematics, i.e. instrumental, platonist, and problem solving. Those teachers were selected from an interview using a belief-related task from purposively selected teachers in Surabaya and Sidoarjo. While the interviews about knowledge examine teachers’ problem solving content and pedagogical knowledge, the interviews about beliefs examine their views on several cases extracted from each of such mathematics-related beliefs. Analysis included the categorization and comparison on each of beliefs and knowledge as well as their interaction. Results indicate that all the teachers did not show a high consistency in responding views of their mathematics-related beliefs, while they showed weaknesses primarily on problem solving content knowledge. Findings also point out that teachers’ beliefs have a strong relationship with teachers’ knowledge about problem solving. In particular, the instrumental teacher’s beliefs were consistent with his insufficient knowledge about problem-solving, while both platonist and problem-solving teacher’s beliefs were consistent with their sufficient knowledge of either content or pedagogical problem solving.

  16. Improved Detection System Description and New Method for Accurate Calibration of Micro-Channel Plate Based Instruments and Its Use in the Fast Plasma Investigation on NASA's Magnetospheric MultiScale Mission

    NASA Technical Reports Server (NTRS)

    Gliese, U.; Avanov, L. A.; Barrie, A. C.; Kujawski, J. T.; Mariano, A. J.; Tucker, C. J.; Chornay, D. J.; Cao, N. T.; Gershman, D. J.; Dorelli, J. C.; hide

    2015-01-01

    system calibration method that enables accurate and repeatable measurement and calibration of MCP gain, MCP efficiency, signal loss due to variation in gain and efficiency, crosstalk from effects both above and below the MCP, noise margin, and stability margin in one single measurement. More precise calibration is highly desirable as the instruments will produce higher quality raw data that will require less post-acquisition data correction using results from in-flight pitch angle distribution measurements and ground calibration measurements. The detection system description and the fundamental concepts of this new calibration method, named threshold scan, will be presented. It will be shown how to derive all the individual detection system parameters and how to choose the optimum detection system operating point. This new method has been successfully applied to achieve a highly accurate calibration of the DESs and DISs of the MMS mission. The practical application of the method will be presented together with the achieved calibration results and their significance. Finally, it will be shown that, with further detailed modeling, this method can be extended for use in flight to achieve and maintain a highly accurate detection system calibration across a large number of instruments during the mission.

  17. Middle School Mathematics Students' Perspectives on the Study of Mathematics

    ERIC Educational Resources Information Center

    Vaughn, Christy H.

    2012-01-01

    This qualitative study addressed the perceptions toward the study of mathematics by middle school students who had formerly been in a remedial mathematics program. The purpose of the study was to explore the past experiences of nine students in order to determine what is needed for them to feel successful in mathematics. The conceptual framework…

  18. Mathematics disorder

    MedlinePlus

    ... this page: //medlineplus.gov/ency/article/001534.htm Mathematics disorder To use the sharing features on this page, please enable JavaScript. Mathematics disorder is a condition in which a child's ...

  19. From Searle's Chinese Room to the Mathematics Classroom: Technical and Cognitive Mathematics

    ERIC Educational Resources Information Center

    Gavalas, Dimitris

    2007-01-01

    Employing Searle's views, I begin by arguing that students of Mathematics behave similarly to machines that manage symbols using a set of rules. I then consider two types of Mathematics, which I call "Cognitive Mathematics" and "Technical Mathematics" respectively. The former type relates to concepts and meanings, logic and sense, whilst the…

  20. Effects of a Training Package to Improve the Accuracy of Descriptive Analysis Data Recording

    ERIC Educational Resources Information Center

    Mayer, Kimberly L.; DiGennaro Reed, Florence D.

