Mathematical modeling relevant to closed artificial ecosystems

USGS Publications Warehouse

DeAngelis, D.L.

2003-01-01

The mathematical modeling of ecosystems has contributed much to the understanding of the dynamics of such systems. Ecosystems can include not only the natural variety, but also artificial systems designed and controlled by humans. These can range from agricultural systems and activated sludge plants, down to mesocosms, microcosms, and aquaria, which may have practical or research applications. Some purposes may require the design of systems that are completely closed, as far as material cycling is concerned. In all cases, mathematical modeling can help not only to understand the dynamics of the system, but also to design methods of control to keep the system operating in desired ranges. This paper reviews mathematical modeling relevant to the simulation and control of closed or semi-closed artificial ecosystems designed for biological production and recycling in applications in space. Published by Elsevier Science Ltd on behalf of COSPAR.

Authentic Integration: a model for integrating mathematics and science in the classroom

NASA Astrophysics Data System (ADS)

Treacy, Páraic; O'Donoghue, John

2014-07-01

Attempts at integrating mathematics and science have been made previously but no definitive, widely adopted teaching model has been developed to date. Research suggests that hands-on, practical, student-centred tasks should form a central element when designing an effective model for the integration of mathematics and science. Aided by this research, the author created a new model entitled 'Authentic Integration' which caters for the specific needs of integration of mathematics and science. This model requires that each lesson be based around a rich task which relates to the real world and ensures that hands-on group work, inquiry, and discussion are central to the lesson. It was found that Authentic Integration, when applied in four Irish post-primary schools, positively affected pupil understanding. The teachers who completed the intervention displayed a very positive attitude towards the approach, intimating that they would continue to implement the practice in their classrooms.

Gamma Ray Observatory (GRO) dynamics simulator requirements and mathematical specifications, revision 1

NASA Technical Reports Server (NTRS)

Harman, R.; Blejer, D.

1990-01-01

The requirements and mathematical specifications for the Gamma Ray Observatory (GRO) Dynamics Simulator are presented. The complete simulator system, which consists of the profie subsystem, simulation control and input/output subsystem, truth model subsystem, onboard computer model subsystem, and postprocessor, is described. The simulator will be used to evaluate and test the attitude determination and control models to be used on board GRO under conditions that simulate the expected in-flight environment.

The image of mathematics held by Irish post-primary students

NASA Astrophysics Data System (ADS)

Lane, Ciara; Stynes, Martin; O'Donoghue, John

2014-08-01

The image of mathematics held by Irish post-primary students was examined and a model for the image found was constructed. Initially, a definition for 'image of mathematics' was adopted with image of mathematics hypothesized as comprising attitudes, beliefs, self-concept, motivation, emotions and past experiences of mathematics. Research focused on students studying ordinary level mathematics for the Irish Leaving Certificate examination - the final examination for students in second-level or post-primary education. Students were aged between 15 and 18 years. A questionnaire was constructed with both quantitative and qualitative aspects. The questionnaire survey was completed by 356 post-primary students. Responses were analysed quantitatively using Statistical Package for the Social Sciences (SPSS) and qualitatively using the constant comparative method of analysis and by reviewing individual responses. Findings provide an insight into Irish post-primary students' images of mathematics and offer a means for constructing a theoretical model of image of mathematics which could be beneficial for future research.

Mathematical modeling of high and low temperature heat pipes

NASA Technical Reports Server (NTRS)

Chi, S. W.

1971-01-01

Mathematical models are developed for calculating heat-transfer limitations of high-temperature heat pipes and heat-transfer limitations and temperature gradient of low temperature heat pipes. Calculated results are compared with the available experimental data from various sources to increase confidence in the present math models. Complete listings of two computer programs for high- and low-temperature heat pipes respectively are appended. These programs enable the performance of heat pipes with wrapped-screen, rectangular-groove or screen-covered rectangular-groove wick to be predicted.

Mathematical model of an air-filled alpha stirling refrigerator

NASA Astrophysics Data System (ADS)

McFarlane, Patrick; Semperlotti, Fabio; Sen, Mihir

2013-10-01

This work develops a mathematical model for an alpha Stirling refrigerator with air as the working fluid and will be useful in optimizing the mechanical design of these machines. Two pistons cyclically compress and expand air while moving sinusoidally in separate chambers connected by a regenerator, thus creating a temperature difference across the system. A complete non-linear mathematical model of the machine, including air thermodynamics, and heat transfer from the walls, as well as heat transfer and fluid resistance in the regenerator, is developed. Non-dimensional groups are derived, and the mathematical model is numerically solved. The heat transfer and work are found for both chambers, and the coefficient of performance of each chamber is calculated. Important design parameters are varied and their effect on refrigerator performance determined. This sensitivity analysis, which shows what the significant parameters are, is a useful tool for the design of practical Stirling refrigeration systems.

A Quantitative Analysis of Methods Used for Avoidance and Acceleration of Developmental Mathematics Sequences in Community College

ERIC Educational Resources Information Center

Travers, Steven T.

2017-01-01

Many developmental mathematics programs at community colleges in recent years have undergone a process of redesign in an attempt increase the historical poor rate of student successful completion of required developmental coursework. Various curriculum and instructional design models that incorporate methods of avoiding and accelerating the…

Mathematical modeling of reflectance and intrinsic fluorescence for cancer detection in human pancreatic tissue

NASA Astrophysics Data System (ADS)

Wilson, Robert H.; Chandra, Malavika; Scheiman, James; Simeone, Diane; McKenna, Barbara; Purdy, Julianne; Mycek, Mary-Ann

2009-02-01

Pancreatic adenocarcinoma has a five-year survival rate of only 4%, largely because an effective procedure for early detection has not been developed. In this study, mathematical modeling of reflectance and fluorescence spectra was utilized to quantitatively characterize differences between normal pancreatic tissue, pancreatitis, and pancreatic adenocarcinoma. Initial attempts at separating the spectra of different tissue types involved dividing fluorescence by reflectance, and removing absorption artifacts by applying a "reverse Beer-Lambert factor" when the absorption coefficient was modeled as a linear combination of the extinction coefficients of oxy- and deoxy-hemoglobin. These procedures demonstrated the need for a more complete mathematical model to quantitatively describe fluorescence and reflectance for minimally-invasive fiber-based optical diagnostics in the pancreas.

Differential equations with applications in cancer diseases.

PubMed

Ilea, M; Turnea, M; Rotariu, M

2013-01-01

Mathematical modeling is a process by which a real world problem is described by a mathematical formulation. The cancer modeling is a highly challenging problem at the frontier of applied mathematics. A variety of modeling strategies have been developed, each focusing on one or more aspects of cancer. The vast majority of mathematical models in cancer diseases biology are formulated in terms of differential equations. We propose an original mathematical model with small parameter for the interactions between these two cancer cell sub-populations and the mathematical model of a vascular tumor. We work on the assumption that, the quiescent cells' nutrient consumption is long. One the equations system includes small parameter epsilon. The smallness of epsilon is relative to the size of the solution domain. MATLAB simulations obtained for transition rate from the quiescent cells' nutrient consumption is long, we show a similar asymptotic behavior for two solutions of the perturbed problem. In this system, the small parameter is an asymptotic variable, different from the independent variable. The graphical output for a mathematical model of a vascular tumor shows the differences in the evolution of the tumor populations of proliferating, quiescent and necrotic cells. The nutrient concentration decreases sharply through the viable rim and tends to a constant level in the core due to the nearly complete necrosis in this region. Many mathematical models can be quantitatively characterized by ordinary differential equations or partial differential equations. The use of MATLAB in this article illustrates the important role of informatics in research in mathematical modeling. The study of avascular tumor growth cells is an exciting and important topic in cancer research and will profit considerably from theoretical input. Interpret these results to be a permanent collaboration between math's and medical oncologists.

Preparation of Students Completing a Core-Plus or Commercially Developed High School Mathematics Curriculum for Intense College Mathematics Coursework

ERIC Educational Resources Information Center

Harwell, Michael R.; Medhanie, Amanuel; Post, Thomas R.; Norman, Ke; Dupuis, Danielle N.

2012-01-01

The purpose of this study was to examine the college mathematics achievement and course-taking of students at a large public research university who completed a commercially developed or standards-based (Core-Plus) high school mathematics curriculum, and who subsequently completed at least 2 college mathematics courses of difficulty level at or…

Design and evaluation of the computer-based training program Calcularis for enhancing numerical cognition

PubMed Central

Käser, Tanja; Baschera, Gian-Marco; Kohn, Juliane; Kucian, Karin; Richtmann, Verena; Grond, Ursina; Gross, Markus; von Aster, Michael

2013-01-01

This article presents the design and a first pilot evaluation of the computer-based training program Calcularis for children with developmental dyscalculia (DD) or difficulties in learning mathematics. The program has been designed according to insights on the typical and atypical development of mathematical abilities. The learning process is supported through multimodal cues, which encode different properties of numbers. To offer optimal learning conditions, a user model completes the program and allows flexible adaptation to a child's individual learning and knowledge profile. Thirty-two children with difficulties in learning mathematics completed the 6–12-weeks computer training. The children played the game for 20 min per day for 5 days a week. The training effects were evaluated using neuropsychological tests. Generally, children benefited significantly from the training regarding number representation and arithmetic operations. Furthermore, children liked to play with the program and reported that the training improved their mathematical abilities. PMID:23935586

The Role of Anxiety and Working Memory in Gender Differences in Mathematics

ERIC Educational Resources Information Center

Ganley, Colleen M.; Vasilyeva, Marina

2014-01-01

This research examined a potential mechanism underlying gender differences in math performance by testing a mediation model in which women's higher anxiety taxes their working memory resources, leading to underperformance on a mathematics test. Participants for the 2 studies were college students (N = 87, N = 118) who completed an anxiety measure,…

A Better Model for Residential High Schools for Talented Youths.

ERIC Educational Resources Information Center

Stanley, Julian C.

1991-01-01

Describes the Texas Academy of Mathematics and Science, a residential school for youths talented in mathematics and science. TAMS students, who come as eleventh graders, take only regular college courses taught by university faculty members. They complete the last two years and the first two years of college in just two academic years. (MLH)

Modeling eBook acceptance: A study on mathematics teachers

NASA Astrophysics Data System (ADS)

Jalal, Azlin Abd; Ayub, Ahmad Fauzi Mohd; Tarmizi, Rohani Ahmad

2014-12-01

The integration and effectiveness of eBook utilization in Mathematics teaching and learning greatly relied upon the teachers, hence the need to understand their perceptions and beliefs. The eBook, an individual laptop completed with digitized textbook sofwares, were provided for each students in line with the concept of 1 student:1 laptop. This study focuses on predicting a model on the acceptance of the eBook among Mathematics teachers. Data was collected from 304 mathematics teachers in selected schools using a survey questionnaire. The selection were based on the proportionate stratified sampling. Structural Equation Modeling (SEM) were employed where the model was tested and evaluated and was found to have a good fit. The variance explained for the teachers' attitude towards eBook is approximately 69.1% where perceived usefulness appeared to be a stronger determinant compared to perceived ease of use. This study concluded that the attitude of mathematics teachers towards eBook depends largely on the perception of how useful the eBook is on improving their teaching performance, implying that teachers should be kept updated with the latest mathematical application and sofwares to use with the eBook to ensure positive attitude towards using it in class.

Does the cognitive reflection test measure cognitive reflection? A mathematical modeling approach.

PubMed

Campitelli, Guillermo; Gerrans, Paul

2014-04-01

We used a mathematical modeling approach, based on a sample of 2,019 participants, to better understand what the cognitive reflection test (CRT; Frederick In Journal of Economic Perspectives, 19, 25-42, 2005) measures. This test, which is typically completed in less than 10 min, contains three problems and aims to measure the ability or disposition to resist reporting the response that first comes to mind. However, since the test contains three mathematically based problems, it is possible that the test only measures mathematical abilities, and not cognitive reflection. We found that the models that included an inhibition parameter (i.e., the probability of inhibiting an intuitive response), as well as a mathematical parameter (i.e., the probability of using an adequate mathematical procedure), fitted the data better than a model that only included a mathematical parameter. We also found that the inhibition parameter in males is best explained by both rational thinking ability and the disposition toward actively open-minded thinking, whereas in females this parameter was better explained by rational thinking only. With these findings, this study contributes to the understanding of the processes involved in solving the CRT, and will be particularly useful for researchers who are considering using this test in their research.

Respiratory protective device design using control system techniques

NASA Technical Reports Server (NTRS)

Burgess, W. A.; Yankovich, D.

1972-01-01

The feasibility of a control system analysis approach to provide a design base for respiratory protective devices is considered. A system design approach requires that all functions and components of the system be mathematically identified in a model of the RPD. The mathematical notations describe the operation of the components as closely as possible. The individual component mathematical descriptions are then combined to describe the complete RPD. Finally, analysis of the mathematical notation by control system theory is used to derive compensating component values that force the system to operate in a stable and predictable manner.

An analysis of mathematical connection ability based on student learning style on visualization auditory kinesthetic (VAK) learning model with self-assessment

NASA Astrophysics Data System (ADS)

Apipah, S.; Kartono; Isnarto

2018-03-01

This research aims to analyze the quality of VAK learning with self-assessment toward the ability of mathematical connection performed by students and to analyze students’ mathematical connection ability based on learning styles in VAK learning model with self-assessment. This research applies mixed method type with concurrent embedded design. The subject of this research consists of VIII grade students from State Junior High School 9 Semarang who apply visual learning style, auditory learning style, and kinesthetic learning style. The data of learning style is collected by using questionnaires, the data of mathematical connection ability is collected by performing tests, and the data of self-assessment is collected by using assessment sheets. The quality of learning is qualitatively valued from planning stage, realization stage, and valuation stage. The result of mathematical connection ability test is analyzed quantitatively by mean test, conducting completeness test, mean differentiation test, and mean proportional differentiation test. The result of the research shows that VAK learning model results in well-qualified learning regarded from qualitative and quantitative sides. Students with visual learning style perform the highest mathematical connection ability, students with kinesthetic learning style perform average mathematical connection ability, and students with auditory learning style perform the lowest mathematical connection ability.

Analysis mathematical literacy skills in terms of the students’ metacognition on PISA-CPS model

NASA Astrophysics Data System (ADS)

Ovan; Waluya, S. B.; Nugroho, S. E.

2018-03-01

This research was aimed to know the effectiveness of PISA-CPS model and desceibe the mathematical literacy skills (KLM) in terms of the students’ metacognition. This study used Mixed Methods approaches with the concurrent embedded desaign. The technique of data analysis on quantitative research done analysis of lesson plan, prerequisite test, test hypotesis 1 and hypotesis test. While qualitative research done data reduction, data presentation, and drawing conclution and data verification. The subject of this study was the students of Grade Eight (VIII) of SMP Islam Sultan Agung 4 Semarang, Central Java. The writer analyzed the data with quantitative and qualitative approaches based on the metacognition of the students in low, medium and high groups. Subsequently, taken the mathematical literacy skills (KLM) from students’ metacognition in low, medium, and high . The results of the study showed that the PISA-CPS model was complete and the students’ mathematical literacy skills in terms of the students’ metacognition taught by the PISA-CPS model was higher than the expository learning. metacognitions’ students classified low hadmathematical literacy skills (KLM) less good, metacognitions’ students classified medium had mathematical literacy skills (KLM) good enough, metacognitions’ students classified high had mathematical literacy skills (KLM) very good. Based onresult analysis got conclusion that the PISA-CPS model was effective toward the students’ mathematical literacy skills (KLM). To increase the students’ mathematical literacy skills (KLM), the teachers need to provide reinforcements in the form of the exercises so that the student’s mathematical literacy was achieved at level 5 and level 6.

A Time Hazard Analysis of Student Persistence: A US University Undergraduate Mathematics Major Experience

ERIC Educational Resources Information Center

Bahi, Saïd; Higgins, Devin; Staley, Patrick

2015-01-01

Individual level data for the entire cohort of undergraduate mathematics students of a relatively small US public university was used to estimate the risk that a student will switch major to another one before degree completion. The data set covers the period from 1999 to 2006. Survival tables and logistic models were estimated and used to discuss…

Mathematical Modelling of Optimization of Structures of Monolithic Coverings Based on Liquid Rubbers

NASA Astrophysics Data System (ADS)

Turgumbayeva, R. Kh; Abdikarimov, M. N.; Mussabekov, R.; Sartayev, D. T.

2018-05-01

The paper considers optimization of monolithic coatings compositions using a computer and MPE methods. The goal of the paper was to construct a mathematical model of the complete factorial experiment taking into account its plan and conditions. Several regression equations were received. Dependence between content components and parameters of rubber, as well as the quantity of a rubber crumb, was considered. An optimal composition for manufacturing the material of monolithic coatings compositions was recommended based on experimental data.

Structural equation modeling assessing relationship between mathematics beliefs, teachers' attitudes and teaching practices among novice teachers in Malaysia

NASA Astrophysics Data System (ADS)

Borhan, Noziati; Zakaria, Effandi

2017-05-01

This quantitative study was conducted to investigate the perception level of novice teachers about mathematics belief, teachers' attitude towards mathematics and teaching practices of mathematics in the classroom. In addition, it also aims to identify whether there is a correspondence model with the data obtained and to identify the relationship between the variables of beliefs, attitudes and practices among novice teachers in Malaysia. A total of 263 primary novice teachers throughout the country were involved in this study were selected randomly. Respondents are required to provide a response to the questionnaire of 66 items related to mathematics beliefs, attitudes and practices of the teaching mathematics. There are ten sub-factors which have been established in this instrument for three major constructs using a Likert scale rating of five points. The items of the constructs undergo the exploratory factor analysis (EFA) and confirmatory factor analysis (CFA) procedure involve of unidimensionality test, convergent validity, construct validity and discriminant validity. Descriptive statistics were used to describe the frequency, percentage, the mean and standard deviation for completing some research questions that have been expressed. As for inferential statistical analysis, the researchers used structural equation modeling (SEM) to answer the question of correspondents model and the relationship between these three variables. The results of the study were found that there exist a correspondence measurement and structural model with the data obtained. While the relationship between variable found that mathematics beliefs have a significant influence on teachers' attitudes towards mathematics as well as the relationship between the attitudes with teaching practices. Meanwhile, mathematics belief had no significant relationship with mathematics teaching practices among novice teachers in Malaysia.

A Method for Calculating the Probability of Successfully Completing a Rocket Propulsion Ground Test

NASA Technical Reports Server (NTRS)

Messer, Bradley

2007-01-01

Propulsion ground test facilities face the daily challenge of scheduling multiple customers into limited facility space and successfully completing their propulsion test projects. Over the last decade NASA s propulsion test facilities have performed hundreds of tests, collected thousands of seconds of test data, and exceeded the capabilities of numerous test facility and test article components. A logistic regression mathematical modeling technique has been developed to predict the probability of successfully completing a rocket propulsion test. A logistic regression model is a mathematical modeling approach that can be used to describe the relationship of several independent predictor variables X(sub 1), X(sub 2),.., X(sub k) to a binary or dichotomous dependent variable Y, where Y can only be one of two possible outcomes, in this case Success or Failure of accomplishing a full duration test. The use of logistic regression modeling is not new; however, modeling propulsion ground test facilities using logistic regression is both a new and unique application of the statistical technique. Results from this type of model provide project managers with insight and confidence into the effectiveness of rocket propulsion ground testing.

Two-dimensional coupled mathematical modeling of fluvial processes with intense sediment transport and rapid bed evolution

NASA Astrophysics Data System (ADS)

Yue, Zhiyuan; Cao, Zhixian; Li, Xin; Che, Tao

2008-09-01

Alluvial rivers may experience intense sediment transport and rapid bed evolution under a high flow regime, for which traditional decoupled mathematical river models based on simplified conservation equations are not applicable. A two-dimensional coupled mathematical model is presented, which is generally applicable to the fluvial processes with either intense or weak sediment transport. The governing equations of the model comprise the complete shallow water hydrodynamic equations closed with Manning roughness for boundary resistance and empirical relationships for sediment exchange with the erodible bed. The second-order Total-Variation-Diminishing version of the Weighted-Average-Flux method, along with the HLLC approximate Riemann Solver, is adapted to solve the governing equations, which can properly resolve shock waves and contact discontinuities. The model is applied to the pilot study of the flooding due to a sudden outburst of a real glacial-lake.

An update of input instructions to TEMOD

NASA Technical Reports Server (NTRS)

1973-01-01

The theory and operation of a FORTRAN 4 computer code, designated as TEMOD, used to calcuate tubular thermoelectric generator performance is described in WANL-TME-1906. The original version of TEMOD was developed in 1969. A description is given of additions to the mathematical model and an update of the input instructions to the code. Although the basic mathematical model described in WANL-TME-1906 has remained unchanged, a substantial number of input/output options were added to allow completion of module performance parametrics as required in support of the compact thermoelectric converter system technology program.

Application of technology developed for flight simulation at NASA. Langley Research Center

NASA Technical Reports Server (NTRS)

Cleveland, Jeff I., II

1991-01-01

In order to meet the stringent time-critical requirements for real-time man-in-the-loop flight simulation, computer processing operations including mathematical model computation and data input/output to the simulators must be deterministic and be completed in as short a time as possible. Personnel at NASA's Langley Research Center are currently developing the use of supercomputers for simulation mathematical model computation for real-time simulation. This, coupled with the use of an open systems software architecture, will advance the state-of-the-art in real-time flight simulation.

A model for closing the inviscid form of the average-passage equation system

NASA Technical Reports Server (NTRS)

Adamczyk, J. J.; Mulac, R. A.; Celestina, M. L.

1985-01-01

A mathematical model is proposed for closing or mathematically completing the system of equations which describes the time average flow field through the blade passages of multistage turbomachinery. These equations referred to as the average passage equation system govern a conceptual model which has proven useful in turbomachinery aerodynamic design and analysis. The closure model is developed so as to insure a consistency between these equations and the axisymmetric through flow equations. The closure model was incorporated into a computer code for use in simulating the flow field about a high speed counter rotating propeller and a high speed fan stage. Results from these simulations are presented.

The role of mathematical models in understanding pattern formation in developmental biology.

PubMed

Umulis, David M; Othmer, Hans G

2015-05-01

In a Wall Street Journal article published on April 5, 2013, E. O. Wilson attempted to make the case that biologists do not really need to learn any mathematics-whenever they run into difficulty with numerical issues, they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilsons Principle No. 1: "It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations." This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson, mathematics is mere number crunching, but as Galileo said long ago, "The laws of Nature are written in the language of mathematics[Formula: see text] the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word." Mathematics has moved beyond the geometry-based model of Galileo's time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science (Both point and counter-point are available in Wilson and Frenkel in Notices Am Math Soc 60(7):837-838, 2013). We will take this a step further and show how mathematics has been used to make new and experimentally verified discoveries in developmental biology and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades-that of how organisms can scale in size. Mathematical analysis alone cannot "solve" these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. Herein, we discuss a few examples of the productive intercourse between mathematics and biology.

Effects of an Additional Mathematics Content Course on Elementary Teachers' Mathematical Beliefs and Knowledge for Teaching

ERIC Educational Resources Information Center

Smith, Marvin E.; Swars, Susan L.; Smith, Stephanie Z.; Hart, Lynn C.; Haardorfer, Regine

2012-01-01

This longitudinal study examines the effects of changes in an elementary teacher preparation program on mathematics beliefs and content knowledge for teaching of two groups of prospective teachers (N = 276): (1) those who completed a program with three mathematics content courses and two mathematics methods courses and (2) those who completed a…

Evidence for shared genetic risk between ADHD symptoms and reduced mathematics ability: a twin study

PubMed Central

Greven, Corina U.; Kovas, Yulia; Willcutt, Erik G.; Petrill, Stephen A.; Plomin, Robert

2013-01-01

Background Attention-deficit/hyperactivity disorder (ADHD) symptoms and mathematics ability are associated, but little is known about the genetic and environmental influences underlying this association. Methods Data came from more than 6,000 12-year-old twin pairs from the U.K. population-representative Twins Early Development Study. Parents rated each twin’s behaviour using a DSM-IV-based 18-item questionnaire of inattentive and hyperactive-impulsive ADHD symptoms. Mathematics tests based on the U.K. National Curriculum were completed by each twin. The twins also completed standardised tests of reading and general cognitive ability. Multivariate twin model fitting was applied. Results Inattentive and hyperactive-impulsive ADHD symptoms were highly heritable (67% and 73%, respectively). Mathematics ability was moderately heritable (46%). Mathematics ability and inattentiveness showed a significantly greater phenotypic correlation (rp=−0.26) and genetic correlation (rA=−0.41) than mathematics ability and hyperactivity-impulsivity (rp=−0.18; rA=−0.22). The genetic correlation between inattentiveness and mathematics ability was largely independent from hyperactivity-impulsivity, and was only partially accounted for by genetic influences related to reading and general cognitive ability. Conclusions Results revealed the novel finding that mathematics ability shows significantly stronger phenotypic and genetic associations with inattentiveness than with hyperactivity-impulsivity. Genetic associations between inattentiveness and mathematics ability could only partially be accounted for by hyperactivity-impulsivity, reading and general cognitive ability. Results suggest that mathematics ability is associated with ADHD symptoms largely because it shares genetic risk factors with inattentiveness, and provide further evidence for considering inattentiveness and hyperactivity-impulsivity separately. DNA markers for ADHD symptoms (especially inattentiveness) may also be candidate risk factors for mathematics ability and vice versa. PMID:23731013

Evidence for shared genetic risk between ADHD symptoms and reduced mathematics ability: a twin study.

PubMed

Greven, Corina U; Kovas, Yulia; Willcutt, Erik G; Petrill, Stephen A; Plomin, Robert

2014-01-01

Attention-deficit/hyperactivity disorder (ADHD) symptoms and mathematics ability are associated, but little is known about the genetic and environmental influences underlying this association. Data came from more than 6,000 twelve-year-old twin pairs from the UK population-representative Twins Early Development Study. Parents rated each twin's behaviour using a DSM-IV-based 18-item questionnaire of inattentive and hyperactive-impulsive ADHD symptoms. Mathematics tests based on the UK National Curriculum were completed by each twin. The twins also completed standardised tests of reading and general cognitive ability. Multivariate twin model fitting was applied. Inattentive and hyperactive-impulsive ADHD symptoms were highly heritable (67% and 73% respectively). Mathematics ability was moderately heritable (46%). Mathematics ability and inattentiveness showed a significantly greater phenotypic correlation (r(p) = -.26) and genetic correlation (r(A) = -.41) than mathematics ability and hyperactivity-impulsivity (r(p) = -.18; r(A) = -.22). The genetic correlation between inattentiveness and mathematics ability was largely independent from hyperactivity-impulsivity, and was only partially accounted for by genetic influences related to reading and general cognitive ability. Results revealed the novel finding that mathematics ability shows significantly stronger phenotypic and genetic associations with inattentiveness than with hyperactivity-impulsivity. Genetic associations between inattentiveness and mathematics ability could only partially be accounted for by hyperactivity-impulsivity, reading and general cognitive ability. Results suggest that mathematics ability is associated with ADHD symptoms largely because it shares genetic risk factors with inattentiveness, and provide further evidence for considering inattentiveness and hyperactivity-impulsivity separately. DNA markers for ADHD symptoms (especially inattentiveness) may also be candidate risk factors for mathematics ability and vice versa. © 2013 The Authors. Journal of Child Psychology and Psychiatry © 2013 Association for Child and Adolescent Mental Health.

Effects of rotor model degradation on the accuracy of rotorcraft real time simulation

NASA Technical Reports Server (NTRS)

Houck, J. A.; Bowles, R. L.

1976-01-01

The effects are studied of degrading a rotating blade element rotor mathematical model to meet various real-time simulation requirements of rotorcraft. Three methods of degradation were studied: reduction of number of blades, reduction of number of blade segments, and increasing the integration interval, which has the corresponding effect of increasing blade azimuthal advance angle. The three degradation methods were studied through static trim comparisons, total rotor force and moment comparisons, single blade force and moment comparisons over one complete revolution, and total vehicle dynamic response comparisons. Recommendations are made concerning model degradation which should serve as a guide for future users of this mathematical model, and in general, they are in order of minimum impact on model validity: (1) reduction of number of blade segments, (2) reduction of number of blades, and (3) increase of integration interval and azimuthal advance angle. Extreme limits are specified beyond which the rotating blade element rotor mathematical model should not be used.

Mathematical problems of quantum teleportation

NASA Astrophysics Data System (ADS)

Tanaka, Yoshiharu; Asano, Masanari; Ohya, Masanori

2011-03-01

It has been considered that a maximal entangled state is needed for complete quantum teleportation. However, Kossakowski and Ohya proposed a scheme of complete teleportation for nonmaximal entangled state [1]. Basing on their scheme, we proposed a teleportation model of 2-level state with a non-maximal entangled state [2]. In the present study, we construct its expanded model, in which Alice can teleport m-level state even if non-maximal entangled state is used.

Stable same-sex friendships with higher achieving partners promote mathematical reasoning in lower achieving primary school children.

PubMed

DeLay, Dawn; Laursen, Brett; Kiuru, Noona; Poikkeus, Anna-Maija; Aunola, Kaisa; Nurmi, Jari-Erik

2015-11-01

This study was designed to investigate friend influence over mathematical reasoning in a sample of 374 children in 187 same-sex friend dyads (184 girls in 92 friendships; 190 boys in 95 friendships). Participants completed surveys that measured mathematical reasoning in the 3rd grade (approximately 9 years old) and 1 year later in the 4th grade (approximately 10 years old). Analyses designed for dyadic data (i.e., longitudinal actor-partner interdependence model) indicated that higher achieving friends influenced the mathematical reasoning of lower achieving friends, but not the reverse. Specifically, greater initial levels of mathematical reasoning among higher achieving partners in the 3rd grade predicted greater increases in mathematical reasoning from 3rd grade to 4th grade among lower achieving partners. These effects held after controlling for peer acceptance and rejection, task avoidance, interest in mathematics, maternal support for homework, parental education, length of the friendship, and friendship group norms on mathematical reasoning. © 2015 The British Psychological Society.

Stable Same-Sex Friendships with Higher Achieving Partners Promote Mathematical Reasoning in Lower Achieving Primary School Children

PubMed Central

DeLay, Dawn; Laursen, Brett; Kiuru, Noona; Poikkeus, Anna-Maija; Aunola, Kaisa; Nurmi, Jari-Erik

2015-01-01

This study is designed to investigate friend influence over mathematical reasoning in a sample of 374 children in 187 same-sex friend dyads (184 girls in 92 friendships; 190 boys in 95 friendships). Participants completed surveys that measured mathematical reasoning in the 3rd grade (approximately 9 years old) and one year later in the 4th grade (approximately 10 years old). Analyses designed for dyadic data (i.e., longitudinal Actor-Partner Interdependence Models) indicated that higher achieving friends influenced the mathematical reasoning of lower achieving friends, but not the reverse. Specifically, greater initial levels of mathematical reasoning among higher achieving partners in the 3rd grade predicted greater increases in mathematical reasoning from 3rd grade to 4th grade among lower achieving partners. These effects held after controlling for peer acceptance and rejection, task avoidance, interest in mathematics, maternal support for homework, parental education, length of the friendship, and friendship group norms on mathematical reasoning. PMID:26402901

A hybrid model of mathematics support for science students emphasizing basic skills and discipline relevance

NASA Astrophysics Data System (ADS)

Jackson, Deborah C.; Johnson, Elizabeth D.

2013-09-01

The problem of students entering university lacking basic mathematical skills is a critical issue in the Australian higher-education sector and relevant globally. The Maths Skills programme at La Trobe University has been developed to address under preparation in the first-year science cohort in the absence of an institutional mathematics support centre. The programme was delivered through first-year science and statistics subjects with large enrolments and focused on basic mathematical skills relevant to each science discipline. The programme offered a new approach to the traditional mathematical support centre or class. It was designed through close collaboration between science subject coordinators and the project leader, a mathematician, and includes resources relevant to science and mathematics questions written in context. Evaluation of the programme showed it improved the confidence of the participating students who found it helpful and relevant. The programme was delivered through three learning modes to allow students to select activities most suitable for them, which was appreciated by students. Mathematics skills appeared to increase following completion of the programme and student participation in the programme correlated positively and highly with academic grades in their relevant science subjects. This programme offers an alternative model for mathematics support tailored to science disciplines.

Analysis of satellite multibeam antennas’ performances

NASA Astrophysics Data System (ADS)

Sterbini, Guido

2006-07-01

In this work, we discuss the application of frequency reuse's concept in satellite communications, stressing the importance for a design-oriented mathematical model as first step for dimensioning antenna systems. We consider multibeam reflector antennas. The first part of the work consists in reorganizing, making uniform and completing the models already developed in the scientific literature. In doing it, we adopt the multidimensional Taylor development formalism. For computing the spillover efficiency of the antenna, we consider different feed's illuminations and we propose a completely original mathematical model, obtained by the interpolation of simulator results. The second part of the work is dedicated to characterize the secondary far field pattern. Combining this model together with the information on the cellular coverage geometry is possible to evaluate the isolation and the minimum directivity on the cell. As third part, in order to test the model and its analysis and synthesis capabilities, we implement a software tool that helps the designer in the rapid tuning of the fundamental quantities for the optimization of the performance: the proposed model shows an optimum agreement with the results of the simulations.

The Modulus of Rupture from a Mathematical Point of View

NASA Astrophysics Data System (ADS)

Quintela, P.; Sánchez, M. T.

2007-04-01

The goal of this work is to present a complete mathematical study about the three-point bending experiments and the modulus of rupture of brittle materials. We will present the mathematical model associated to three-point bending experiments and we will use the asymptotic expansion method to obtain a new formula to calculate the modulus of rupture. We will compare the modulus of rupture of porcelain obtained with the previous formula with that obtained by using the classic theoretical formula. Finally, we will also present one and three-dimensional numerical simulations to compute the modulus of rupture.

Sifting noisy data for truths about noisy systems. Comment on "Extracting physics of life at the molecular level: A review of single-molecule data analyses" by W. Colomb and S.K. Sarkar

NASA Astrophysics Data System (ADS)

Flyvbjerg, Henrik; Mortensen, Kim I.

2015-06-01

With each new aspect of nature that becomes accessible to quantitative science, new needs arise for data analysis and mathematical modeling. The classical example is Tycho Brahe's accurate and comprehensive observations of planets, which made him hire Kepler for his mathematical skills to assist with the data analysis. We all learned what that lead to: Kepler's three laws of planetary motion, phenomenology in purely mathematical form. Newton built on this, and the scientific revolution was over, completed.

Inferring pathological states in cortical neuron microcircuits.

PubMed

Rydzewski, Jakub; Nowak, Wieslaw; Nicosia, Giuseppe

2015-12-07

The brain activity is to a large extent determined by states of neural cortex microcircuits. Unfortunately, accuracy of results from neural circuits׳ mathematical models is often biased by the presence of uncertainties in underlying experimental data. Moreover, due to problems with uncertainties identification in a multidimensional parameters space, it is almost impossible to classify states of the neural cortex, which correspond to a particular set of the parameters. Here, we develop a complete methodology for determining uncertainties and the novel protocol for classifying all states in any neuroinformatic model. Further, we test this protocol on the mathematical, nonlinear model of such a microcircuit developed by Giugliano et al. (2008) and applied in the experimental data analysis of Huntington׳s disease. Up to now, the link between parameter domains in the mathematical model of Huntington׳s disease and the pathological states in cortical microcircuits has remained unclear. In this paper we precisely identify all the uncertainties, the most crucial input parameters and domains that drive the system into an unhealthy state. The scheme proposed here is general and can be easily applied to other mathematical models of biological phenomena. Copyright © 2015 Elsevier Ltd. All rights reserved.

Computational aspects of real-time simulation of rotary-wing aircraft. M.S. Thesis

NASA Technical Reports Server (NTRS)

Houck, J. A.

1976-01-01

A study was conducted to determine the effects of degrading a rotating blade element rotor mathematical model suitable for real-time simulation of rotorcraft. Three methods of degradation were studied, reduction of number of blades, reduction of number of blade segments, and increasing the integration interval, which has the corresponding effect of increasing blade azimuthal advance angle. The three degradation methods were studied through static trim comparisons, total rotor force and moment comparisons, single blade force and moment comparisons over one complete revolution, and total vehicle dynamic response comparisons. Recommendations are made concerning model degradation which should serve as a guide for future users of this mathematical model, and in general, they are in order of minimum impact on model validity: (1) reduction of number of blade segments; (2) reduction of number of blades; and (3) increase of integration interval and azimuthal advance angle. Extreme limits are specified beyond which a different rotor mathematical model should be used.

[Mathematic modeling for prediction of waning immunity and timing of booster doses].

PubMed

Matuo, Fujio; Okada, Kenji

2008-10-01

Under an environment that a vaccination rate is low and an infectious disease is prevalent, it is thought that most vaccinee got additional immunity by natural infection. On the other hand, in the area where the incidence of disease has been reduced by high rate vaccination, it is also decreased the chance of additional immunity by natural infection. Therefore susceptible individuals are increased because of the waning immunity. In the community where a vaccination rate is high, it may be necessary to consider the booster vaccination for adolescent and adult even if one completed the primary vaccinations. It may also be important to explore the timing of booster dose. In this paper, we attempt to give a comprehensive explanation of mathematical model for predicting the antibody duration, and we introduce the role of mathematical model on a consideration to the need and timing of booster doses after the primary series.

Use of Total Possibilistic Uncertainty as a Measure of Students' Modelling Capacities

ERIC Educational Resources Information Center

Voskoglou, Michael Gr.

2010-01-01

We represent the main stages of the process of mathematical modelling as fuzzy sets in the set of the linguistic labels of negligible, low intermediate, high and complete success by students in each of these stages and we use the total possibilistic uncertainty as a measure of students' modelling capacities. A classroom experiment is also…

Mathematic modeling of the Earth's surface and the process of remote sensing

NASA Technical Reports Server (NTRS)

Balter, B. M.

1979-01-01

It is shown that real data from remote sensing of the Earth from outer space are not best suited to the search for optimal procedures with which to process such data. To work out the procedures, it was proposed that data synthesized with the help of mathematical modeling be used. A criterion for simularity to reality was formulated. The basic principles for constructing methods for modeling the data from remote sensing are recommended. A concrete method is formulated for modeling a complete cycle of radiation transformations in remote sensing. A computer program is described which realizes the proposed method. Some results from calculations are presented which show that the method satisfies the requirements imposed on it.

Statistical models of lunar rocks and regolith

NASA Technical Reports Server (NTRS)

Marcus, A. H.

1973-01-01

The mathematical, statistical, and computational approaches used in the investigation of the interrelationship of lunar fragmental material, regolith, lunar rocks, and lunar craters are described. The first two phases of the work explored the sensitivity of the production model of fragmental material to mathematical assumptions, and then completed earlier studies on the survival of lunar surface rocks with respect to competing processes. The third phase combined earlier work into a detailed statistical analysis and probabilistic model of regolith formation by lithologically distinct layers, interpreted as modified crater ejecta blankets. The fourth phase of the work dealt with problems encountered in combining the results of the entire project into a comprehensive, multipurpose computer simulation model for the craters and regolith. Highlights of each phase of research are given.

Perfection Of Methods Of Mathematical Analysis For Increasing The Completeness Of Subsoil Development

NASA Astrophysics Data System (ADS)

Fokina, Mariya

2017-11-01

The economy of Russia is based around the mineral-raw material complex to the highest degree. The mining industry is a prioritized and important area. Given the high competitiveness of businesses in this sector, increasing the efficiency of completed work and manufactured products will become a central issue. Improvement of planning and management in this sector should be based on multivariant study and the optimization of planning decisions, the appraisal of their immediate and long-term results, taking the dynamic of economic development into account. All of this requires the use of economic mathematic models and methodsApplying an economic-mathematic model to determine optimal ore mine production capacity, we receive a figure of 4,712,000 tons. The production capacity of the Uchalinsky ore mine is 1560 thousand tons, and the Uzelginsky ore mine - 3650 thousand. Conducting a corresponding analysis of the production of OAO "Uchalinsky Gok", an optimal production plan was received: the optimal production of copper - 77961,4 rubles; the optimal production of zinc - 17975.66 rubles. The residual production volume of the two main ore mines of OAO "UGOK" is 160 million tons of ore.