    2013-01-01

    Functional behavior assessment is an important precursor to developing interventions to address a problem behavior. Descriptive analysis, a type of functional behavior assessment, is effective in informing intervention design only if the gathered data accurately capture relevant events and behaviors. We investigated a training procedure to improve…

  1. Explorations in Mathematics

    ERIC Educational Resources Information Center

    Muses, Charles

    1977-01-01

    Mathematics provides a language by which man can explore, and describe precisely and profoundly, any possible set of characteristics or relationships in nature. Discussed in this article are several mathematical topics including some historical perspectives in mathematics and new pioneering in hypernumbers. Supplementary sections include…

  2. Accurate estimation of object location in an image sequence using helicopter flight data

    NASA Technical Reports Server (NTRS)

    Tang, Yuan-Liang; Kasturi, Rangachar

    1994-01-01

    In autonomous navigation, it is essential to obtain a three-dimensional (3D) description of the static environment in which the vehicle is traveling. For a rotorcraft conducting low-latitude flight, this description is particularly useful for obstacle detection and avoidance. In this paper, we address the problem of 3D position estimation for static objects from a monocular sequence of images captured from a low-latitude flying helicopter. Since the environment is static, it is well known that the optical flow in the image will produce a radiating pattern from the focus of expansion. We propose a motion analysis system which utilizes the epipolar constraint to accurately estimate 3D positions of scene objects in a real world image sequence taken from a low-altitude flying helicopter. Results show that this approach gives good estimates of object positions near the rotorcraft's intended flight-path.

  3. Rethinking Mathematics.

    ERIC Educational Resources Information Center

    Abad, Ernesto A.

    1994-01-01

    Poses solutions for our failure to show students how well mathematics interlocks with the physical structures of the Universe. Some examples are provided to illustrate the natural integration of mathematics and science. (ZWH)

  4. How directions of route descriptions influence orientation specificity: the contribution of spatial abilities.

    PubMed

    Meneghetti, Chiara; Muffato, Veronica; Varotto, Diego; De Beni, Rossana

    2017-03-01

    Previous studies found mental representations of route descriptions north-up oriented when egocentric experience (given by the protagonist's initial view) was congruent with the global reference system. This study examines: (a) the development and maintenance of representations derived from descriptions when the egocentric and global reference systems are congruent or incongruent; and (b) how spatial abilities modulate these representations. Sixty participants (in two groups of 30) heard route descriptions of a protagonist's moves starting from the bottom of a layout and headed mainly northwards (SN description) in one group, and headed south from the top (NS description, the egocentric view facing in the opposite direction to the canonical north) in the other. Description recall was tested with map drawing (after hearing the description a first and second time; i.e. Time 1 and 2) and South-North (SN) or North-South (NS) pointing tasks; and spatial objective tasks were administered. The results showed that: (a) the drawings were more rotated in NS than in SN descriptions, and performed better at Time 2 than at Time 1 for both types of description; SN pointing was more accurate than NS pointing for the SN description, while SN and NS pointing accuracy did not differ for the NS description; (b) spatial (rotation) abilities were related to recall accuracy for both types of description, but were more so for the NS ones. Overall, our results showed that the way in which spatial information is conveyed (with/without congruence between the egocentric and global reference systems) and spatial abilities influence the development and maintenance of mental representations.

  5. Didactical Design Material Units of Distance and Speed to Developed Mathematical Connection in Elementary School

    NASA Astrophysics Data System (ADS)

    Jannah, R. R.; Apriliya, S.; Karlimah

    2017-03-01

    This study aims to develop alternative instructional design based of barriers learning which identified by developing mathematical connection capabilities to the material unit of distance and speed. The research was conducted in the fifth grade elementary school Instructional design is complemented with a hypothetical learning trajectory in the form of a pedagogical didactic anticipation. The method used is descriptive method with qualitative approach. Techniques data collection used were observation, interviews, and documentation. The instrument used the researchers themselves are equipped with an instrument written test. The data were analyzed qualitatively to determine the student learning obstacles, then arrange hypothetical learning trajectory and pedagogical didactic anticipation. Learning obstacle are identified, it is learning obstacle related the connections between mathematical topics, learning obstacle related with other disciplines, and learning obstacle related with everyday life. The results of this research are improvement and development of didactic design in mathematics which has activities mathematical connection to the material unit of distance and speed in elementary school. The learning activities are carried out is using varied methods include method lectures, demonstrations, practice and exercise, as well as using the modified instructional media.