Complete Systematic Error Model of SSR for Sensor Registration in ATC Surveillance Networks

PubMed Central

Besada, Juan A.

2017-01-01

In this paper, a complete and rigorous mathematical model for secondary surveillance radar systematic errors (biases) is developed. The model takes into account the physical effects systematically affecting the measurement processes. The azimuth biases are calculated from the physical error of the antenna calibration and the errors of the angle determination dispositive. Distance bias is calculated from the delay of the signal produced by the refractivity index of the atmosphere, and from clock errors, while the altitude bias is calculated taking into account the atmosphere conditions (pressure and temperature). It will be shown, using simulated and real data, that adapting a classical bias estimation process to use the complete parametrized model results in improved accuracy in the bias estimation. PMID:28934157

The Abstract Selection Task: New Data and an Almost Comprehensive Model

ERIC Educational Resources Information Center

Klauer, Karl Christoph; Stahl, Christoph; Erdfelder, Edgar

2007-01-01

A complete quantitative account of P. Wason's (1966) abstract selection task is proposed. The account takes the form of a mathematical model. It is assumed that some response patterns are caused by inferential reasoning, whereas other responses reflect cognitive processes that affect each card selection separately and independently of other card…

Reciprocal Relationships between Math Self-Concept and Math Anxiety

ERIC Educational Resources Information Center

Ahmed, Wondimu; Minnaert, Alexander; Kuyper, Hans; van der Werf, Greetje

2012-01-01

The present study examined the reciprocal relationships between self-concept and anxiety in mathematics. A sample of 495 grade 7 students (51% girls) completed self-report measures assessing self-concept and anxiety three times in a school year. Structural equation modeling was used to test a cross-lagged panel model of reciprocal effects between…

Effectiveness of a Corequisite Delivery Model for Developmental Mathematics

ERIC Educational Resources Information Center

Fair, Katherine Eileen

2017-01-01

The purpose of this quantitative quasi-experimental study is to determine the effectiveness of a corequisite delivery model for developmental math students at a 4-year public institution. Nationally, close to fifty percent of incoming college students are placed in non-credit bearing remedial courses (Complete College America, 2012). Students must…

A comparison of cognitive skills between completes and dropouts in a college physics course

NASA Astrophysics Data System (ADS)

Hudson, H. T.

Separate tests of mathematics skills, proportions and translations between words, and mathematical expression given the first week of class were correlated with performance for students who completed a college physics course (completes) and students who dropped the course (drops). None of the measures used discriminated between completes and drops as groups. However, the correlations between score on the test of math skills and on both of the measures involving mathematical reasoning (proportions, and translations) were dramatically different for the two groups. For the completes, these correlations were slightly negative, but not significant. For the drops, the correlation was positive and signficant at the p < 0.01 level. This suggests the possibility that the students who complete the course tend to have independent cognitive skills for the mechanical mathematical operations and for questions requiring some degree of reasoning, while, in contrast, the same skills for students at high risk for dropping overlap significantly. The study also found that when students are given the results of mathematics skills tests in a diagnostic mode, with feedback on specific areas of weakness and time to remediate with self study, the correlation between mathematics and physics is lower than previously reported values.Received: 2 April 1985

Unsteady Aerodynamic Modeling in Roll for the NASA Generic Transport Model

NASA Technical Reports Server (NTRS)

Murphy, Patrick C.; Klein, Vladislav; Frink, Neal T.

2012-01-01

Reducing the impact of loss-of-control conditions on commercial transport aircraft is a primary goal of the NASA Aviation Safety Program. One aspect in developing the supporting technologies is to improve the aerodynamic models that represent these adverse conditions. Aerodynamic models appropriate for loss of control conditions require a more general mathematical representation to predict nonlinear unsteady behaviors. In this paper, a more general mathematical model is proposed for the subscale NASA Generic Transport Model (GTM) that covers both low and high angles of attack. Particular attention is devoted to the stall region where full-scale transports have demonstrated a tendency for roll instability. The complete aerodynamic model was estimated from dynamic wind-tunnel data. Advanced computational methods are used to improve understanding and visualize the flow physics within the region where roll instability is a factor.

A Model Comparison for Count Data with a Positively Skewed Distribution with an Application to the Number of University Mathematics Courses Completed

ERIC Educational Resources Information Center

Liou, Pey-Yan

2009-01-01

The current study examines three regression models: OLS (ordinary least square) linear regression, Poisson regression, and negative binomial regression for analyzing count data. Simulation results show that the OLS regression model performed better than the others, since it did not produce more false statistically significant relationships than…

Self-Perceptions of Pre-Service Mathematics Teachers Completing a Graduate Diploma of Secondary Education

ERIC Educational Resources Information Center

Hine, Gregory S. C.

2015-01-01

This qualitative research project explored the self-perceptions of pre-service secondary mathematics teachers completing a Graduate Diploma of Secondary Education. Specifically, the researcher investigated the extent to which teachers perceived their readiness to commence a secondary mathematics teaching position. The project relied principally on…

Treatment of control data in lunar phototriangulation. [application of statistical procedures and development of mathematical and computer techniques

NASA Technical Reports Server (NTRS)

Wong, K. W.

1974-01-01

In lunar phototriangulation, there is a complete lack of accurate ground control points. The accuracy analysis of the results of lunar phototriangulation must, therefore, be completely dependent on statistical procedure. It was the objective of this investigation to examine the validity of the commonly used statistical procedures, and to develop both mathematical techniques and computer softwares for evaluating (1) the accuracy of lunar phototriangulation; (2) the contribution of the different types of photo support data on the accuracy of lunar phototriangulation; (3) accuracy of absolute orientation as a function of the accuracy and distribution of both the ground and model points; and (4) the relative slope accuracy between any triangulated pass points.

Predicting human chronically paralyzed muscle force: a comparison of three mathematical models.

PubMed

Frey Law, Laura A; Shields, Richard K

2006-03-01

Chronic spinal cord injury (SCI) induces detrimental musculoskeletal adaptations that adversely affect health status, ranging from muscle paralysis and skin ulcerations to osteoporosis. SCI rehabilitative efforts may increasingly focus on preserving the integrity of paralyzed extremities to maximize health quality using electrical stimulation for isometric training and/or functional activities. Subject-specific mathematical muscle models could prove valuable for predicting the forces necessary to achieve therapeutic loading conditions in individuals with paralyzed limbs. Although numerous muscle models are available, three modeling approaches were chosen that can accommodate a variety of stimulation input patterns. To our knowledge, no direct comparisons between models using paralyzed muscle have been reported. The three models include 1) a simple second-order linear model with three parameters and 2) two six-parameter nonlinear models (a second-order nonlinear model and a Hill-derived nonlinear model). Soleus muscle forces from four individuals with complete, chronic SCI were used to optimize each model's parameters (using an increasing and decreasing frequency ramp) and to assess the models' predictive accuracies for constant and variable (doublet) stimulation trains at 5, 10, and 20 Hz in each individual. Despite the large differences in modeling approaches, the mean predicted force errors differed only moderately (8-15% error; P=0.0042), suggesting physiological force can be adequately represented by multiple mathematical constructs. The two nonlinear models predicted specific force characteristics better than the linear model in nearly all stimulation conditions, with minimal differences between the two nonlinear models. Either nonlinear mathematical model can provide reasonable force estimates; individual application needs may dictate the preferred modeling strategy.

Effects of intracerebroventricular administration of beta-amyloid on the dynamics of learning in purebred and mongrel rats.

PubMed

Stepanov, I I; Kuznetsova, N N; Klement'ev, B I; Sapronov, N S

2007-07-01

The effects of intracerebroventricular administration of the beta-amyloid peptide fragment Abeta(25-35) on the dynamics of the acquisition of a conditioned reflex in a Y maze were studied in Wistar and mongrel rats. The dynamics of decreases in the number of errors were assessed using an exponential mathematical model describing the transfer function of a first-order system in response to stepped inputs using non-linear regression analysis. This mathematical model provided a good approximation to the learning dynamics in inbred and mongrel mice. In Wistar rats, beta-amyloid impaired learning, with reduced memory between the first and second training sessions, but without complete blockade of learning. As a result, learning dynamics were no longer approximated by the mathematical model. At the same time, comparison of the number of errors in each training sessions between the control group of Wistar rats and the group given beta-amyloid showed no significant differences (Student's t test). This result demonstrates the advantage of regression analysis based on a mathematical model over the traditionally used statistical methods. In mongrel rats, the effect of beta-amyloid was limited to an a slowing of the process of learning as compared with control mongrel rats, with retention of the approximation by the mathematical model. It is suggested that mongrel animals have some kind of innate, genetically determined protective mechanism against the harmful effects of beta-amyloid.

Towards A Complete Model Of Photopic Visual Threshold Performance

NASA Astrophysics Data System (ADS)

Overington, I.

1982-02-01

Based on a wide variety of fragmentary evidence taken from psycho-physics, neurophysiology and electron microscopy, it has been possible to put together a very widely applicable conceptual model of photopic visual threshold performance. Such a model is so complex that a single comprehensive mathematical version is excessively cumbersome. It is, however, possible to set up a suite of related mathematical models, each of limited application but strictly known envelope of usage. Such models may be used for assessment of a variety of facets of visual performance when using display imagery, including effects and interactions of image quality, random and discrete display noise, viewing distance, image motion, etc., both for foveal interrogation tasks and for visual search tasks. The specific model may be selected from the suite according to the assessment task in hand. The paper discusses in some depth the major facets of preperceptual visual processing and their interaction with instrumental image quality and noise. It then highlights the statistical nature of visual performance before going on to consider a number of specific mathematical models of partial visual function. Where appropriate, these are compared with widely popular empirical models of visual function.

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…

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…

Designing for Improvement in Professional Development for Community College Developmental Mathematics Faculty

ERIC Educational Resources Information Center

Edwards, Ann R.; Sandoval, Carlos; McNamara, Haley

2015-01-01

More than 60% of the nation's 14 million community college students are required to complete at least one developmental mathematics class before enrolling in college-credit courses; however, 80% of them do not successfully complete any college-level mathematics course within 3 years. To address this problem, the Community College Pathways…

Role of Mathematics Learning Development Centres in HEIs

ERIC Educational Resources Information Center

Nzekwe-Excel, C.

2010-01-01

Background and Rationale: Student withdrawal and non-completion in institutions have been an issue of considerable concern. The lack of mathematical ability has been identified as a factor resulting to non-completion in higher institutions. Several students in higher education approach mathematics with a lot of anxiety. This has created the need…

Mathematical modeling and analysis of heat pipe start-up from the frozen state

NASA Technical Reports Server (NTRS)

Jang, Jong Hoon; Faghri, Amir; Chang, Won Soon; Mahefkey, Edward T.

1989-01-01

The start-up process of a frozen heat pipe is described and a complete mathematical model for the start-up of the frozen heat pipe is developed based on the existing experimental data, which is simplified and solved numerically. The two-dimensional transient model for the wall and wick is coupled with the one-dimensional transient model for the vapor flow when vaporization and condensation occur at the interface. A parametric study is performed to examine the effect of the boundary specification at the surface of the outer wall on the successful start-up from the frozen state. For successful start-up, the boundary specification at the outer wall surface must melt the working substance in the condenser before dry-out takes place in the evaporator.

Mathematical modeling and analysis of heat pipe start-up from the frozen state

NASA Technical Reports Server (NTRS)

Jang, J. H.; Faghri, A.; Chang, W. S.; Mahefkey, E. T.

1990-01-01

The start-up process of a frozen heat pipe is described and a complete mathematical model for the start-up of the frozen heat pipe is developed based on the existing experimental data, which is simplified and solved numerically. The two-dimensional transient model for the wall and wick is coupled with the one-dimensional transient model for the vapor flow when vaporization and condensation occur at the interface. A parametric study is performed to examine the effect of the boundary specification at the surface of the outer wall on the successful start-up from the frozen state. For successful start-up, the boundary specification at the outer wall surface must melt the working substance in the condenser before dry-out takes place in the evaporator.

Mathematical Methods of Subjective Modeling in Scientific Research: I. The Mathematical and Empirical Basis

NASA Astrophysics Data System (ADS)

Pyt'ev, Yu. P.

2018-01-01

mathematical formalism for subjective modeling, based on modelling of uncertainty, reflecting unreliability of subjective information and fuzziness that is common for its content. The model of subjective judgments on values of an unknown parameter x ∈ X of the model M( x) of a research object is defined by the researcher-modeler as a space1 ( X, p( X), P{I^{\\bar x}}, Be{l^{\\bar x}}) with plausibility P{I^{\\bar x}} and believability Be{l^{\\bar x}} measures, where x is an uncertain element taking values in X that models researcher—modeler's uncertain propositions about an unknown x ∈ X, measures P{I^{\\bar x}}, Be{l^{\\bar x}} model modalities of a researcher-modeler's subjective judgments on the validity of each x ∈ X: the value of P{I^{\\bar x}}(\\tilde x = x) determines how relatively plausible, in his opinion, the equality (\\tilde x = x) is, while the value of Be{l^{\\bar x}}(\\tilde x = x) determines how the inequality (\\tilde x = x) should be relatively believed in. Versions of plausibility Pl and believability Bel measures and pl- and bel-integrals that inherit some traits of probabilities, psychophysics and take into account interests of researcher-modeler groups are considered. It is shown that the mathematical formalism of subjective modeling, unlike "standard" mathematical modeling, •enables a researcher-modeler to model both precise formalized knowledge and non-formalized unreliable knowledge, from complete ignorance to precise knowledge of the model of a research object, to calculate relative plausibilities and believabilities of any features of a research object that are specified by its subjective model M(\\tilde x), and if the data on observations of a research object is available, then it: •enables him to estimate the adequacy of subjective model to the research objective, to correct it by combining subjective ideas and the observation data after testing their consistency, and, finally, to empirically recover the model of a research object.

Computational Control of Flexible Aerospace Systems

NASA Technical Reports Server (NTRS)

Sharpe, Lonnie, Jr.; Shen, Ji Yao

1994-01-01

The main objective of this project is to establish a distributed parameter modeling technique for structural analysis, parameter estimation, vibration suppression and control synthesis of large flexible aerospace structures. This report concentrates on the research outputs produced in the last two years of the project. The main accomplishments can be summarized as follows. A new version of the PDEMOD Code had been completed. A theoretical investigation of the NASA MSFC two-dimensional ground-based manipulator facility by using distributed parameter modelling technique has been conducted. A new mathematical treatment for dynamic analysis and control of large flexible manipulator systems has been conceived, which may provide a embryonic form of a more sophisticated mathematical model for future modified versions of the PDEMOD Codes.

Design and Development Computer-Based E-Learning Teaching Material for Improving Mathematical Understanding Ability and Spatial Sense of Junior High School Students

NASA Astrophysics Data System (ADS)

Nurjanah; Dahlan, J. A.; Wibisono, Y.

2017-02-01

This paper aims to make a design and development computer-based e-learning teaching material for improving mathematical understanding ability and spatial sense of junior high school students. Furthermore, the particular aims are (1) getting teaching material design, evaluation model, and intrument to measure mathematical understanding ability and spatial sense of junior high school students; (2) conducting trials computer-based e-learning teaching material model, asessment, and instrument to develop mathematical understanding ability and spatial sense of junior high school students; (3) completing teaching material models of computer-based e-learning, assessment, and develop mathematical understanding ability and spatial sense of junior high school students; (4) resulting research product is teaching materials of computer-based e-learning. Furthermore, the product is an interactive learning disc. The research method is used of this study is developmental research which is conducted by thought experiment and instruction experiment. The result showed that teaching materials could be used very well. This is based on the validation of computer-based e-learning teaching materials, which is validated by 5 multimedia experts. The judgement result of face and content validity of 5 validator shows that the same judgement result to the face and content validity of each item test of mathematical understanding ability and spatial sense. The reliability test of mathematical understanding ability and spatial sense are 0,929 and 0,939. This reliability test is very high. While the validity of both tests have a high and very high criteria.

Completing the Remedial Sequence and College-Level Credit-Bearing Math: Comparing Binary, Cumulative, and Continuation Ratio Logistic Regression Models

ERIC Educational Resources Information Center

Davidson, J. Cody

2016-01-01

Mathematics is the most common subject area of remedial need and the majority of remedial math students never pass a college-level credit-bearing math class. The majorities of studies that investigate this phenomenon are conducted at community colleges and use some type of regression model; however, none have used a continuation ratio model. The…

A unique large-scale undergraduate research experience in molecular systems biology for non-mathematics majors.

PubMed

Kappler, Ulrike; Rowland, Susan L; Pedwell, Rhianna K

2017-05-01

Systems biology is frequently taught with an emphasis on mathematical modeling approaches. This focus effectively excludes most biology, biochemistry, and molecular biology students, who are not mathematics majors. The mathematical focus can also present a misleading picture of systems biology, which is a multi-disciplinary pursuit requiring collaboration between biochemists, bioinformaticians, and mathematicians. This article describes an authentic large-scale undergraduate research experience (ALURE) in systems biology that incorporates proteomics, bacterial genomics, and bioinformatics in the one exercise. This project is designed to engage students who have a basic grounding in protein chemistry and metabolism and no mathematical modeling skills. The pedagogy around the research experience is designed to help students attack complex datasets and use their emergent metabolic knowledge to make meaning from large amounts of raw data. On completing the ALURE, participants reported a significant increase in their confidence around analyzing large datasets, while the majority of the cohort reported good or great gains in a variety of skills including "analysing data for patterns" and "conducting database or internet searches." An environmental scan shows that this ALURE is the only undergraduate-level system-biology research project offered on a large-scale in Australia; this speaks to the perceived difficulty of implementing such an opportunity for students. We argue however, that based on the student feedback, allowing undergraduate students to complete a systems-biology project is both feasible and desirable, even if the students are not maths and computing majors. © 2016 by The International Union of Biochemistry and Molecular Biology, 45(3):235-248, 2017. © 2016 The International Union of Biochemistry and Molecular Biology.

Task allocation model for minimization of completion time in distributed computer systems

NASA Astrophysics Data System (ADS)

Wang, Jai-Ping; Steidley, Carl W.

1993-08-01

A task in a distributed computing system consists of a set of related modules. Each of the modules will execute on one of the processors of the system and communicate with some other modules. In addition, precedence relationships may exist among the modules. Task allocation is an essential activity in distributed-software design. This activity is of importance to all phases of the development of a distributed system. This paper establishes task completion-time models and task allocation models for minimizing task completion time. Current work in this area is either at the experimental level or without the consideration of precedence relationships among modules. The development of mathematical models for the computation of task completion time and task allocation will benefit many real-time computer applications such as radar systems, navigation systems, industrial process control systems, image processing systems, and artificial intelligence oriented systems.

The Role of Mathematical Models in Understanding Pattern Formation in Developmental Biology

PubMed Central

Umulis, David M.

2016-01-01

In a Wall Street Journal article published on April 5, 2013, E. O. Wilson attempted to make the case that biologists do not really need to learn any mathematics—whenever they run into difficulty with numerical issues, they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilsons Principle No. 1: “It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations.” This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson, mathematics is mere number crunching, but as Galileo said long ago, “The laws of Nature are written in the language of mathematics…the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word.” Mathematics has moved beyond the geometry-based model of Galileo’s time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science (Both point and counter-point are available in Wilson and Frenkel in Notices Am Math Soc 60(7):837–838, 2013). We will take this a step further and show how mathematics has been used to make new and experimentally verified discoveries in developmental biology and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades—that of how organisms can scale in size. Mathematical analysis alone cannot “solve” these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. Herein, we discuss a few examples of the productive intercourse between mathematics and biology. PMID:25280665

Modeling the Growth of Filamentous Fungi at the Particle Scale in Solid-State Fermentation Systems.

PubMed

Sugai-Guérios, Maura Harumi; Balmant, Wellington; Furigo, Agenor; Krieger, Nadia; Mitchell, David Alexander

2015-01-01

Solid-state fermentation (SSF) with filamentous fungi is a promising technique for the production of a range of biotechnological products and has the potential to play an important role in future biorefineries. The performance of such processes is intimately linked with the mycelial mode of growth of these fungi: Not only is the production of extracellular enzymes related to morphological characteristics, but also the mycelium can affect bed properties and, consequently, the efficiency of heat and mass transfer within the bed. A mathematical model that describes the development of the fungal mycelium in SSF systems at the particle scale would be a useful tool for investigating these phenomena, but, as yet, a sufficiently complete model has not been proposed. This review presents the biological and mass transfer phenomena that should be included in such a model and then evaluates how these phenomena have been modeled previously in the SSF and related literature. We conclude that a discrete lattice-based model that uses differential equations to describe the mass balances of the components within the system would be most appropriate and that mathematical expressions for describing the individual phenomena are available in the literature. It remains for these phenomena to be integrated into a complete model describing the development of fungal mycelia in SSF systems.

Multiscale Mathematics for Biomass Conversion to Renewable Hydrogen

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

Plechac, Petr; Vlachos, Dionisios; Katsoulakis, Markos

2013-09-05

The overall objective of this project is to develop multiscale models for understanding and eventually designing complex processes for renewables. To the best of our knowledge, our work is the first attempt at modeling complex reacting systems, whose performance relies on underlying multiscale mathematics. Our specific application lies at the heart of biofuels initiatives of DOE and entails modeling of catalytic systems, to enable economic, environmentally benign, and efficient conversion of biomass into either hydrogen or valuable chemicals. Specific goals include: (i) Development of rigorous spatio-temporal coarse-grained kinetic Monte Carlo (KMC) mathematics and simulation for microscopic processes encountered in biomassmore » transformation. (ii) Development of hybrid multiscale simulation that links stochastic simulation to a deterministic partial differential equation (PDE) model for an entire reactor. (iii) Development of hybrid multiscale simulation that links KMC simulation with quantum density functional theory (DFT) calculations. (iv) Development of parallelization of models of (i)-(iii) to take advantage of Petaflop computing and enable real world applications of complex, multiscale models. In this NCE period, we continued addressing these objectives and completed the proposed work. Main initiatives, key results, and activities are outlined.« less

Reliable before-fabrication forecasting of normal and touch mode MEMS capacitive pressure sensor: modeling and simulation

NASA Astrophysics Data System (ADS)

Jindal, Sumit Kumar; Mahajan, Ankush; Raghuwanshi, Sanjeev Kumar

2017-10-01

An analytical model and numerical simulation for the performance of MEMS capacitive pressure sensors in both normal and touch modes is required for expected behavior of the sensor prior to their fabrication. Obtaining such information should be based on a complete analysis of performance parameters such as deflection of diaphragm, change of capacitance when the diaphragm deflects, and sensitivity of the sensor. In the literature, limited work has been carried out on the above-stated issue; moreover, due to approximation factors of polynomials, a tolerance error cannot be overseen. Reliable before-fabrication forecasting requires exact mathematical calculation of the parameters involved. A second-order polynomial equation is calculated mathematically for key performance parameters of both modes. This eliminates the approximation factor, and an exact result can be studied, maintaining high accuracy. The elimination of approximation factors and an approach of exact results are based on a new design parameter (δ) that we propose. The design parameter gives an initial hint to the designers on how the sensor will behave once it is fabricated. The complete work is aided by extensive mathematical detailing of all the parameters involved. Next, we verified our claims using MATLAB® simulation. Since MATLAB® effectively provides the simulation theory for the design approach, more complicated finite element method is not used.

Model correlation and damage location for large space truss structures: Secant method development and evaluation

NASA Technical Reports Server (NTRS)

Smith, Suzanne Weaver; Beattie, Christopher A.

1991-01-01

On-orbit testing of a large space structure will be required to complete the certification of any mathematical model for the structure dynamic response. The process of establishing a mathematical model that matches measured structure response is referred to as model correlation. Most model correlation approaches have an identification technique to determine structural characteristics from the measurements of the structure response. This problem is approached with one particular class of identification techniques - matrix adjustment methods - which use measured data to produce an optimal update of the structure property matrix, often the stiffness matrix. New methods were developed for identification to handle problems of the size and complexity expected for large space structures. Further development and refinement of these secant-method identification algorithms were undertaken. Also, evaluation of these techniques is an approach for model correlation and damage location was initiated.

Longitudinal development of number line estimation and mathematics performance in primary school children.

PubMed

Friso-van den Bos, Ilona; Kroesbergen, Evelyn H; Van Luit, Johannes E H; Xenidou-Dervou, Iro; Jonkman, Lisa M; Van der Schoot, Menno; Van Lieshout, Ernest C D M

2015-06-01

Children's ability to relate number to a continuous quantity abstraction visualized as a number line is widely accepted to be predictive of mathematics achievement. However, a debate has emerged with respect to how children's placements are distributed on this number line across development. In the current study, different models were applied to children's longitudinal number placement data to get more insight into the development of number line representations in kindergarten and early primary school years. In addition, longitudinal developmental relations between number line placements and mathematical achievement, measured with a national test of mathematics, were investigated using cross-lagged panel modeling. A group of 442 children participated in a 3-year longitudinal study (ages 5-8 years) in which they completed a number-to-position task every 6 months. Individual number line placements were fitted to various models, of which a one-anchor power model provided the best fit for many of the placements at a younger age (5 or 6 years) and a two-anchor power model provided better fit for many of the children at an older age (7 or 8 years). The number of children who made linear placements also grew with age. Cross-lagged panel analyses indicated that the best fit was provided with a model in which number line acuity and mathematics performance were mutually predictive of each other rather than models in which one ability predicted the other in a non-reciprocal way. This indicates that number line acuity should not be seen as a predictor of math but that both skills influence each other during the developmental process. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

Mathematical Modeling of Rotary Blood Pumps in a Pulsatile In Vitro Flow Environment.

PubMed

Pirbodaghi, Tohid

2017-08-01

Nowadays, sacrificing animals to develop medical devices and receive regulatory approval has become more common, which increases ethical concerns. Although in vivo tests are necessary for development and evaluation of new devices, nonetheless, with appropriate in vitro setups and mathematical models, a part of the validation process can be performed using these models to reduce the number of sacrificed animals. The main aim of this study is to present a mathematical model simulating the hydrodynamic function of a rotary blood pump (RBP) in a pulsatile in vitro flow environment. This model relates the pressure head of the RBP to the flow rate, rotational speed, and time derivatives of flow rate and rotational speed. To identify the model parameters, an in vitro setup was constructed consisting of a piston pump, a compliance chamber, a throttle, a buffer reservoir, and the CentriMag RBP. A 40% glycerin-water mixture as a blood analog fluid and deionized water were used in the hydraulic circuit to investigate the effect of viscosity and density of the working fluid on the model parameters. First, model variables were physically measured and digitally acquired. Second, an identification algorithm based on regression analysis was used to derive the model parameters. Third, the completed model was validated with a totally different set of in vitro data. The model is usable for both mathematical simulations of the interaction between the pump and heart and indirect pressure measurement in a clinical context. © 2017 International Center for Artificial Organs and Transplantation and Wiley Periodicals, Inc.

Mathematical Modeling and Dynamic Simulation of Metabolic Reaction Systems Using Metabolome Time Series Data.

PubMed

Sriyudthsak, Kansuporn; Shiraishi, Fumihide; Hirai, Masami Yokota

2016-01-01

The high-throughput acquisition of metabolome data is greatly anticipated for the complete understanding of cellular metabolism in living organisms. A variety of analytical technologies have been developed to acquire large-scale metabolic profiles under different biological or environmental conditions. Time series data are useful for predicting the most likely metabolic pathways because they provide important information regarding the accumulation of metabolites, which implies causal relationships in the metabolic reaction network. Considerable effort has been undertaken to utilize these data for constructing a mathematical model merging system properties and quantitatively characterizing a whole metabolic system in toto. However, there are technical difficulties between benchmarking the provision and utilization of data. Although, hundreds of metabolites can be measured, which provide information on the metabolic reaction system, simultaneous measurement of thousands of metabolites is still challenging. In addition, it is nontrivial to logically predict the dynamic behaviors of unmeasurable metabolite concentrations without sufficient information on the metabolic reaction network. Yet, consolidating the advantages of advancements in both metabolomics and mathematical modeling remain to be accomplished. This review outlines the conceptual basis of and recent advances in technologies in both the research fields. It also highlights the potential for constructing a large-scale mathematical model by estimating model parameters from time series metabolome data in order to comprehensively understand metabolism at the systems level.

Mathematical Modeling of Torsional Surface Wave Propagation in a Non-Homogeneous Transverse Isotropic Elastic Solid Semi-Infinite Medium Under a Layer

NASA Astrophysics Data System (ADS)

Sethi, M.; Sharma, A.; Vasishth, A.

2017-05-01

The present paper deals with the mathematical modeling of the propagation of torsional surface waves in a non-homogeneous transverse isotropic elastic half-space under a rigid layer. Both rigidities and density of the half-space are assumed to vary inversely linearly with depth. Separation of variable method has been used to get the analytical solutions for the dispersion equation of the torsional surface waves. Also, the effects of nonhomogeneities on the phase velocity of torsional surface waves have been shown graphically. Also, dispersion equations have been derived for some particular cases, which are in complete agreement with some classical results.

The Mathematics of Navigating the Solar System

NASA Technical Reports Server (NTRS)

Hintz, Gerald

2000-01-01

In navigating spacecraft throughout the solar system, the space navigator relies on three academic disciplines - optimization, estimation, and control - that work on mathematical models of the real world. Thus, the navigator determines the flight path that will consume propellant and other resources in an efficient manner, determines where the craft is and predicts where it will go, and transfers it onto the optimal trajectory that meets operational and mission constraints. Mission requirements, for example, demand that observational measurements be made with sufficient precision that relativity must be modeled in collecting and fitting (the estimation process) the data, and propagating the trajectory. Thousands of parameters are now determined in near real-time to model the gravitational forces acting on a spacecraft in the vicinity of an irregularly shaped body. Completing these tasks requires mathematical models, analyses, and processing techniques. Newton, Gauss, Lambert, Legendre, and others are justly famous for their contributions to the mathematics of these tasks. More recently, graduate students participated in research to update the gravity model of the Saturnian system, including higher order gravity harmonics, tidal effects, and the influence of the rings. This investigation was conducted for the Cassini project to incorporate new trajectory modeling features in the navigation software. The resulting trajectory model will be used in navigating the 4-year tour of the Saturnian satellites. Also, undergraduate students are determining the ephemerides (locations versus time) of asteroids that will be used as reference objects in navigating the New Millennium's Deep Space 1 spacecraft autonomously.

A Multisite Study of High School Mathematics Curricula and the Impact of Taking a Developmental Mathematics Course in College

ERIC Educational Resources Information Center

Harwell, Michael; Dupuis, Danielle; Post, Thomas R.; Medhanie, Amanuel; LeBeau, Brandon

2014-01-01

The relationship between high school mathematics curricula and the likelihood of students who enroll in a developmental (non-credit bearing) course in college taking additional mathematics courses was studied. The results showed that high school mathematics curriculum, years of high school mathematics completed, and ACT mathematics scores were…

Abrupt Strategy Change Underlies Gradual Performance Change: Bayesian Hierarchical Models of Component and Aggregate Strategy Use

ERIC Educational Resources Information Center

Wynton, Sarah K. A.; Anglim, Jeromy

2017-01-01

While researchers have often sought to understand the learning curve in terms of multiple component processes, few studies have measured and mathematically modeled these processes on a complex task. In particular, there remains a need to reconcile how abrupt changes in strategy use can co-occur with gradual changes in task completion time. Thus,…

Multivariate Dynamical Modeling to Investigate Human Adaptation to Space Flight: Initial Concepts

NASA Technical Reports Server (NTRS)

Shelhamer, Mark; Mindock, Jennifer; Zeffiro, Tom; Krakauer, David; Paloski, William H.; Lumpkins, Sarah

2014-01-01

The array of physiological changes that occur when humans venture into space for long periods presents a challenge to future exploration. The changes are conventionally investigated independently, but a complete understanding of adaptation requires a conceptual basis founded in intergrative physiology, aided by appropriate mathematical modeling. NASA is in the early stages of developing such an approach.

Multivariate Dynamic Modeling to Investigate Human Adaptation to Space Flight: Initial Concepts

NASA Technical Reports Server (NTRS)

Shelhamer, Mark; Mindock, Jennifer; Zeffiro, Tom; Krakauer, David; Paloski, William H.; Lumpkins, Sarah

2014-01-01

The array of physiological changes that occur when humans venture into space for long periods presents a challenge to future exploration. The changes are conventionally investigated independently, but a complete understanding of adaptation requires a conceptual basis founded in integrative physiology, aided by appropriate mathematical modeling. NASA is in the early stages of developing such an approach.

An Examination of Interactive Whiteboard Perceptions using the Concerns-Based Adoption Model Stages of Concern and the Apple Classrooms of Tomorrow Model of Instructional Evolution

ERIC Educational Resources Information Center

Hall, Jeffrey; Chamblee, Gregory; Slough, Scott

2013-01-01

Two high school mathematics teachers who use Interactive Whiteboards (IWBs) in the classroom were interviewed annually over the course of three years regarding their perceptions of the technology. During the third year, the two teachers were asked to complete the Concerns-Based Adoption Model Stages of Concern Questionnaire. The data obtained from…

Temporal Subtraction of Digital Breast Tomosynthesis Images for Improved Mass Detection

DTIC Science & Technology

2009-11-01

imaging using two distinct methods7-15: mathematically based models defined by geometric primitives and voxelized models derived from real human...trees to complete them. We also plan to add further detail by defining the Cooper’s ligaments using geometrical NURBS surfaces. Realistic...generated model for the coronary arterial tree based on multislice CT and morphometric data," Medical Imaging 2006: Physics of Medical Imaging 6142

Heat pipe dynamic behavior

NASA Technical Reports Server (NTRS)

Issacci, F.; Roche, G. L.; Klein, D. B.; Catton, I.

1988-01-01

The vapor flow in a heat pipe was mathematically modeled and the equations governing the transient behavior of the core were solved numerically. The modeled vapor flow is transient, axisymmetric (or two-dimensional) compressible viscous flow in a closed chamber. The two methods of solution are described. The more promising method failed (a mixed Galerkin finite difference method) whereas a more common finite difference method was successful. Preliminary results are presented showing that multi-dimensional flows need to be treated. A model of the liquid phase of a high temperature heat pipe was developed. The model is intended to be coupled to a vapor phase model for the complete solution of the heat pipe problem. The mathematical equations are formulated consistent with physical processes while allowing a computationally efficient solution. The model simulates time dependent characteristics of concern to the liquid phase including input phase change, output heat fluxes, liquid temperatures, container temperatures, liquid velocities, and liquid pressure. Preliminary results were obtained for two heat pipe startup cases. The heat pipe studied used lithium as the working fluid and an annular wick configuration. Recommendations for implementation based on the results obtained are presented. Experimental studies were initiated using a rectangular heat pipe. Both twin beam laser holography and laser Doppler anemometry were investigated. Preliminary experiments were completed and results are reported.

Differences in the Mathematics-Vocabulary Knowledge of Fifth-Grade Students with and without Learning Difficulties

ERIC Educational Resources Information Center

Forsyth, Suzanne R.; Powell, Sarah R.

2017-01-01

The purpose of this pilot study was to explore the impact of mathematics and reading learning difficulties on the mathematics-vocabulary understanding of fifth-grade students. Students (n = 114) completed three measures: mathematics computation, general vocabulary, and mathematics vocabulary. Based on performance on the mathematics computation and…

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.

Perceptual Creativity: Where Inner and Outer Reality Come Together

ERIC Educational Resources Information Center

Dayton, Glenn C.

1976-01-01

Investigates two opposing views of creativity, that of the Freudian psychologists vs. the interpretation of humanistic psychologists, and offers a compromising, perhaps more gestalt solution, along with a new mathematical model and ideas for research in developing a more complete theory of creativity. (Author/RK)

Performance characteristics of the Cooper PC-9 centrifugal compressor

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

Foster, R.E.; Neely, R.F.

1988-06-30

Mathematical performance modeling of the PC-9 centrifugal compressor has been completed. Performance characteristics curves have never been obtained for them in test loops with the same degree of accuracy as for the uprated axial compressors and, consequently, computer modeling of the top cascade and purge cascades has been very difficult and of limited value. This compressor modeling work has been carried out in an attempt to generate data which would more accurately define the compressor's performance and would permit more accurate cascade modeling. A computer code, COMPAL, was used to mathematically model the PC-9 performance with variations in gas composition,more » flow ratios, pressure ratios, speed and temperature. The results of this effort, in the form of graphs, with information about the compressor and the code, are the subject of this report. Compressor characteristic curves are featured. 13 figs.« less

Simulating Bone Loss in Microgravity Using Mathematical Formulations of Bone Remodeling

NASA Technical Reports Server (NTRS)

Pennline, James A.

2009-01-01

Most mathematical models of bone remodeling are used to simulate a specific bone disease, by disrupting the steady state or balance in the normal remodeling process, and to simulate a therapeutic strategy. In this work, the ability of a mathematical model of bone remodeling to simulate bone loss as a function of time under the conditions of microgravity is investigated. The model is formed by combining a previously developed set of biochemical, cellular dynamics, and mechanical stimulus equations in the literature with two newly proposed equations; one governing the rate of change of the area of cortical bone tissue in a cross section of a cylindrical section of bone and one governing the rate of change of calcium in the bone fluid. The mechanical stimulus comes from a simple model of stress due to a compressive force on a cylindrical section of bone which can be reduced to zero to mimic the effects of skeletal unloading in microgravity. The complete set of equations formed is a system of first order ordinary differential equations. The results of selected simulations are displayed and discussed. Limitations and deficiencies of the model are also discussed as well as suggestions for further research.

Development and validation of a model of bio-barriers for remediation of Cr(VI) contaminated aquifers using laboratory column experiments.

PubMed

Shashidhar, T; Bhallamudi, S Murty; Philip, Ligy

2007-07-16

Bench scale transport and biotransformation experiments and mathematical model simulations were carried out to study the effectiveness of bio-barriers for the containment of hexavalent chromium in contaminated confined aquifers. Experimental results showed that a 10cm thick bio-barrier with an initial biomass concentration of 0.205mg/g of soil was able to completely contain a Cr(VI) plume of 25mg/L concentration. It was also observed that pore water velocity and initial biomass concentration are the most significant parameters in the containment of Cr(VI). The mathematical model developed is based on one-dimensional advection-dispersion reaction equations for Cr(VI) and molasses in saturated, homogeneous porous medium. The transport of Cr(VI) and molasses is coupled with adsorption and Monod's inhibition kinetics for immobile bacteria. It was found that, in general, the model was able to simulate the experimental results satisfactorily. However, there was disparity between the numerically simulated and experimental breakthrough curves for Cr(VI) and molasses in cases where there was high clay content and high microbial activity. The mathematical model could contribute towards improved designs of future bio-barriers for the remediation of Cr(VI) contaminated aquifers.

The Relation Between Inattentive and Hyperactive/Impulsive Behaviors and Early Mathematics Skills.

PubMed

Sims, Darcey M; Purpura, David J; Lonigan, Christopher J

2016-08-01

Despite strong evidence that inattentive and hyperactive/impulsive behaviors are associated with mathematical difficulties in school-age children, little research has been conducted to examine the link between these constructs before the start of formal education. The purpose of this study was to examine how different manifestations of inattentive and hyperactive/impulsive behaviors, as measured by different assessment tools, are related to early mathematics skills in preschoolers. Eighty-two preschool children completed a measure of early mathematics and the Continuous Performance Test (CPT). Teachers rated children's behaviors using the Conners' Teacher Rating Scale-15 Item. Sixty-five of these children completed mathematics assessments 1 year later. Teacher ratings of inattention were uniquely related to concurrent early mathematics skills, whereas CPT errors were uniquely predictive of early mathematics skills 1 year later. Findings have implications for the understanding and assessment of behavior problems that are associated with early mathematics difficulties. © The Author(s) 2012.

Birationality and Landau-Ginzburg Models

NASA Astrophysics Data System (ADS)

Clarke, Patrick

2017-08-01

We introduce a new technique for approaching birationality questions that arise in the mirror symmetry of complete intersections in toric varieties. As an application we answer affirmatively and conclusively the question of Batyrev-Nill (Integer points in polyhedra—geometry, number theory, representation theory, algebra, optimization, statistics, volume 452 of Contemporary mathematics. American Mathematical Society, Providence, pp 35-66, 2008) about the birationality of Calabi-Yau families associated to multiple mirror nef-partitions. This completes the progress in this direction made by Li's breakthrough (Li in Adv Math 299:71-107, 2016). In the process, we obtain results in the theory of Borisov's nef-partitions (Borisov in Towards the mirror symmetry for Calabi-Yau complete intersections in Gorenstein toric Fano varieties, 1993. arXiv:alg-geom/9310001 ) and provide new insight into the geometric content of the multiple mirror phenomenon.

Mathematics Problems from Ancient Egyptian Papyri

ERIC Educational Resources Information Center

Howard, Christopher A.

2009-01-01

Most high school mathematics teachers completed a mathematics history course in college, and many of them likely found it intriguing. Unfortunately, very few of them find the time to allow much, if any, mathematics history to trickle into their instruction. However, if mathematics history is taught effectively, students can see the connections…

"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…

``SO what Will you do if String Theory is WRONG?''

NASA Astrophysics Data System (ADS)

Emam, Moataz H.

2008-07-01

I briefly discuss the accomplishments of string theory that would survive a complete falsification of the theory as a model of nature and argue the possibility that such a survival may necessarily mean that string theory would become its own discipline, independently of both physics and mathematics.

Determining Dissolved Oxygen Levels

ERIC Educational Resources Information Center

Boucher, Randy

2010-01-01

This project was used in a mathematical modeling and introduction to differential equations course for first-year college students. The students worked in two-person groups and were given three weeks to complete the project. Students were given this project three weeks into the course, after basic first order linear differential equation and…

The Impact of Prior Mathematics Achievement on the Relationship between High School Mathematics Curricula and Postsecondary Mathematics Performance, Course-Taking, and Persistence

ERIC Educational Resources Information Center

Post, Thomas R.; Medhanie, Amanuel; Harwell, Michael; Norman, Ke Wu; Dupuis, Danielle N.; Muchlinski, Thomas; Andersen, Edwin; Monson, Debra

2010-01-01

This retrospective study examined the impact of prior mathematics achievement on the relationship between high school mathematics curricula and student postsecondary mathematics performance. The sample (N = 4,144 from 266 high schools) was partitioned into 3 strata by ACT mathematics scores. Students completing 3 or more years of a commercially…

Application of DIVWAG at Rodman Laboratory

DTIC Science & Technology

1976-03-01

Continue on reveree eide It neceaemry mnd identify by block number) DIVWAG War Game Simulation Mathematical Model 20. ABSTRACT (Continue on...parameters. Rodman Laboratory is using DIVWAG in a simulation mode. In this model of operation, once a game has been completed, a representative...a period of play by a blue (red) artillery battery as a function of range and game time). t Ü UNCLASSIFIED SECURITY CLASSIFICATION OF THIS

Development of a predictive model to estimate the effect of soil solarization on survival of soilborne inoculum of Phytophthora ramorum and Phytophthora pini

Treesearch

Fumiaki Funahashi; Jennifer L. Parke

2017-01-01

Soil solarization has been shown to be an effective tool to manage Phytophthora spp. within surface soils, but estimating the minimum time required to complete local eradication under variable weather conditions remains unknown. A mathematical model could help predict the effectiveness of solarization at different sites and soil depths....

Using a mathematical model to evaluate the efficacy of TB control measures.

PubMed Central

Gammaitoni, L.; Nucci, M. C.

1997-01-01

We evaluated the efficacy of recommended tuberculosis (TB) infection control measures by using a deterministic mathematical model for airborne contagion. We examined the percentage of purified protein derivative conversions under various exposure conditions, environmental controlstrategies, and respiratory protective devices. We conclude that environmental control cannot eliminate the risk for TB transmission during high-risk procedures; respiratory protective devices, and particularly high-efficiency particulate air masks, may provide nearly complete protection if used with air filtration or ultraviolet irradiation. Nevertheless, the efficiency of these control measures decreases as the infectivity of the source case increases. Therefore, administrative control measures (e.g., indentifying and isolating patients with infectious TB) are the most effective because they substantially reduce the rate of infection. PMID:9284378

Mathematical model for HIV spreads control program with ART treatment

NASA Astrophysics Data System (ADS)

Maimunah; Aldila, Dipo

2018-03-01

In this article, using a deterministic approach in a seven-dimensional nonlinear ordinary differential equation, we establish a mathematical model for the spread of HIV with an ART treatment intervention. In a simplified model, when no ART treatment is implemented, disease-free and the endemic equilibrium points were established analytically along with the basic reproduction number. The local stability criteria of disease-free equilibrium and the existing criteria of endemic equilibrium were analyzed. We find that endemic equilibrium exists when the basic reproduction number is larger than one. From the sensitivity analysis of the basic reproduction number of the complete model (with ART treatment), we find that the increased number of infected humans who follow the ART treatment program will reduce the basic reproduction number. We simulate this result also in the numerical experiment of the autonomous system to show how treatment intervention impacts the reduction of the infected population during the intervention time period.

Vicissitudes of Children's Mathematical Knowledge: Implications of Developmental Research for Early Childhood Mathematics Education

ERIC Educational Resources Information Center

Sophian, Catherine

2013-01-01

Hachey's (2013) article celebrates a revolution that is taking place in early childhood mathematics education, fueled in part by developmental research demonstrating the mathematical capabilities of young children. At the same time, Hachey notes that the mathematics revolution she describes is not yet complete. In this commentary, the author…

Computer Mathematics: An Introduction. Part II.

ERIC Educational Resources Information Center

New York City Board of Education, Brooklyn, NY. Div. of Curriculum and Instruction.

This document describes a mathematics course that uses the computer to solve mathematics problems. It was developed to be used with students who have completed at least one year of general mathematics or are not achieving success in the traditional mathematics program. The course is intended to review, reinforce, and extend concepts included in…

Romance of a Mathematician: Celebrating St Valentine's Day in a Mathematics Class

ERIC Educational Resources Information Center

Hekimoglu, Serkan

2005-01-01

Mathematics should not be studied simply because it is useful; mathematics should be also studied because it nurtures both the mind and soul with its beauty. By completing the four activities described in this paper, students will appreciate mathematical ideas both rationally and emotionally. Since students' appreciation of mathematical ideas…

32 CFR 901.5 - Academic examination requirements.

Code of Federal Regulations, 2010 CFR

2010-07-01

... Level 1 (Standard) Mathematics or Level II (Intensive) Mathematics. (Level 1 recommended for candidates without advanced high school mathematics.) (b) ACT. Candidates who elect to use the ACT tests must take the complete battery of tests: English, mathematics, social studies, and natural sciences. ...

Determination of minimum enzymatic decolorization time of reactive dye solution by spectroscopic & mathematical approach.

PubMed

Celebi, Mithat; Ozdemir, Zafer Omer; Eroglu, Emre; Altikatoglu, Melda; Guney, Ibrahim

2015-02-01

Synthetic dyes are very important for textile dyeing, paper printing, color photography and petroleum products. Traditional methods of dye removal include biodegradation, precipitation, adsorption, chemical degradation, photo degradation, and chemical coagulation. Dye decolorization with enzymatic reaction is an important issue for several research field (chemistry, environment) In this study, minimum decolorization time of Remazol Brilliant Blue R dye with Horseradish peroxidase enzyme was calculated using with mathematical equation depending on experimental data. Dye decolorization was determined by monitoring the absorbance decrease at the specific maximum wavelength for dye. All experiments were carried out with different initial dye concentrations of Remazol Brilliant Blue R at 25 degrees C constant temperature for 30 minutes. The development of the least squares estimators for a nonlinear model brings about complications not encountered in the case of the linear model. Decolorization times for completely removal of dye were calculated according to equation. It was shown that mathematical equation was conformed exponential curve for dye degradation.

Poly (lactic-co-glycolic acid) controlled release systems: experimental and modeling insights

PubMed Central

Hines, Daniel J.; Kaplan, David L.

2013-01-01

Poly-lactic-co-glycolic acid (PLGA) has been the most successful polymeric biomaterial for use in controlled drug delivery systems. There are several different chemical and physical properties of PLGA that impact the release behavior of drugs from PLGA delivery devices. These properties must be considered and optimized in drug release device formulation. Mathematical modeling is a useful tool for identifying, characterizing, and predicting the mechanisms of controlled release. The advantages and limitations of poly (lactic-co-glycolic acid) for controlled release are reviewed, followed by a review of current approaches in controlled release technology that utilize PLGA. Mathematical modeling applied towards controlled release rates from PLGA-based devices will also be discussed to provide a complete picture of state of the art understanding of the control achievable with this polymeric system, as well as the limitations. PMID:23614648

Predicting Scientific Understanding of Prospective Elementary Teachers: Role of Gender, Education Level, Courses in Science, and Attitudes Toward Science and Mathematics

NASA Astrophysics Data System (ADS)

Kumar, David D.; Morris, John D.

2005-12-01

A multiple regression analysis of the relationship between prospective teachers' scientific understanding and Gender, Education Level (High School, College), Courses in Science (Biology, Chemistry, Physics, Earth Science, Astronomy, and Agriculture), Attitude Towards Science, and Attitude Towards Mathematics is reported. Undergraduate elementary science students ( N = 176) in an urban doctoral-level university in the United States participated in this study. The results of this study showed Gender, completion of courses in High School Chemistry and Physics, College Chemistry and Physics, and Attitudes Toward Mathematics and Science significantly correlated with scientific understanding. Based on a regression model, Gender, and College Chemistry and Physics experiences added significant predictive accuracy to scientific understanding among prospective elementary teachers compared to the other variables.

On two mathematical problems of canonical quantization. IV

NASA Astrophysics Data System (ADS)

Kirillov, A. I.

1992-11-01

A method for solving the problem of reconstructing a measure beginning with its logarithmic derivative is presented. The method completes that of solving the stochastic differential equation via Dirichlet forms proposed by S. Albeverio and M. Rockner. As a result one obtains the mathematical apparatus for the stochastic quantization. The apparatus is applied to prove the existence of the Feynman-Kac measure of the sine-Gordon and λφ2n/(1 + K2φ2n)-models. A synthesis of both mathematical problems of canonical quantization is obtained in the form of a second-order martingale problem for vacuum noise. It is shown that in stochastic mechanics the martingale problem is an analog of Newton's second law and enables us to find the Nelson's stochastic trajectories without determining the wave functions.

Integrability in heavy quark effective theory

NASA Astrophysics Data System (ADS)

Braun, Vladimir M.; Ji, Yao; Manashov, Alexander N.

2018-06-01

It was found that renormalization group equations in the heavy-quark effective theory (HQET) for the operators involving one effective heavy quark and light degrees of freedom are completely integrable in some cases and are related to spin chain models with the Hamiltonian commuting with the nondiagonal entry C( u) of the monodromy matrix. In this work we provide a more complete mathematical treatment of such spin chains in the QISM framework. We also discuss the relation of integrable models that appear in the HQET context with the large-spin limit of integrable models in QCD with light quarks. We find that the conserved charges and the "ground state" wave functions in HQET models can be obtained from the light-quark counterparts in a certain scaling limit.

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 modelling process for large metabolic networks. From this, users can simulate their pathway of interest and obtain a better understanding of how altering conditions influences cellular dynamics. By testing the effects of different parameterisations we are also able to provide suggestions to help construct more accurate models of complete metabolic systems in the future.

Truth, models, model sets, AIC, and multimodel inference: a Bayesian perspective

USGS Publications Warehouse

Barker, Richard J.; Link, William A.

2015-01-01

Statistical inference begins with viewing data as realizations of stochastic processes. Mathematical models provide partial descriptions of these processes; inference is the process of using the data to obtain a more complete description of the stochastic processes. Wildlife and ecological scientists have become increasingly concerned with the conditional nature of model-based inference: what if the model is wrong? Over the last 2 decades, Akaike's Information Criterion (AIC) has been widely and increasingly used in wildlife statistics for 2 related purposes, first for model choice and second to quantify model uncertainty. We argue that for the second of these purposes, the Bayesian paradigm provides the natural framework for describing uncertainty associated with model choice and provides the most easily communicated basis for model weighting. Moreover, Bayesian arguments provide the sole justification for interpreting model weights (including AIC weights) as coherent (mathematically self consistent) model probabilities. This interpretation requires treating the model as an exact description of the data-generating mechanism. We discuss the implications of this assumption, and conclude that more emphasis is needed on model checking to provide confidence in the quality of inference.

Pre-service science teachers' perceptions of mathematics courses in a science teacher education programme

NASA Astrophysics Data System (ADS)

Incikabi, Lutfi; Serin, Mehmet Koray

2017-08-01

Most science departments offer compulsory mathematics courses to their students with the expectation that students can apply their experience from the mathematics courses to other fields of study, including science. The current study first aims to investigate the views of pre-service science teachers of science-teaching preparation degrees and their expectations regarding the difficulty level of mathematics courses in science-teaching education programmes. Second, the study investigates changes and the reasons behind the changes in their interest regarding mathematics after completing these courses. Third, the current study seeks to reveal undergraduate science teachers' opinions regarding the contribution of undergraduate mathematics courses to their professional development. Being qualitative in nature, this study was a case study. According to the results, almost all of the students considered that undergraduate mathematics courses were 'difficult' because of the complex and intensive content of the courses and their poor background mathematical knowledge. Moreover, the majority of science undergraduates mentioned that mathematics would contribute to their professional development as a science teacher. On the other hand, they declared a negative change in their attitude towards mathematics after completing the mathematics courses due to continuous failure at mathematics and their teachers' lack of knowledge in terms of teaching mathematics.

Physiological responses at five estimates of critical velocity.

PubMed

Bull, Anthony J; Housh, Terry J; Johnson, Glen O; Rana, Sharon R

2008-04-01

The purpose of this study was to compare critical velocity (CV) estimates from five mathematical models, and to examine the oxygen uptake (VO(2)) and heart rate (HR) responses during treadmill runs at the five estimates of CV. Ten subjects (six males and four females) performed one incremental test to determine maximal oxygen consumption (VO(2max)) and four or five randomly ordered constant-velocity trials on a treadmill for the estimation of CV. Five mathematical models were used to estimate CV for each subject including two linear, two nonlinear, and an exponential model. Up to five randomly ordered runs to exhaustion were performed by each subject at treadmill velocities that corresponded to the five CV estimates, and VO(2) and HR responses were monitored throughout each trial. The 3-parameter, nonlinear (Non-3) model produced CV estimates that were significantly (P < 0.05) less than the other four models. During runs at CV estimates, five subjects did not complete 60 min at the their estimate from the Non-3 model, nine did not complete 60 min at their estimate from the Non-2 model, and no subjects completed 60 min at any estimate from the other three models. The mean HR value (179 +/- 18 beats min(-1), HR(peak)) at the end of runs at CV using the Non-3 model was significantly less than the maximal HR (195 +/- 7 beats min(-1), HR(max)) achieved during the incremental trial to exhaustion. However, mean HR(peak) values from runs at all other CV estimates were not significantly different from HR(max). Furthermore, data indicated that mean HR(peak) values increased during runs at CV estimates from the third minute to the end of exercise for all models, and that these increases in VO(2) (range = 367-458 ml min(-1)) were significantly greater than that typically associated with O(2) drift ( approximately 200 ml min(-1)) for all but the exponential model, indicating a VO(2) slow component associated with CV estimates from four of the five models. However, the mean VO(2) values at the end of exercise during the runs at CV estimates for all five mathematical models were significantly less than the mean VO(2max) value. These results suggest that, in most cases, CV estimated from the five models does not represent a fatigueless task. In addition, the mean CV estimates from the five models varied by 18%, and four of the five mean CV estimates were within the heavy exercise domain. Therefore, CV would not represent the demarcation point between heavy and severe exercise domains.

Mathematical and computational model for the analysis of micro hybrid rocket motor

NASA Astrophysics Data System (ADS)

Stoia-Djeska, Marius; Mingireanu, Florin

2012-11-01

The hybrid rockets use a two-phase propellant system. In the present work we first develop a simplified model of the coupling of the hybrid combustion process with the complete unsteady flow, starting from the combustion port and ending with the nozzle. The physical and mathematical model are adapted to the simulations of micro hybrid rocket motors. The flow model is based on the one-dimensional Euler equations with source terms. The flow equations and the fuel regression rate law are solved in a coupled manner. The platform of the numerical simulations is an implicit fourth-order Runge-Kutta second order cell-centred finite volume method. The numerical results obtained with this model show a good agreement with published experimental and numerical results. The computational model developed in this work is simple, computationally efficient and offers the advantage of taking into account a large number of functional and constructive parameters that are used by the engineers.

Comparison of Virginia's 2009 Mathematics Standards of Learning with the Common Core State Standards for Mathematics

ERIC Educational Resources Information Center

Virginia Department of Education, 2011

2011-01-01

This first draft of the "Comparison of Virginia's 2009 Mathematics Standards of Learning (SOL) with the Common Core State Standards (CCSS) for Mathematics" provides a side-by-side overview demonstrating how the 2009 Mathematics SOL are aligned to the CCSS. The comparison was made using Virginia's complete standards program for supporting…

The Effects of Motivation, Perceived Learning Strategy Use, and Mathematics Anxiety on the Mathematics Competency of Postsecondary Developmental Mathematics Students

ERIC Educational Resources Information Center

Grassl, Rebecca

2010-01-01

Mathematics competency continues to limit the success of many students and prevents their completion of a postsecondary degree, which ultimately prevents access to education, jobs, and upward social mobility. Furthermore, many postsecondary institutions admit students who do not meet the institution's mathematics proficiency requirements and then…

Mathematics Anxiety and Statistics Anxiety. Shared but Also Unshared Components and Antagonistic Contributions to Performance in Statistics

PubMed Central

Paechter, Manuela; Macher, Daniel; Martskvishvili, Khatuna; Wimmer, Sigrid; Papousek, Ilona

2017-01-01

In many social science majors, e.g., psychology, students report high levels of statistics anxiety. However, these majors are often chosen by students who are less prone to mathematics and who might have experienced difficulties and unpleasant feelings in their mathematics courses at school. The present study investigates whether statistics anxiety is a genuine form of anxiety that impairs students' achievements or whether learners mainly transfer previous experiences in mathematics and their anxiety in mathematics to statistics. The relationship between mathematics anxiety and statistics anxiety, their relationship to learning behaviors and to performance in a statistics examination were investigated in a sample of 225 undergraduate psychology students (164 women, 61 men). Data were recorded at three points in time: At the beginning of term students' mathematics anxiety, general proneness to anxiety, school grades, and demographic data were assessed; 2 weeks before the end of term, they completed questionnaires on statistics anxiety and their learning behaviors. At the end of term, examination scores were recorded. Mathematics anxiety and statistics anxiety correlated highly but the comparison of different structural equation models showed that they had genuine and even antagonistic contributions to learning behaviors and performance in the examination. Surprisingly, mathematics anxiety was positively related to performance. It might be that students realized over the course of their first term that knowledge and skills in higher secondary education mathematics are not sufficient to be successful in statistics. Part of mathematics anxiety may then have strengthened positive extrinsic effort motivation by the intention to avoid failure and may have led to higher effort for the exam preparation. However, via statistics anxiety mathematics anxiety also had a negative contribution to performance. Statistics anxiety led to higher procrastination in the structural equation model and, therefore, contributed indirectly and negatively to performance. Furthermore, it had a direct negative impact on performance (probably via increased tension and worry in the exam). The results of the study speak for shared but also unique components of statistics anxiety and mathematics anxiety. They are also important for instruction and give recommendations to learners as well as to instructors. PMID:28790938

Mathematics Anxiety and Statistics Anxiety. Shared but Also Unshared Components and Antagonistic Contributions to Performance in Statistics.

PubMed

Paechter, Manuela; Macher, Daniel; Martskvishvili, Khatuna; Wimmer, Sigrid; Papousek, Ilona

2017-01-01

In many social science majors, e.g., psychology, students report high levels of statistics anxiety. However, these majors are often chosen by students who are less prone to mathematics and who might have experienced difficulties and unpleasant feelings in their mathematics courses at school. The present study investigates whether statistics anxiety is a genuine form of anxiety that impairs students' achievements or whether learners mainly transfer previous experiences in mathematics and their anxiety in mathematics to statistics. The relationship between mathematics anxiety and statistics anxiety, their relationship to learning behaviors and to performance in a statistics examination were investigated in a sample of 225 undergraduate psychology students (164 women, 61 men). Data were recorded at three points in time: At the beginning of term students' mathematics anxiety, general proneness to anxiety, school grades, and demographic data were assessed; 2 weeks before the end of term, they completed questionnaires on statistics anxiety and their learning behaviors. At the end of term, examination scores were recorded. Mathematics anxiety and statistics anxiety correlated highly but the comparison of different structural equation models showed that they had genuine and even antagonistic contributions to learning behaviors and performance in the examination. Surprisingly, mathematics anxiety was positively related to performance. It might be that students realized over the course of their first term that knowledge and skills in higher secondary education mathematics are not sufficient to be successful in statistics. Part of mathematics anxiety may then have strengthened positive extrinsic effort motivation by the intention to avoid failure and may have led to higher effort for the exam preparation. However, via statistics anxiety mathematics anxiety also had a negative contribution to performance. Statistics anxiety led to higher procrastination in the structural equation model and, therefore, contributed indirectly and negatively to performance. Furthermore, it had a direct negative impact on performance (probably via increased tension and worry in the exam). The results of the study speak for shared but also unique components of statistics anxiety and mathematics anxiety. They are also important for instruction and give recommendations to learners as well as to instructors.

Vocational Assessment of Students with Disadvantages: Their Peculiar Needs.

ERIC Educational Resources Information Center

Nolte, Deborah

A study examined the underlying factor structure of the aptitude tests and work samples being completed by students with educational disadvantages (limited reading and mathematics skills) who were assessed with the current assessment model in the Akron (Ohio) Public Schools. The amount of variance accounted for by the factors was also…

The Influence of Race-Ethnicity and Physical Activity Levels on Elementary School Achievement

ERIC Educational Resources Information Center

Caldas, Stephen J.; Reilly, Monique S.

2018-01-01

The authors used structural equation modeling to map the relationships between student race-ethnicity via the mediating variable physical activity on English language arts (ELA) and mathematics achievement among 964 fourth- and fifth-grade students. The students attended a New York City Metropolitan area school district and completed the Physical…

Increasing Persistence in Undergraduate Science Majors: A Model for Institutional Support of Underrepresented Students

ERIC Educational Resources Information Center

Toven-Lindsey, Brit; Levis-Fitzgerald, Marc; Barber, Paul H.; Hasson, Tama

2015-01-01

The 6-yr degree-completion rate of undergraduate science, technology, engineering, and mathematics (STEM) majors at U.S. colleges and universities is less than 40%. Persistence among women and underrepresented minorities (URMs), including African-American, Latino/a, Native American, and Pacific Islander students, is even more troubling, as these…

Effects of physical activity and breaks on mathematics engagement in adolescents.

PubMed

Owen, Katherine B; Parker, Philip D; Astell-Burt, Thomas; Lonsdale, Chris

2018-01-01

The purpose of this study was to determine whether physical activity has a positive relationship with school engagement regardless of the presence or absence of a recess or lunch break before the classroom lesson. Data were collected over three ten-week periods: January-April 2014 (Time 1), October-December 2014 (Time 2), and April-June 2015 (Time 3). A cohort of 2194 adolescents (mean age=13.40years, SD=.73) wore an accelerometer during the hour before a mathematics lesson and completed a questionnaire following the mathematics lesson to assess school engagement in that lesson. Linear mixed models indicated that moderate-intensity activity before a mathematics lesson had a positive linear relationship with cognitive engagement (β=.40, p<.05). Recess breaks before a mathematics lesson had a negative relationship with overall, behavioural, emotional, and cognitive engagement (β=-.18, p<.01, β=-.19, p<.01, β=-.13, p=.03, and β=-.13, p=.04, respectively). Promoting moderate-intensity activity prior to mathematics lessons could improve students' cognitive engagement. Educators should be aware that students tend to demonstrate the lowest levels of school engagement after recess breaks. Crown Copyright © 2017. Published by Elsevier Ltd. All rights reserved.

Integrating First-Year Technology and Finite Mathematics Courses

ERIC Educational Resources Information Center

Shafii-Mousavi, Morteza; Kochanowski, Paul

2006-01-01

This paper describes an interdisciplinary project-based mathematics course linked to a computer technology course. The linkage encourages an appreciation of mathematics and technology as students see an immediate use for these skills in completing actual real-world projects. Linking mathematics and technology integrates subjects taught in…

Middle School Children's Mathematical Reasoning and Proving Schemes

ERIC Educational Resources Information Center

Liu, Yating; Manouchehri, Azita

2013-01-01

In this work we explored proof schemes used by 41 middle school students when confronted with four mathematical propositions that demanded verification of accuracy of statements. The students' perception of mathematically complete vs. convincing arguments in different mathematics branches was also elicited. Lastly, we considered whether the…

Flawed Mathematical Conceptualizations: Marlon's Dilemma

ERIC Educational Resources Information Center

Garrett, Lauretta

2013-01-01

Adult developmental mathematics students often work under great pressure to complete the mathematics sequences designed to help them achieve success (Bryk & Treisman, 2010). Results of a teaching experiment demonstrate how the ability to reason can be impeded by flaws in students' mental representations of mathematics. The earnestness of the…

Mathematics Intervention for Prevention of Neurocognitive Deficits in Childhood Leukemia

PubMed Central

Moore (Ki), Ida M.; Hockenberry, Marilyn J.; Anhalt, Cynthia; McCarthy, Kathy; Krull, Kevin R.

2011-01-01

Background Despite evidence that CNS treatment is associated with cognitive and academic impairment, interventions to prevent or mitigate these problems are limited. The purpose was to determine if early intervention can prevent declines in mathematics abilities. Procedures Fifty-seven children with ALL were enrolled and randomized to a Mathematics Intervention or Standard Care. Subjects completed neurocognitive assessments prior to the intervention, post intervention, and one year later. Parents received written results and recommendations for use with their school. The Mathematics Intervention was based on Multiple Representation Theory and delivered individually over one year. Results Thirty-two of 57 subjects completed the study and were included in data analyses. These 32 subjects completed all neurocognitive assessments and, for those in the intervention group, 40–50 hours of the mathematics intervention. There were no group differences on relevant demographic variables; risk stratification; number of intrathecal methotrexate injections or high dose systemic methotrexate. Significant improvements in calculation and applied mathematics from baseline to post-intervention (p = 0.003 and 0.002, respectively) and in visual working memory from baseline to one year follow-up (p = 0.02) were observed in the Intervention but not the Standard Care group. Results from repeated measures ANOVA demonstrated significant between group differences for applied mathematics (F[2, 29] 12.47, p<0.001) and visual working memory (F[2 29]= 5.53, p=0.009). Conclusions The Mathematics Intervention improved mathematics abilities and visual working memory compared to standard care. Future studies are needed to translate the Mathematics Intervention into a “virtual” delivery method more readily available to parents and children. PMID:21938763

Mathematics intervention for prevention of neurocognitive deficits in childhood leukemia.

PubMed

Moore, Ida M; Hockenberry, Marilyn J; Anhalt, Cynthia; McCarthy, Kathy; Krull, Kevin R

2012-08-01

Despite evidence that CNS treatment is associated with cognitive and academic impairment, interventions to prevent or mitigate these problems are limited. The purpose was to determine if early intervention can prevent declines in mathematics abilities. Fifty-seven children with ALL were enrolled and randomized to a Mathematics Intervention or Standard Care. Subjects completed neurocognitive assessments prior to the intervention, post-intervention, and 1 year later. Parents received written results and recommendations for use with their school. The Mathematics Intervention was based on Multiple Representation Theory and delivered individually over 1 year. Thirty-two of 57 subjects completed the study and were included in data analyses. These 32 subjects completed all neurocognitive assessments and, for those in the Intervention Group, 40-50 hours of the Mathematics Intervention. There were no group differences on relevant demographic variables; risk stratification; number of intrathecal methotrexate injections; or high dose systemic methotrexate. Significant improvements in calculation and applied mathematics from Baseline to Post-Intervention (P = 0.003 and 0.002, respectively) and in visual working memory from Baseline to 1 year Follow-up (P = 0.02) were observed in the Intervention but not the Standard Care Group. Results from repeated measures ANOVA demonstrated significant between group differences for applied mathematics [F(2,29) = 12.47, P < 0.001] and visual working memory [F(2,29) = 5.53, P = 0.009]. The Mathematics Intervention improved mathematics abilities and visual working memory compared to standard care. Future studies are needed to translate the Mathematics Intervention into a "virtual" delivery method more readily available to parents and children. Copyright © 2011 Wiley Periodicals, Inc.

Dynamics of Cooperation in a Task Completion Social Dilemma

PubMed Central

Passino, Kevin M.

2017-01-01

We study the situation where the members of a community have the choice to participate in the completion of a common task. The process of completing the task involves only costs and no benefits to the individuals that participate in this process. However, completing the task results in changes that significantly benefit the community and that exceed the participation efforts. A task completion social dilemma arises when the short-term participation costs dissipate any interest in the community members to contribute to the task completion process and therefore to obtain the benefits that result from completing the task. In this work, we model the task completion problem using a dynamical system that characterizes the participation dynamics in the community and the task completion process. We show how this model naturally allows for the incorporation of several mechanisms that facilitate the emergence of cooperation and that have been studied in previous research on social dilemmas, including communication across a network, and indirect reciprocity through relative reputation. We provide mathematical analyses and computer simulations to study the qualitative properties of the participation dynamics in the community for different scenarios. PMID:28125721

Using confirmatory factor analysis to validate the Chamberlin affective instrument for mathematical problem solving with academically advanced students.

PubMed

Chamberlin, Scott A; Moore, Alan D; Parks, Kelly

2017-09-01

Student affect plays a considerable role in mathematical problem solving performance, yet is rarely formally assessed. In this manuscript, an instrument and its properties are discussed to enable educational psychologists the opportunity to assess student affect. The study was conducted to norm the CAIMPS (instrument) with gifted students. In so doing, educational psychologists are informed of the process and the instrument's properties. The sample was comprised of 160 middle-grade (7 and 8) students, identified as gifted, in the United States. After completing one of four model-eliciting activities (MEAs), all participants completed the CAIMPS (Chamberlin Affective Instrument for Mathematical Problem Solving). Data were analysed using confirmatory factor analysis to ascertain the number of factors in the instrument. The normed fit index (0.6939), non-normed fit index (0.8072), and root mean square error approximation (.076) were at or near the acceptable levels. Alpha levels for factors were also robust (.637-.923). Data suggest that the instrument was a good fit for use with mathematics students in middle grades when solving problems. Perhaps the most impressive characteristic of the instrument was that the four factors (AVI: anxiety, value, and interest), SS (self-efficacy and self-esteem), ASP (aspiration), and ANX (anxiety) did not correlate highly with one another, which defies previous hypotheses in educational psychology. © 2017 The British Psychological Society.

From Parental Involvement to Children's Mathematical Performance: The Role of Mathematics Anxiety

ERIC Educational Resources Information Center

Vukovic, Rose K.; Roberts, Steven O.; Green Wright, Linnie

2013-01-01

This study examined whether children's mathematics anxiety serves as an underlying pathway between parental involvement and children's mathematics achievement. Participants included 78 low-income, ethnic minority parents and their children residing in a large urban center in the northeastern United States. Parents completed a short survey tapping…

Applied Mathematics in the Undergraduate Curriculum.

ERIC Educational Resources Information Center

Committee on the Undergraduate Program in Mathematics, Berkeley, CA.

After considering the growth in the use of mathematics in the past 25 years, this report makes four major recommendations regarding the undergraduate curriculum: (1) The mathematics department should offer a course or two in applied mathematics which treat some realistic situations completely, including the steps of problem formulation, model…

Undergraduate Students' Conceptions of Mathematics: An International Study

ERIC Educational Resources Information Center

Petocz, Peter; Reid, Anna; Wood, Leigh N.; Smith, Geoff H.; Mather, Glyn; Harding, Ansie; Engelbrecht, Johann; Houston, Ken; Hillel, Joel; Perrett, Gillian

2007-01-01

In this paper, we report on an international study of undergraduate mathematics students; conceptions of mathematics. Almost 1,200 students in five countries completed a short survey including three open-ended questions asking about their views of mathematics and its role in their future studies and planned professions. Responses were analysed…

Educational Research and Planning as a Career Option for a Mathematics Major.

ERIC Educational Resources Information Center

Tatham, Elaine L.

The author describes her career development from mathematics instructor to director of institutional research at a large community college. She discusses the impact of mathematics on her career, illustrates her present job by describing three recently completed research projects, and strongly recommends that mathematics instructors encourage some…

Friend Influence and Susceptibility to Influence: Changes in Mathematical Reasoning as a Function of Relative Peer Acceptance and Interest in Mathematics

ERIC Educational Resources Information Center

DeLay, Dawn; Laursen, Brett; Kiuru, Noona; Poikkeus, Anna-Maija; Aunola, Kaisa

2016-01-01

This study investigated friend influence over mathematics achievement in 202 same-sex friendship dyads (106 girl dyads). Participants were in the third grade (around age 9) at the outset. Each friend completed a questionnaire describing interest in mathematics and a standardized mathematical reasoning assessment. Peer nominations provided a…

A Core Curriculum: Making Mathematics Count for Everyone. Curriculum and Evaluation Standards for School Mathematics Addenda Series, Grades 9-12.

ERIC Educational Resources Information Center

Meiring, Steven P.; And Others

The 1989 document, "Curriculum and Evaluation Standards for School Mathematics," provides a vision and a framework for revising and strengthening the K-12 mathematics curriculum in North American schools and for evaluating both the mathematics curriculum and students' progress. When completed, it is expected that the Addenda Series will…

In-vitro development of vitrified-warmed bovine oocytes after activation may be predicted based on mathematical modelling of cooling and warming rates during vitrification, storage and sample removal.

PubMed

Sansinena, Marina; Santos, Maria Victoria; Chirife, Jorge; Zaritzky, Noemi

2018-05-01

Heat transfer during cooling and warming is difficult to measure in cryo-devices; mathematical modelling is an alternative method that can describe these processes. In this study, we tested the validity of one such model by assessing in-vitro development of vitrified and warmed bovine oocytes after parthenogenetic activation and culture. The viability of oocytes vitrified in four different cryo-devices was assessed. Consistent with modelling predictions, oocytes vitrified using cryo-devices with the highest modelled cooling rates had significantly (P < 0.05) better cleavage and blastocyst formation rates. We then evaluated a two-step sample removal process, in which oocytes were held in nitrogen vapour for 15 s to simulate sample identification during clinical application, before being removed completely and warmed. Oocytes exposed to this procedure showed reduced developmental potential, according to the model, owing to thermodynamic instability and devitrification at relatively low temperatures. These findings suggest that cryo-device selection and handling, including method of removal from nitrogen storage, are critical to survival of vitrified oocytes. Limitations of the study include use of parthenogenetically activated rather than fertilized ova and lack of physical measurement of recrystallization. We suggest mathematical modelling could be used to predict the effect of critical steps in cryopreservation. Copyright © 2018 Reproductive Healthcare Ltd. Published by Elsevier Ltd. All rights reserved.

Effects of role models from films on short-term ratings of intent, interest, and self-assessment of ability by high school youth: a study of gender-stereotyped academic subjects.

PubMed

Ziegler, Albert; Stoeger, Heidrun

2008-04-01

The effects of cinematic female role models on self-confidence in own abilities, interest, and academic elective intents of secondary school pupils were analyzed in two studies. In Study 1 the participants (N = 283) were randomly assigned to 1 of 3 groups. Each group watched a film after which they completed a questionnaire. In Film 1 the lead female character demonstrated conventional female characteristics and was discernibly untalented in mathematics and the natural sciences, in Film 2 the lead female character did not exhibit conventional female characteristics and was gifted in mathematics and the natural sciences, and in Film 3 the lead female character was typically female and gifted in mathematics and the natural sciences. Film 3, in which the lead female character not only contradicted the stereotype of women not being gifted at mathematics and the natural sciences but also should not have elicited subtyping processes, turned out to be effective among girls with High prior interest and boys in general. In contrast, this film had unexpected effects among girls with Low prior interest. Instead of showing, as expected, merely weaker effects than those found for the other groups, this role model even had a deterrent effect on girls with Low prior interest. In Study 2 (N = 55) an investigation assessed whether Film 3 could exercise a similarly positive effect on female pupils with Low prior interest were a female role model to depict constructive coping with difficulties in mathematics and the natural sciences prior to the presentation of the film. Results show this is possible.

An experimental investigation of the unsteady response of a stator located downstream of a propeller ingesting broadband turbulence

NASA Astrophysics Data System (ADS)

Lynch, Denis Aloysius, III

This experimental investigation examined the unsteady response of a stator located downstream of a four- or ten-bladed propeller encountering broadband turbulence. The response is manifested in a radiated acoustic field which can be directly attributed to the unsteady surface pressure loading on the stator by the turbulent flowfield. In order to characterize the unsteady response of the stator, a thorough analysis of the turbulent flowfield downstream of the propeller was completed. The analysis of the turbulent flowfield is organized in a manner which reflects the causal relationship between influences on the flowfield and the evolution of the flowfield itself. Mathematical models for each of these contributions, including the broadband and periodic contributions of the propeller wakes and modification of the inflow turbulence by the propeller, are presented and analyzed. A further mathematical model involving the prediction of correlation length scale aids in the accurate prediction of the radiated acoustic pressure based solely on fundamental turbulent flowfield measurements. Unsteady surface pressure measurements, originally intended to provide additional information about the response of the stator as it relates to the incoming flowfield, were found to be heavily contaminated by vibrational effects. Therefore, techniques involving cross-correlation measurements are developed to mathematically isolate the unsteady pressure signal. The success of these techniques suggests the strong possibility of future application in this area. Finally, the mathematical models developed to describe the flowfield downstream of the propeller are applied to the case of a twenty-bladed propeller. This case was selected due to the anticipated increased levels of modification of the inflow turbulence. Results provide further evidence that this complex flowfield may be fully and accurately represented using simple mathematical models supported by baseline empirical information.

A generalized network flow model for the multi-mode resource-constrained project scheduling problem with discounted cash flows

NASA Astrophysics Data System (ADS)

Chen, Miawjane; Yan, Shangyao; Wang, Sin-Siang; Liu, Chiu-Lan

2015-02-01

An effective project schedule is essential for enterprises to increase their efficiency of project execution, to maximize profit, and to minimize wastage of resources. Heuristic algorithms have been developed to efficiently solve the complicated multi-mode resource-constrained project scheduling problem with discounted cash flows (MRCPSPDCF) that characterize real problems. However, the solutions obtained in past studies have been approximate and are difficult to evaluate in terms of optimality. In this study, a generalized network flow model, embedded in a time-precedence network, is proposed to formulate the MRCPSPDCF with the payment at activity completion times. Mathematically, the model is formulated as an integer network flow problem with side constraints, which can be efficiently solved for optimality, using existing mathematical programming software. To evaluate the model performance, numerical tests are performed. The test results indicate that the model could be a useful planning tool for project scheduling in the real world.

Shedding light on El Farol

NASA Astrophysics Data System (ADS)

Challet, Damien; Marsili, M.; Ottino, Gabriele

2004-02-01

We mathematize El Farol bar problem and transform it into a workable model. We find general conditions on the predictor space under which the convergence of the average attendance to the resource level does not require any intelligence on the side of the agents. Secondly, specializing to a particular ensemble of continuous strategies yields a model similar to the Minority Game. Statistical physics of disordered systems allows us to derive a complete understanding of the complex behavior of this model, on the basis of its phase diagram.

Mathematical models of real geometrical factors in restricted blood vessels for the analysis of CAD (coronary artery diseases) using Legendre, Boubaker and Bessel polynomials.