  6. Mathematics Teaching Today

    ERIC Educational Resources Information Center

    Martin, Tami S.; Speer, William R.

    2009-01-01

    This article describes features, consistent messages, and new components of "Mathematics Teaching Today: Improving Practice, Improving Student Learning" (NCTM 2007), an updated edition of "Professional Standards for Teaching Mathematics" (NCTM 1991). The new book describes aspects of high-quality mathematics teaching; offers a model for observing,…

  7. Mathematics and the surgeon.

    PubMed Central

    Crank, J.

    1976-01-01

    The surgeon uses elementary mathematics just as much as any other educated layman. In his professional life, however, much of the knowledge and skill on which he relies has had a mathematical strand in its development, possibly woven into the supporting disciplines such as physics, chemistry, biology, and bioengineering. The valves and limitations of mathematical models are examined briefly in the general medical field and particularly in relation to the surgeon. Arithmetic and statistics are usually regarded as the most immediately useful parts of mathematics. Examples are cited, however, of medical postgraduate work which uses other highly advanced mathematical techniques. The place of mathematics in postgraduate and postexperience teaching courses is touched on. The role of a mathematical consultant in the medical team is discussed. PMID:942167

  8. Water immersion facility general description, spacecraft design division, crew station branch

    NASA Technical Reports Server (NTRS)

    1978-01-01

    The Water Immersion Facility provides an accurate, safe, neutral buoyancy simulation of zero gravity conditions for development of equipment and procedures, and the training of crews. A detailed description is given of some of the following systems: (1) water tank and support equipment; (2) communications systems; (3) environmental control and liquid cooled garment system (EcS/LCG); (4) closed circuit television system; and (5) medical support system.

  9. The Effects of Differing Presentations of Mathematical Word Problems Upon the Achievement of Tenth Grade Students.

    ERIC Educational Resources Information Center

    Sherrill, James M.

    Described is a study concerned with the mode of presentation of printed mathematical word problems. Tenth grade students were given twenty word problems to solve, presented in one of three ways: (1) prose only, (2) prose with an accurate picture included, or (3) prose with a distorted picture. Experimental results showed that the group with an…

  10. Wrist electrogoniometry: are current mathematical correction procedures effective in reducing crosstalk in functional assessment?

    PubMed

    Foltran, Fabiana A; Silva, Luciana C C B; Sato, Tatiana O; Coury, Helenice J C G

    2013-01-01

    The recording of human movement is an essential requirement for biomechanical, clinical, and occupational analysis, allowing assessment of postural variation, occupational risks, and preventive programs in physical therapy and rehabilitation. The flexible electrogoniometer (EGM), considered a reliable and accurate device, is used for dynamic recordings of different joints. Despite these advantages, the EGM is susceptible to measurement errors, known as crosstalk. There are two known types of crosstalk: crosstalk due to sensor rotation and inherent crosstalk. Correction procedures have been proposed to correct these errors; however no study has used both procedures in clinical measures for wrist movements with the aim to optimize the correction. To evaluate the effects of mathematical correction procedures on: 1) crosstalk due to forearm rotation, 2) inherent sensor crosstalk; and 3) the combination of these two procedures. 43 healthy subjects had their maximum range of motion of wrist flexion/extension and ulnar/radials deviation recorded by EGM. The results were analyzed descriptively, and procedures were compared by differences. There was no significant difference in measurements before and after the application of correction procedures (P<0.05). Furthermore, the differences between the correction procedures were less than 5° in most cases, having little impact on the measurements. Considering the time-consuming data analysis, the specific technical knowledge involved, and the inefficient results, the correction procedures are not recommended for wrist recordings by EGM.