PubMed

Awojoyogbe, O B; Faromika, O P; Dada, M; Boubaker, Karem; Ojambati, O S

2011-12-01

Most cardiovascular emergencies are directly caused by coronary artery disease. Coronary arteries can become clogged or occluded, leading to damage to the heart muscle supplied by the artery. Modem cardiovascular medicine can certainly be improved by meticulous analysis of geometrical factors closely associated with the degenerative disease that results in narrowing of the coronary arteries. There are, however, inherent difficulties in developing this type of mathematical models to completely describe the real or ideal geometries that are very critical in plaque formation and thickening of the vessel wall. Neither the mathematical models of the blood vessels with arthrosclerosis generated by the heart and blood flow or the NMR/MRI data to construct them are available. In this study, a mathematical formulation for the geometrical factors that are very critical for the understanding of coronary artery disease is presented. Based on the Bloch NMR flow equations, we derive analytical expressions to describe in detail the NMR transverse magnetizations and signals as a function of some NMR flow and geometrical parameters which are invaluable for the analysis of blood flow in restricted blood vessels. The procedure would apply to the situations in which the geometry of the fatty deposits, (plague) on the interior walls of the coronary arteries is spherical. The boundary conditions are introduced based on Bessel, Boubaker and Legendre polynomials.

Efforts to Recruit Secondary STEM Teachers at Columbus State University

NASA Astrophysics Data System (ADS)

Webster, Zodiac T.; MaSST Preparation Council

2006-12-01

Physics as a discipline is not alone in having difficulty finding qualified teachers. Under-qualified teachers are present in high school Mathematics, Chemistry, Biology, and Earth-science classrooms as well. Columbus State University (CSU) has formed the Mathematics and Science Secondary Teachers (MaSST) Preparation Council to recruit more majors into our existing secondary teaching programs: Mathematics, Biology, Chemistry, and Geology. College of Education and College of Science faculty are working together to create a higher profile for these majors at our institution within the state of Georgia. In addition, we are planning an aggressive campaign to recruit from within by implementing a peer-tutoring program using outstanding students who have completed introductory math and science courses. Our group’s organization and initiatives can serve as a model for other institutions concerned about recruiting more high-school teachers.

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.

A review on the modelling of collection and distribution of blood donation based on vehicle routing problem

NASA Astrophysics Data System (ADS)

Azezan, Nur Arif; Ramli, Mohammad Fadzli; Masran, Hafiz

2017-11-01

In this paper, we discussed a literature on blood collection-distribution that based on vehicle routing problem. This problem emergence when the process from collection to stock up must be completed in timely manner. We also modified the mathematical model so that it will suited to general collection of blood. A discussion on its algorithm and solution methods are also pointed out briefly in this paper.

Regression Analysis as a Cost Estimation Model for Unexploded Ordnance Cleanup at Former Military Installations

DTIC Science & Technology

2002-06-01

fits our actual data . To determine the goodness of fit, statisticians typically use the following four measures: R2 Statistic. The R2 statistic...reviewing instruction, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of...mathematical model is developed to better estimate cleanup costs using historical cost data that could be used by the Defense Department prior to placing

Gaining control: changing relations between executive control and processing speed and their relevance for mathematics achievement over course of the preschool period

PubMed Central

Clark, Caron A. C.; Nelson, Jennifer Mize; Garza, John; Sheffield, Tiffany D.; Wiebe, Sandra A.; Espy, Kimberly Andrews

2014-01-01

Early executive control (EC) predicts a range of academic outcomes and shows particularly strong associations with children's mathematics achievement. Nonetheless, a major challenge for EC research lies in distinguishing EC from related cognitive constructs that also are linked to achievement outcomes. Developmental cascade models suggest that children's information processing speed is a driving mechanism in cognitive development that supports gains in working memory, inhibitory control and associated cognitive abilities. Accordingly, individual differences in early executive task performance and their relation to mathematics may reflect, at least in part, underlying variation in children's processing speed. The aims of this study were to: (1) examine the degree of overlap between EC and processing speed at different preschool age points; and (2) determine whether EC uniquely predicts children's mathematics achievement after accounting for individual differences in processing speed. As part of a longitudinal, cohort-sequential study, 388 children (50% boys; 44% from low income households) completed the same battery of EC tasks at ages 3, 3.75, 4.5, and 5.25 years. Several of the tasks incorporated baseline speeded naming conditions with minimal EC demands. Multidimensional latent models were used to isolate the variance in executive task performance that did not overlap with baseline processing speed, covarying for child language proficiency. Models for separate age points showed that, while EC did not form a coherent latent factor independent of processing speed at age 3 years, it did emerge as a distinct factor by age 5.25. Although EC at age 3 showed no distinct relation with mathematics achievement independent of processing speed, EC at ages 3.75, 4.5, and 5.25 showed independent, prospective links with mathematics achievement. Findings suggest that EC and processing speed are tightly intertwined in early childhood. As EC becomes progressively decoupled from processing speed with age, it begins to take on unique, discriminative importance for children's mathematics achievement. PMID:24596563

Assessing adult mortality in HIV-1-afflicted Zimbabwe (1998 -2003).

PubMed Central

Lopman, Ben A.; Barnabas, Ruanne; Hallett, Timothy B.; Nyamukapa, Constance; Mundandi, Costa; Mushati, Phyllis; Garnett, Geoff P.; Gregson, Simon

2006-01-01

OBJECTIVE: To compare alternative methods to vital registration systems for estimating adult mortality, and describe patterns of mortality in Manicaland, Zimbabwe, which has been severely affected by HIV. METHODS: We compared estimates of adult mortality from (1) a single question on household mortality, (2) repeated household censuses, and (3) an adult cohort study with linked HIV testing from Manicaland, with a mathematical model fitted to local age-specific HIV prevalence (1998 -2000). FINDINGS: The crude death rate from the single question (29 per 1000 person-years) was roughly consistent with that from the mathematical model (22 -25 per 1000 person-years), but much higher than that from the household censuses (12 per 1000 person-years). Adult mortality in the household censuses (males 0.65; females 0.51) was lower than in the cohort study (males 0.77; females 0.57), while mathematical models gave a much higher estimate, especially for females (males 0.80 -0.83; females 0.75 -0.80). The population attributable fraction of adult deaths due to HIV was 0.61 for men and 0.70 for women, with life expectancy estimated to be 34.3 years for males and 38.2 years for females. CONCLUSION: Each method for estimating adult mortality had limitations in terms of loss to follow-up (cohort study), under-ascertainment (household censuses), transparency of underlying processes (single question), and sensitivity to parameterization (mathematical model). However, these analyses make clear the advantages of longitudinal cohort data, which provide more complete ascertainment than household censuses, highlight possible inaccuracies in model assumptions, and allow direct quantification of the impact of HIV. PMID:16583077

[Chest modelling and automotive accidents].

PubMed

Trosseille, Xavier

2011-11-01

Automobile development is increasingly based on mathematical modeling. Accurate models of the human body are now available and serve to develop new means of protection. These models used to consist of rigid, articulated bodies but are now made of several million finite elements. They are now capable of predicting some risks of injury. To develop these models, sophisticated tests were conducted on human cadavers. For example, chest modeling started with material characterization and led to complete validation in the automobile environment. Model personalization, based on medical imaging, will permit studies of the behavior and tolerances of the entire population.

An Investigation into Pre-Service Special Education Teachers' Mathematical Skills, Self-Efficacy, and Teaching Methodology

ERIC Educational Resources Information Center

Hinton, Vanessa; Flores, Margaret; Burton, Megan; Curtis, Rebecca

2015-01-01

The purpose of this mixed method study was to investigate future special education teachers' preparation for effectively teaching mathematics. During the last semester of their program, pre-service special education teachers completed elementary level mathematics computation and problem solving assessments, a mathematics efficacy beliefs survey,…

SPATIAL VISUALIZATION ABILITIES OF CENTRAL WASHINGTON STATE COLLEGE PROSPECTIVE ELEMENTARY AND SECONDARY TEACHERS OF MATHEMATICS.

ERIC Educational Resources Information Center

MARTIN, BERNARD LOYAL

INVESTIGATED WAS THE EXTENT TO WHICH STUDENTS COMPLETING PLANNED MATHEMATICS EDUCATION PROGRAMS (1) WERE PROFICIENT IN SPATIAL VISUALIZATION ABILITIES, AND (2) HAD DEVELOPED MATHEMATICAL UNDERSTANDINGS. THE EFFECTS OF THE MATHEMATICS CURRICULA UPON SUCH DEVELOPMENT WERE INVESTIGATED BY COMPARING GROUP MEAN TEST SCORES OF PROSPECTIVE ELEMENTARY AND…

The Construction of Deductive Warrant Derived from Inductive Warrant in Preservice-Teacher Mathematical Argumentations

ERIC Educational Resources Information Center

Tristanti, Lia Budi; Sutawidjaja, Akbar; As'ari, Abdur Rahman; Muskar, Makbul

2016-01-01

This study discusses the construction of deductive warrant derived from inductive warrant in mathematical argumentations expressed by pre-service teacher. In completing a mathematics task, a problem solver needs argumentation to determine, reveal, and support a reasonable solution. A mathematical argumentation can be analyzed by Toulmin scheme…

The Status of Proving among US Secondary Mathematics Teachers

ERIC Educational Resources Information Center

Kotelawala, Usha

2016-01-01

This report examines teachers' self-espoused attitudes and beliefs on proving in the secondary mathematics classroom. Conclusions were based on a questionnaire of 78 US mathematics teachers who had completed at least 2 years of teaching mathematics at the secondary level. While these teachers placed importance on proving as a general mathematical…

How Flipping Much? Consecutive Flipped Mathematics Courses and Their Influence on Students' Anxieties and Perceptions of Learning

ERIC Educational Resources Information Center

Dove, Anthony; Dove, Emily

2017-01-01

While studies have shown positive attributes related to flipped learning, especially in mathematics and statistics, there is limited understanding of how taking multiple flipped courses may impact students' learning of mathematics and their perceptions of mathematics. Specifically, this study examined how completing consecutive flipped mathematics…

Persistence in STEM: An investigation of the relationship between high school experiences in science and mathematics and college degree completion in STEM fields

NASA Astrophysics Data System (ADS)

Maltese, Adam V.

While the number of Bachelor's degrees awarded annually has nearly tripled over the past 40 years (NSF, 2008), the same cannot be said for degrees in the STEM (science, technology, engineering and mathematics) fields. The Bureau of Labor Statistics projects that by the year 2014 the combination of new positions and retirements will lead to 2 million job openings in STEM (BLS, 2005). Thus, the research questions I sought to answer with this study were: (1)What are the most common enrollment patterns for students who enter into and exit from the STEM pipeline during high school and college? (2) Controlling for differences in student background and early interest in STEM careers, what are the high school science and mathematics classroom experiences that characterize student completion of a college major in STEM? Using data from NELS:88 I analyzed descriptive statistics and completed logistic regressions to gain an understanding of factors related to student persistence in STEM. Approximately 4700 students with transcript records and who participated in all survey rounds were included in the analyses. The results of the descriptive analysis demonstrated that most students who went on to complete majors in STEM completed at least three or four years of STEM courses during high school, and enrolled in advanced high school mathematics and science courses at higher rates. At almost every pipeline checkpoint indicators of the level of coursework and achievement were significant in predicting student completion of a STEM degree. The results also support previous research that showed demographic variables have little effect on persistence once the sample is limited to those who have the intrinsic ability and desire to complete a college degree. The most significant finding is that measures of student interest and engagement in science and mathematics were significant in predicting completion of a STEM degree, above and beyond the effects of course enrollment and performance. A final analysis, which involved the comparison of descriptive statistics for students who switched into and out of the STEM pipeline during high school, suggested that attitudes toward mathematics and science play a major role in choices regarding pipeline persistence.

The mathematical model of dynamic stabilization system for autonomous car

NASA Astrophysics Data System (ADS)

Saikin, A. M.; Buznikov, S. E.; Shabanov, N. S.; Elkin, D. S.

2018-02-01

Leading foreign companies and domestic enterprises carry out extensive researches and developments in the field of control systems for autonomous cars and in the field of improving driver assistance systems. The search for technical solutions, as a rule, is based on heuristic methods and does not always lead to satisfactory results. The purpose of this research is to formalize the road safety problem in the terms of modern control theory, to construct the adequate mathematical model for solving it, including the choice of software and hardware environment. For automatic control of the object, it is necessary to solve the problem of dynamic stabilization in the most complete formulation. The solution quality of the problem on a finite time interval is estimated by the value of the quadratic functional. Car speed, turn angle and additional yaw rate (during car drift or skidding) measurements are performed programmatically by the original virtual sensors. The limit speeds at which drift, skidding or rollover begins are calculated programmatically taking into account the friction coefficient identified in motion. The analysis of the results confirms both the adequacy of the mathematical models and the algorithms and the possibility of implementing the system in the minimal technical configuration.

Comparison Of Models Of Metal-Matrix Composites

NASA Technical Reports Server (NTRS)

Bigelow, C. A.; Johnson, W. S.; Naik, R. A.

1994-01-01

Report presents comparative review of four mathematical models of micromechanical behaviors of fiber/metal-matrix composite materials. Models differ in various details, all based on properties of fiber and matrix constituent materials, all involve square arrays of fibers continuous and parallel and all assume complete bonding between constituents. Computer programs implementing models used to predict properties and stress-vs.-strain behaviors of unidirectional- and cross-ply laminated composites made of boron fibers in aluminum matrices and silicon carbide fibers in titanium matrices. Stresses in fiber and matrix constituent materials also predicted.

Mathematical model of the competition life cycle under limited resources conditions: Problem statement for business community

NASA Astrophysics Data System (ADS)

Shelomentsev, A. G.; Medvedev, M. A.; Berg, D. B.; Lapshina, S. N.; Taubayev, A. A.; Davletbaev, R. H.; Savina, D. V.

2017-12-01

Present study is devoted to the development of competition life cycle mathematical model in the closed business community with limited resources. Growth of each agent is determined by the balance of input and output resource flows: input (cash) flow W is covering the variable V and constant C costs and growth dA/dt of the agent's assets A. Value of V is proportional to assets A that allows us to write down a first order non-stationary differential equation of the agent growth. Model includes the number of such equations due to the number of agents. The amount of resources that is available for agents vary in time. The balances of their input and output flows are changing correspondingly to the different stages of the competition life cycle. According to the theory of systems, the most complete description of any object or process is the model of its life cycle. Such a model describes all stages of its development: from the appearance ("birth") through development ("growth") to extinction ("death"). The model of the evolution of an individual firm, not contradicting the economic meaning of events actually observed in the market, is the desired result from modern AVMs for applied use. With a correct description of the market, rules for participants' actions, restrictions, forecasts can be obtained, which modern mathematics and the economy can not give.

DAISY: a new software tool to test global identifiability of biological and physiological systems.

PubMed

Bellu, Giuseppina; Saccomani, Maria Pia; Audoly, Stefania; D'Angiò, Leontina

2007-10-01

A priori global identifiability is a structural property of biological and physiological models. It is considered a prerequisite for well-posed estimation, since it concerns the possibility of recovering uniquely the unknown model parameters from measured input-output data, under ideal conditions (noise-free observations and error-free model structure). Of course, determining if the parameters can be uniquely recovered from observed data is essential before investing resources, time and effort in performing actual biomedical experiments. Many interesting biological models are nonlinear but identifiability analysis for nonlinear system turns out to be a difficult mathematical problem. Different methods have been proposed in the literature to test identifiability of nonlinear models but, to the best of our knowledge, so far no software tools have been proposed for automatically checking identifiability of nonlinear models. In this paper, we describe a software tool implementing a differential algebra algorithm to perform parameter identifiability analysis for (linear and) nonlinear dynamic models described by polynomial or rational equations. Our goal is to provide the biological investigator a completely automatized software, requiring minimum prior knowledge of mathematical modelling and no in-depth understanding of the mathematical tools. The DAISY (Differential Algebra for Identifiability of SYstems) software will potentially be useful in biological modelling studies, especially in physiology and clinical medicine, where research experiments are particularly expensive and/or difficult to perform. Practical examples of use of the software tool DAISY are presented. DAISY is available at the web site http://www.dei.unipd.it/~pia/.

Temperature and solute-transport simulation in streamflow using a Lagrangian reference frame

USGS Publications Warehouse

Jobson, Harvey E.

1980-01-01

A computer program for simulating one-dimensional, unsteady temperature and solute transport in a river has been developed and documented for general use. The solution approach to the convective-diffusion equation uses a moving reference frame (Lagrangian) which greatly simplifies the mathematics of the solution procedure and dramatically reduces errors caused by numerical dispersion. The model documentation is presented as a series of four programs of increasing complexity. The conservative transport model can be used to route a single conservative substance. The simplified temperature model is used to predict water temperature in rivers when only temperature and windspeed data are available. The complete temperature model is highly accurate but requires rather complete meteorological data. Finally, the 10-parameter model can be used to route as many as 10 interacting constituents through a river reach. (USGS)

Rate of Change: AP Calculus Students' Understandings and Misconceptions after Completing Different Curricular Paths

ERIC Educational Resources Information Center

Teuscher, Dawn; Reys, Robert E.

2012-01-01

This study examined Advanced Placement Calculus students' mathematical understanding of rate of change, after studying four years of college preparatory (integrated or single-subject) mathematics. Students completed the Precalculus Concept Assessment (PCA) and two open-ended tasks with questions about rates of change. After adjusting for prior…

Teaching Mathematics to Students With Learning Disabilities: A Review Of Literature

ERIC Educational Resources Information Center

Obudo, Francis

2008-01-01

The purpose of this study was to review and synthesize available literature to draw a comprehensive picture of what is necessary to teach mathematics to students with learning disabilities. A systematic search was conducted through 5 computerized databases (Academic Search Complete, ERIC, Education Research Complete, and Primary Search) The…

Child development at 5 years of age predicted mathematics ability and schooling outcomes in Malawian adolescents.

PubMed

Gandhi, Mihir; Teivaanmaki, Tiina; Maleta, Kenneth; Duan, Xiaolian; Ashorn, Per; Cheung, Yin Bun

2013-01-01

This study aimed to examine the association between child development at 5 years of age and mathematics ability and schooling outcomes at 12 years of age in Malawian children. A prospective cohort study looking at 609 rural Malawian children. Outcome measures were percentage of correctly answered mathematics questions, highest school grade completed and number of times repeating school grades at 12 years of age. A child development summary score obtained at 5 years of age was the main exposure variable. Regression analyses were used to estimate the association and adjust for confounders. Sensitivity analysis was performed by handling losses to follow-up with multiple imputation (MI) method. The summary score was positively associated with percentage of correctly answered mathematics questions (p = 0.057; p = 0.031 MI) and with highest school grade completed (p = 0.096; p = 0.070 MI), and negatively associated with number of times repeating school grades (p = 0.834; p = 0.339 MI). Fine motor score at 5 years was independently associated with the mathematic score (p = 0.032; p = 0.011 MI). The association between child development and mathematics ability did not depend on school attendance. Child development at 5 years of age showed signs of positive association with mathematics ability and possibly with highest school grade completed at 12 years of age. © 2012 The Author(s)/Acta Paediatrica © 2012 Foundation Acta Paediatrica.

The operating diagram of a model of two competitors in a chemostat with an external inhibitor.

PubMed

Dellal, Mohamed; Lakrib, Mustapha; Sari, Tewfik

2018-05-24

Understanding and exploiting the inhibition phenomenon, which promotes the stable coexistence of species, is a major challenge in the mathematical theory of the chemostat. Here, we study a model of two microbial species in a chemostat competing for a single resource in the presence of an external inhibitor. The model is a four-dimensional system of ordinary differential equations. Using general monotonic growth rate functions of the species and absorption rate of the inhibitor, we give a complete analysis for the existence and local stability of all steady states. We focus on the behavior of the system with respect of the three operating parameters represented by the dilution rate and the input concentrations of the substrate and the inhibitor. The operating diagram has the operating parameters as its coordinates and the various regions defined in it correspond to qualitatively different asymptotic behavior: washout, competitive exclusion of one species, coexistence of the species around a stable steady state and coexistence around a stable cycle. This bifurcation diagram which determines the effect of the operating parameters, is very useful to understand the model from both the mathematical and biological points of view, and is often constructed in the mathematical and biological literature. Copyright © 2018 Elsevier Inc. All rights reserved.

The beliefs of `Tomorrow's Teachers' about mathematics: precipitating change in beliefs as a result of participation in an Initial Teacher Education programme

NASA Astrophysics Data System (ADS)

Leavy, Aisling; Hourigan, Mairead

2018-07-01

Mathematics education research has given increasing attention to the role of affective factors in the learning process. While 'affect' is used to refer to a variety of aspects including feelings, emotions, beliefs, attitudes and conceptions, this paper focuses on 'beliefs' of elementary pre-service teachers. In particular, the study evaluates the effect of participation in a reform-based elementary pre-service teacher education (referred to as Initial Teacher Education (ITE)) programme on participants' 'beliefs about the nature of mathematics'. This was completed using two (sub)scales of the Aiken's Revised Mathematics Scale measuring Enjoyment of Mathematics (E) and belief in the Value of Mathematics (V). Both scales were administered before and after participants completed the mathematics education programme, which consisted of 5 compulsory and consecutive modules. This study reveals that entry-level pre-service teachers report generally positive beliefs about the value of and enjoyment in doing mathematics. The findings challenge previous research, which report the tendency of teachers' beliefs to be resistant to change while in teacher education and suggest that it is possible for ITE mathematics education programmes to stimulate improvement in beliefs and attitudes among participants. Particular programme features are identified as instrumental in this positive change in beliefs about mathematics.

Secondary School Advanced Mathematics, Chapter 8, Systems of Equations. Teacher's Commentary.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This manual was designed for use with the last of five texts in the Secondary School Advanced Mathematics (SSAM) series. Developed for students who have completed the Secondary School Mathematics (SSM) program and wish to continue their studies in mathematics, this series is designed to review, strengthen, and fill gaps in the material covered in…

Secondary School Advanced Mathematics, Chapter 3, Formal Geometry. Teacher's Commentary.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This manual was designed for use with the second of five texts in the Secondary School Advanced Mathematics (SSAM) series. Developed for students who have completed the Secondary School Mathematics (SSM) program and wish to continue their studies in mathematics, this series is designed to review, strengthen, and fill gaps in the material covered…

Secondary School Advanced Mathematics, Chapter 3, Formal Geometry. Student's Text.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This text is the second of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. This volume is devoted to a rigorous development of theorems in plane geometry from 22…

Secondary School Advanced Mathematics, Chapter 8, Systems of Equations. Student's Text.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This text is the last of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. In this volume the solution of systems of linear and quadratic equations and inequalities in…

Defective Number Module or Impaired Access? Numerical Magnitude Processing in First Graders with Mathematical Difficulties

ERIC Educational Resources Information Center

De Smedt, Bert; Gilmore, Camilla K.

2011-01-01

This study examined numerical magnitude processing in first graders with severe and mild forms of mathematical difficulties, children with mathematics learning disabilities (MLD) and children with low achievement (LA) in mathematics, respectively. In total, 20 children with MLD, 21 children with LA, and 41 regular achievers completed a numerical…

Are College Student Success Courses Effective Corequisites to Developmental Mathematics in Community Colleges?

ERIC Educational Resources Information Center

Reilly, Karen L.

2014-01-01

The purpose of this study was to examine the differences in the achievement rates of developmental mathematics students when a student success course was taken in combination with mathematics. The study investigated changes that occurred in the developmental mathematics completion rates of the learners by examining age and the course sequence of…

Impact of Online Summer Mathematics Bridge Program on Placement Scores and Pass Rates

ERIC Educational Resources Information Center

Frost, Jodi L.; Dreher, J. P.

2017-01-01

An online four-week summer mathematics bridge program was implemented at a Midwest university with historically low pass rates in College Algebra and Remedial Mathematics. Students who completed the four week program significantly increased their mathematics placement exam scores. These students also had a higher pass rate in their initial college…

The Relation between Mathematics and Working Memory in Young Children with Fetal Alcohol Spectrum Disorders

ERIC Educational Resources Information Center

Rasmussen, Carmen; Bisanz, Jeffrey

2011-01-01

The goal of this study was to examine the relation between mathematics and working memory in young children with Fetal Alcohol Spectrum Disorders (FASD). Children with FASD and comparison children (4 to 6 years old) completed standardized tests of mathematics and working memory. Children with FASD showed impairments on mathematics (applied…

The Influence of University Courses and Field Experiences on Chinese Elementary Candidates' Mathematical Knowledge for Teaching

ERIC Educational Resources Information Center

Youngs, Peter; Qian, Hong

2013-01-01

In this article, we draw on survey data to investigate associations between Chinese elementary teaching candidates’ mathematical knowledge for teaching (MKT) and their experiences in mathematics courses, mathematics methods courses, and student teaching. In our study, we found that (a) Chinese teaching candidates' completion of courses in number…

A Highly Capable Year 6 Student's Response to a Challenging Mathematical Task

ERIC Educational Resources Information Center

Livy, Sharyn; Holmes, Marilyn; Ingram, Naomi; Linsell, Chris; Sullivan, Peter

2016-01-01

Highly capable mathematics students are not usually considered strugglers. This paper reports on a case study of a Year 6 student, Debbie, her response to a lesson, and her learning involving a challenging mathematical task. Debbie, usually a highly capable student, struggled to complete a challenging mathematical task by herself, but as the…

Challenging Transitions and Crossing Borders: Preparing Novice Mathematics Teacher Educators to Support Novice K-12 Mathematics Teachers

ERIC Educational Resources Information Center

Yow, Jan A.; Eli, Jennifer A.; Beisiegel, Mary; McCloskey, Andrea; Welder, Rachael M.

2016-01-01

Sixty-nine recently graduated doctoral students in mathematics education completed a survey to determine their perceptions of transitioning from a doctoral program into an academic position at an institution of higher education. Research literature for novice mathematics school teachers was also reviewed to document their experiences transitioning…

Data Analysis and Statistics across the Curriculum. Curriculum and Evaluation Standards for School Mathematics Addenda Series. Grades 9-12.

ERIC Educational Resources Information Center

Burrill, Gail; And Others

The 1989 document, "Curriculum and Evaluation Standards for School Mathematics" (the "Standards"), provides a vision and a framework for revising and strengthening the K-12 mathematics curriculum in North American schools and for evaluating both the mathematics curriculum and students' progress. When completed, it is expected…

Quantitative imaging with Fucci and mathematics to uncover temporal dynamics of cell cycle progression.

PubMed

Saitou, Takashi; Imamura, Takeshi

2016-01-01

Cell cycle progression is strictly coordinated to ensure proper tissue growth, development, and regeneration of multicellular organisms. Spatiotemporal visualization of cell cycle phases directly helps us to obtain a deeper understanding of controlled, multicellular, cell cycle progression. The fluorescent ubiquitination-based cell cycle indicator (Fucci) system allows us to monitor, in living cells, the G1 and the S/G2/M phases of the cell cycle in red and green fluorescent colors, respectively. Since the discovery of Fucci technology, it has found numerous applications in the characterization of the timing of cell cycle phase transitions under diverse conditions and various biological processes. However, due to the complexity of cell cycle dynamics, understanding of specific patterns of cell cycle progression is still far from complete. In order to tackle this issue, quantitative approaches combined with mathematical modeling seem to be essential. Here, we review several studies that attempted to integrate Fucci technology and mathematical models to obtain quantitative information regarding cell cycle regulatory patterns. Focusing on the technological development of utilizing mathematics to retrieve meaningful information from the Fucci producing data, we discuss how the combined methods advance a quantitative understanding of cell cycle regulation. © 2015 Japanese Society of Developmental Biologists.

A Formal Model of Partitioning for Integrated Modular Avionics

NASA Technical Reports Server (NTRS)

DiVito, Ben L.

1998-01-01

The aviation industry is gradually moving toward the use of integrated modular avionics (IMA) for civilian transport aircraft. An important concern for IMA is ensuring that applications are safely partitioned so they cannot interfere with one another. We have investigated the problem of ensuring safe partitioning and logical non-interference among separate applications running on a shared Avionics Computer Resource (ACR). This research was performed in the context of ongoing standardization efforts, in particular, the work of RTCA committee SC-182, and the recently completed ARINC 653 application executive (APEX) interface standard. We have developed a formal model of partitioning suitable for evaluating the design of an ACR. The model draws from the mathematical modeling techniques developed by the computer security community. This report presents a formulation of partitioning requirements expressed first using conventional mathematical notation, then formalized using the language of SRI'S Prototype Verification System (PVS). The approach is demonstrated on three candidate designs, each an abstraction of features found in real systems.

Mathematical model of gas plasma applied to chronic wounds

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

Wang, J. G.; Liu, X. Y.; Liu, D. W.

2013-11-15

Chronic wounds are a major burden for worldwide health care systems, and patients suffer pain and discomfort from this type of wound. Recently gas plasmas have been shown to safely speed chronic wounds healing. In this paper, we develop a deterministic mathematical model formulated by eight-species reaction-diffusion equations, and use it to analyze the plasma treatment process. The model follows spatial and temporal concentration within the wound of oxygen, chemoattractants, capillary sprouts, blood vessels, fibroblasts, extracellular matrix material, nitric oxide (NO), and inflammatory cell. Two effects of plasma, increasing NO concentration and reducing bacteria load, are considered in this model.more » The plasma treatment decreases the complete healing time from 25 days (normal wound healing) to 17 days, and the contributions of increasing NO concentration and reducing bacteria load are about 1/4 and 3/4, respectively. Increasing plasma treatment frequency from twice to three times per day accelerates healing process. Finally, the response of chronic wounds of different etiologies to treatment with gas plasmas is analyzed.« less

Application of remote sensing for prediction and detection of thermal pollution

NASA Technical Reports Server (NTRS)

Veziroglu, T. N.; Lee, S. S.

1974-01-01

The first phase is described of a three year project for the development of a mathematical model for predicting thermal pollution by use of remote sensing measurements. A rigid-lid model was developed, and results were obtained for different wind conditions at Biscayne Bay in South Florida. The design of the measurement system was completed, and instruments needed for the first stage of experiment were acquired, tested, and calibrated. A preliminary research flight was conducted.

Time-Dependent Simulations of Incompressible Flow in a Turbopump Using Overset Grid Approach

NASA Technical Reports Server (NTRS)

Kiris, Cetin; Kwak, Dochan

2001-01-01

This viewgraph presentation provides information on mathematical modelling of the SSME (space shuttle main engine). The unsteady SSME-rig1 start-up procedure from the pump at rest has been initiated by using 34.3 million grid points. The computational model for the SSME-rig1 has been completed. Moving boundary capability is obtained by using DCF module in OVERFLOW-D. MPI (Message Passing Interface)/OpenMP hybrid parallel code has been benchmarked.

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

Lai, Jih-Sheng

This paper introduces control system design based softwares, SIMNON and MATLAB/SIMULINK, for power electronics system simulation. A complete power electronics system typically consists of a rectifier bridge along with its smoothing capacitor, an inverter, and a motor. The system components, featuring discrete or continuous, linear or nonlinear, are modeled in mathematical equations. Inverter control methods,such as pulse-width-modulation and hysteresis current control, are expressed in either computer algorithms or digital circuits. After describing component models and control methods, computer programs are then developed for complete systems simulation. Simulation results are mainly used for studying system performances, such as input and outputmore » current harmonics, torque ripples, and speed responses. Key computer programs and simulation results are demonstrated for educational purposes.« less

Finite Dimensional Approximations for Continuum Multiscale Problems

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

Berlyand, Leonid

2017-01-24

The completed research project concerns the development of novel computational techniques for modeling nonlinear multiscale physical and biological phenomena. Specifically, it addresses the theoretical development and applications of the homogenization theory (coarse graining) approach to calculation of the effective properties of highly heterogenous biological and bio-inspired materials with many spatial scales and nonlinear behavior. This theory studies properties of strongly heterogeneous media in problems arising in materials science, geoscience, biology, etc. Modeling of such media raises fundamental mathematical questions, primarily in partial differential equations (PDEs) and calculus of variations, the subject of the PI’s research. The focus of completed researchmore » was on mathematical models of biological and bio-inspired materials with the common theme of multiscale analysis and coarse grain computational techniques. Biological and bio-inspired materials offer the unique ability to create environmentally clean functional materials used for energy conversion and storage. These materials are intrinsically complex, with hierarchical organization occurring on many nested length and time scales. The potential to rationally design and tailor the properties of these materials for broad energy applications has been hampered by the lack of computational techniques, which are able to bridge from the molecular to the macroscopic scale. The project addressed the challenge of computational treatments of such complex materials by the development of a synergistic approach that combines innovative multiscale modeling/analysis techniques with high performance computing.« less

The Nature of Quantum Truth: Logic, Set Theory, & Mathematics in the Context of Quantum Theory

NASA Astrophysics Data System (ADS)

Frey, Kimberly

The purpose of this dissertation is to construct a radically new type of mathematics whose underlying logic differs from the ordinary classical logic used in standard mathematics, and which we feel may be more natural for applications in quantum mechanics. Specifically, we begin by constructing a first order quantum logic, the development of which closely parallels that of ordinary (classical) first order logic --- the essential differences are in the nature of the logical axioms, which, in our construction, are motivated by quantum theory. After showing that the axiomatic first order logic we develop is sound and complete (with respect to a particular class of models), this logic is then used as a foundation on which to build (axiomatic) mathematical systems --- and we refer to the resulting new mathematics as "quantum mathematics." As noted above, the hope is that this form of mathematics is more natural than classical mathematics for the description of quantum systems, and will enable us to address some foundational aspects of quantum theory which are still troublesome --- e.g. the measurement problem --- as well as possibly even inform our thinking about quantum gravity. After constructing the underlying logic, we investigate properties of several mathematical systems --- e.g. axiom systems for abstract algebras, group theory, linear algebra, etc. --- in the presence of this quantum logic. In the process, we demonstrate that the resulting quantum mathematical systems have some strange, but very interesting features, which indicates a richness in the structure of mathematics that is classically inaccessible. Moreover, some of these features do indeed suggest possible applications to foundational questions in quantum theory. We continue our investigation of quantum mathematics by constructing an axiomatic quantum set theory, which we show satisfies certain desirable criteria. Ultimately, we hope that such a set theory will lead to a foundation for quantum mathematics in a sense which parallels the foundational role of classical set theory in classical mathematics. One immediate application of the quantum set theory we develop is to provide a foundation on which to construct quantum natural numbers, which are the quantum analog of the classical counting numbers. It turns out that in a special class of models, there exists a 1-1 correspondence between the quantum natural numbers and bounded observables in quantum theory whose eigenvalues are (ordinary) natural numbers. This 1-1 correspondence is remarkably satisfying, and not only gives us great confidence in our quantum set theory, but indicates the naturalness of such models for quantum theory itself. We go on to develop a Peano-like arithmetic for these new "numbers," as well as consider some of its consequences. Finally, we conclude by summarizing our results, and discussing directions for future work.

A complete dynamic model of primary sedimentation.

PubMed

Paraskevas, P; Kolokithas, G; Lekkas, T

1993-11-01

A dynamic mathematical model for the primary clarifier of a wastewater treatment plant is described, which is represented by a general tanks-in-series model, to simulate insufficient mixing. The model quantifies successfully the diurnal response of both the suspended and dissolved species. It is general enough, so that the values of the parameters can be replaced with those applicable to a specific case. The model was verified through data from the Biological Centre of Metamorfosi, in Athens, Greece, and can be used to assist in the design of new plants or in the analysis and output predictions of existing ones.

A Mathematical Model to Predict and Maintain the Neutral Buoyancy of Suited Astronauts

NASA Technical Reports Server (NTRS)

Clowers, Kurt; Jaramillo, Marcos; Nguyen, Daniel; Sweet, Robert; Rajulu, Sudhakar

2006-01-01

A previous study reported that inadequate weigh outs of suited subjects contribute to fatigue and the risk of injury during training in the Neutral Buoyancy Laboratory (NBL). Another study suggested that shoulder injuries observed in suited subjects who train in the NBL may be attributed to excessive righting moments caused by a non-optimal weigh out. The purpose of this study was to develop a mathematical model to predict and maintain the neutral buoyancy of suited subjects during training operations at the NBL. Due to time constraints, one certified NBL support diver served as a subject (height: 66.54 in; weight: 182 lbs) for this study and only one complete test was conducted. The study was divided into two runs for which the first run required the NBL divers to perform a weigh out similar to a suited astronaut on a scuba diver wearing a mock Portable Life Support System and a Displays and Control Module. For the second run, the same subject and equipment were weighed out according to the mathematical model. The objective of each run was to achieve a neutrally buoyant subject floating 450 to the pool floor. Motion data was collected using two underwater cameras and analyzed using Dartfish video analysis software while force and moment data were recorded using an AMTI force plate. The results from the NBL divers visual run indicate that the subject was floating at an angle of 29.50 while the resultant force and moment data were 1.139 lb and 1.125 ft-lb respectively. The mathematical model s weigh out resulted in the subject floating at an angle of 37.40 and a resultant force of 0.765 lb and resultant moment of 1.248 ft-lb. The mathematical model was better able to orient the subject and reduce resultant moment and force as compared to the NBL divers.

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.

Interactions Between the Cross-Shore Structure of Small Pelagic Fish Population, Offshore Industrial Fisheries and Near Shore Artisanal Fisheries: A Mathematical Approach.

PubMed

Mchich, Rachid; Brochier, Timothée; Auger, Pierre; Brehmer, Patrice

2016-12-01

This work presents a mathematical model describing the interactions between the cross-shore structure of small pelagic fish population an their exploitation by coastal and offshore fisheries. The complete model is a system of seven ODE's governing three stocks of small pelagic fish population moving and growing between three zones. Two types of fishing fleets are inter-acting with the fish population, industrial boats, constrained to offshore area, and artisanal boats, operating from the shore. Two time scales were considered and we use aggregation methods that allow us to reduce the dimension of the model and to obtain an aggregated model, which is a four dimension one. The analysis of the aggregated model is performed. We discuss the possible equilibriums and their meaning in terms of fishery management. An interesting equilibrium state can be obtained for which we can expect coexistence and a stable equilibrium state between fish stocks and fishing efforts. Some identification parameters are also given in the discussion part of the model.

Isotonic designs for phase I trials in partially ordered groups.

PubMed

Conaway, Mark

2017-10-01

Dose-finding trials can be conducted such that patients are first stratified into multiple risk groups before doses are allocated. The risk groups are often completely ordered in that, for a fixed dose, the probability of toxicity is monotonically increasing across groups. In some trials, the groups are only partially ordered. For example, one of several groups in a trial may be known to have the least risk of toxicity for a given dose, but the ordering of the risk among the remaining groups may not be known. The aim of the article is to introduce a method for designing dose-finding trials of cytotoxic agents in completely or partially ordered groups of patients. This article presents a method for dose-finding that combines previously proposed mathematical models, augmented with results using order restricted inference. The resulting method is computationally convenient and allows for dose-finding in trials with completely or partially ordered groups. Extensive simulations are done to evaluate the performance of the method, using randomly generated dose-toxicity curves where, within each group, the risk of toxicity is an increasing function of dose. Our simulations show that the hybrid method, in which order-restricted estimation is applied to parameters of a parsimonious mathematical model, gives results that are similar to previously proposed methods for completely ordered groups. Our method generalizes to a wide range of partial orders among the groups. The problem of dose-finding in partially ordered groups has not been extensively studied in the statistical literature. The proposed method is computationally feasible, and provides a potential solution to the design of dose-finding studies in completely or partially ordered groups.

Mathematical model for the growth of phases in binary multiphase systems upon isothermic annealing

NASA Astrophysics Data System (ADS)

Molokhina, L. A.; Rogalin, V. E.; Filin, S. A.; Kaplunov, I. A.

2017-09-01

A phenomenological mathematical model of the formation and growth of phases in a binary multiphase system with allowance for factors influencing the process of diffusion in a binary system is presented. It is shown that phases can grow for a certain time at different ratios between diffusion parameters according to a parabolic law that depends on the duration of isothermic annealing. They then slow their growth after successor phases appear at their interface with one component and can completely disappear from a diffusion layer or begin to grow again, but only at a rate slower than during their initial formation. The dependence of the thickness of each phase layer in a multiphase diffusion zone on the duration of isothermic annealing and the ratio between the diffusion parameters in neighboring phases is obtained. It is established that a certain ratio between the phase growth and rates of dissolution with allowance for the coefficients of diffusion in each phase and the periods of incubation can result in the complete disappearance of one phase as early as the onset of the growth of phase nuclei and be interpreted as a process of reaction diffusion.

A mathematical model for expected time to extinction of pathogenic bacteria through antibiotic

NASA Astrophysics Data System (ADS)

Ghosh, M. K.; Nandi, S.; Roy, P. K.

2016-04-01

Application of antibiotics in human system to prevent bacterial diseases like Gastritis, Ulcers, Meningitis, Pneumonia and Gonorrhea are indispensable. Antibiotics saved innumerable lives and continue to be a strong support for therapeutic application against pathogenic bacteria. In human system, bacterial diseases occur when pathogenic bacteria gets into the body and begin to reproduce and crowd out healthy bacteria. In this process, immature bacteria releases enzyme which is essential for bacterial cell-wall biosynthesis. After complete formation of cell wall, immature bacteria are converted to mature or virulent bacteria which are harmful to us during bacterial infections. Use of antibiotics as drug inhibits the bacterial cell wall formation. After application of antibiotics within body, the released bacterial enzyme binds with antibiotic molecule instead of its functional site during the cell wall synthesis in a competitive inhibition approach. As a consequence, the bacterial cell-wall formation as well as maturation process of pathogenic bacteria is halted and the disease is cured with lysis of bacterial cells. With this idea, a mathematical model has been developed in the present research investigation to review the inhibition of biosynthesis of bacterial cell wall by the application of antibiotics as drug in the light of enzyme kinetics. This approach helps to estimate the expected time to extinction of the pathogenic bacteria. Our mathematical approach based on the enzyme kinetic model for finding out expected time to extinction contributes favorable results for understanding of disease dynamics. Analytical and numerical results based on simulated findings validate our mathematical model.

Readiness, Behavior, and Foundational Mathematics Course Success

ERIC Educational Resources Information Center

Li, Kevin; Zelenka, Richard; Buonaguidi, Larry; Beckman, Robert; Casillas, Alex; Crouse, Jill; Allen, Jeff; Hanson, Mary Ann; Acton, Tara; Robbins, Steve

2013-01-01

This study examines the effects of math readiness and student course behavior (e.g., attendance, participation, homework completion) on knowledge gain and course success using two samples of students enrolled in foundational skills (noncredit-bearing) mathematics courses. As hypothesized, entering student mathematics readiness and course behavior…

Secondary School Advanced Mathematics, Chapter 1, Organizing Geometric Knowledge, Chapter 2, Concepts and Skills in Algebra. Student's Text.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This text is the first of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. The first chapter, devoted to organizing geometric knowledge, deals with the distinction…

"I Think I Can, but I'm Afraid to Try": The Role of Self-Efficacy Beliefs and Mathematics Anxiety in Mathematics Problem-Solving Efficiency

ERIC Educational Resources Information Center

Hoffman, Bobby

2010-01-01

This study investigated the role of self-efficacy beliefs, mathematics anxiety, and working memory capacity in problem-solving accuracy, response time, and efficiency (the ratio of problem-solving accuracy to response time). Pre-service teachers completed a mathematics anxiety inventory measuring cognitive and affective dispositions for…

A physiome standards-based model publication paradigm.

PubMed

Nickerson, David P; Buist, Martin L

2009-05-28

In this era of widespread broadband Internet penetration and powerful Web browsers on most desktops, a shift in the publication paradigm for physiome-style models is envisaged. No longer will model authors simply submit an essentially textural description of the development and behaviour of their model. Rather, they will submit a complete working implementation of the model encoded and annotated according to the various standards adopted by the physiome project, accompanied by a traditional human-readable summary of the key scientific goals and outcomes of the work. While the final published, peer-reviewed article will look little different to the reader, in this new paradigm, both reviewers and readers will be able to interact with, use and extend the models in ways that are not currently possible. Here, we review recent developments that are laying the foundations for this new model publication paradigm. Initial developments have focused on the publication of mathematical models of cellular electrophysiology, using technology based on a CellML- or Systems Biology Markup Language (SBML)-encoded implementation of the mathematical models. Here, we review the current state of the art and what needs to be done before such a model publication becomes commonplace.

Derivation of an applied nonlinear Schroedinger equation

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

Pitts, Todd Alan; Laine, Mark Richard; Schwarz, Jens

We derive from first principles a mathematical physics model useful for understanding nonlinear optical propagation (including filamentation). All assumptions necessary for the development are clearly explained. We include the Kerr effect, Raman scattering, and ionization (as well as linear and nonlinear shock, diffraction and dispersion). We explain the phenomenological sub-models and each assumption required to arrive at a complete and consistent theoretical description. The development includes the relationship between shock and ionization and demonstrates why inclusion of Drude model impedance effects alters the nature of the shock operator. Unclassified Unlimited Release

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…

Automation of closed environments in space for human comfort and safety

NASA Technical Reports Server (NTRS)

1992-01-01

This report culminates the work accomplished during a three year design project on the automation of an Environmental Control and Life Support System (ECLSS) suitable for space travel and colonization. The system would provide a comfortable living environment in space that is fully functional with limited human supervision. A completely automated ECLSS would increase astronaut productivity while contributing to their safety and comfort. The first section of this report, section 1.0, briefly explains the project, its goals, and the scheduling used by the team in meeting these goals. Section 2.0 presents an in-depth look at each of the component subsystems. Each subsection describes the mathematical modeling and computer simulation used to represent that portion of the system. The individual models have been integrated into a complete computer simulation of the CO2 removal process. In section 3.0, the two simulation control schemes are described. The classical control approach uses traditional methods to control the mechanical equipment. The expert control system uses fuzzy logic and artificial intelligence to control the system. By integrating the two control systems with the mathematical computer simulation, the effectiveness of the two schemes can be compared. The results are then used as proof of concept in considering new control schemes for the entire ECLSS. Section 4.0 covers the results and trends observed when the model was subjected to different test situations. These results provide insight into the operating procedures of the model and the different control schemes. The appendix, section 5.0, contains summaries of lectures presented during the past year, homework assignments, and the completed source code used for the computer simulation and control system.

Mathematics Is?--A Journey Completed

ERIC Educational Resources Information Center

Turner, Laura

2011-01-01

In this article, the author explores her personal views on mathematics and how she solves problems. She experiences some personal revelations while attending a "Mathsjam". Organised by some of the more prominent names in the popularisation of mathematics, "Mathsjam" was billed as the UK's first Gathering for Gardner, an event…

The analysis of student’s critical thinking ability on discovery learning by using hand on activity based on the curiosity

NASA Astrophysics Data System (ADS)

Sulistiani, E.; Waluya, S. B.; Masrukan

2018-03-01

This study aims to determine (1) the effectiveness of Discovery Learning model by using Hand on Activity toward critical thinking abilities, and (2) to describe students’ critical thinking abilities in Discovery Learning by Hand on Activity based on curiosity. This study is mixed method research with concurrent embedded design. Sample of this study are students of VII A and VII B of SMP Daarul Qur’an Ungaran. While the subject in this study is based on the curiosity of the students groups are classified Epistemic Curiosity (EC) and Perceptual Curiosity (PC). The results showed that the learning of Discovery Learning by using Hand on Activity is effective toward mathematics critical thinking abilities. Students of the EC type are able to complete six indicators of mathematics critical thinking abilities, although there are still two indicators that the result is less than the maximum. While students of PC type have not fully been able to complete the indicator of mathematics critical thinking abilities. They are only strong on indicators formulating questions, while on the other five indicators they are still weak. The critical thinking abilities of EC’s students is better than the critical thinking abilities of the PC’s students.

Neutral gas sympathetic cooling of an ion in a Paul trap.

PubMed

Chen, Kuang; Sullivan, Scott T; Hudson, Eric R

2014-04-11

A single ion immersed in a neutral buffer gas is studied. An analytical model is developed that gives a complete description of the dynamics and steady-state properties of the ions. An extension of this model, using techniques employed in the mathematics of economics and finance, is used to explain the recent observation of non-Maxwellian statistics for these systems. Taken together, these results offer an explanation of the long-standing issues associated with sympathetic cooling of an ion by a neutral buffer gas.

Neutral Gas Sympathetic Cooling of an Ion in a Paul Trap

NASA Astrophysics Data System (ADS)

Chen, Kuang; Sullivan, Scott T.; Hudson, Eric R.

2014-04-01

A single ion immersed in a neutral buffer gas is studied. An analytical model is developed that gives a complete description of the dynamics and steady-state properties of the ions. An extension of this model, using techniques employed in the mathematics of economics and finance, is used to explain the recent observation of non-Maxwellian statistics for these systems. Taken together, these results offer an explanation of the long-standing issues associated with sympathetic cooling of an ion by a neutral buffer gas.

Control of Supercavitation Flow and Stability of Supercavitating Motion of Bodies

DTIC Science & Technology

2001-02-01

sign opposite to a sign of angle Vf - accidental deflection of the model Sgn M = -Sgn i. 4.3. EQUATIONS OF THE SCM DYNAMICS The most effective method of...the motion stability in interactive regime "researcher - computer" [ 16]. The complete mathematical model of the SCM motion includes a set of equations ...of solid body dynamics, equations to calculate the unsteady cavity shape and relations to calculate the acting forces. A set of dynamic equations of

DAISY: a new software tool to test global identifiability of biological and physiological systems

PubMed Central

Bellu, Giuseppina; Saccomani, Maria Pia; Audoly, Stefania; D’Angiò, Leontina

2009-01-01

A priori global identifiability is a structural property of biological and physiological models. It is considered a prerequisite for well-posed estimation, since it concerns the possibility of recovering uniquely the unknown model parameters from measured input-output data, under ideal conditions (noise-free observations and error-free model structure). Of course, determining if the parameters can be uniquely recovered from observed data is essential before investing resources, time and effort in performing actual biomedical experiments. Many interesting biological models are nonlinear but identifiability analysis for nonlinear system turns out to be a difficult mathematical problem. Different methods have been proposed in the literature to test identifiability of nonlinear models but, to the best of our knowledge, so far no software tools have been proposed for automatically checking identifiability of nonlinear models. In this paper, we describe a software tool implementing a differential algebra algorithm to perform parameter identifiability analysis for (linear and) nonlinear dynamic models described by polynomial or rational equations. Our goal is to provide the biological investigator a completely automatized software, requiring minimum prior knowledge of mathematical modelling and no in-depth understanding of the mathematical tools. The DAISY (Differential Algebra for Identifiability of SYstems) software will potentially be useful in biological modelling studies, especially in physiology and clinical medicine, where research experiments are particularly expensive and/or difficult to perform. Practical examples of use of the software tool DAISY are presented. DAISY is available at the web site http://www.dei.unipd.it/~pia/. PMID:17707944

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…

Elementary Preservice Teachers' and Elementary Inservice Teachers' Knowledge of Mathematical Modeling

ERIC Educational Resources Information Center

Schwerdtfeger, Sara

2017-01-01

This study examined the differences in knowledge of mathematical modeling between a group of elementary preservice teachers and a group of elementary inservice teachers. Mathematical modeling has recently come to the forefront of elementary mathematics classrooms because of the call to add mathematical modeling tasks in mathematics classes through…

Secondary School Advanced Mathematics, Chapter 4, Equations, Inequalities, and Radicals, Chapter 5, Circles and Spheres. Teacher's Commentary.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This manual was designed for use with the third of five texts in the Secondary School Advanced Mathematics (SSAM) series. Developed for students who have completed the Secondary School Mathematics (SSM) program and wish to continue their studies in mathematics, this series is designed to review, strengthen, and fill gaps in the material covered in…

Secondary School Advanced Mathematics, Chapter 1, Organizing Geometric Knowledge, Chapter 2, Concepts and Skills in Algebra. Teacher's Commentary.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This manual was designed for use with the first of five texts in the Secondary School Advanced Mathematics (SSAM) series. Developed for students who have completed the Secondary School Mathematics (SSM) program and wish to continue their studies in mathematics, this series is designed to review, strengthen, and fill gaps in the material covered in…

Secondary School Advanced Mathematics, Chapter 4, Equations, Inequalities, and Radicals, Chapter 5, Circles and Spheres. Student's Text.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This text is the third of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. The first of the two chapters in this text deals with equations, inequalities and radicals.…

Attitudinal and Motivational Variables Related to Mathematics Achievement in Jordan: Findings from the Third International Mathematics and Science Study (TIMSS)

ERIC Educational Resources Information Center

Hammouri, Hind

2004-01-01

The purpose of the present study was to examine the effects of student-related variables on achievement in mathematics. The sample consisted of 3736 13-year-old Jordanian 8th-graders who participated in the Third International Mathematics and Science Study (TIMSS). The participants completed a student questionnaire and participated in the…

A Case Study of Teachers' Development of Well-Structured Mathematical Modelling Activities

ERIC Educational Resources Information Center

Stohlmann, Micah; Maiorca, Cathrine; Allen, Charlie

2017-01-01

This case study investigated how three teachers developed mathematical modelling activities integrated with content standards through participation in a course on mathematical modelling. The class activities involved experiencing a mathematical modelling activity, reading and rating example mathematical modelling activities, reading articles about…

All complete intersection Calabi-Yau four-folds

NASA Astrophysics Data System (ADS)

Gray, James; Haupt, Alexander S.; Lukas, Andre

2013-07-01

We present an exhaustive, constructive, classification of the Calabi-Yau four-folds which can be described as complete intersections in products of projective spaces. A comprehensive list of 921,497 configuration matrices which represent all topologically distinct types of complete intersection Calabi-Yau four-folds is provided and can be downloaded from http://www-thphys.physics.ox.ac.uk/projects/CalabiYau/Cicy4folds/index.html. The manifolds have non-negative Euler characteristics in the range 0 ≤ χ ≤ 2610. This data set will be of use in a wide range of physical and mathematical applications. Nearly all of these four-folds are elliptically fibered and are thus of interest for F-theory model building.

The Worm Propagation Model with Dual Dynamic Quarantine Strategy

NASA Astrophysics Data System (ADS)

Yao, Yu; Xie, Xiao-Wu; Guo, Hao; Gao, Fu-Xiang; Yu, Ge

Internet worms are becoming more and more harmful with the rapid development of the Internet. Due to the extremely fast spread and great destructive power of network worms, strong dynamic quarantine strategies are necessary. Inspired by the real-world approach to the prevention and treatment of infectious diseases, this paper proposes a quarantine strategy based on dynamic worm propagation model: the SIQRV dual quarantine model. This strategy uses dynamic quarantine method to make the vulnerable host and infected host quarantined, and then release them after a certain period of time, regardless of whether quarantined host security is checked. Through mathematic modeling, it has been found that when the basic reproduction number R0 is less than a critical value, the system will stabilize in the disease-free equilibrium, that is, in theory, the infected hosts will be completely immune. Finally, by comparing the simulation results and numerical analysis, the basic agreement between the two curves supports the validity of the mathematical model. Our future work will be focusing on taking both the delay and double-quarantine strategy into account and further expanding the scale of our simulation work.

Mathematical Ability Relies on Knowledge, Too

ERIC Educational Resources Information Center

Sweller, John; Clark, Richard E.; Kirschner, Paul A.

2011-01-01

Recent "reform" curricula both ignore the absence of supporting data and completely misunderstand the role of problem solving in cognition. If, the argument goes, teachers are not really teaching people mathematics but rather are teaching them some form of general problem solving, then mathematical content can be reduced in importance. According…

Recommendations for Alternative Credit.

ERIC Educational Resources Information Center

Lenderman, Ed; And Others

Following a review of the mathematics topics taught in accounting, electronics, auto, food and clothing, and metals courses at Linn-Benton Community College, Albany, Oregon, recommendations were made to grant one semester of mathematics credit for completing a two-year sequence of these courses. The other required semester of mathematics should be…

Elementary Mathematics Specialists: Ensuring the Intersection of Research and Practice

ERIC Educational Resources Information Center

McGatha, Maggie B.

2017-01-01

This paper provides a historical overview of the role and impact of elementary mathematics specialists as well as current implications and opportunities for the field. Furthermore, suggestions are offered for the mathematics education field for ensuring the intersection of practice and research. [For complete proceedings, see ED581294.

Applied Mathematics. Florida Teaching Supplement.

ERIC Educational Resources Information Center

Florida State Dept. of Education, Tallahassee. Div. of Vocational, Adult, and Community Education.

The information in this supplementary notebook is intended to provide teachers with additional materials, ideas and suggestions, and activities to help in implementing the first 21 units of the Applied Mathematics modules that help develop and refine job-related mathematics skills. An introduction lists the 36 units of the complete Applied…

Strength in Numbers? Women and Mathematics

ERIC Educational Resources Information Center

Beaton, Ann; Tougas, Francine; Rinfret, Natalie; Huard, Nathalie; Delisle, Marie-Noelle

2007-01-01

Two studies were conducted to test the link between numerical distinctiveness, stereotype threat and mathematical performance among women. In the first study, stereotype threat was measured with a stereotype activation task. Women in a solo, non-solo or control condition completed word fragments and a mathematical activity. Solo women, rather than…

Mathematics from High School to Community College: Preparation, Articulation, and College Un-Readiness

ERIC Educational Resources Information Center

Jaffe, Louise

2012-01-01

This research studied the role of mathematics as a roadblock to college completion for community college-bound students in California. Using longitudinal quantitative analysis, I observed the educational pipeline between high school and community college and analyzed how different high school mathematics histories predicted readiness, or…

Mathematical Thinking: Challenging Prospective Teachers to Do More than "Talk the Talk"

ERIC Educational Resources Information Center

Prendergast, Mark; Johnson, Patrick; Fitzmaurice, Olivia; Liston, Miriam; O'Keeffe, Lisa; O'Meara, Niamh

2014-01-01

This paper reports on a research project which aims to improve prospective mathematics teachers' relational understanding and pedagogical beliefs for teaching in second-level Irish classrooms. Prospective mathematics teachers complete their teacher education training with varying pedagogical beliefs, and often little relational understanding of…

Young Children's Block Play and Mathematical Learning

ERIC Educational Resources Information Center

Park, Boyoung; Chae, Jeong-Lim; Boyd, Barbara Foulks

2008-01-01

This qualitative study investigated young children's mathematical engagement in play with wooden unit blocks. Two boys, ages 6 and 7, were independently observed completing the task of filling outlined regions with the various sets of blocks. Three major mathematical actions were observed: categorizing geometric shapes, composing a larger shape…

Mathematics Teacher Educators' Perceptions and Use of Cognitive Research

ERIC Educational Resources Information Center

Laski, Elida V.; Reeves, Todd D.; Ganley, Colleen M.; Mitchell, Rebecca

2013-01-01

Instructors ("N"?=?204) of elementary mathematics methods courses completed a survey assessing the extent to which they value cognitive research and incorporate it into their courses. Instructors' responses indicated that they view cognitive research to be fairly important for mathematics education, particularly studies of domain-specific topics,…

A Multi-Method Investigation of Mathematics Motivation for Elementary Age Students

ERIC Educational Resources Information Center

Linder, Sandra M.; Smart, Julie B.; Cribbs, Jennifer

2015-01-01

This paper presents the results of a multi-method study examining elementary students with high self-reported levels of mathematics motivation. Second- through fifth-grade students at a Title One school in the southeastern United States completed the Elementary Mathematics Motivation Instrument (EMMI), which examines levels of mathematics…

Closing the Gap: First Year Success in College Mathematics at an HBCU

ERIC Educational Resources Information Center

Harrington, Melissa A.; Lloyd, Andrew; Smolinski, Tomasz; Shahin, Mazen

2016-01-01

At our Historically-Black University, about 89% of first-year students place into developmental mathematics, negatively impacting retention and degree completion. In 2012, an NSF-funded learning enrichment project began offering the introductory and developmental mathematics courses on-line over the summer to incoming science, technology,…

Internal consistency reliability and validity of the Arabic translation of the Mathematics Teaching Efficacy Beliefs Instrument.

PubMed

Alkhateeb, Haitham M

2004-06-01

The Arabic translation of the Mathematics Teaching Efficacy Beliefs was completed by 144 undergraduate students (M age=20.6) in Jordan. The findings support the internal reliability of the Arabic translation of the Mathematics Teaching Efficacy Beliefs as well as its construct validity.

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…

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…

Mathematics teachers' conceptions about modelling activities and its reflection on their beliefs about mathematics

NASA Astrophysics Data System (ADS)

Shahbari, Juhaina Awawdeh

2018-07-01

The current study examines whether the engagement of mathematics teachers in modelling activities and subsequent changes in their conceptions about these activities affect their beliefs about mathematics. The sample comprised 52 mathematics teachers working in small groups in four modelling activities. The data were collected from teachers' Reports about features of each activity, interviews and questionnaires on teachers' beliefs about mathematics. The findings indicated changes in teachers' conceptions about the modelling activities. Most teachers referred to the first activity as a mathematical problem but emphasized only the mathematical notions or the mathematical operations in the modelling process; changes in their conceptions were gradual. Most of the teachers referred to the fourth activity as a mathematical problem and emphasized features of the whole modelling process. The results of the interviews indicated that changes in the teachers' conceptions can be attributed to structure of the activities, group discussions, solution paths and elicited models. These changes about modelling activities were reflected in teachers' beliefs about mathematics. The quantitative findings indicated that the teachers developed more constructive beliefs about mathematics after engagement in the modelling activities and that the difference was significant, however there was no significant difference regarding changes in their traditional beliefs.

On dynamics of integrate-and-fire neural networks with conductance based synapses.

PubMed

Cessac, Bruno; Viéville, Thierry

2008-01-01

We present a mathematical analysis of networks with integrate-and-fire (IF) neurons with conductance based synapses. Taking into account the realistic fact that the spike time is only known within some finite precision, we propose a model where spikes are effective at times multiple of a characteristic time scale delta, where delta can be arbitrary small (in particular, well beyond the numerical precision). We make a complete mathematical characterization of the model-dynamics and obtain the following results. The asymptotic dynamics is composed by finitely many stable periodic orbits, whose number and period can be arbitrary large and can diverge in a region of the synaptic weights space, traditionally called the "edge of chaos", a notion mathematically well defined in the present paper. Furthermore, except at the edge of chaos, there is a one-to-one correspondence between the membrane potential trajectories and the raster plot. This shows that the neural code is entirely "in the spikes" in this case. As a key tool, we introduce an order parameter, easy to compute numerically, and closely related to a natural notion of entropy, providing a relevant characterization of the computational capabilities of the network. This allows us to compare the computational capabilities of leaky and IF models and conductance based models. The present study considers networks with constant input, and without time-dependent plasticity, but the framework has been designed for both extensions.

Non-linear analytic and coanalytic problems ( L_p-theory, Clifford analysis, examples)

NASA Astrophysics Data System (ADS)

Dubinskii, Yu A.; Osipenko, A. S.

2000-02-01

Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the "orthogonal" sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented.

Physico-chemical study of some areas of fundamental significance to biophysics. Final report, 1974--1977

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

McGlynn, S.P.

1977-08-18

The comprehensive report includes a complete list of publications resulting from the work and a review of studies made in the vacuum ultraviolet, photoelectron spectroscopy, excited states and electron structure of inorganic salts, a model for polar molecules, application of abstract mathematics to the genetic code, the orbital approximation in which orbital properties are related to state properties. (JSR)

Utilizing Structural Equation Modeling and Social Cognitive Career Theory to Identify Factors in Choice of It as a Major

ERIC Educational Resources Information Center

Luse, Andy; Rursch, Julie A.; Jacobson, Doug

2014-01-01

In the United States, the number of students entering into and completing degrees in science, technology, engineering, and mathematics (STEM) areas has declined significantly over the past decade. Although modest increases have been shown in enrollments in computer-related majors in the past 4 years, the prediction is that even in 3 to 4 years…

The 24-Hour Mathematical Modeling Challenge

ERIC Educational Resources Information Center

Galluzzo, Benjamin J.; Wendt, Theodore J.

2015-01-01

Across the mathematics curriculum there is a renewed emphasis on applications of mathematics and on mathematical modeling. Providing students with modeling experiences beyond the ordinary classroom setting remains a challenge, however. In this article, we describe the 24-hour Mathematical Modeling Challenge, an extracurricular event that exposes…

Condensation of Forced Convection Two-Phase Flow in a Miniature Tube

NASA Technical Reports Server (NTRS)

Begg, E.; Faghri, A.; Krustalev, D.

1999-01-01

A physical/mathematical model of annular film condensation at the inlet of a miniature tube has been developed. In the model, the liquid flow is coupled with the vapor flow along the liquid-vapor interface through the interfacial temperature, heat flux, shear stress, and pressure jump conditions due to surface tension effects. The model predicts the shape of the liquid-vapor interface along the condenser and leads to the conclusion that there is complete condensation at a certain distance from the condenser inlet. The numerical results show that complete condensation of the incoming vapor is possible at comparatively low heat loads and that this is a special case of a more general condensation regime with two-phase bubbly flow downstream of the initial annular film condensation region. Observations from the flow visualization experiment confirm the existence and qualitative features of annular film condensation leading to the complete condensation phenomenon in a small diameter (3.25 mm) circular tube condenser.

College Students' Persistence and Degree Completion in Science, Technology, Engineering, and Mathematics (STEM): The Role of Non-Cognitive Attributes of Self-Efficacy, Outcome Expectations, and Interest

ERIC Educational Resources Information Center

Aryee, Michael

2017-01-01

The lack of students' persistence (or student's effort to continue their academic studies until degree completion) in Science, Technology, Engineering, and Mathematics (STEM) and the attrition of STEM students as well as the shortage of STEM workers have gathered much attention from policy makers, governmental agencies, higher education…

Tensor and Spin Representations of SO(4) and Discrete Quantum Gravity

NASA Astrophysics Data System (ADS)

Lorente, M.; Kramer, P.

Starting from the defining transformations of complex matrices for the SO(4) group, we construct the fundamental representation and the tensor and spinor representations of the group SO(4). Given the commutation relations for the corresponding algebra, the unitary representations of the group in terms of the generalized Euler angles are constructed. These mathematical results help us to a more complete description of the Barret-Crane model in Quantum Gravity. In particular a complete realization of the weight function for the partition function is given and a new geometrical interpretation of the asymptotic limit for the Regge action is presented.

Theoretical Fluid Mechanics

NASA Astrophysics Data System (ADS)

Fitzpatrick, Richard

2017-12-01

'Theoretical Fluid Mechanics' has been written to aid physics students who wish to pursue a course of self-study in fluid mechanics. It is a comprehensive, completely self-contained text with equations of fluid mechanics derived from first principles, and any required advanced mathematics is either fully explained in the text, or in an appendix. It is accompanied by about 180 exercises with completely worked out solutions. It also includes extensive sections on the application of fluid mechanics to topics of importance in astrophysics and geophysics. These topics include the equilibrium of rotating, self-gravitating, fluid masses; tidal bores; terrestrial ocean tides; and the Eddington solar model.

Report on the formal specification and partial verification of the VIPER microprocessor

NASA Technical Reports Server (NTRS)

Brock, Bishop; Hunt, Warren A., Jr.

1991-01-01

The formal specification and partial verification of the VIPER microprocessor is reviewed. The VIPER microprocessor was designed by RSRE, Malvern, England, for safety critical computing applications (e.g., aircraft, reactor control, medical instruments, armaments). The VIPER was carefully specified and partially verified in an attempt to provide a microprocessor with completely predictable operating characteristics. The specification of VIPER is divided into several levels of abstraction, from a gate-level description up to an instruction execution model. Although the consistency between certain levels was demonstrated with mechanically-assisted mathematical proof, the formal verification of VIPER was never completed.

Secondary School Advanced Mathematics, Chapter 6, The Complex Number System, Chapter 7, Equations of the First and Second Degree in Two Variables. Student's Text.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This text is the fourth of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. This text begins with a brief discussion of quadratic equations which motivates the…

Secondary School Advanced Mathematics, Chapter 6, The Complex Number System, Chapter 7, Equations of the First and Second Degree in Two Variables. Teacher's Commentary.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This manual was designed for use with the fourth of five texts in the Secondary School Advanced Mathematics (SSAM) series. Developed for students who have completed the Secondary School Mathematics (SSM) program and wish to continue their studies in mathematics, this series is designed to review, strengthen, and fill gaps in the material covered…

The Relationship between Students' Performance on Conventional Standardized Mathematics Assessments and Complex Mathematical Modeling Problems

ERIC Educational Resources Information Center

Kartal, Ozgul; Dunya, Beyza Aksu; Diefes-Dux, Heidi A.; Zawojewski, Judith S.

2016-01-01

Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…

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…

Modeling and numerical simulations of the influenced Sznajd model

NASA Astrophysics Data System (ADS)

Karan, Farshad Salimi Naneh; Srinivasan, Aravinda Ramakrishnan; Chakraborty, Subhadeep

2017-08-01

This paper investigates the effects of independent nonconformists or influencers on the behavioral dynamic of a population of agents interacting with each other based on the Sznajd model. The system is modeled on a complete graph using the master equation. The acquired equation has been numerically solved. Accuracy of the mathematical model and its corresponding assumptions have been validated by numerical simulations. Regions of initial magnetization have been found from where the system converges to one of two unique steady-state PDFs, depending on the distribution of influencers. The scaling property and entropy of the stationary system in presence of varying level of influence have been presented and discussed.

Modeling and numerical simulations of the influenced Sznajd model.

PubMed

Karan, Farshad Salimi Naneh; Srinivasan, Aravinda Ramakrishnan; Chakraborty, Subhadeep

2017-08-01

This paper investigates the effects of independent nonconformists or influencers on the behavioral dynamic of a population of agents interacting with each other based on the Sznajd model. The system is modeled on a complete graph using the master equation. The acquired equation has been numerically solved. Accuracy of the mathematical model and its corresponding assumptions have been validated by numerical simulations. Regions of initial magnetization have been found from where the system converges to one of two unique steady-state PDFs, depending on the distribution of influencers. The scaling property and entropy of the stationary system in presence of varying level of influence have been presented and discussed.

Mathematics in Power Technology.

ERIC Educational Resources Information Center

Trombley, Carl; And Others

This mathematics curriculum is designed to be taught by the technology education teacher during the power technology class over a period of 2 years. It is intended to be elective in nature; upon successful completion of both years, one-half credit in mathematics is to be awarded. A list of the academic competencies contained in the curriculum…

Connecting Research to Teaching: Integrated Curricula and Preparation for College Mathematics

ERIC Educational Resources Information Center

Post, Thomas R.; Monson, Debra S.; Andersen, Edwin; Harwell, Michael R.

2012-01-01

In the early 1990s, after a long series of disappointing results on national and international mathematics achievement tests the National Science Foundation (NSF) funded the development of thirteen complete mathematics programs at the elementary school, middle school, and secondary school levels. Many teachers were quite happy with the new…

Constructive Metacognitive Activity Shift in Mathematical Problem Solving

ERIC Educational Resources Information Center

Hastuti, Intan Dwi; Nusantara, Toto; Subanji; Susanto, Hery

2016-01-01

This study aims to describe the constructive metacognitive activity shift of eleventh graders in solving a mathematical problem. Subjects in this study were 10 students in grade 11 of SMAN 1 Malang. They were divided into 4 groups. Three types of metacognitive activity undertaken by students when completing mathematical problem are awareness,…

Community College Pathways: A Descriptive Report of Summative Assessments and Student Learning

ERIC Educational Resources Information Center

Strother, Scott; Sowers, Nicole

2014-01-01

Carnegie's Community College Pathways (CCP) offers two pathways, Statway® and Quantway®, that reduce the amount of time required to complete developmental mathematics and earn college-level mathematics credit. The Pathways aim to improve student success in mathematics while maintaining rigorous content, pedagogy, and learning outcomes. It is…

Demonstration Lessons in Mathematics Education: Teachers' Observation Foci and Intended Changes in Practice

ERIC Educational Resources Information Center

Clarke, Doug; Roche, Anne; Wilkie, Karina; Wright, Vince; Brown, Jill; Downton, Ann; Horne, Marj; Knight, Rose; McDonough, Andrea; Sexton, Matthew; Worrall, Chris

2013-01-01

As part of a teacher professional learning project in mathematics education, university mathematics educators taught demonstration lessons in project primary schools. These lessons were part of a "pre-brief, teaching, and debrief" process, in which up to eight teachers observed each lesson. Using brief questionnaires completed in advance of the…

A Case Study of Two Groups of Elementary Prospective Teachers' Experiences in Distinct Mathematics Content Courses

ERIC Educational Resources Information Center

Auslander, Susan Swars; Smith, Stephanie Z.; Smith, Marvin E.; Hart, Lynn C.; Carothers, Jody

2016-01-01

This multiple case study examined two groups of elementary prospective teachers (n=12) completing distinct mathematics content courses. Data were collected via two belief surveys, one content knowledge assessment, and individual interviews. The findings revealed differences in specialized content knowledge and mathematical beliefs between the two…

Relating Aspects of Motivation to Facets of Mathematical Competence Varying in Cognitive Demand

ERIC Educational Resources Information Center

Gilbert, Melissa C.

2016-01-01

The author investigated the relationship between aspects of student motivation and performance on mathematical tasks varying in cognitive demand relevant to meeting the expectations of the Common Core State Standards for Mathematics (CCSS-M). A sample of 479 primarily Latino middle school students completed established survey measures of…

Case Study of a College Mathematics Instructor: Patterns of Classroom Discourse

ERIC Educational Resources Information Center

Tsay, Jenq-Jong; Judd, April B.; Hauk, Shandy; Davis, Mark K.

2011-01-01

In the United States, undergraduates--regardless of their field of study--generally must complete a mathematics course to meet breadth-of-study requirements. This report is aimed at providing a research foundation for practical efforts to improve teaching and learning in such college mathematics service courses (e.g., college algebra, liberal arts…

Mathematical Modeling: A Bridge to STEM Education

ERIC Educational Resources Information Center

Kertil, Mahmut; Gurel, Cem

2016-01-01

The purpose of this study is making a theoretical discussion on the relationship between mathematical modeling and integrated STEM education. First of all, STEM education perspective and the construct of mathematical modeling in mathematics education is introduced. A review of literature is provided on how mathematical modeling literature may…

The influence of mathematics learning using SAVI approach on junior high school students’ mathematical modelling ability

NASA Astrophysics Data System (ADS)

Khusna, H.; Heryaningsih, N. Y.

2018-01-01

The aim of this research was to examine mathematical modeling ability who learn mathematics by using SAVI approach. This research was a quasi-experimental research with non-equivalent control group designed by using purposive sampling technique. The population of this research was the state junior high school students in Lembang while the sample consisted of two class at 8th grade. The instrument used in this research was mathematical modeling ability. Data analysis of this research was conducted by using SPSS 20 by Windows. The result showed that students’ ability of mathematical modeling who learn mathematics by using SAVI approach was better than students’ ability of mathematical modeling who learn mathematics using conventional learning.

Beyond Motivation: Exploring Mathematical Modeling as a Context for Deepening Students' Understandings of Curricular Mathematics

ERIC Educational Resources Information Center

Zbiek, Rose Mary; Conner, Annamarie

2006-01-01

Views of mathematical modeling in empirical, expository, and curricular references typically capture a relationship between real-world phenomena and mathematical ideas from the perspective that competence in mathematical modeling is a clear goal of the mathematics curriculum. However, we work within a curricular context in which mathematical…

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…

Genomic signal processing: from matrix algebra to genetic networks.

PubMed

Alter, Orly

2007-01-01

DNA microarrays make it possible, for the first time, to record the complete genomic signals that guide the progression of cellular processes. Future discovery in biology and medicine will come from the mathematical modeling of these data, which hold the key to fundamental understanding of life on the molecular level, as well as answers to questions regarding diagnosis, treatment, and drug development. This chapter reviews the first data-driven models that were created from these genome-scale data, through adaptations and generalizations of mathematical frameworks from matrix algebra that have proven successful in describing the physical world, in such diverse areas as mechanics and perception: the singular value decomposition model, the generalized singular value decomposition model comparative model, and the pseudoinverse projection integrative model. These models provide mathematical descriptions of the genetic networks that generate and sense the measured data, where the mathematical variables and operations represent biological reality. The variables, patterns uncovered in the data, correlate with activities of cellular elements such as regulators or transcription factors that drive the measured signals and cellular states where these elements are active. The operations, such as data reconstruction, rotation, and classification in subspaces of selected patterns, simulate experimental observation of only the cellular programs that these patterns represent. These models are illustrated in the analyses of RNA expression data from yeast and human during their cell cycle programs and DNA-binding data from yeast cell cycle transcription factors and replication initiation proteins. Two alternative pictures of RNA expression oscillations during the cell cycle that emerge from these analyses, which parallel well-known designs of physical oscillators, convey the capacity of the models to elucidate the design principles of cellular systems, as well as guide the design of synthetic ones. In these analyses, the power of the models to predict previously unknown biological principles is demonstrated with a prediction of a novel mechanism of regulation that correlates DNA replication initiation with cell cycle-regulated RNA transcription in yeast. These models may become the foundation of a future in which biological systems are modeled as physical systems are today.

Reflective Modeling in Teacher Education.

ERIC Educational Resources Information Center

Shealy, Barry E.

This paper describes mathematical modeling activities from a secondary mathematics teacher education course taken by fourth-year university students. Experiences with mathematical modeling are viewed as important in helping teachers develop a more intuitive understanding of mathematics, generate and evaluate mathematical interpretations, and…

Applications of numerical methods to simulate the movement of contaminants in groundwater.

PubMed Central

Sun, N Z

1989-01-01

This paper reviews mathematical models and numerical methods that have been extensively used to simulate the movement of contaminants through the subsurface. The major emphasis is placed on the numerical methods of advection-dominated transport problems and inverse problems. Several mathematical models that are commonly used in field problems are listed. A variety of numerical solutions for three-dimensional models are introduced, including the multiple cell balance method that can be considered a variation of the finite element method. The multiple cell balance method is easy to understand and convenient for solving field problems. When the advection transport dominates the dispersion transport, two kinds of numerical difficulties, overshoot and numerical dispersion, are always involved in solving standard, finite difference methods and finite element methods. To overcome these numerical difficulties, various numerical techniques are developed, such as upstream weighting methods and moving point methods. A complete review of these methods is given and we also mention the problems of parameter identification, reliability analysis, and optimal-experiment design that are absolutely necessary for constructing a practical model. PMID:2695327

Effect of particle size, polydispersity and polymer degradation on progesterone release from PLGA microparticles: Experimental and mathematical modeling.

PubMed

Busatto, Carlos; Pesoa, Juan; Helbling, Ignacio; Luna, Julio; Estenoz, Diana

2018-01-30

Poly(lactic-co-glycolic acid) (PLGA) microparticles containing progesterone were prepared by the solvent extraction/evaporation and microfluidic techniques. Microparticles were characterized by their size distribution, encapsulation efficiency, morphology and thermal properties. The effect of particle size, polydispersity and polymer degradation on the in vitro release of the hormone was studied. A triphasic release profile was observed for larger microparticles, while smaller microspheres showed a biphasic release profile. This behavior is related to the fact that complete drug release was achieved in a few days for smaller microparticles, during which polymer degradation effects are still negligible. A mathematical model was developed that predicts the progesterone release profiles from different-sized PLGA microspheres. The model takes into account both the dissolution and diffusion of the drug in the polymeric matrix as well as the autocatalytic effect of polymer degradation. The model was adjusted and validated with novel experimental data. Simulation results are in very good agreement with experimental results. Copyright © 2017 Elsevier B.V. All rights reserved.

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…

Three-Dimensional Model for Preservation and Restoration of Architectural Heritage

NASA Technical Reports Server (NTRS)

Marchis, Elena

2011-01-01

Thc aim of the research will be to create a model, three-dimensional mathematical. implementation. consultation and assistance to "large" restoration projects that will assist the structural analysis, allowing easier display of dynamic strain. analysis and lighting noise. It could also be a valuable tool for decision support. therefore. may simulate several possible scenarios for intervention, This model appears therefore an excellent support for recovering. ordering and monitoring information about materials and data (stage of restoration. photographs. sampling points. results of diagnostic tests, etc.) collected dynamically during the "life" of the cultural heritage. allowing to document its complete history

Mathematical modeling of high and low temperature heat pipes

NASA Technical Reports Server (NTRS)

Chi, S. W.

1971-01-01

Following a review of heat and mass transfer theory relevant to heat pipe performance, math models are developed for calculating heat-transfer limitations of high-temperature heat pipes and heat-transfer limitations and temperature gradient of low temperature heat pipes. Calculated results are compared with the available experimental data from various sources to increase confidence in the present math models. Complete listings of two computer programs for high- and low-temperature heat pipes respectively are included. These programs enable the performance to be predicted of heat pipes with wrapped-screen, rectangular-groove, or screen-covered rectangular-groove wick.

Pharmacy students' perceptions of natural science and mathematics subjects.