  11. A mathematical model of insulin resistance in Parkinson's disease.

    PubMed

    Braatz, Elise M; Coleman, Randolph A

    2015-06-01

    This paper introduces a mathematical model representing the biochemical interactions between insulin signaling and Parkinson's disease. The model can be used to examine the changes that occur over the course of the disease as well as identify which processes would be the most effective targets for treatment. The model is mathematized using biochemical systems theory (BST). It incorporates a treatment strategy that includes several experimental drugs along with current treatments. In the past, BST models of neurodegeneration have used power law analysis and simulation (PLAS) to model the system. This paper recommends the use of MATLAB instead. MATLAB allows for more flexibility in both the model itself and in data analysis. Previous BST analyses of neurodegeneration began treatment at disease onset. As shown in this model, the outcomes of delayed, realistic treatment and full treatment at disease onset are significantly different. The delayed treatment strategy is an important development in BST modeling of neurodegeneration. It emphasizes the importance of early diagnosis, and allows for a more accurate representation of disease and treatment interactions. Copyright © 2015 Elsevier Ltd. All rights reserved.

  12. Techniques Use by Science, Technology and Mathematics (STM) Teachers for Controlling Undesirable Classroom Behaviours in Anambra State Secondary Schools

    ERIC Educational Resources Information Center

    Chinelo, Okigbo Ebele; Nwanneka, Okoli Josephine

    2016-01-01

    This study investigated the techniques used by secondary school Science Technology and Mathematics (STM) teachers in controlling undesirable behaviours in their classrooms. It adopted descriptive survey design in which 178 Anambra State teachers teaching STM subjects in senior secondary were involved in the research. Two sections of questionnaire…

  13. Coupling geostatistics to detailed reservoir description allows better visualization and more accurate characterization/simulation of turbidite reservoirs: Elk Hills oil field, California

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Allan, M.E.; Wilson, M.L.; Wightman, J.

    1996-12-31

    The Elk Hills giant oilfield, located in the southern San Joaquin Valley of California, has produced 1.1 billion barrels of oil from Miocene and shallow Pliocene reservoirs. 65% of the current 64,000 BOPD production is from the pressure-supported, deeper Miocene turbidite sands. In the turbidite sands of the 31 S structure, large porosity & permeability variations in the Main Body B and Western 31 S sands cause problems with the efficiency of the waterflooding. These variations have now been quantified and visualized using geostatistics. The end result is a more detailed reservoir characterization for simulation. Traditional reservoir descriptions based onmore » marker correlations, cross-sections and mapping do not provide enough detail to capture the short-scale stratigraphic heterogeneity needed for adequate reservoir simulation. These deterministic descriptions are inadequate to tie with production data as the thinly bedded sand/shale sequences blur into a falsely homogenous picture. By studying the variability of the geologic & petrophysical data vertically within each wellbore and spatially from well to well, a geostatistical reservoir description has been developed. It captures the natural variability of the sands and shales that was lacking from earlier work. These geostatistical studies allow the geologic and petrophysical characteristics to be considered in a probabilistic model. The end-product is a reservoir description that captures the variability of the reservoir sequences and can be used as a more realistic starting point for history matching and reservoir simulation.« less

  14. Coupling geostatistics to detailed reservoir description allows better visualization and more accurate characterization/simulation of turbidite reservoirs: Elk Hills oil field, California

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Allan, M.E.; Wilson, M.L.; Wightman, J.

    1996-01-01

    The Elk Hills giant oilfield, located in the southern San Joaquin Valley of California, has produced 1.1 billion barrels of oil from Miocene and shallow Pliocene reservoirs. 65% of the current 64,000 BOPD production is from the pressure-supported, deeper Miocene turbidite sands. In the turbidite sands of the 31 S structure, large porosity permeability variations in the Main Body B and Western 31 S sands cause problems with the efficiency of the waterflooding. These variations have now been quantified and visualized using geostatistics. The end result is a more detailed reservoir characterization for simulation. Traditional reservoir descriptions based on markermore » correlations, cross-sections and mapping do not provide enough detail to capture the short-scale stratigraphic heterogeneity needed for adequate reservoir simulation. These deterministic descriptions are inadequate to tie with production data as the thinly bedded sand/shale sequences blur into a falsely homogenous picture. By studying the variability of the geologic petrophysical data vertically within each wellbore and spatially from well to well, a geostatistical reservoir description has been developed. It captures the natural variability of the sands and shales that was lacking from earlier work. These geostatistical studies allow the geologic and petrophysical characteristics to be considered in a probabilistic model. The end-product is a reservoir description that captures the variability of the reservoir sequences and can be used as a more realistic starting point for history matching and reservoir simulation.« less

  15. A brief history of the most remarkable numbers e, i and γ in mathematical sciences with applications

    NASA Astrophysics Data System (ADS)

    Debnath, Lokenath

    2015-08-01

    This paper deals with a brief history of the most remarkable Euler numbers e, i and γ in mathematical sciences. Included are many properties of the constants e, i and γ and their applications in algebra, geometry, physics, chemistry, ecology, business and industry. Special attention is given to the growth and decay phenomena in many real-world problems including stability and instability of their solutions. Some specific and modern applications of logarithms, complex numbers and complex exponential functions to electrical circuits and mechanical systems are presented with examples. Included are the use of complex numbers and complex functions in the description and analysis of chaos and fractals with the aid of modern computer technology. In addition, the phasor method is described with examples of applications in engineering science. The major focus of this paper is to provide basic information through historical approach to mathematics teaching and learning of the fundamental knowledge and skills required for students and teachers at all levels so that they can understand the concepts of mathematics, and mathematics education in science and technology.

  16. Defining Mathematical Giftedness

    ERIC Educational Resources Information Center

    Parish, Linda

    2014-01-01

    This theoretical paper outlines the process of defining "mathematical giftedness" for a present study on how primary school teaching shapes the mindsets of children who are mathematically gifted. Mathematical giftedness is not a badge of honour or some special value attributed to a child who has achieved something exceptional.…

  17. Making Mathematics Phenomenal

    ERIC Educational Resources Information Center

    Pratt, Dave

    2012-01-01

    Mathematics is often portrayed as an "abstract" cerebral subject, beyond the reach of many. In response, research with digital technology has led to innovative design in which mathematics can be experienced much like everyday phenomena. This lecture examines how careful design can "phenomenalise" mathematics and support not only engagement but…

  18. Conceptions and Images of Mathematics Professors on Teaching Mathematics in School.

    ERIC Educational Resources Information Center

    Pehkonen, Erkki

    1999-01-01

    Clarifies what kind of mathematical beliefs are conveyed to student teachers during their studies. Interviews mathematics professors (n=7) from five Finnish universities who were responsible for mathematics teacher education. Professors estimated that teachers' basic knowledge was poor and old-fashioned, requiring improvement, and they emphasized…

  19. The Use of the History of Mathematics in the Teaching Pre-Service Mathematics Teachers

    ERIC Educational Resources Information Center

    Galante, Dianna

    2014-01-01

    Many scholars have written about using the history of mathematics in the teaching of pre-service mathematics teachers. For this study, pre-service mathematics teachers developed an electronic journal of reflections based on presentations in the history of mathematics in a secondary mathematics education course. The main purpose of the…

  20. Construction of mathematical knowledge using graphic calculators (CAS) in the mathematics classroom

    NASA Astrophysics Data System (ADS)

    Hitt, Fernando

    2011-09-01

    Mathematics education researchers are asking themselves about why technology has impacted heavily on the social environment and not in the mathematics classroom. The use of technology in the mathematics classroom has not had the expected impact, as it has been its use in everyday life (i.e. cell phone). What about teachers' opinions? Mathematics teachers can be divided into three categories: those with a boundless overflow (enthusiasm) who want to use the technology without worrying much about the construction of mathematical concepts, those who reject outright the use of technology because they think that their use inhibits the development of mathematical skills and others that reflect on the balance that must exist between paper-pencil activities and use of technology. The mathematics teacher, by not having clear examples that support this last option about the balance of paper-pencil activities and technology, opt for one of the extreme positions outlined above. In this article, we show the results of research on a methodology based on collaborative learning (ACODESA) in the training of mathematics teachers in secondary schools and implementation of activities in an environment of paper-pencil and CAS in the mathematics classroom. We also note that with the development of technology on the use of electronic tablets and interactive whiteboards, these activities will take on greater momentum in the near future.