PubMed

Prescott, Julie; Wilson, Sarah Ellen; Wan, Kai-Wai

2014-08-15

To determine the level of importance pharmacy students placed on science and mathematics subjects for pursuing a career in pharmacy. Two hundred fifty-four students completed a survey instrument developed to investigate students' perceptions of the relevance of science and mathematics subjects to a career in pharmacy. Pharmacy students in all 4 years of a master of pharmacy (MPharm) degree program were invited to complete the survey instrument. Students viewed chemistry-based and biology-based subjects as relevant to a pharmacy career, whereas mathematics subjects such as physics, logarithms, statistics, and algebra were not viewed important to a career in pharmacy. Students' experience in pharmacy and year of study influenced their perceptions of subjects relevant to a pharmacy career. Pharmacy educators need to consider how they can help students recognize the importance of scientific knowledge earlier in the pharmacy curriculum.

Assessment of Galileo modal test results for mathematical model verification

NASA Technical Reports Server (NTRS)

Trubert, M.

1984-01-01

The modal test program for the Galileo Spacecraft was completed at the Jet Propulsion Laboratory in the summer of 1983. The multiple sine dwell method was used for the baseline test. The Galileo Spacecraft is a rather complex 2433 kg structure made of a central core on which seven major appendages representing 30 percent of the total mass are attached, resulting in a high modal density structure. The test revealed a strong nonlinearity in several major modes. This nonlinearity discovered in the course of the test necessitated running additional tests at the unusually high response levels of up to about 21 g. The high levels of response were required to obtain a model verification valid at the level of loads for which the spacecraft was designed. Because of the high modal density and the nonlinearity, correlation between the dynamic mathematical model and the test results becomes a difficult task. Significant changes in the pre-test analytical model are necessary to establish confidence in the upgraded analytical model used for the final load verification. This verification, using a test verified model, is required by NASA to fly the Galileo Spacecraft on the Shuttle/Centaur launch vehicle in 1986.

The implementation of multiple intelligences based teaching model to improve mathematical problem solving ability for student of junior high school

NASA Astrophysics Data System (ADS)

Fasni, Nurli; Fatimah, Siti; Yulanda, Syerli

2017-05-01

This research aims to achieve some purposes such as: to know whether mathematical problem solving ability of students who have learned mathematics using Multiple Intelligences based teaching model is higher than the student who have learned mathematics using cooperative learning; to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using Multiple Intelligences based teaching model., to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using cooperative learning; to know the attitude of the students to Multiple Intelligences based teaching model. The method employed here is quasi-experiment which is controlled by pre-test and post-test. The population of this research is all of VII grade in SMP Negeri 14 Bandung even-term 2013/2014, later on two classes of it were taken for the samples of this research. A class was taught using Multiple Intelligences based teaching model and the other one was taught using cooperative learning. The data of this research were gotten from the test in mathematical problem solving, scale questionnaire of the student attitudes, and observation. The results show the mathematical problem solving of the students who have learned mathematics using Multiple Intelligences based teaching model learning is higher than the student who have learned mathematics using cooperative learning, the mathematical problem solving ability of the student who have learned mathematics using cooperative learning and Multiple Intelligences based teaching model are in intermediate level, and the students showed the positive attitude in learning mathematics using Multiple Intelligences based teaching model. As for the recommendation for next author, Multiple Intelligences based teaching model can be tested on other subject and other ability.

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…

Longitudinal Associations between Executive Control and Developing Mathematical Competence in Preschool Boys and Girls

ERIC Educational Resources Information Center

Clark, Caron A. C.; Sheffield, Tiffany D.; Wiebe, Sandra A.; Espy, Kimberly A.

2013-01-01

Executive control (EC) is related to mathematics performance in middle childhood. However, little is known regarding how EC and informal numeracy differentially support mathematics skill acquisition in preschoolers. A sample of preschoolers (115 girls, 113 boys), stratified by social risk, completed an EC task battery at 3 years, informal numeracy…

Effects of Improvements in Interval Timing on the Mathematics Achievement of Elementary School Students

ERIC Educational Resources Information Center

Taub, Gordon E.; McGrew, Kevin S.; Keith, Timothy Z.

2015-01-01

This article examines the effect of improvements in timing/rhythmicity on mathematics achievement. A total of 86 participants attending 1st through 4th grades completed pre- and posttest measures of mathematics achievement from the Woodcock-Johnson III Tests of Achievement. Students in the experimental group participated in a 4-week intervention…

Integrating Multicultural Children's Math Books into Kindergarten through Sixth-Grade Classrooms: Preservice Teachers' Reflections

ERIC Educational Resources Information Center

Harding, Jenni; Hbaci, Ilham; Loyd, Stacy; Hamilton, Boni

2017-01-01

This case study of mathematics instruction using children's literature reports on the experiences 47 elementary preservice teachers had in their mathematics methods course while completing a microteaching assignment. As part of the microteaching assignment, preservice teachers were required to plan and teach mathematics lessons based on children's…

Mathematical Literacy in Undergraduates: Role of Gender, Emotional Intelligence and Emotional Self-Efficacy

ERIC Educational Resources Information Center

Tariq, Vicki N.; Qualter, Pamela; Roberts, Sian; Appleby, Yvon; Barnes, Lynne

2013-01-01

This empirical study explores the roles that Emotional Intelligence (EI) and Emotional Self-Efficacy (ESE) play in undergraduates' mathematical literacy, and the influence of EI and ESE on students' attitudes towards and beliefs about mathematics. A convenience sample of 93 female and 82 male first-year undergraduates completed a test of…

Objects, Signs, and Representations in the Semio-Cognitive Analysis of the Processes Involved in Teaching and Learning Mathematics: A Duvalian Perspective

ERIC Educational Resources Information Center

Iori, Maura

2017-01-01

In mathematical activities and in the analysis of mathematics teaching-learning processes, "objects," "signs", and "representations" are often mentioned, where the meaning assigned to those words is sometimes very broad, sometimes limited, other times intuitive, allusive, or not completely clear. On the other hand, as…

Geometric Probability. New Topics for Secondary School Mathematics. Materials and Software.

ERIC Educational Resources Information Center

National Council of Teachers of Mathematics, Inc., Reston, VA.

These materials on geometric probability are the first unit in a course being developed by the Mathematics Department at the North Carolina School of Science and Mathematics. This course is designed to prepare high school students who have completed Algebra 2 for the variety of math courses they will encounter in college. Assuming only a knowledge…

Results from the Fourth Mathematics Assessment of the National Assessment of Educational Progress.

ERIC Educational Resources Information Center

Lindquist, Mary Montgomery, Ed.

The National Assessment of Educational Progress (NAEP) completed its fourth mathematics assessment during the 1985-86 school year and finished the analyses of the results in 1988. This monograph, prepared by an interpretive team of the National Council of Teachers of Mathematics, represents a comprehensive discussion of the results of the fourth…

Becoming Mathematicians: Women and Students of Color Choosing and Leaving Doctoral Mathematics

ERIC Educational Resources Information Center

Herzig, Abbe H.

2004-01-01

Few women and even fewer African Americans, Latinos, and Native Americans complete doctoral degrees in mathematics in the United States. This article proposes a framework for understanding the small numbers of women and students of color who persist in doctoral mathematics based on the notion that academic and social integration are critical to…

Reading for Pleasure and Progress in Vocabulary and Mathematics

ERIC Educational Resources Information Center

Sullivan, Alice; Brown, Matt

2015-01-01

This paper examines inequalities in attainment in vocabulary and mathematics at age 16 for a nationally representative cohort of people born in Britain in 1970 (the 1970 British Cohort Study). Our analytical sample is n = 3,583 cohort members who completed vocabulary and mathematics tests at age 16. We explore whether inequalities as a result of…

The Teaching Practices Inventory: A New Tool for Characterizing College and University Teaching in Mathematics and Science

ERIC Educational Resources Information Center

Wieman, Carl; Gilbert, Sarah

2014-01-01

We have created an inventory to characterize the teaching practices used in science and mathematics courses. This inventory can aid instructors and departments in reflecting on their teaching. It has been tested with several hundred university instructors and courses from mathematics and four science disciplines. Most instructors complete the…

The Mathematical Abilities and Personality of Undergraduate Psychology Students Relative to Other Student Groups

ERIC Educational Resources Information Center

Bhakta, Roy; Wood, Clare; Lawson, Duncan

2010-01-01

This study examined differences in personality and mathematical ability between students studying Business, Psychology, Sports and Nursing. There were 286 participants who each completed a mathematics diagnostics test and a Revised Eysenck Personality Questionnaire (EPQ-R) during the first term of their first year of study. There was a significant…

Test Anxiety in Mathematics among Early Undergraduate Students in a British University in Malaysia

ERIC Educational Resources Information Center

Karjanto, Natanael; Yong, Su Ting

2013-01-01

The level of test anxiety in mathematics subjects among early undergraduate students at the University of Nottingham Malaysia Campus is studied in this article. The sample consists of 206 students taking several mathematics modules who completed the questionnaires on test anxiety just before they entered the venue for midterm examinations. The…

Preservice Teachers of High School Mathematics: Success, Failure, and Persistence in the Face of Mathematical Challenges

ERIC Educational Resources Information Center

Sinicrope, Rose; Eppler, Marion; Preston, Ronald V.; Ironsmith, Marsha

2015-01-01

The goal of this study was to identify variables related to success and resilience in an undergraduate, high school mathematics teacher education program. Over a five-year period, we tracked the academic performance and achievement motivation goals of multiple cohorts of students. Students who successfully completed their degrees had higher grade…

An Investigation of Preservice Teachers' Perceptions of African American Students' Ability To Achieve in Mathematics and Science.

ERIC Educational Resources Information Center

Lewis, Bradford F.; Collins, Alicia; Pitts, Vanessa

This study investigated the perceptions of 30 predominantly white pre-service teachers about African American students' ability to achieve in mathematics and science. Participants completed a three-part, open-ended questionnaire that asked them about their experiences with and awareness of African American students' mathematics and science…

The Priorities and Challenges of Primary Teachers' Knowledge in Their Mathematics Planning

ERIC Educational Resources Information Center

Davidson, Aylie

2016-01-01

There is growing consensus that the process of planning mathematics lessons is as complex as teaching them, yet there is limited research on this. This paper reports on one aspect of a project examining issues in primary teachers' mathematics planning. The results, taken from a questionnaire completed by 62 primary teachers, indicate that when…

University Students' Metacognitive Failures in Mathematical Proving Investigated Based on the Framework of Assimilation and Accommodation

ERIC Educational Resources Information Center

Huda, Nizlel; Subanji; Nusantar, Toto; Susiswo; Sutawidjaja, Akbar; Rahardjo, Swasono

2016-01-01

This study aimed to determine students' metacognitive failure in Mathematics Education Program of FKIP in Jambi University investigated based on assimilation and accommodation Mathematical framework. There were 35 students, five students did not answer the question, three students completed the questions correctly and 27 students tried to solve…

Evaluation of the Effectiveness of a Tablet Computer Application (App) in Helping Students with Visual Impairments Solve Mathematics Problems

ERIC Educational Resources Information Center

Beal, Carole R.; Rosenblum, L. Penny

2018-01-01

Introduction: The authors examined a tablet computer application (iPad app) for its effectiveness in helping students studying prealgebra to solve mathematical word problems. Methods: Forty-three visually impaired students (that is, those who are blind or have low vision) completed eight alternating mathematics units presented using their…

Gifted Students' Metaphor Images about Mathematics

ERIC Educational Resources Information Center

Arikan, Elif Esra; Unal, Hasan

2015-01-01

The aim of this study is to investigate the metaphors images of gifted students about mathematics. The sample of the study consists of 82 gifted students, which are 2, 3, 4, 5, 6, 7 graders, from Istanbul. Data were collected by asking students to complete the sentence: "Mathematics is as …, because…". In the study content analysis was…

A Cross-Cultural Investigation into How Tasks Influence Seatwork Activities in Mathematics Lessons

ERIC Educational Resources Information Center

Serrano, Ana M.

2012-01-01

This study examined how types of tasks influenced student activities/thinking and defined the role of Seatwork in mathematics lessons. It used 60 lessons from the TIMSS videotaped Study. These data indicated that practice was the most prevalent form of tasks in the U.S. In Germany, students completed mathematical calculations after a complex…

Pre-Service Teachers' Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

ERIC Educational Resources Information Center

Cetinkaya, Bulent; Kertil, Mahmut; Erbas, Ayhan Kursat; Korkmaz, Himmet; Alacaci, Cengiz; Cakiroglu, Erdinc

2016-01-01

Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers' developing conceptions about (a) the nature of mathematical modeling in simulations of "real life" problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike…

Evolution of Mathematics Teachers' Pedagogical Knowledge When They Are Teaching through Modeling

ERIC Educational Resources Information Center

Aydogan Yenmez, Arzu; Erbas, Ayhan Kursat; Alacaci, Cengiz; Cakiroglu, Erdinc; Cetinkaya, Bulent

2017-01-01

Use of mathematical modeling in mathematics education has been receiving significant attention as a way to develop students' mathematical knowledge and skills. As effective use of modeling in classes depends on the competencies of teachers we need to know more about the nature of teachers' knowledge to use modeling in mathematics education and how…

Mathematical Modeling in Science: Using Spreadsheets to Create Mathematical Models and Address Scientific Inquiry

ERIC Educational Resources Information Center

Horton, Robert M.; Leonard, William H.

2005-01-01

In science, inquiry is used as students explore important and interesting questions concerning the world around them. In mathematics, one contemporary inquiry approach is to create models that describe real phenomena. Creating mathematical models using spreadsheets can help students learn at deep levels in both science and mathematics, and give…

The Genesis of Cyberscience and its Mathematical Models (CYBERSCIENCE)

DTIC Science & Technology

2005-02-01

Of course, the idea of maintaining a complete development record has other advantages , and has frequently been proposed in the past as a solution to...system development. There is no question that this offers certain advantages . For exam- ple, if systems that satisfy a standard frequently prove...some substantial practical advantages . First, providing wildly 2Unfortunately, this terminology has not been standardized. For example, in the Safety

Radar for Measuring Soil Moisture Under Vegetation

NASA Technical Reports Server (NTRS)

Moghaddam, Mahta; Moller, Delwyn; Rodriguez, Ernesto; Rahmat-Samii, Yahya

2004-01-01

A two-frequency, polarimetric, spaceborne synthetic-aperture radar (SAR) system has been proposed for measuring the moisture content of soil as a function of depth, even in the presence of overlying vegetation. These measurements are needed because data on soil moisture under vegetation canopies are not available now and are necessary for completing mathematical models of global energy and water balance with major implications for global variations in weather and climate.

AAFE man-made noise experiment project. Volume 3: Appendices

NASA Technical Reports Server (NTRS)

1974-01-01

Management and operational considerations involved in the project to measure man-made electromagnetic noise at earth orbital altitudes are discussed. The subjects considered are: (1) launch and orbit of the Scout D vehicles, (2) experiment management, (3) receiver scanning considerations, (4) data handling, and (5) threshold measurements. The storage requirements for a high resolution, complete data storage library are defined. Mathematical models of signal detection probability are developed.

Use of high performance networks and supercomputers for real-time flight simulation

NASA Technical Reports Server (NTRS)

Cleveland, Jeff I., II

1993-01-01

In order to meet the stringent time-critical requirements for real-time man-in-the-loop flight simulation, computer processing operations must be consistent in processing time and be completed in as short a time as possible. These operations include simulation mathematical model computation and data input/output to the simulators. In 1986, in response to increased demands for flight simulation performance, NASA's Langley Research Center (LaRC), working with the contractor, developed extensions to the Computer Automated Measurement and Control (CAMAC) technology which resulted in a factor of ten increase in the effective bandwidth and reduced latency of modules necessary for simulator communication. This technology extension is being used by more than 80 leading technological developers in the United States, Canada, and Europe. Included among the commercial applications are nuclear process control, power grid analysis, process monitoring, real-time simulation, and radar data acquisition. Personnel at LaRC are completing the development of the use of supercomputers for mathematical model computation to support real-time flight simulation. This includes the development of a real-time operating system and development of specialized software and hardware for the simulator network. This paper describes the data acquisition technology and the development of supercomputing for flight simulation.

Dynamic Uncertain Causality Graph for Knowledge Representation and Probabilistic Reasoning: Directed Cyclic Graph and Joint Probability Distribution.

PubMed

Zhang, Qin

2015-07-01

Probabilistic graphical models (PGMs) such as Bayesian network (BN) have been widely applied in uncertain causality representation and probabilistic reasoning. Dynamic uncertain causality graph (DUCG) is a newly presented model of PGMs, which can be applied to fault diagnosis of large and complex industrial systems, disease diagnosis, and so on. The basic methodology of DUCG has been previously presented, in which only the directed acyclic graph (DAG) was addressed. However, the mathematical meaning of DUCG was not discussed. In this paper, the DUCG with directed cyclic graphs (DCGs) is addressed. In contrast, BN does not allow DCGs, as otherwise the conditional independence will not be satisfied. The inference algorithm for the DUCG with DCGs is presented, which not only extends the capabilities of DUCG from DAGs to DCGs but also enables users to decompose a large and complex DUCG into a set of small, simple sub-DUCGs, so that a large and complex knowledge base can be easily constructed, understood, and maintained. The basic mathematical definition of a complete DUCG with or without DCGs is proved to be a joint probability distribution (JPD) over a set of random variables. The incomplete DUCG as a part of a complete DUCG may represent a part of JPD. Examples are provided to illustrate the methodology.

Ultrasensitive dual phosphorylation dephosphorylation cycle kinetics exhibits canonical competition behavior

NASA Astrophysics Data System (ADS)

Huang, Qingdao; Qian, Hong

2009-09-01

We establish a mathematical model for a cellular biochemical signaling module in terms of a planar differential equation system. The signaling process is carried out by two phosphorylation-dephosphorylation reaction steps that share common kinase and phosphatase with saturated enzyme kinetics. The pair of equations is particularly simple in the present mathematical formulation, but they are singular. A complete mathematical analysis is developed based on an elementary perturbation theory. The dynamics exhibits the canonical competition behavior in addition to bistability. Although widely understood in ecological context, we are not aware of a full range of biochemical competition in a simple signaling network. The competition dynamics has broad implications to cellular processes such as cell differentiation and cancer immunoediting. The concepts of homogeneous and heterogeneous multisite phosphorylation are introduced and their corresponding dynamics are compared: there is no bistability in a heterogeneous dual phosphorylation system. A stochastic interpretation is also provided that further gives intuitive understanding of the bistable behavior inside the cells.

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…

Understanding Prospective Teachers' Mathematical Modeling Processes in the Context of a Mathematical Modeling Course

ERIC Educational Resources Information Center

Zeytun, Aysel Sen; Cetinkaya, Bulent; Erbas, Ayhan Kursat

2017-01-01

This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future…

A mathematical model of atherogenesis as an inflammatory response.

PubMed

Ibragimov, A I; McNeal, C J; Ritter, L R; Walton, J R

2005-12-01

We construct a mathematical model of the early formation of an atherosclerotic lesion based on a simplification of Russell Ross' paradigm of atherosclerosis as a chronic inflammatory response. Atherosclerosis is a disease characterized by the accumulation of lipid-laden cells in the arterial wall. This disease results in lesions within the artery that may grow into the lumen restricting blood flow and, in critical cases, can rupture causing complete, sudden occlusion of the artery resulting in heart attack, stroke and possibly death. It is now understood that when chemically modified low-density lipoproteins (LDL cholesterol) enter into the wall of the human artery, they can trigger an immune response mediated by biochemical signals sent and received by immune and other cells indigenous to the vasculature. The presence of modified LDL can also corrupt the normal immune function triggering further immune response and ultimately chronic inflammation. In the construction of our mathematical model, we focus on the inflammatory component of the pathogenesis of cardiovascular disease (CVD). Because this study centres on the interplay between chemical and cellular species in the human artery and bloodstream, we employ a model of chemotaxis first given by E. F. Keller and Lee Segel in 1970 and present our model as a coupled system of non-linear reaction diffusion equations describing the state of the various species involved in the disease process. We perform numerical simulations demonstrating that our model captures certain observed features of CVD such as the localization of immune cells, the build-up of lipids and debris and the isolation of a lesion by smooth muscle cells.

Advanced semi-active engine and transmission mounts: tools for modelling, analysis, design, and tuning

NASA Astrophysics Data System (ADS)

Farjoud, Alireza; Taylor, Russell; Schumann, Eric; Schlangen, Timothy

2014-02-01

This paper is focused on modelling, design, and testing of semi-active magneto-rheological (MR) engine and transmission mounts used in the automotive industry. The purpose is to develop a complete analysis, synthesis, design, and tuning tool that reduces the need for expensive and time-consuming laboratory and field tests. A detailed mathematical model of such devices is developed using multi-physics modelling techniques for physical systems with various energy domains. The model includes all major features of an MR mount including fluid dynamics, fluid track, elastic components, decoupler, rate-dip, gas-charged chamber, MR fluid rheology, magnetic circuit, electronic driver, and control algorithm. Conventional passive hydraulic mounts can also be studied using the same mathematical model. The model is validated using standard experimental procedures. It is used for design and parametric study of mounts; effects of various geometric and material parameters on dynamic response of mounts can be studied. Additionally, this model can be used to test various control strategies to obtain best vibration isolation performance by tuning control parameters. Another benefit of this work is that nonlinear interactions between sub-components of the mount can be observed and investigated. This is not possible by using simplified linear models currently available.

Introducing Modeling Transition Diagrams as a Tool to Connect Mathematical Modeling to Mathematical Thinking

ERIC Educational Resources Information Center

Czocher, Jennifer A.

2016-01-01

This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…

An Experimental Approach to Mathematical Modeling in Biology

ERIC Educational Resources Information Center

Ledder, Glenn

2008-01-01

The simplest age-structured population models update a population vector via multiplication by a matrix. These linear models offer an opportunity to introduce mathematical modeling to students of limited mathematical sophistication and background. We begin with a detailed discussion of mathematical modeling, particularly in a biological context.…

Mathematical Modeling with Middle School Students: The Robot Art Model-Eliciting Activity

ERIC Educational Resources Information Center

Stohlmann, Micah S.

2017-01-01

Internationally mathematical modeling is garnering more attention for the benefits associated with it. Mathematical modeling can develop students' communication skills and the ability to demonstrate understanding through different representations. With the increased attention on mathematical modeling, there is a need for more curricula to be…

Changing Pre-Service Mathematics Teachers' Beliefs about Using Computers for Teaching and Learning Mathematics: The Effect of Three Different Models

ERIC Educational Resources Information Center

Karatas, Ilhan

2014-01-01

This study examines the effect of three different computer integration models on pre-service mathematics teachers' beliefs about using computers in mathematics education. Participants included 104 pre-service mathematics teachers (36 second-year students in the Computer Oriented Model group, 35 fourth-year students in the Integrated Model (IM)…

Impact of a Required Pharmaceutical Calculations Course on Mathematics Ability and Knowledge Retention

PubMed Central

Buring, Shauna M.; Papas, Elizabeth

2013-01-01

Objective. To assess doctor of pharmacy (PharmD) students’ mathematics ability by content area before and after completing a required pharmaceutical calculations course and to analyze changes in scores. Methods. A mathematics skills assessment was administered to 2 cohorts of pharmacy students (class of 2013 and 2014) before and after completing a pharmaceutical calculations course. The posttest was administered to the second cohort 6 months after completing the course to assess knowledge retention. Results. Both cohorts performed significantly better on the posttest (cohort 1, 13% higher scores; cohort 2, 15.9% higher scores). Significant improvement on posttest scores was observed in 6 of the 10 content areas for cohorts 1 and 2. Both cohorts scored lower in percentage calculations on the posttest than on the pretest. Conclusions. A required, 1-credit-hour pharmaceutical calculations course improved PharmD students’ overall ability to perform fundamental and application-based calculations. PMID:23966727

Impact of a required pharmaceutical calculations course on mathematics ability and knowledge retention.

PubMed

Hegener, Michael A; Buring, Shauna M; Papas, Elizabeth

2013-08-12

To assess doctor of pharmacy (PharmD) students' mathematics ability by content area before and after completing a required pharmaceutical calculations course and to analyze changes in scores. A mathematics skills assessment was administered to 2 cohorts of pharmacy students (class of 2013 and 2014) before and after completing a pharmaceutical calculations course. The posttest was administered to the second cohort 6 months after completing the course to assess knowledge retention. Both cohorts performed significantly better on the posttest (cohort 1, 13% higher scores; cohort 2, 15.9% higher scores). Significant improvement on posttest scores was observed in 6 of the 10 content areas for cohorts 1 and 2. Both cohorts scored lower in percentage calculations on the posttest than on the pretest. A required, 1-credit-hour pharmaceutical calculations course improved PharmD students' overall ability to perform fundamental and application-based calculations.

Mathematical Modeling: A Structured Process

ERIC Educational Resources Information Center

Anhalt, Cynthia Oropesa; Cortez, Ricardo

2015-01-01

Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…

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…

To Assess Students' Attitudes, Skills and Competencies in Mathematical Modeling

ERIC Educational Resources Information Center

Lingefjard, Thomas; Holmquist, Mikael

2005-01-01

Peer-to-peer assessment, take-home exams and a mathematical modeling survey were used to monitor and assess students' attitudes, skills and competencies in mathematical modeling. The students were all in a secondary mathematics, teacher education program with a comprehensive amount of mathematics studies behind them. Findings indicate that…

Mathematical Modeling in the Undergraduate Curriculum

ERIC Educational Resources Information Center

Toews, Carl

2012-01-01

Mathematical modeling occupies an unusual space in the undergraduate mathematics curriculum: typically an "advanced" course, it nonetheless has little to do with formal proof, the usual hallmark of advanced mathematics. Mathematics departments are thus forced to decide what role they want the modeling course to play, both as a component of the…

Teachers' Conceptions of Mathematical Modeling

ERIC Educational Resources Information Center

Gould, Heather

2013-01-01

The release of the "Common Core State Standards for Mathematics" in 2010 resulted in a new focus on mathematical modeling in United States curricula. Mathematical modeling represents a way of doing and understanding mathematics new to most teachers. The purpose of this study was to determine the conceptions and misconceptions held by…

Experimentation of cooperative learning model Numbered Heads Together (NHT) type by concept maps and Teams Games Tournament (TGT) by concept maps in terms of students logical mathematics intellegences

NASA Astrophysics Data System (ADS)

Irawan, Adi; Mardiyana; Retno Sari Saputro, Dewi

2017-06-01

This research is aimed to find out the effect of learning model towards learning achievement in terms of students’ logical mathematics intelligences. The learning models that were compared were NHT by Concept Maps, TGT by Concept Maps, and Direct Learning model. This research was pseudo experimental by factorial design 3×3. The population of this research was all of the students of class XI Natural Sciences of Senior High School in all regency of Karanganyar in academic year 2016/2017. The conclusions of this research were: 1) the students’ achievements with NHT learning model by Concept Maps were better than students’ achievements with TGT model by Concept Maps and Direct Learning model. The students’ achievements with TGT model by Concept Maps were better than the students’ achievements with Direct Learning model. 2) The students’ achievements that exposed high logical mathematics intelligences were better than students’ medium and low logical mathematics intelligences. The students’ achievements that exposed medium logical mathematics intelligences were better than the students’ low logical mathematics intelligences. 3) Each of student logical mathematics intelligences with NHT learning model by Concept Maps has better achievement than students with TGT learning model by Concept Maps, students with NHT learning model by Concept Maps have better achievement than students with the direct learning model, and the students with TGT by Concept Maps learning model have better achievement than students with Direct Learning model. 4) Each of learning model, students who have logical mathematics intelligences have better achievement then students who have medium logical mathematics intelligences, and students who have medium logical mathematics intelligences have better achievement than students who have low logical mathematics intelligences.

Pre-Service Teachers' Modelling Processes through Engagement with Model Eliciting Activities with a Technological Tool

ERIC Educational Resources Information Center

Daher, Wajeeh M.; Shahbari, Juhaina Awawdeh

2015-01-01

Engaging mathematics students with modelling activities helps them learn mathematics meaningfully. This engagement, in the case of model eliciting activities, helps the students elicit mathematical models by interpreting real-world situation in mathematical ways. This is especially true when the students utilize technology to build the models.…

Mathematical E-Learning: State of the Art and Experiences at the Open University of Catalonia

ERIC Educational Resources Information Center

Juan, A.; Huertas, A.; Steegmann, C.; Corcoles, C.; Serrat, C.

2008-01-01

In this article we present a review of the state of the art in mathematical e-learning and some personal experiences on this area developed during the last eleven years at the Open University of Catalonia (UOC), a completely online university located in Spain. The article discusses important aspects related to online mathematics courses offered in…

Separate but Correlated: The Latent Structure of Space and Mathematics across Development

ERIC Educational Resources Information Center

Mix, Kelly S.; Levine, Susan C.; Cheng, Yi-Ling; Young, Chris; Hambrick, D. Zachary; Ping, Raedy

2016-01-01

The relations among various spatial and mathematics skills were assessed in a cross-sectional study of 854 children from kindergarten, third, and sixth grades (i.e., 5 to 13 years of age). Children completed a battery of spatial mathematics tests and their scores were submitted to exploratory factor analyses both within and across domains. In the…

An Investigation of Preservice Teachers' Use of Guess and Check in Solving a Semi Open-Ended Mathematics Problem

ERIC Educational Resources Information Center

Capraro, Mary Margaret; An, Song A.; Ma, Tingting; Rangel-Chavez, A. Fabiola; Harbaugh, Adam

2012-01-01

Open-ended problems have been regarded as powerful tools for teaching mathematics. This study examined the problem solving of eight mathematics/science middle-school teachers. A semi-structured interview was conducted with (PTs) after completing an open-ended triangle task with four unique solutions. Of particular emphasis was how the PTs used a…

Live Lectures or Online Videos: Students' Resource Choices in a First-Year University Mathematics Module

ERIC Educational Resources Information Center

Howard, Emma; Meehan, Maria; Parnell, Andrew

2018-01-01

In "Maths for Business", a mathematics module for non-mathematics specialists, students are given the choice of completing the module content via short online videos, live lectures or a combination of both. In this study, we identify students' specific usage patterns with both of these resources and discuss their reasons for the…

Mathematical Preparedness for Tertiary Mathematics--A Need for Focused Intervention in the First Year?

ERIC Educational Resources Information Center

Du Preez, Jeanetta; Steyn, Tobia; Owen, Rina

2008-01-01

Ongoing action research at the University of Pretoria investigates first-year students' preparedness for a study in calculus. In 2005 first-year engineering students completed a mathematics diagnostic survey at the beginning and end of the year. In this article the results of the 2005 survey are compared with the students' final school marks in…

Grade 9 Pilot Test. Mathematics. June 1988 = 9e Annee Test Pilote. Mathematiques. Juin 1988.

ERIC Educational Resources Information Center

Alberta Dept. of Education, Edmonton.

This pilot test for ninth grade mathematics is written in both French and English. The test consists of 75 multiple-choice items. Students are given 90 minutes to complete the examination and the use of a calculator is highly recommended. The test content covers a wide range of mathematical topics including: decimals; exponents; arithmetic word…

Underprepared Students' Performance on Algebra in a Double-Period High School Mathematics Program

ERIC Educational Resources Information Center

Martinez, Mara V.; Bragelman, John; Stoelinga, Timothy

2016-01-01

The primary goal of the Intensified Algebra I (IA) program is to enable mathematically underprepared students to successfully complete Algebra I in 9th grade and stay on track to meet increasingly rigorous high school mathematics graduation requirements. The program was designed to bring a range of both cognitive and non-cognitive supports to bear…

Using Mental Imagery Processes for Teaching and Research in Mathematics and Computer Science

ERIC Educational Resources Information Center

Arnoux, Pierre; Finkel, Alain

2010-01-01

The role of mental representations in mathematics and computer science (for teaching or research) is often downplayed or even completely ignored. Using an ongoing work on the subject, we argue for a more systematic study and use of mental representations, to get an intuition of mathematical concepts, and also to understand and build proofs. We…

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.

Mathematical Problem Solving Ability of Junior High School Students through Ang’s Framework for Mathematical Modelling Instruction

NASA Astrophysics Data System (ADS)

Fasni, N.; Turmudi, T.; Kusnandi, K.

2017-09-01

This research background of this research is the importance of student problem solving abilities. The purpose of this study is to find out whether there are differences in the ability to solve mathematical problems between students who have learned mathematics using Ang’s Framework for Mathematical Modelling Instruction (AFFMMI) and students who have learned using scientific approach (SA). The method used in this research is a quasi-experimental method with pretest-postest control group design. Data analysis of mathematical problem solving ability using Indepent Sample Test. The results showed that there was a difference in the ability to solve mathematical problems between students who received learning with Ang’s Framework for Mathematical Modelling Instruction and students who received learning with a scientific approach. AFFMMI focuses on mathematical modeling. This modeling allows students to solve problems. The use of AFFMMI is able to improve the solving ability.

Equilibrium stability of a cylindrical body subject to the internal structure of the material and inelastic behaviour of the completely compressed matrix

NASA Astrophysics Data System (ADS)

Gotsev, D. V.; Perunov, N. S.; Sviridova, E. N.

2018-03-01

The mathematical model describing the stress-strain state of a cylindrical body under the uniform radial compression effect is constructed. The model of the material is the porous medium model. The compressed skeleton of the porous medium possesses hardening elastic-plastic properties. Deforming of the porous medium under the specified compressive loads is divided into two stages: elastic deforming of the porous medium and further elastic-plastic deforming of the material with completely compressed matrix. The analytical relations that define the fields of stress and displacement at each stage of the deforming are obtained. The influence of the porosity and other physical, mechanical and geometric parameters of the construction on the size of the plastic zone is evaluated. The question of the ground state equilibrium instability is investigated within the framework of the three-dimensional linearized relationships of the stability theory of deformed bodies.

Mathematics beliefs and instructional strategies in achievement of elementary-school students in Japan: results from the TIMSS 2003 assessment.

PubMed

House, J Daniel

2007-04-01

Recent findings concerning mathematics assessment indicate that students in Japan consistently score above international averages. Researchers have examined specific mathematics beliefs and instructional strategies associated with mathematics achievement for students in Japan. This study examined relationships among self-beliefs, classroom instructional strategies, and mathematics achievement for a large national sample of students (N=4,207) from the TIMSS 2003 international sample of fourth graders in Japan. Several significant relationships between mathematics beliefs and test scores were found; a number of classroom teaching strategies were also significantly associated with test scores. However, multiple regression using the complete set of five mathematics beliefs and five instructional strategies explained only 25.1% of the variance in mathematics achievement test scores.

Pharmacy Students’ Perceptions of Natural Science and Mathematics Subjects

PubMed Central

Wilson, Sarah Ellen; Wan, Kai-Wai

2014-01-01

Objective. To determine the level of importance pharmacy students placed on science and mathematics subjects for pursuing a career in pharmacy. Method. Two hundred fifty-four students completed a survey instrument developed to investigate students’ perceptions of the relevance of science and mathematics subjects to a career in pharmacy. Pharmacy students in all 4 years of a master of pharmacy (MPharm) degree program were invited to complete the survey instrument. Results. Students viewed chemistry-based and biology-based subjects as relevant to a pharmacy career, whereas mathematics subjects such as physics, logarithms, statistics, and algebra were not viewed important to a career in pharmacy. Conclusion. Students’ experience in pharmacy and year of study influenced their perceptions of subjects relevant to a pharmacy career. Pharmacy educators need to consider how they can help students recognize the importance of scientific knowledge earlier in the pharmacy curriculum. PMID:25147390

Characterization, scaling, and partial representation of diffuse and discrete input junctions to CA3 hippocampus.

PubMed

Ascarrunz, F G; Kisley, M A; Flach, K A; Hamilton, R W; MacGregor, R J

1995-07-01

This paper applies a general mathematical system for characterizing and scaling functional connectivity and information flow across the diffuse (EC) and discrete (DG) input junctions to the CA3 hippocampus. Both gross connectivity and coordinated multiunit informational firing patterns are quantitatively characterized in terms of 32 defining parameters interrelated by 17 equations, and then scaled down according to rules for uniformly proportional scaling and for partial representation. The diffuse EC-CA3 junction is shown to be uniformly scalable with realistic representation of both essential spatiotemporal cooperativity and coordinated firing patterns down to populations of a few hundred neurons. Scaling of the discrete DG-CA3 junction can be effected with a two-step process, which necessarily deviates from uniform proportionality but nonetheless produces a valuable and readily interpretable reduced model, also utilizing a few hundred neurons in the receiving population. Partial representation produces a reduced model of only a portion of the full network where each model neuron corresponds directly to a biological neuron. The mathematical analysis illustrated here shows that although omissions and distortions are inescapable in such an application, satisfactorily complete and accurate models the size of pattern modules are possible. Finally, the mathematical characterization of these junctions generates a theory which sees the DG as a definer of the fine structure of embedded traces in the hippocampus and entire coordinated patterns of sequences of 14-cell links in CA3 as triggered by the firing of sequences of individual neurons in DG.

How can mathematical models advance tuberculosis control in high HIV prevalence settings?

PubMed

Houben, R M G J; Dowdy, D W; Vassall, A; Cohen, T; Nicol, M P; Granich, R M; Shea, J E; Eckhoff, P; Dye, C; Kimerling, M E; White, R G

2014-05-01

Existing approaches to tuberculosis (TB) control have been no more than partially successful in areas with high human immunodeficiency virus (HIV) prevalence. In the context of increasingly constrained resources, mathematical modelling can augment understanding and support policy for implementing those strategies that are most likely to bring public health and economic benefits. In this paper, we present an overview of past and recent contributions of TB modelling in this key area, and suggest a way forward through a modelling research agenda that supports a more effective response to the TB-HIV epidemic, based on expert discussions at a meeting convened by the TB Modelling and Analysis Consortium. The research agenda identified high-priority areas for future modelling efforts, including 1) the difficult diagnosis and high mortality of TB-HIV; 2) the high risk of disease progression; 3) TB health systems in high HIV prevalence settings; 4) uncertainty in the natural progression of TB-HIV; and 5) combined interventions for TB-HIV. Efficient and rapid progress towards completion of this modelling agenda will require co-ordination between the modelling community and key stakeholders, including advocates, health policy makers, donors and national or regional finance officials. A continuing dialogue will ensure that new results are effectively communicated and new policy-relevant questions are addressed swiftly.

An imaging-based stochastic model for simulation of tumour vasculature

NASA Astrophysics Data System (ADS)

Adhikarla, Vikram; Jeraj, Robert

2012-10-01

A mathematical model which reconstructs the structure of existing vasculature using patient-specific anatomical, functional and molecular imaging as input was developed. The vessel structure is modelled according to empirical vascular parameters, such as the mean vessel branching angle. The model is calibrated such that the resultant oxygen map modelled from the simulated microvasculature stochastically matches the input oxygen map to a high degree of accuracy (R2 ≈ 1). The calibrated model was successfully applied to preclinical imaging data. Starting from the anatomical vasculature image (obtained from contrast-enhanced computed tomography), a representative map of the complete vasculature was stochastically simulated as determined by the oxygen map (obtained from hypoxia [64Cu]Cu-ATSM positron emission tomography). The simulated microscopic vasculature and the calculated oxygenation map successfully represent the imaged hypoxia distribution (R2 = 0.94). The model elicits the parameters required to simulate vasculature consistent with imaging and provides a key mathematical relationship relating the vessel volume to the tissue oxygen tension. Apart from providing an excellent framework for visualizing the imaging gap between the microscopic and macroscopic imagings, the model has the potential to be extended as a tool to study the dynamics between the tumour and the vasculature in a patient-specific manner and has an application in the simulation of anti-angiogenic therapies.

The Effect of Teacher Beliefs on Student Competence in Mathematical Modeling--An Intervention Study

ERIC Educational Resources Information Center

Mischo, Christoph; Maaß, Katja

2013-01-01

This paper presents an intervention study whose aim was to promote teacher beliefs about mathematics and learning mathematics and student competences in mathematical modeling. In the intervention, teachers received written curriculum materials about mathematical modeling. The concept underlying the materials was based on constructivist ideas and…

Leaning on Mathematical Habits of Mind

ERIC Educational Resources Information Center

Sword, Sarah; Matsuura, Ryota; Cuoco, Al; Kang, Jane; Gates, Miriam

2018-01-01

Mathematical modeling has taken on increasing curricular importance in the past decade due in no small measure to the Common Core State Standards in Mathematics (CCSSM) identifying modeling as one of the Standards for Mathematical Practice (SMP 4, CCSSI 2010, p. 7). Although researchers have worked on mathematical modeling (Lesh and Doerr 2003;…

V/STOL tilt rotor study. Volume 5: A mathematical model for real time flight simulation of the Bell model 301 tilt rotor research aircraft

NASA Technical Reports Server (NTRS)

Harendra, P. B.; Joglekar, M. J.; Gaffey, T. M.; Marr, R. L.

1973-01-01

A mathematical model for real-time flight simulation of a tilt rotor research aircraft was developed. The mathematical model was used to support the aircraft design, pilot training, and proof-of-concept aspects of the development program. The structure of the mathematical model is indicated by a block diagram. The mathematical model differs from that for a conventional fixed wing aircraft principally in the added requirement to represent the dynamics and aerodynamics of the rotors, the interaction of the rotor wake with the airframe, and the rotor control and drive systems. The constraints imposed on the mathematical model are defined.

The influence of a wind tunnel on helicopter rotational noise: Formulation of analysis

NASA Technical Reports Server (NTRS)

Mosher, M.

1984-01-01

An analytical model is discussed that can be used to examine the effects of wind tunnel walls on helicopter rotational noise. A complete physical model of an acoustic source in a wind tunnel is described and a simplified version is then developed. This simplified model retains the important physical processes involved, yet it is more amenable to analysis. The simplified physical model is then modeled as a mathematical problem. An inhomogeneous partial differential equation with mixed boundary conditions is set up and then transformed into an integral equation. Details of generating a suitable Green's function and integral equation are included and the equation is discussed and also given for a two-dimensional case.

Developing Students' Reflections on the Function and Status of Mathematical Modeling in Different Scientific Practices: History as a Provider of Cases

ERIC Educational Resources Information Center

Kjeldsen, Tinne Hoff; Blomhøj, Morten

2013-01-01

Mathematical models and mathematical modeling play different roles in the different areas and problems in which they are used. The function and status of mathematical modeling and models in the different areas depend on the scientific practice as well as the underlying philosophical and theoretical position held by the modeler(s) and the…

How Ordinary Meaning Underpins the Meaning of Mathematics.

ERIC Educational Resources Information Center

Ormell, Christopher

1991-01-01

Discusses the meaning of mathematics by looking at its uses in the real world. Offers mathematical modeling as a way to represent mathematical applications in real or potential situations. Presents levels of applicability, modus operandi, relationship to "pure mathematics," and consequences for education for mathematical modeling. (MDH)

Using expectancy-value theory to explore aspects of motivation and engagement in inquiry-based learning in primary mathematics

NASA Astrophysics Data System (ADS)

Fielding-Wells, Jill; O'Brien, Mia; Makar, Katie

2017-03-01

Inquiry-based learning (IBL) is a pedagogical approach in which students address complex, ill-structured problems set in authentic contexts. While IBL is gaining ground in Australia as an instructional practice, there has been little research that considers implications for student motivation and engagement. Expectancy-value theory (Eccles and Wigfield 2002) provides a framework through which children's beliefs about their mathematical competency and their expectation of success are able to be examined and interpreted, alongside students' perceptions of task value. In this paper, Eccles and Wigfield's expectancy-value model has been adopted as a lens to examine a complete unit of mathematical inquiry as undertaken with a class of 9-10-year-old students. Data were sourced from a unit (˜10 lessons) based on geometry and geometrical reasoning. The units were videotaped in full, transcribed, and along with field notes and student work samples, subjected to theoretical coding using the dimensions of Eccles and Wigfield's model. The findings provide insight into aspects of IBL that may impact student motivation and engagement. The study is limited to a single unit; however, the results provide a depth of insight into IBL in practice while identifying features of IBL that may be instrumental in bringing about increased motivation and engagement of students in mathematics. Identifying potentially motivating aspects of IBL enable these to be integrated and more closely studied in IBL practises.

Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century.

PubMed

Ganusov, Vitaly V

2016-01-01

While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest "strong inference in mathematical modeling" as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century.

Summer Camp of Mathematical Modeling in China

ERIC Educational Resources Information Center

Tian, Xiaoxi; Xie, Jinxing

2013-01-01

The Summer Camp of Mathematical Modeling in China is a recently created experience designed to further Chinese students' academic pursuits in mathematical modeling. Students are given more than three months to research on a mathematical modeling project. Researchers and teams with outstanding projects are invited to the Summer Camp to present…

A Review of Research on Bird Impacting on Jet Engines

NASA Astrophysics Data System (ADS)

Jin, Yuecheng

2018-03-01

Bird strikes can lead to permanent deformations, sudden decrease of thrust, even engine failure during the flight. Bird strikes on rotating blades can also cause slices of birds hitting other parts which may lead to greater damages. Bird strikes cannot be completely avoided. However, reduction of bird impacting on jet engines can be achieved by suitable design and manufacturing, through the mathematical modelling, simulation analysis and practical experiment of jet engines.

Dynamic analysis for shuttle design verification

NASA Technical Reports Server (NTRS)

Fralich, R. W.; Green, C. E.; Rheinfurth, M. H.

1972-01-01

Two approaches that are used for determining the modes and frequencies of space shuttle structures are discussed. The first method, direct numerical analysis, involves finite element mathematical modeling of the space shuttle structure in order to use computer programs for dynamic structural analysis. The second method utilizes modal-coupling techniques of experimental verification made by vibrating only spacecraft components and by deducing modes and frequencies of the complete vehicle from results obtained in the component tests.

SSME structural dynamic model development, phase 2

NASA Technical Reports Server (NTRS)

Foley, M. J.; Wilson, V. L.

1985-01-01

A set of test correlated mathematical models of the SSME High Pressure Oxygen Turbopump (HPOTP) housing and rotor assembly was produced. New analysis methods within the EISI/EAL and SPAR systems were investigated and runstreams for future use were developed. The LOX pump models have undergone extensive modification since the first phase of this effort was completed. The rotor assembly from the original model was abandoned and a new, more detailed model constructed. A description of the new rotor math model is presented. Also, the pump housing model was continually modified as additional test data have become available. This model is documented along with measured test results. Many of the more advanced features of the EAL/SPAR finite element analysis system were exercised. These included the cyclic symmetry option, the macro-element procedures, and the fluid analysis capability. In addition, a new tool was developed that allows an automated analysis of a disjoint structure in terms of its component modes. A complete description of the implementation of the Craig-Bampton method is given along with two worked examples.

Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century

PubMed Central

Ganusov, Vitaly V.

2016-01-01

While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest “strong inference in mathematical modeling” as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century. PMID:27499750

Using Covariation Reasoning to Support Mathematical Modeling

ERIC Educational Resources Information Center

Jacobson, Erik

2014-01-01

For many students, making connections between mathematical ideas and the real world is one of the most intriguing and rewarding aspects of the study of mathematics. In the Common Core State Standards for Mathematics (CCSSI 2010), mathematical modeling is highlighted as a mathematical practice standard for all grades. To engage in mathematical…

An Examination of Pre-Service Mathematics Teachers' Approaches to Construct and Solve Mathematical Modelling Problems

ERIC Educational Resources Information Center

Bukova-Guzel, Esra

2011-01-01

This study examines the approaches displayed by pre-service mathematics teachers in their experiences of constructing mathematical modelling problems and the extent to which they perform the modelling process when solving the problems they construct. This case study was carried out with 35 pre-service teachers taking the Mathematical Modelling…

Spatial modeling of cell signaling networks.

PubMed

Cowan, Ann E; Moraru, Ion I; Schaff, James C; Slepchenko, Boris M; Loew, Leslie M

2012-01-01

The shape of a cell, the sizes of subcellular compartments, and the spatial distribution of molecules within the cytoplasm can all control how molecules interact to produce a cellular behavior. This chapter describes how these spatial features can be included in mechanistic mathematical models of cell signaling. The Virtual Cell computational modeling and simulation software is used to illustrate the considerations required to build a spatial model. An explanation of how to appropriately choose between physical formulations that implicitly or explicitly account for cell geometry and between deterministic versus stochastic formulations for molecular dynamics is provided, along with a discussion of their respective strengths and weaknesses. As a first step toward constructing a spatial model, the geometry needs to be specified and associated with the molecules, reactions, and membrane flux processes of the network. Initial conditions, diffusion coefficients, velocities, and boundary conditions complete the specifications required to define the mathematics of the model. The numerical methods used to solve reaction-diffusion problems both deterministically and stochastically are then described and some guidance is provided in how to set up and run simulations. A study of cAMP signaling in neurons ends the chapter, providing an example of the insights that can be gained in interpreting experimental results through the application of spatial modeling. Copyright © 2012 Elsevier Inc. All rights reserved.

Identifying parameter regions for multistationarity

PubMed Central

Conradi, Carsten; Mincheva, Maya; Wiuf, Carsten

2017-01-01

Mathematical modelling has become an established tool for studying the dynamics of biological systems. Current applications range from building models that reproduce quantitative data to identifying systems with predefined qualitative features, such as switching behaviour, bistability or oscillations. Mathematically, the latter question amounts to identifying parameter values associated with a given qualitative feature. We introduce a procedure to partition the parameter space of a parameterized system of ordinary differential equations into regions for which the system has a unique or multiple equilibria. The procedure is based on the computation of the Brouwer degree, and it creates a multivariate polynomial with parameter depending coefficients. The signs of the coefficients determine parameter regions with and without multistationarity. A particular strength of the procedure is the avoidance of numerical analysis and parameter sampling. The procedure consists of a number of steps. Each of these steps might be addressed algorithmically using various computer programs and available software, or manually. We demonstrate our procedure on several models of gene transcription and cell signalling, and show that in many cases we obtain a complete partitioning of the parameter space with respect to multistationarity. PMID:28972969

Identifying potential misfit items in cognitive process of learning engineering mathematics based on Rasch model

NASA Astrophysics Data System (ADS)

Ataei, Sh; Mahmud, Z.; Khalid, M. N.

2014-04-01

The students learning outcomes clarify what students should know and be able to demonstrate after completing their course. So, one of the issues on the process of teaching and learning is how to assess students' learning. This paper describes an application of the dichotomous Rasch measurement model in measuring the cognitive process of engineering students' learning of mathematics. This study provides insights into the perspective of 54 engineering students' cognitive ability in learning Calculus III based on Bloom's Taxonomy on 31 items. The results denote that some of the examination questions are either too difficult or too easy for the majority of the students. This analysis yields FIT statistics which are able to identify if there is data departure from the Rasch theoretical model. The study has identified some potential misfit items based on the measurement of ZSTD where the removal misfit item was accomplished based on the MNSQ outfit of above 1.3 or less than 0.7 logit. Therefore, it is recommended that these items be reviewed or revised to better match the range of students' ability in the respective course.

Examining My Window and Mirror: A Pedagogical Reflection from a White Mathematics Teacher Educator about Her Experiences with Immigrant Latina Pre-Service Teachers

ERIC Educational Resources Information Center

Kalinec-Craig, Crystal A.

2014-01-01

In this pedagogical reflection, a White mathematics teacher educator describes what she learned from three Latina pre-service teachers who were recent immigrants from Mexico while they completed an elementary mathematics methods course. Using Rochelle Gutierrez's (2012) metaphor of a window and mirror, the author interrogates her own identity and…

Additive and Multiplicative Effects of Working Memory and Test Anxiety on Mathematics Performance in Grade 3 Students

ERIC Educational Resources Information Center

Korhonen, Johan; Nyroos, Mikaela; Jonsson, Bert; Eklöf, Hanna

2018-01-01

The aim of this study was to investigate the interplay between test anxiety and working memory (WM) on mathematics performance in younger children. A sample of 624 grade 3 students completed a test battery consisting of a test anxiety scale, WM tasks and the Swedish national examination in mathematics for grade 3. The main effects of test anxiety…

Learning to teach mathematical modelling in secondary and tertiary education

NASA Astrophysics Data System (ADS)

Ferri, Rita Borromeo

2017-07-01

Since 2003 mathematical modelling in Germany is not only a topic for scientific disciplines in university mathematics courses, but also in school starting with primary school. This paper shows what mathematical modelling means in school and how it can be taught as a basis for complex modeling problems in tertiary education.

Development of a Multidisciplinary Middle School Mathematics Infusion Model

ERIC Educational Resources Information Center

Russo, Maria; Hecht, Deborah; Burghardt, M. David; Hacker, Michael; Saxman, Laura

2011-01-01

The National Science Foundation (NSF) funded project "Mathematics, Science, and Technology Partnership" (MSTP) developed a multidisciplinary instructional model for connecting mathematics to science, technology and engineering content areas at the middle school level. Specifically, the model infused mathematics into middle school curriculum…

Frequencies as Proportions: Using a Teaching Model Based on Pirie and Kieren's Model of Mathematical Understanding

ERIC Educational Resources Information Center

Wright, Vince

2014-01-01

Pirie and Kieren (1989 "For the learning of mathematics", 9(3)7-11, 1992 "Journal of Mathematical Behavior", 11, 243-257, 1994a "Educational Studies in Mathematics", 26, 61-86, 1994b "For the Learning of Mathematics":, 14(1)39-43) created a model (P-K) that describes a dynamic and recursive process by which…

Detecting Strengths and Weaknesses in Learning Mathematics through a Model Classifying Mathematical Skills

ERIC Educational Resources Information Center

Karagiannakis, Giannis N.; Baccaglini-Frank, Anna E.; Roussos, Petros

2016-01-01

Through a review of the literature on mathematical learning disabilities (MLD) and low achievement in mathematics (LA) we have proposed a model classifying mathematical skills involved in learning mathematics into four domains (Core number, Memory, Reasoning, and Visual-spatial). In this paper we present a new experimental computer-based battery…

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…

Teaching Mathematical Modelling for Earth Sciences via Case Studies

NASA Astrophysics Data System (ADS)

Yang, Xin-She

2010-05-01

Mathematical modelling is becoming crucially important for earth sciences because the modelling of complex systems such as geological, geophysical and environmental processes requires mathematical analysis, numerical methods and computer programming. However, a substantial fraction of earth science undergraduates and graduates may not have sufficient skills in mathematical modelling, which is due to either limited mathematical training or lack of appropriate mathematical textbooks for self-study. In this paper, we described a detailed case-study-based approach for teaching mathematical modelling. We illustrate how essential mathematical skills can be developed for students with limited training in secondary mathematics so that they are confident in dealing with real-world mathematical modelling at university level. We have chosen various topics such as Airy isostasy, greenhouse effect, sedimentation and Stokes' flow,free-air and Bouguer gravity, Brownian motion, rain-drop dynamics, impact cratering, heat conduction and cooling of the lithosphere as case studies; and we use these step-by-step case studies to teach exponentials, logarithms, spherical geometry, basic calculus, complex numbers, Fourier transforms, ordinary differential equations, vectors and matrix algebra, partial differential equations, geostatistics and basic numeric methods. Implications for teaching university mathematics for earth scientists for tomorrow's classroom will also be discussed. Refereces 1) D. L. Turcotte and G. Schubert, Geodynamics, 2nd Edition, Cambridge University Press, (2002). 2) X. S. Yang, Introductory Mathematics for Earth Scientists, Dunedin Academic Press, (2009).

Mathematics Literacy on Problem Based Learning with Indonesian Realistic Mathematics Education Approach Assisted E-Learning Edmodo

NASA Astrophysics Data System (ADS)

Wardono; Waluya, S. B.; Mariani, Scolastika; Candra D, S.

2016-02-01

This study aims to find out that there are differences in mathematical literacy ability in content Change and Relationship class VII Junior High School 19, Semarang by Problem Based Learning (PBL) model with an Indonesian Realistic Mathematics Education (called Pendidikan Matematika Realistik Indonesia or PMRI in Indonesia) approach assisted Elearning Edmodo, PBL with a PMRI approach, and expository; to know whether the group of students with learning PBL models with PMRI approach and assisted E-learning Edmodo can improve mathematics literacy; to know that the quality of learning PBL models with a PMRI approach assisted E-learning Edmodo has a good category; to describe the difficulties of students in working the problems of mathematical literacy ability oriented PISA. This research is a mixed methods study. The population was seventh grade students of Junior High School 19, Semarang Indonesia. Sample selection is done by random sampling so that the selected experimental class 1, class 2 and the control experiment. Data collected by the methods of documentation, tests and interviews. From the results of this study showed average mathematics literacy ability of students in the group PBL models with a PMRI approach assisted E-learning Edmodo better than average mathematics literacy ability of students in the group PBL models with a PMRI approach and better than average mathematics literacy ability of students in the expository models; Mathematics literacy ability in the class using the PBL model with a PMRI approach assisted E-learning Edmodo have increased and the improvement of mathematics literacy ability is higher than the improvement of mathematics literacy ability of class that uses the model of PBL learning with PMRI approach and is higher than the improvement of mathematics literacy ability of class that uses the expository models; The quality of learning using PBL models with a PMRI approach assisted E-learning Edmodo have very good category.

A Gravitational, Mathematical Model for the Energy, Emitted Power and Longevity of the Sun and Stars that does not use E=mc^2

NASA Astrophysics Data System (ADS)

Morse Kingsley, James

2017-08-01

A gravitational mathematical model for the energy, radiated power and lifetime of the sun and stars is derived that does not use E=mc^2. The speed of solar flares, 200 to 1000km/sec is used to derive the surface temperature of the sun as 1.4(10^6)degrees K. Optical radiation results as gamma rays leave the sun's surface and traverse and lose energy to the ~10^6km of the sun's corona. The corona is a result of solar flares with a speed component of 424km/sec parallel to the sun's surface placing their atoms into gravitational orbit about the sun. The temperature, density, and pressure of the sun are derived as a function of r, i.e. the distance from the center of the sun. The complete article is chapter 11 of my text that can be found on my website www.jmkingsleyiii.info

A Mathematical Formulation of the SCOLE Control Problem. Part 2: Optimal Compensator Design

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.

1988-01-01

The study initiated in Part 1 of this report is concluded and optimal feedback control (compensator) design for stability augmentation is considered, following the mathematical formulation developed in Part 1. Co-located (rate) sensors and (force and moment) actuators are assumed, and allowing for both sensor and actuator noise, stabilization is formulated as a stochastic regulator problem. Specializing the general theory developed by the author, a complete, closed form solution (believed to be new with this report) is obtained, taking advantage of the fact that the inherent structural damping is light. In particular, it is possible to solve in closed form the associated infinite-dimensional steady-state Riccati equations. The SCOLE model involves associated partial differential equations in a single space variable, but the compensator design theory developed is far more general since it is given in the abstract wave equation formulation. The results thus hold for any multibody system so long as the basic model is linear.

Mathematical modeling of control subsystems for CELSS: Application to diet

NASA Technical Reports Server (NTRS)

Waleh, Ahmad; Nguyen, Thoi K.; Kanevsky, Valery

1991-01-01

The dynamic control of a Closed Ecological Life Support System (CELSS) in a closed space habitat is of critical importance. The development of a practical method of control is also a necessary step for the selection and design of realistic subsystems and processors for a CELSS. Diet is one of the dynamic factors that strongly influences, and is influenced, by the operational states of all major CELSS subsystems. The problems of design and maintenance of a stable diet must be obtained from well characterized expert subsystems. The general description of a mathematical model that forms the basis of an expert control program for a CELSS is described. The formulation is expressed in terms of a complete set of time dependent canonical variables. System representation is dynamic and includes time dependent storage buffers. The details of the algorithm are described. The steady state results of the application of the method for representative diets made from wheat, potato, and soybean are presented.

Tracing Growth of Teachers' Classroom Interactions with Representations of Functions in the Connected Classroom

NASA Astrophysics Data System (ADS)

Morton, Brian Lee

The purpose of this study is to create an empirically based theoretic model of change of the use and treatment of representations of functions with the use of Connected Classroom Technology (CCT) using data previously collected for the Classroom Connectivity in Promoting Mathematics and Science Achievement (CCMS) project. Qualitative analysis of videotapes of three algebra teachers' instruction focused on different categories thought to influence teaching representations with technology: representations, discourse, technology, and decisions. Models for rating teachers low, medium, or high for each of these categories were created using a priori codes and grounded methodology. A cross case analysis was conducted after the completion of the case studies by comparing and contrasting the three cases. Data revealed that teachers' decisions shifted to incorporate the difference in student ideas/representations made visible by the CCT into their instruction and ultimately altered their orientation to mathematics teaching. The shift in orientation seemed to lead to the teachers' growth with regards to representations, discourse, and technology.

Improvement of sand filter and constructed wetland design using an environmental decision support system.

PubMed

Turon, Clàudia; Comas, Joaquim; Torrens, Antonina; Molle, Pascal; Poch, Manel

2008-01-01

With the aim of improving effluent quality of waste stabilization ponds, different designs of vertical flow constructed wetlands and intermittent sand filters were tested on an experimental full-scale plant within the framework of a European project. The information extracted from this study was completed and updated with heuristic and bibliographic knowledge. The data and knowledge acquired were difficult to integrate into mathematical models because they involve qualitative information and expert reasoning. Therefore, it was decided to develop an environmental decision support system (EDSS-Filter-Design) as a tool to integrate mathematical models and knowledge-based techniques. This paper describes the development of this support tool, emphasizing the collection of data and knowledge and representation of this information by means of mathematical equations and a rule-based system. The developed support tool provides the main design characteristics of filters: (i) required surface, (ii) media type, and (iii) media depth. These design recommendations are based on wastewater characteristics, applied load, and required treatment level data provided by the user. The results of the EDSS-Filter-Design provide appropriate and useful information and guidelines on how to design filters, according to the expert criteria. The encapsulation of the information into a decision support system reduces the design period and provides a feasible, reasoned, and positively evaluated proposal.

A Review of Mathematical Models for Leukemia and Lymphoma

PubMed Central

Clapp, Geoffrey; Levy, Doron

2014-01-01

Recently, there has been significant activity in the mathematical community, aimed at developing quantitative tools for studying leukemia and lymphoma. Mathematical models have been applied to evaluate existing therapies and to suggest novel therapies. This article reviews the recent contributions of mathematical modeling to leukemia and lymphoma research. These developments suggest that mathematical modeling has great potential in this field. Collaboration between mathematicians, clinicians, and experimentalists can significantly improve leukemia and lymphoma therapy. PMID:26744598

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.

Executive functioning predicts reading, mathematics, and theory of mind during the elementary years.

PubMed

Cantin, Rachelle H; Gnaedinger, Emily K; Gallaway, Kristin C; Hesson-McInnis, Matthew S; Hund, Alycia M

2016-06-01

The goal of this study was to specify how executive functioning components predict reading, mathematics, and theory of mind performance during the elementary years. A sample of 93 7- to 10-year-old children completed measures of working memory, inhibition, flexibility, reading, mathematics, and theory of mind. Path analysis revealed that all three executive functioning components (working memory, inhibition, and flexibility) mediated age differences in reading comprehension, whereas age predicted mathematics and theory of mind directly. In addition, reading mediated the influence of executive functioning components on mathematics and theory of mind, except that flexibility also predicted mathematics directly. These findings provide important details about the development of executive functioning, reading, mathematics, and theory of mind during the elementary years. Copyright © 2016 Elsevier Inc. All rights reserved.

Longitudinal Associations between Executive Control and Developing Mathematical Competence in Preschool Boys and Girls

PubMed Central

Clark, Caron A.C.; Sheffield, Tiffany D.; Wiebe, Sandra A.; Espy, Kimberly Andrews

2012-01-01

Executive control (EC) is related to mathematics performance in middle childhood. However, little is known regarding how EC and informal numeracy differentially support mathematics skill acquisition in preschoolers. A sample of preschoolers (115 girls, 113 boys), stratified by social risk, completed an EC task battery at 3 years, informal numeracy assessments at 3.75 and 4.5 years, and a broad mathematics assessment during kindergarten. Strong associations were observed between latent EC at 3 and mathematics achievement in kindergarten, which remained robust after accounting for earlier informal numeracy, socio-economic status, language and processing speed. Relations between EC and mathematics achievement were stronger in girls than boys. Findings highlight the unique role of EC in predicting which children may have difficulty transitioning to formal mathematics instruction. PMID:23006040

Preservice Secondary Teachers' Conceptions from a Mathematical Modeling Activity and Connections to the Common Core State Standards

ERIC Educational Resources Information Center

Stohlmann, Micah; Maiorca, Cathrine; Olson, Travis A.

2015-01-01

Mathematical modeling is an essential integrated piece of the Common Core State Standards. However, researchers have shown that mathematical modeling activities can be difficult for teachers to implement. Teachers are more likely to implement mathematical modeling activities if they have their own successful experiences with such activities. This…

Investigating and Developing Engineering Students' Mathematical Modelling and Problem-Solving Skills

ERIC Educational Resources Information Center

Wedelin, Dag; Adawi, Tom; Jahan, Tabassum; Andersson, Sven

2015-01-01

How do engineering students approach mathematical modelling problems and how can they learn to deal with such problems? In the context of a course in mathematical modelling and problem solving, and using a qualitative case study approach, we found that the students had little prior experience of mathematical modelling. They were also inexperienced…

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.

Transmission Dinamics Model Of Dengue Fever

NASA Astrophysics Data System (ADS)

Debora; Rendy; Rahmi

2018-01-01

Dengue fever is an endemic disease that is transmitted through the Aedes aegypti mosquito vector. The disease is present in more than 100 countries in America, Africa, and Asia, especially tropical countries. Differential equations can be used to represent the spread of dengue virus occurring in time intervals and model in the form of mathematical models. The mathematical model in this study tries to represent the spread of dengue fever based on the data obtained and the assumptions used. The mathematical model used is a mathematical model consisting of Susceptible (S), Infected (I), Viruses (V) subpopulations. The SIV mathematical model is then analyzed to see the solution behaviour of the system.

Mathematical Modeling: Convoying Merchant Ships

ERIC Educational Resources Information Center

Mathews, Susann M.

2004-01-01

This article describes a mathematical model that connects mathematics with social studies. Students use mathematics to model independent versus convoyed ship deployments and sinkings to determine if the British should have convoyed their merchant ships during World War I. During the war, the British admiralty opposed sending merchant ships grouped…

Mathematical model for Dengue with three states of infection

NASA Astrophysics Data System (ADS)

Hincapie, Doracelly; Ospina, Juan

2012-06-01

A mathematical model for dengue with three states of infection is proposed and analyzed. The model consists in a system of differential equations. The three states of infection are respectively asymptomatic, partially asymptomatic and fully asymptomatic. The model is analyzed using computer algebra software, specifically Maple, and the corresponding basic reproductive number and the epidemic threshold are computed. The resulting basic reproductive number is an algebraic synthesis of all epidemic parameters and it makes clear the possible control measures. The microscopic structure of the epidemic parameters is established using the quantum theory of the interactions between the atoms and radiation. In such approximation, the human individual is represented by an atom and the mosquitoes are represented by radiation. The force of infection from the mosquitoes to the humans is considered as the transition probability from the fundamental state of atom to excited states. The combination of computer algebra software and quantum theory provides a very complete formula for the basic reproductive number and the possible control measures tending to stop the propagation of the disease. It is claimed that such result may be important in military medicine and the proposed method can be applied to other vector-borne diseases.

Modal analysis of human body vibration model for Indian subjects under sitting posture.

PubMed

Singh, Ishbir; Nigam, S P; Saran, V H

2015-01-01

Need and importance of modelling in human body vibration research studies are well established. The study of biodynamic responses of human beings can be classified into experimental and analytical methods. In the past few decades, plenty of mathematical models have been developed based on the diverse field measurements to describe the biodynamic responses of human beings. In this paper, a complete study on lumped parameter model derived from 50th percentile anthropometric data for a seated 54- kg Indian male subject without backrest support under free un-damped conditions has been carried out considering human body segments to be of ellipsoidal shape. Conventional lumped parameter modelling considers the human body as several rigid masses interconnected by springs and dampers. In this study, concept of mass of interconnecting springs has been incorporated and eigenvalues thus obtained are found to be closer to the values reported in the literature. Results obtained clearly establish decoupling of vertical and fore-and-aft oscillations. The mathematical modelling of human body vibration studies help in validating the experimental investigations for ride comfort of a sitting subject. This study clearly establishes the decoupling of vertical and fore-and-aft vibrations and helps in better understanding of possible human response to single and multi-axial excitations.

Commentary on the statistical properties of noise and its implication on general linear models in functional near-infrared spectroscopy.

PubMed

Huppert, Theodore J

2016-01-01

Functional near-infrared spectroscopy (fNIRS) is a noninvasive neuroimaging technique that uses low levels of light to measure changes in cerebral blood oxygenation levels. In the majority of NIRS functional brain studies, analysis of this data is based on a statistical comparison of hemodynamic levels between a baseline and task or between multiple task conditions by means of a linear regression model: the so-called general linear model. Although these methods are similar to their implementation in other fields, particularly for functional magnetic resonance imaging, the specific application of these methods in fNIRS research differs in several key ways related to the sources of noise and artifacts unique to fNIRS. In this brief communication, we discuss the application of linear regression models in fNIRS and the modifications needed to generalize these models in order to deal with structured (colored) noise due to systemic physiology and noise heteroscedasticity due to motion artifacts. The objective of this work is to present an overview of these noise properties in the context of the linear model as it applies to fNIRS data. This work is aimed at explaining these mathematical issues to the general fNIRS experimental researcher but is not intended to be a complete mathematical treatment of these concepts.

Improving mathematical problem solving ability through problem-based learning and authentic assessment for the students of Bali State Polytechnic

NASA Astrophysics Data System (ADS)

Darma, I. K.

2018-01-01

This research is aimed at determining: 1) the differences of mathematical problem solving ability between the students facilitated with problem-based learning model and conventional learning model, 2) the differences of mathematical problem solving ability between the students facilitated with authentic and conventional assessment model, and 3) interaction effect between learning and assessment model on mathematical problem solving. The research was conducted in Bali State Polytechnic, using the 2x2 experiment factorial design. The samples of this research were 110 students. The data were collected using a theoretically and empirically-validated test. Instruments were validated by using Aiken’s approach of technique content validity and item analysis, and then analyzed using anova stylistic. The result of the analysis shows that the students facilitated with problem-based learning and authentic assessment models get the highest score average compared to the other students, both in the concept understanding and mathematical problem solving. The result of hypothesis test shows that, significantly: 1) there is difference of mathematical problem solving ability between the students facilitated with problem-based learning model and conventional learning model, 2) there is difference of mathematical problem solving ability between the students facilitated with authentic assessment model and conventional assessment model, and 3) there is interaction effect between learning model and assessment model on mathematical problem solving. In order to improve the effectiveness of mathematics learning, collaboration between problem-based learning model and authentic assessment model can be considered as one of learning models in class.

Influence of Problem-Based Learning Model of Learning to the Mathematical Communication Ability of Students of Grade XI IPA SMAN 14 Padang

NASA Astrophysics Data System (ADS)

Nisa, I. M.

2018-04-01

The ability of mathematical communication is one of the goals of learning mathematics expected to be mastered by students. However, reality in the field found that the ability of mathematical communication the students of grade XI IPA SMA Negeri 14 Padang have not developed optimally. This is evident from the low test results of communication skills mathematically done. One of the factors that causes this happens is learning that has not been fully able to facilitate students to develop mathematical communication skills well. By therefore, to improve students' mathematical communication skills required a model in the learning activities. One of the models learning that can be used is Problem Based learning model Learning (PBL). The purpose of this study is to see whether the ability the students' mathematical communication using the PBL model better than the students' mathematical communication skills of the learning using conventional learning in Class XI IPA SMAN 14 Padang. This research type is quasi experiment with design Randomized Group Only Design. Population in this research that is student of class XI IPA SMAN 14 Padang with sample class XI IPA 3 and class XI IPA 4. Data retrieval is done by using communication skill test mathematically shaped essay. To test the hypothesis used U-Mann test Whitney. Based on the results of data analysis, it can be concluded that the ability mathematical communication of students whose learning apply more PBL model better than the students' mathematical communication skills of their learning apply conventional learning in class XI IPA SMA 14 Padang at α = 0.05. This indicates that the PBL learning model effect on students' mathematical communication ability.

78 FR 34671 - Invitation for Membership on Advisory Committee

Federal Register 2010, 2011, 2012, 2013, 2014

2013-06-10

... by successful completion of Joint Board examinations in basic actuarial mathematics and methodology and in actuarial mathematics and methodology relating to pension plans qualifying under ERISA. The... (ERISA), is responsible for the enrollment of individuals who wish to perform actuarial services under...

Are Universities Providing Non-STEM Students the Mathematics Preparation Required by Their Programs?: A Case Study of A Quantitative Literacy Pathway and Vertical Alignment from Remediation to Degree Completion

ERIC Educational Resources Information Center

Allen, Charles

2017-01-01

Informed by Gagne's belief in the necessity of prerequisite knowledge for new learning, and Bruner's Spiral Curriculum Theory, the objective of this case study was to explore the postsecondary pathway from remedial mathematics, through one gateway mathematics course, and into the quantitative literacy requirements of various non-STEM programs of…

The Real and the Mathematical in Quantum Modeling: From Principles to Models and from Models to Principles

NASA Astrophysics Data System (ADS)

Plotnitsky, Arkady

2017-06-01

The history of mathematical modeling outside physics has been dominated by the use of classical mathematical models, C-models, primarily those of a probabilistic or statistical nature. More recently, however, quantum mathematical models, Q-models, based in the mathematical formalism of quantum theory have become more prominent in psychology, economics, and decision science. The use of Q-models in these fields remains controversial, in part because it is not entirely clear whether Q-models are necessary for dealing with the phenomena in question or whether C-models would still suffice. My aim, however, is not to assess the necessity of Q-models in these fields, but instead to reflect on what the possible applicability of Q-models may tell us about the corresponding phenomena there, vis-à-vis quantum phenomena in physics. In order to do so, I shall first discuss the key reasons for the use of Q-models in physics. In particular, I shall examine the fundamental principles that led to the development of quantum mechanics. Then I shall consider a possible role of similar principles in using Q-models outside physics. Psychology, economics, and decision science borrow already available Q-models from quantum theory, rather than derive them from their own internal principles, while quantum mechanics was derived from such principles, because there was no readily available mathematical model to handle quantum phenomena, although the mathematics ultimately used in quantum did in fact exist then. I shall argue, however, that the principle perspective on mathematical modeling outside physics might help us to understand better the role of Q-models in these fields and possibly to envision new models, conceptually analogous to but mathematically different from those of quantum theory, helpful or even necessary there or in physics itself. I shall suggest one possible type of such models, singularized probabilistic, SP, models, some of which are time-dependent, TDSP-models. The necessity of using such models may change the nature of mathematical modeling in science and, thus, the nature of science, as it happened in the case of Q-models, which not only led to a revolutionary transformation of physics but also opened new possibilities for scientific thinking and mathematical modeling beyond physics.

A Primer for Mathematical Modeling

ERIC Educational Resources Information Center

Sole, Marla

2013-01-01

With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school…

Strategies to Support Students' Mathematical Modeling

ERIC Educational Resources Information Center

Jung, Hyunyi

2015-01-01

An important question for mathematics teachers is this: "How can we help students learn mathematics to solve everyday problems, rather than teaching them only to memorize rules and practice mathematical procedures?" Teaching students using modeling activities can help them learn mathematics in real-world problem-solving situations that…

Mathematical Modeling in the High School Curriculum

ERIC Educational Resources Information Center

Hernández, Maria L.; Levy, Rachel; Felton-Koestler, Mathew D.; Zbiek, Rose Mary

2016-01-01

In 2015, mathematics leaders and instructors from the Society for Industrial and Applied Mathematics (SIAM) and the Consortium for Mathematics and Its Applications (COMAP), with input from NCTM, came together to write the "Guidelines for Assessment and Instruction in Mathematical Modeling Education" (GAIMME) report as a resource for…

Quantitative Studies in Planetary Volcanism

NASA Technical Reports Server (NTRS)

Baloga, Stephen M.

2004-01-01

Proxemy Research has a research grant to perform scientific investigations of volcanism and volcanic-related process on other planets. Part of this research involves mathematical modeling of specific volcanic transport processes and the use of terrestrial analogs. This report contains a summary of activities conducted over the time period indicated. In addition, a synopsis of science research conducted during the period is given. A complete listing of publications and scientific abstracts that were presented at scientific conferences is contained in the report.

Computer simulation of space station computer steered high gain antenna

NASA Technical Reports Server (NTRS)

Beach, S. W.

1973-01-01

The mathematical modeling and programming of a complete simulation program for a space station computer-steered high gain antenna are described. The program provides for reading input data cards, numerically integrating up to 50 first order differential equations, and monitoring up to 48 variables on printed output and on plots. The program system consists of a high gain antenna, an antenna gimbal control system, an on board computer, and the environment in which all are to operate.

USSR and Eastern Europe Scientific Abstracts, Cybernetics, Computers and Automation Technology, Number 29.

DTIC Science & Technology

1978-01-17

approach to designing computers: Formal mathematical methods were applied and computers themselves began to be widely used in designing other...capital, labor resources and the funds of consumers. Analysis of the model indicates that at the present time the average complexity of production of...ALGORITHMIC COMPLETENESS AND COMPLEXITY OF MICROPROGRAMS Kiev KIBERNETIKA in Russian No 3, May/Jun 77 pp 1-15 manuscript received 22 Dec 76 G0LUNK0V

Analysis of swimming motions.

NASA Technical Reports Server (NTRS)

Gallenstein, J.; Huston, R. L.

1973-01-01

This paper presents an analysis of swimming motion with specific attention given to the flutter kick, the breast-stroke kick, and the breast stroke. The analysis is completely theoretical. It employs a mathematical model of the human body consisting of frustrums of elliptical cones. Dynamical equations are written for this model including both viscous and inertia forces. These equations are then applied with approximated swimming strokes and solved numerically using a digital computer. The procedure is to specify the input of the swimming motion. The computer solution then provides the output displacement, velocity, and rotation or body roll of the swimmer.

Maple

NASA Astrophysics Data System (ADS)

Nicolaides, Roy A.; Walkington, Noel J.

1996-06-01

A knowledge of one or more high level symbolic mathematics programs is rapidly becoming a necessity for mathematics users from all fields of science. The aim of this book is to provide a solid grounding in Maple, one of the best known of these programs. The authors combine efficiency and economy of exposition with a complete coverage of Maple. The book has twelve chapters, of which eight are completely accessible to anyone who has completed calculus and linear sequences as taught in American universities. These chapters cover the great majority of Maple's capabilities. There are also three chapters on Maple programming that can be read without prior programming experience, although knowledge of a high level programming language (Basic, Fortran, C etc.) will help. There is also a chapter on some relevant aspects of algebra. Above all, the book allows the reader to extract value from Maple without wasting time and effort in the learning process. It is the fastest track to expertise for Maple users in mathematics and computer science.

Particle tracking velocimetry in three-dimensional flows

NASA Astrophysics Data System (ADS)

Maas, H. G.; Gruen, A.; Papantoniou, D.

1993-07-01

Particle Tracking Velocimetry (PTV) is a well-known technique for the determination of velocity vectors within an observation volume. However, for a long time it has rarely been applied because of the intensive effort necessary to measure coordinates of a large number of flow marker particles in many images. With today's imaging hardware in combination with the methods of digital image processing and digital photogrammetry, however, new possibilities have arisen for the design of completely automatic PTV systems. A powerful 3 D PTV has been developed in a cooperation of the Institute of Geodesy and Photogrammetry with the Institute of Hydromechanics and Water Resources Management at the Swiss Federal Institute of Technology. In this paper hardware components for 3 D PTV systems wil be discussed, and a strict mathematical model of photogrammetric 3 D coordinate determination, taking into account the different refractive indices in the optical path, will be presented. The system described is capable of determining coordinate sets of some 1000 particles in a flow field at a time resolution of 25 datasets per second and almost arbitrary sequence length completely automatically after an initialization by an operator. The strict mathematical modelling of the measurement geometry, together with a thorough calibration of the system provide for a coordinate accuracy of typically 0.06 mm in X, Y and 0.18 mm in Z (depth coordinate) in a volume of 200 × 160 × 50 mm3.

The Effect of Instruction through Mathematical Modelling on Modelling Skills of Prospective Elementary Mathematics Teachers

ERIC Educational Resources Information Center

Ciltas, Alper; Isik, Ahmet

2013-01-01

The aim of this study was to examine the modelling skills of prospective elementary mathematics teachers who were studying the mathematical modelling method. The research study group was composed of 35 prospective teachers. The exploratory case analysis method was used in the study. The data were obtained via semi-structured interviews and a…

Electrode Models for Electric Current Computed Tomography

PubMed Central

CHENG, KUO-SHENG; ISAACSON, DAVID; NEWELL, J. C.; GISSER, DAVID G.

2016-01-01

This paper develops a mathematical model for the physical properties of electrodes suitable for use in electric current computed tomography (ECCT). The model includes the effects of discretization, shunt, and contact impedance. The complete model was validated by experiment. Bath resistivities of 284.0, 139.7, 62.3, 29.5 Ω · cm were studied. Values of “effective” contact impedance z used in the numerical approximations were 58.0, 35.0, 15.0, and 7.5 Ω · cm2, respectively. Agreement between the calculated and experimentally measured values was excellent throughout the range of bath conductivities studied. It is desirable in electrical impedance imaging systems to model the observed voltages to the same precision as they are measured in order to be able to make the highest resolution reconstructions of the internal conductivity that the measurement precision allows. The complete electrode model, which includes the effects of discretization of the current pattern, the shunt effect due to the highly conductive electrode material, and the effect of an “effective” contact impedance, allows calculation of the voltages due to any current pattern applied to a homogeneous resistivity field. PMID:2777280

Electrode models for electric current computed tomography.

PubMed

Cheng, K S; Isaacson, D; Newell, J C; Gisser, D G

1989-09-01

This paper develops a mathematical model for the physical properties of electrodes suitable for use in electric current computed tomography (ECCT). The model includes the effects of discretization, shunt, and contact impedance. The complete model was validated by experiment. Bath resistivities of 284.0, 139.7, 62.3, 29.5 omega.cm were studied. Values of "effective" contact impedance zeta used in the numerical approximations were 58.0, 35.0, 15.0, and 7.5 omega.cm2, respectively. Agreement between the calculated and experimentally measured values was excellent throughout the range of bath conductivities studied. It is desirable in electrical impedance imaging systems to model the observed voltages to the same precision as they are measured in order to be able to make the highest resolution reconstructions of the internal conductivity that the measurement precision allows. The complete electrode model, which includes the effects of discretization of the current pattern, the shunt effect due to the highly conductive electrode material, and the effect of an "effective" contact impedance, allows calculation of the voltages due to any current pattern applied to a homogeneous resistivity field.

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…

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…

Mathematical Modelling at Secondary School: The MACSI-Clongowes Wood College Experience

ERIC Educational Resources Information Center

Charpin, J. P. F.; O'Hara, S.; Mackey, D.

2013-01-01

In Ireland, to encourage the study of STEM (science, technology, engineering and mathematics) subjects and particularly mathematics, the Mathematics Applications Consortium for Science and Industry (MACSI) and Clongowes Wood College (County Kildare, Ireland) organized a mathematical modelling workshop for senior cycle secondary school students.…

Mathematical models of thermoregulation and heat transfer in mammals. A compendium of research

NASA Technical Reports Server (NTRS)

Shitzer, A.

1972-01-01

An annotated compendium on mathematical modeling of mammal thermoregulation systems is presented. Author abstracts, tables containing the more used mathematical models, solutions to these models, and each thermoregulation mechanism considered are included.

Ocular hemodynamics and glaucoma: the role of mathematical modeling.

PubMed

Harris, Alon; Guidoboni, Giovanna; Arciero, Julia C; Amireskandari, Annahita; Tobe, Leslie A; Siesky, Brent A

2013-01-01

To discuss the role of mathematical modeling in studying ocular hemodynamics, with a focus on glaucoma. We reviewed recent literature on glaucoma, ocular blood flow, autoregulation, the optic nerve head, and the use of mathematical modeling in ocular circulation. Many studies suggest that alterations in ocular hemodynamics play a significant role in the development, progression, and incidence of glaucoma. Although there is currently a limited number of studies involving mathematical modeling of ocular blood flow, regulation, and diseases (such as glaucoma), preliminary modeling work shows the potential of mathematical models to elucidate the mechanisms that contribute most significantly to glaucoma progression. Mathematical modeling is a useful tool when used synergistically with clinical and laboratory data in the study of ocular blood flow and glaucoma. The development of models to investigate the relationship between ocular hemodynamic alterations and glaucoma progression will provide a unique and useful method for studying the pathophysiology of glaucoma.

The influence of wind-tunnel walls on discrete frequency noise

NASA Technical Reports Server (NTRS)

Mosher, M.

1984-01-01

This paper describes an analytical model that can be used to examine the effects of wind-tunnel walls on discrete frequency noise. First, a complete physical model of an acoustic source in a wind tunnel is described, and a simplified version is then developed. This simplified model retains the important physical processes involved, yet it is more amenable to analysis. Second, the simplified physical model is formulated as a mathematical problem. An inhomogeneous partial differential equation with mixed boundary conditions is set up and then transformed into an integral equation. The integral equation has been solved with a panel program on a computer. Preliminary results from a simple model problem will be shown and compared with the approximate analytic solution.

Comparison of learning models based on mathematics logical intelligence in affective domain

NASA Astrophysics Data System (ADS)

Widayanto, Arif; Pratiwi, Hasih; Mardiyana

2018-04-01

The purpose of this study was to examine the presence or absence of different effects of multiple treatments (used learning models and logical-mathematical intelligence) on the dependent variable (affective domain of mathematics). This research was quasi experimental using 3x3 of factorial design. The population of this research was VIII grade students of junior high school in Karanganyar under the academic year 2017/2018. Data collected in this research was analyzed by two ways analysis of variance with unequal cells using 5% of significance level. The result of the research were as follows: (1) Teaching and learning with model TS lead to better achievement in affective domain than QSH, teaching and learning with model QSH lead to better achievement in affective domain than using DI; (2) Students with high mathematics logical intelligence have better achievement in affective domain than students with low mathematics logical intelligence have; (3) In teaching and learning mathematics using learning model TS, students with moderate mathematics logical intelligence have better achievement in affective domain than using DI; and (4) In teaching and learning mathematics using learning model TS, students with low mathematics logical intelligence have better achievement in affective domain than using QSH and DI.

The impact of mathematical models of teaching materials on square and rectangle concepts to improve students' mathematical connection ability and mathematical disposition in middle school

NASA Astrophysics Data System (ADS)

Afrizal, Irfan Mufti; Dachlan, Jarnawi Afghani

2017-05-01

The aim of this study was to determine design of mathematical models of teaching materials to improve students' mathematical connection ability and mathematical disposition in middle school through experimental studies. The design in this study was quasi-experimental with non-equivalent control group type. This study consisted of two phases, the first phase was identify students' learning obstacle on square and rectangle concepts to obtain the appropriate design of teaching materials, beside that there were internalization of the values or characters expected to appear on students through the teaching materials. Second phase was experiments on the effectiveness and efficiency of mathematical models of teaching materials to improve students' mathematical connection ability and mathematical disposition. The result of this study are 1) Students' learning obstacle that have identified was categorized as an epistemological obstacle. 2) The improvement of students' mathematical connection ability and mathematical disposition who used mathematical teaching materials is better than the students who used conventional learning.

Mathematical modelling in developmental biology.

PubMed

Vasieva, Olga; Rasolonjanahary, Manan'Iarivo; Vasiev, Bakhtier

2013-06-01

In recent decades, molecular and cellular biology has benefited from numerous fascinating developments in experimental technique, generating an overwhelming amount of data on various biological objects and processes. This, in turn, has led biologists to look for appropriate tools to facilitate systematic analysis of data. Thus, the need for mathematical techniques, which can be used to aid the classification and understanding of this ever-growing body of experimental data, is more profound now than ever before. Mathematical modelling is becoming increasingly integrated into biological studies in general and into developmental biology particularly. This review outlines some achievements of mathematics as applied to developmental biology and demonstrates the mathematical formulation of basic principles driving morphogenesis. We begin by describing a mathematical formalism used to analyse the formation and scaling of morphogen gradients. Then we address a problem of interplay between the dynamics of morphogen gradients and movement of cells, referring to mathematical models of gastrulation in the chick embryo. In the last section, we give an overview of various mathematical models used in the study of the developmental cycle of Dictyostelium discoideum, which is probably the best example of successful mathematical modelling in developmental biology.

Mathematical models for plant-herbivore interactions

USGS Publications Warehouse

Feng, Zhilan; DeAngelis, Donald L.

2017-01-01

Mathematical Models of Plant-Herbivore Interactions addresses mathematical models in the study of practical questions in ecology, particularly factors that affect herbivory, including plant defense, herbivore natural enemies, and adaptive herbivory, as well as the effects of these on plant community dynamics. The result of extensive research on the use of mathematical modeling to investigate the effects of plant defenses on plant-herbivore dynamics, this book describes a toxin-determined functional response model (TDFRM) that helps explains field observations of these interactions. This book is intended for graduate students and researchers interested in mathematical biology and ecology.

Develop and test fuel cell powered on-site integrated total energy system. Phase 3: Full-scale power plant development

NASA Technical Reports Server (NTRS)

Kaufman, A.

1981-01-01

An integrated 5 kW power system based upon methanol fuel and a phosphoric acid fuel cell operating at about 473 K is described. Description includes test results of advanced fuel cell catalysts, a semiautomatic acid replenishment system and a completed 5 kW methanol/system reformer. The results of a preliminary system test on a reformer/stack/inverter combination are reported. An initial design for a 25 kW stack is presented. Experimental plans are outlined for data acquisition necessary for design of a 50 kW methanol/steam reformer. Activities related to complete mathematical modelling of the integrated power system, including wasteheat utilization, are described.

Dealing with dissatisfaction in mathematical modelling to integrate QFD and Kano’s model

NASA Astrophysics Data System (ADS)

Retno Sari Dewi, Dian; Debora, Joana; Edy Sianto, Martinus

2017-12-01

The purpose of the study is to implement the integration of Quality Function Deployment (QFD) and Kano’s Model into mathematical model. Voice of customer data in QFD was collected using questionnaire and the questionnaire was developed based on Kano’s model. Then the operational research methodology was applied to build the objective function and constraints in the mathematical model. The relationship between voice of customer and engineering characteristics was modelled using linier regression model. Output of the mathematical model would be detail of engineering characteristics. The objective function of this model is to maximize satisfaction and minimize dissatisfaction as well. Result of this model is 62% .The major contribution of this research is to implement the existing mathematical model to integrate QFD and Kano’s Model in the case study of shoe cabinet.

Beyond Homework: Science and Mathematics Backpacks.

ERIC Educational Resources Information Center

Kokoski, Teresa M.; Patton, Mary Martin

1997-01-01

Describes classroom-developed science and mathematics backpacks, self-contained educational packets developed around a theme or concept and designed to be completed at home. Presents generalized contents, a sample backpack on colors, and the backpack's advantages, including promotion of active learning, family involvement, curriculum integration,…

Technology to Develop Algebraic Reasoning

ERIC Educational Resources Information Center

Polly, Drew

2011-01-01

Students' use of technology allows them to generate and manipulate multiple representations of a concept, compute numbers with relative ease, and focus more on mathematical concepts and higher-order thinking skills. In elementary school mathematics classrooms, students develop higher-order thinking skills by completing complex tasks that require…

Striking a Balance: Students' Tendencies to Oversimplify or Overcomplicate in Mathematical Modeling

ERIC Educational Resources Information Center

Gould, Heather; Wasserman, Nicholas H.

2014-01-01

With the adoption of the "Common Core State Standards for Mathematics" (CCSSM), the process of mathematical modeling has been given increased attention in mathematics education. This article reports on a study intended to inform the implementation of modeling in classroom contexts by examining students' interactions with the process of…

Attitudes of Pre-Service Mathematics Teachers towards Modelling: A South African Inquiry

ERIC Educational Resources Information Center

Jacobs, Gerrie J.; Durandt, Rina

2017-01-01

This study explores the attitudes of mathematics pre-service teachers, based on their initial exposure to a model-eliciting challenge. The new Curriculum and Assessment Policy Statement determines that mathematics students should be able to identify, investigate and solve problems via modelling. The unpreparedness of mathematics teachers in…

Achilles and the tortoise: Some caveats to mathematical modeling in biology.

PubMed

Gilbert, Scott F

2018-01-31

Mathematical modeling has recently become a much-lauded enterprise, and many funding agencies seek to prioritize this endeavor. However, there are certain dangers associated with mathematical modeling, and knowledge of these pitfalls should also be part of a biologist's training in this set of techniques. (1) Mathematical models are limited by known science; (2) Mathematical models can tell what can happen, but not what did happen; (3) A model does not have to conform to reality, even if it is logically consistent; (4) Models abstract from reality, and sometimes what they eliminate is critically important; (5) Mathematics can present a Platonic ideal to which biologically organized matter strives, rather than a trial-and-error bumbling through evolutionary processes. This "Unity of Science" approach, which sees biology as the lowest physical science and mathematics as the highest science, is part of a Western belief system, often called the Great Chain of Being (or Scala Natura), that sees knowledge emerge as one passes from biology to chemistry to physics to mathematics, in an ascending progression of reason being purification from matter. This is also an informal model for the emergence of new life. There are now other informal models for integrating development and evolution, but each has its limitations. Copyright © 2018 Elsevier Ltd. All rights reserved.

Automatic mathematical modeling for real time simulation program (AI application)

NASA Technical Reports Server (NTRS)

Wang, Caroline; Purinton, Steve

1989-01-01

A methodology is described for automatic mathematical modeling and generating simulation models. The major objective was to create a user friendly environment for engineers to design, maintain, and verify their models; to automatically convert the mathematical models into conventional code for computation; and finally, to document the model automatically.

Vaccine approaches to malaria control and elimination: Insights from mathematical models.

PubMed

White, Michael T; Verity, Robert; Churcher, Thomas S; Ghani, Azra C

2015-12-22

A licensed malaria vaccine would provide a valuable new tool for malaria control and elimination efforts. Several candidate vaccines targeting different stages of the malaria parasite's lifecycle are currently under development, with one candidate, RTS,S/AS01 for the prevention of Plasmodium falciparum infection, having recently completed Phase III trials. Predicting the public health impact of a candidate malaria vaccine requires using clinical trial data to estimate the vaccine's efficacy profile--the initial efficacy following vaccination and the pattern of waning of efficacy over time. With an estimated vaccine efficacy profile, the effects of vaccination on malaria transmission can be simulated with the aid of mathematical models. Here, we provide an overview of methods for estimating the vaccine efficacy profiles of pre-erythrocytic vaccines and transmission-blocking vaccines from clinical trial data. In the case of RTS,S/AS01, model estimates from Phase II clinical trial data indicate a bi-phasic exponential profile of efficacy against infection, with efficacy waning rapidly in the first 6 months after vaccination followed by a slower rate of waning over the next 4 years. Transmission-blocking vaccines have yet to be tested in large-scale Phase II or Phase III clinical trials so we review ongoing work investigating how a clinical trial might be designed to ensure that vaccine efficacy can be estimated with sufficient statistical power. Finally, we demonstrate how parameters estimated from clinical trials can be used to predict the impact of vaccination campaigns on malaria using a mathematical model of malaria transmission. Copyright © 2015 Elsevier Ltd. All rights reserved.

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.

Mathematics anxiety among talented students.

PubMed

Lupkowski, A E; Schumacker, R E

1991-12-01

In order to test the assumption that mathematically talented students show little mathematics anxiety, students participating in an early entrance to college program for talented students were asked to complete the Mathematics Anxiety Rating Scale. Results indicated that these talented students were less math anxious than most unselected college students. However, they were more math anxious than a group of college students majoring in physics. Females in the study showed a tendency to be more math anxious than males (d=-.32), although this finding was not significant. No relationship between level of mathematics anxiety and grades or math anxiety and Scholastic Aptitude Test - Mathematics scores was found for the group of subjects. However, when those relationships were examined for males alone, higher verbal scores and higher grades were associated with lower levels of mathematics anxiety. These relationships were not evident for females.

Think Pair Share Using Realistic Mathematics Education Approach in Geometry Learning

NASA Astrophysics Data System (ADS)

Afthina, H.; Mardiyana; Pramudya, I.

2017-09-01

This research aims to determine the impact of mathematics learning applying Think Pair Share (TPS) using Realistic Mathematics Education (RME) viewed from mathematical-logical intelligence in geometry learning. Method that used in this research is quasi experimental research The result of this research shows that (1) mathematics achievement applying TPS using RME approach gives a better result than those applying direct learning model; (2) students with high mathematical-logical intelligence can reach a better mathematics achievement than those with average and low one, whereas students with average mathematical-logical intelligence can reach a better achievement than those with low one; (3) there is no interaction between learning model and the level of students’ mathematical-logical intelligence in giving a mathematics achievement. The impact of this research is that TPS model using RME approach can be applied in mathematics learning so that students can learn more actively and understand the material more, and mathematics learning become more meaningful. On the other hand, internal factors of students must become a consideration toward the success of students’ mathematical achievement particularly in geometry material.

Preserving Pelicans with Models That Make Sense

ERIC Educational Resources Information Center

Moore, Tamara J.; Doerr, Helen M.; Glancy, Aran W.; Ntow, Forster D.

2015-01-01

Getting students to think deeply about mathematical concepts is not an easy job, which is why we often use problem-solving tasks to engage students in higher-level mathematical thinking. Mathematical modeling, one of the mathematical practices found in the Common Core State Standards for Mathematics (CCSSM), is a type of problem solving that can…

Two Project-Based Strategies in an Interdisciplinary Mathematical Modeling in Biology Course

ERIC Educational Resources Information Center

Ludwig, Patrice; Tongen, Anthony; Walton, Brian

2018-01-01

James Madison University faculty team-teach an interdisciplinary mathematical modeling course for mathematics and biology students. We have used two different project-based approaches to emphasize the mathematical concepts taught in class, while also exposing students to new areas of mathematics not formally covered in class. The first method…

Of Nasa and Neanderthals, Elephants and Machines: Metaphors and the Conceptualization of Homeland Security

DTIC Science & Technology

2013-12-01

study of nature, just as they have in mathematics . Hence, even in our day of hyper abstract thinking , mathematics continues to be the language of...way of thinking . 2. Those successfully completing education and apprenticeship have professed a self-sacrificing commitment to serving society...overreaches. Pinker points out that the contextual school ignores the predictive reality of science and mathematics .73 This does not mean that metaphors

Tracing the role of endogenous carbon in denitrification using wine industry by-product as an external electron donor: Coupling isotopic tools with mathematical modeling.

PubMed

Carrey, R; Rodríguez-Escales, P; Soler, A; Otero, N

2018-02-01

Nitrate removal through enhanced biological denitrification (EBD), consisting of the inoculation of an external electron donor, is a feasible solution for the recovery of groundwater quality. In this context, liquid waste from wine industries (wine industry by-products, WIB) may be feasible for use as a reactant to enhance heterotrophic denitrification. To address the feasibility of WIB as electron donor to promote denitrification, as well as to evaluate the role of biomass as a secondary organic C source, a flow-through experiment was carried out. Chemical and isotopic characterization was performed and coupled with mathematical modeling. Complete nitrate attenuation with no nitrite accumulation was successfully achieved after 10 days. Four different C/N molar ratios (7.0, 2.0, 1.0 and 0) were tested. Progressive decrease of the C/N ratio reduced the remaining C in the outflow and favored biomass migration, producing significant changes in dispersivity in the reactor, which favored efficient nitrate degradation. The applied mathematical model described the general trends for nitrate, ethanol, dissolved organic carbon (DOC) and dissolved inorganic carbon (DIC) concentrations. This model shows how the biomass present in the system is degraded to dissolved organic C (DOC en ) and becomes the main source of DOC for a C/N ratio between 1.0 and 0. The isotopic model developed for organic and inorganic carbon also describes the general trends of δ 13 C of ethanol, DOC and DIC in the outflow water. The study of the evolution of the isotopic fractionation of organic C using a Rayleigh distillation model shows the shift in the organic carbon source from the WIB to the biomass and is in agreement with the isotopic fractionation values used to calibrate the model. Isotopic fractionations (ε) of C-ethanol and C-DOC en were -1‰ and -5‰ (model) and -3.3‰ and -4.8‰ (Rayleigh), respectively. In addition, an inverse isotopic fractionation of +10‰ was observed for biomass degradation to DOC en . Overall, WIB can efficiently promote nitrate reduction in EBD treatments. The conceptual model of the organic C cycle and the developed mathematical model accurately described the chemical and isotopic transformations that occur during this induced denitrification. Copyright © 2017 Elsevier Ltd. All rights reserved.

Delineating the relationship between stress mindset and primary appraisals: preliminary findings.

PubMed

Kilby, Christopher J; Sherman, Kerry A

2016-01-01

Stress mindset theory suggests that positive stress beliefs lead to positive, rather than negative, outcomes when engaging with stressors. Similarly, the Transactional Model of Stress predicts that perceiving a stressor as challenging leads to positive outcomes whereas negative perceptions of the stressor as threatening invoke negative outcomes. The aim of this study was to provide preliminary data examining the nature of the relationship between stress mindset and primary appraisals. It was predicted that positive beliefs about stress would be associated with perceiving a stressful situation as more challenging, and inversely related to perceptions of threat. Participants (N = 124) initially completed measures assessing stress mindset, lifetime and current perceived stress, trait anxiety, and self-efficacy. Then participants received a set of instructions regarding a stressful mathematics task, followed by completion of post-manipulation stress mindset and primary appraisals measures, prior to completing the mathematics task. Multiple linear regression analyses revealed that participants who held a greater number of positive beliefs (as opposed to negative beliefs) about stress also perceived the stressor as being more challenging. However, there was no significant relationship between valence of beliefs and threat appraisals. These findings provide initial evidence for the nature of the relationship between valence of stress beliefs and challenge appraisals. Further research is needed to understand how stress beliefs impact on the way in which an individual copes with stressful situations.

Mathematical models of behavior of individual animals.

PubMed

Tsibulsky, Vladimir L; Norman, Andrew B

2007-01-01

This review is focused on mathematical modeling of behaviors of a whole organism with special emphasis on models with a clearly scientific approach to the problem that helps to understand the mechanisms underlying behavior. The aim is to provide an overview of old and contemporary mathematical models without complex mathematical details. Only deterministic and stochastic, but not statistical models are reviewed. All mathematical models of behavior can be divided into two main classes. First, models that are based on the principle of teleological determinism assume that subjects choose the behavior that will lead them to a better payoff in the future. Examples are game theories and operant behavior models both of which are based on the matching law. The second class of models are based on the principle of causal determinism, which assume that subjects do not choose from a set of possibilities but rather are compelled to perform a predetermined behavior in response to specific stimuli. Examples are perception and discrimination models, drug effects models and individual-based population models. A brief overview of the utility of each mathematical model is provided for each section.

Nonlinear mathematical modeling and sensitivity analysis of hydraulic drive unit

NASA Astrophysics Data System (ADS)

Kong, Xiangdong; Yu, Bin; Quan, Lingxiao; Ba, Kaixian; Wu, Liujie

2015-09-01

The previous sensitivity analysis researches are not accurate enough and also have the limited reference value, because those mathematical models are relatively simple and the change of the load and the initial displacement changes of the piston are ignored, even experiment verification is not conducted. Therefore, in view of deficiencies above, a nonlinear mathematical model is established in this paper, including dynamic characteristics of servo valve, nonlinear characteristics of pressure-flow, initial displacement of servo cylinder piston and friction nonlinearity. The transfer function block diagram is built for the hydraulic drive unit closed loop position control, as well as the state equations. Through deriving the time-varying coefficient items matrix and time-varying free items matrix of sensitivity equations respectively, the expression of sensitivity equations based on the nonlinear mathematical model are obtained. According to structure parameters of hydraulic drive unit, working parameters, fluid transmission characteristics and measured friction-velocity curves, the simulation analysis of hydraulic drive unit is completed on the MATLAB/Simulink simulation platform with the displacement step 2 mm, 5 mm and 10 mm, respectively. The simulation results indicate that the developed nonlinear mathematical model is sufficient by comparing the characteristic curves of experimental step response and simulation step response under different constant load. Then, the sensitivity function time-history curves of seventeen parameters are obtained, basing on each state vector time-history curve of step response characteristic. The maximum value of displacement variation percentage and the sum of displacement variation absolute values in the sampling time are both taken as sensitivity indexes. The sensitivity indexes values above are calculated and shown visually in histograms under different working conditions, and change rules are analyzed. Then the sensitivity indexes values of four measurable parameters, such as supply pressure, proportional gain, initial position of servo cylinder piston and load force, are verified experimentally on test platform of hydraulic drive unit, and the experimental research shows that the sensitivity analysis results obtained through simulation are approximate to the test results. This research indicates each parameter sensitivity characteristics of hydraulic drive unit, the performance-affected main parameters and secondary parameters are got under different working conditions, which will provide the theoretical foundation for the control compensation and structure optimization of hydraulic drive unit.

Problem Posing and Solving with Mathematical Modeling

ERIC Educational Resources Information Center

English, Lyn D.; Fox, Jillian L.; Watters, James J.

2005-01-01

Mathematical modeling is explored as both problem posing and problem solving from two perspectives, that of the child and the teacher. Mathematical modeling provides rich learning experiences for elementary school children and their teachers.

Building Mathematical Models of Simple Harmonic and Damped Motion.

ERIC Educational Resources Information Center

Edwards, Thomas

1995-01-01

By developing a sequence of mathematical models of harmonic motion, shows that mathematical models are not right or wrong, but instead are better or poorer representations of the problem situation. (MKR)

Taking the mystery out of mathematical model applications to karst aquifers—A primer

USGS Publications Warehouse

Kuniansky, Eve L.

2014-01-01

Advances in mathematical model applications toward the understanding of the complex flow, characterization, and water-supply management issues for karst aquifers have occurred in recent years. Different types of mathematical models can be applied successfully if appropriate information is available and the problems are adequately identified. The mathematical approaches discussed in this paper are divided into three major categories: 1) distributed parameter models, 2) lumped parameter models, and 3) fitting models. The modeling approaches are described conceptually with examples (but without equations) to help non-mathematicians understand the applications.

A characterization of linearly repetitive cut and project sets

NASA Astrophysics Data System (ADS)

Haynes, Alan; Koivusalo, Henna; Walton, James

2018-02-01

For the development of a mathematical theory which can be used to rigorously investigate physical properties of quasicrystals, it is necessary to understand regularity of patterns in special classes of aperiodic point sets in Euclidean space. In one dimension, prototypical mathematical models for quasicrystals are provided by Sturmian sequences and by point sets generated by substitution rules. Regularity properties of such sets are well understood, thanks mostly to well known results by Morse and Hedlund, and physicists have used this understanding to study one dimensional random Schrödinger operators and lattice gas models. A key fact which plays an important role in these problems is the existence of a subadditive ergodic theorem, which is guaranteed when the corresponding point set is linearly repetitive. In this paper we extend the one-dimensional model to cut and project sets, which generalize Sturmian sequences in higher dimensions, and which are frequently used in mathematical and physical literature as models for higher dimensional quasicrystals. By using a combination of algebraic, geometric, and dynamical techniques, together with input from higher dimensional Diophantine approximation, we give a complete characterization of all linearly repetitive cut and project sets with cubical windows. We also prove that these are precisely the collection of such sets which satisfy subadditive ergodic theorems. The results are explicit enough to allow us to apply them to known classical models, and to construct linearly repetitive cut and project sets in all pairs of dimensions and codimensions in which they exist. Research supported by EPSRC grants EP/L001462, EP/J00149X, EP/M023540. HK also gratefully acknowledges the support of the Osk. Huttunen foundation.

Sustained virological response with intravenous silibinin: individualized IFN-free therapy via real-time modelling of HCV kinetics.

PubMed

Dahari, Harel; Shteingart, Shimon; Gafanovich, Inna; Cotler, Scott J; D'Amato, Massimo; Pohl, Ralf T; Weiss, Gali; Ashkenazi, Yaakov J; Tichler, Thomas; Goldin, Eran; Lurie, Yoav

2015-02-01

Intravenous silibinin (SIL) is a potent antiviral agent against hepatitis C virus (HCV) genotype-1. In this proof of concept case-study we tested: (i) whether interferon-alfa (IFN)-free treatment with SIL plus ribavirin (RBV) can achieve sustained virological response (SVR); (ii) whether SIL is safe and feasible for prolonged duration of treatment and (iii) whether mathematical modelling of early on-treatment HCV kinetics can guide duration of therapy to achieve SVR. A 44 year-old female HCV-(genotype-1)-infected patient who developed severe psychiatric adverse events to a previous course of pegIFN+RBV, initiated combination treatment with 1200 mg/day of SIL, 1200 mg/day of RBV and 6000 u/day vitamin D. Blood samples were collected frequently till week 4, thereafter every 1-12 weeks until the end of therapy. The standard biphasic mathematical model with time-varying SIL effectiveness was used to predict the duration of therapy to achieve SVR. Based on modelling the observed viral kinetics during the first 3 weeks of treatment, SVR was predicted to be achieved within 34 weeks of therapy. Provided with this information, the patient agreed to complete 34 weeks of treatment. IFN-free treatment with SIL+RBV was feasible, safe and achieved SVR (week-33). We report, for the first time, the use of real-time mathematical modelling of HCV kinetics to individualize duration of IFN-free therapy and to empower a patient to participate in shared decision making regarding length of treatment. SIL-based individualized therapy provides a treatment option for patients who do not respond to or cannot receive other HCV agents and should be further validated. © 2014 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

Sustained virological response with intravenous silibinin: individualized IFN-free therapy via real-time modeling of HCV kinetics

PubMed Central

Dahari, Harel; Shteingart, Shimon; Gafanovich, Inna; Cotler, Scott J.; D'Amato, Massimo; Pohl, Ralf T.; Weiss, Gali; Ashkenazi, Yaakov Jack; Tichler, Thomas; Goldin, Eran; Lurie, Yoav

2014-01-01

Background & Aims Intravenous silibinin (SIL) is a potent antiviral agent against hepatitis C virus (HCV) genotype-1. In this proof of concept case-study we tested: (i) whether interferon-alfa (IFN)-free treatment with SIL plus ribavirin (RBV) can achieve sustained virological response (SVR), (ii) whether SIL is safe and feasible for prolonged duration of treatment, and (iii) whether mathematical modeling of early on-treatment HCV kinetics can guide duration of therapy to achieve SVR. Methods A 44 year-old female HCV-(genotype-1)-infected patient who developed severe psychiatric adverse events to a previous course of pegIFN+RBV, initiated combination treatment with 1200 mg/day of SIL, 1200 mg/day of RBV and 6000 u/day vitamin D. Blood samples were collected frequently till week 4, thereafter every 1 to 12 weeks until the end of therapy. The standard-biphasic-mathematical model was used to predict the duration of therapy to achieve SVR. Results Based on modeling the observed viral kinetics during the first 3 weeks of treatment, SVR was predicted to be achieved within 34 weeks of therapy. Provided with this information, the patient agreed to complete 34 weeks of treatment. IFN-free treatment with SIL+RBV was feasible, safe, and achieved SVR (week-33). Conclusions We report, for the first time, the use of real-time mathematical modeling of HCV kinetics to individualize duration of IFN-free therapy and to empower a patient to participate in shared decision making regarding length of treatment. SIL-based individualized therapy provides a treatment option for patients who do not respond to or cannot receive other HCV agents and should be further validated. PMID:25251042

Accelerating Mathematics Achievement Using Heterogeneous Grouping

ERIC Educational Resources Information Center

Burris, Carol Corbett; Heubert, Jay P.; Levin, Henry M.

2006-01-01

This longitudinal study examined the effects of providing an accelerated mathematics curriculum in heterogeneously grouped middle school classes in a diverse suburban school district. A quasi-experimental cohort design was used to evaluate subsequent completion of advanced high school math courses as well as academic achievement. Results showed…

Using Curriculum-Based Measurement To Monitor Kindergarteners' Mathematics Development

ERIC Educational Resources Information Center

Seethaler, Pamela M.; Fuchs, Lynn S.

2011-01-01

The purpose of this study was to examine technical and instructional features of a kindergarten curriculum-based measurement (CBM) tool designed to track students' mathematics progress in terms of computational concepts, procedures, and counting strategies. Students in 10 kindergarten classrooms in three elementary schools completed alternate…

75 FR 53716 - Invitation for Membership on Advisory Committee

Federal Register 2010, 2011, 2012, 2013, 2014

2010-09-01

... successful completion of Joint Board examinations in basic actuarial mathematics and methodology and in actuarial mathematics and methodology relating to pension plans qualifying under ERISA. The Joint Board, the... Act of 1974 (ERISA), is responsible for the enrollment of individuals who wish to perform actuarial...

How to Teach Verbal Problems

ERIC Educational Resources Information Center

Dahmus, Maurice E.

1970-01-01

Presents a technique for teaching the lower ninety percent in mathematics. Concentrates on converting English statements, both expressed and implied, into one or many mathematical statements. Emphasis on translating in a direct, piecemeal, pure, and complete manner (DPPC). This method differs from others in that it is concrete rather than…

Secondary Teachers' Conceptions and Practices of Assessment Models: The Case for Mathematics Teachers in Jordan

ERIC Educational Resources Information Center

Al Duwairi, Ahmed

2013-01-01

This study aimed at investigating the extent to which secondary schools mathematics teachers practice to assessment models in their mathematics teaching and learning. Definitely, the study aimed at answering the following questions: (1) To what extent do secondary schools mathematics teachers practice each of the assessment models in their…

Reality-Theoretical Models-Mathematics: A Ternary Perspective on Physics Lessons in Upper-Secondary School

ERIC Educational Resources Information Center

Hansson, Lena; Hansson, Örjan; Juter, Kristina; Redfors, Andreas

2015-01-01

This article discusses the role of mathematics during physics lessons in upper-secondary school. Mathematics is an inherent part of theoretical models in physics and makes powerful predictions of natural phenomena possible. Ability to use both theoretical models and mathematics is central in physics. This paper takes as a starting point that the…

Mathematics Student Teachers' Modelling Approaches While Solving the Designed Esme Rug Problem

ERIC Educational Resources Information Center

Hidiroglu, Çaglar Naci; Dede, Ayse Tekin; Ünver, Semiha Kula; Güzel, Esra Bukova

2017-01-01

The purpose of the study is to analyze the mathematics student teachers' solutions on the Esme Rug Problem through 7-stage mathematical modelling process. This problem was designed by the researchers by considering the modelling problems' main properties. The study was conducted with twenty one secondary mathematics student teachers. The data were…

The use of mathematical models in teaching wastewater treatment engineering.

PubMed

Morgenroth, E; Arvin, E; Vanrolleghem, P

2002-01-01

Mathematical modeling of wastewater treatment processes has become increasingly popular in recent years. To prepare students for their future careers, environmental engineering education should provide students with sufficient background and experiences to understand and apply mathematical models efficiently and responsibly. Approaches for introducing mathematical modeling into courses on wastewater treatment engineering are discussed depending on the learning objectives, level of the course and the time available.

Low Dose Radiation Cancer Risks: Epidemiological and Toxicological Models

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

David G. Hoel, PhD

2012-04-19

The basic purpose of this one year research grant was to extend the two stage clonal expansion model (TSCE) of carcinogenesis to exposures other than the usual single acute exposure. The two-stage clonal expansion model of carcinogenesis incorporates the biological process of carcinogenesis, which involves two mutations and the clonal proliferation of the intermediate cells, in a stochastic, mathematical way. The current TSCE model serves a general purpose of acute exposure models but requires numerical computation of both the survival and hazard functions. The primary objective of this research project was to develop the analytical expressions for the survival functionmore » and the hazard function of the occurrence of the first cancer cell for acute, continuous and multiple exposure cases within the framework of the piece-wise constant parameter two-stage clonal expansion model of carcinogenesis. For acute exposure and multiple exposures of acute series, it is either only allowed to have the first mutation rate vary with the dose, or to have all the parameters be dose dependent; for multiple exposures of continuous exposures, all the parameters are allowed to vary with the dose. With these analytical functions, it becomes easy to evaluate the risks of cancer and allows one to deal with the various exposure patterns in cancer risk assessment. A second objective was to apply the TSCE model with varing continuous exposures from the cancer studies of inhaled plutonium in beagle dogs. Using step functions to estimate the retention functions of the pulmonary exposure of plutonium the multiple exposure versions of the TSCE model was to be used to estimate the beagle dog lung cancer risks. The mathematical equations of the multiple exposure versions of the TSCE model were developed. A draft manuscript which is attached provides the results of this mathematical work. The application work using the beagle dog data from plutonium exposure has not been completed due to the fact that the research project did not continue beyond its first year.« less

Semantic language as a mechanism explaining the association between ADHD symptoms and reading and mathematics underachievement.

PubMed

Gremillion, Monica L; Martel, Michelle M

2012-11-01

ADHD is associated with academic underachievement, but it remains unclear what mechanism accounts for this association. Semantic language is an underexplored mechanism that provides a developmental explanation for this association. The present study will examine whether semantic language deficits explain the association between ADHD and reading and mathematics underachievement, taking into account alternative explanations for associations, including verbal working memory (WM) impairments, as well as specificity of effects to inattentive and hyperactive-impulsive ADHD symptom domains. Participants in this cross-sectional study were 546 children (54 % male) ages six to twelve (M = 9.77, SD = 1.49). ADHD symptoms were measured via maternal and teacher report during structured interviews and on standardized rating forms. Children completed standardized semantic language, verbal WM, and academic testing. Semantic language fully mediated the ADHD-reading achievement association and partially mediated the ADHD-mathematics achievement association. Verbal WM also partially mediated the ADHD-mathematics association but did not mediate the ADHD-reading achievement association. Results generalized across inattentive and hyperactive-impulsive ADHD symptom domains. Semantic language explained the association between ADHD and reading underachievement and partially explained the association between ADHD and mathematics underachievement. Together, language impairment and WM fully explained the association between ADHD and reading underachievement, in line with developmental models suggesting that language and WM conjointly influence the development of attention and subsequent academic achievement. This work has implication for the development of tailored interventions for academic underachievement in children with ADHD.

Kinetic models in industrial biotechnology - Improving cell factory performance.

PubMed

Almquist, Joachim; Cvijovic, Marija; Hatzimanikatis, Vassily; Nielsen, Jens; Jirstrand, Mats

2014-07-01

An increasing number of industrial bioprocesses capitalize on living cells by using them as cell factories that convert sugars into chemicals. These processes range from the production of bulk chemicals in yeasts and bacteria to the synthesis of therapeutic proteins in mammalian cell lines. One of the tools in the continuous search for improved performance of such production systems is the development and application of mathematical models. To be of value for industrial biotechnology, mathematical models should be able to assist in the rational design of cell factory properties or in the production processes in which they are utilized. Kinetic models are particularly suitable towards this end because they are capable of representing the complex biochemistry of cells in a more complete way compared to most other types of models. They can, at least in principle, be used to in detail understand, predict, and evaluate the effects of adding, removing, or modifying molecular components of a cell factory and for supporting the design of the bioreactor or fermentation process. However, several challenges still remain before kinetic modeling will reach the degree of maturity required for routine application in industry. Here we review the current status of kinetic cell factory modeling. Emphasis is on modeling methodology concepts, including model network structure, kinetic rate expressions, parameter estimation, optimization methods, identifiability analysis, model reduction, and model validation, but several applications of kinetic models for the improvement of cell factories are also discussed. Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.

A Mathematical Model Development for the Lateral Collapse of Octagonal Tubes

NASA Astrophysics Data System (ADS)

Ghazali Kamardan, M.; Sufahani, Suliadi; Othman, M. Z. M.; Che-Him, Norziha; Khalid, Kamil; Roslan, Rozaini; Ali, Maselan; Zaidi, A. M. A.

2018-04-01

Many researches has been done on the lateral collapse of tube. However, the previous researches only focus on cylindrical and square tubes. Then a research has been done discovering the collapse behaviour of hexagonal tube and the mathematic model of the deformation behaviour had been developed [8]. The purpose of this research is to study the lateral collapse behaviour of symmetric octagonal tubes and hence to develop a mathematical model of the collapse behaviour of these tubes. For that, a predictive mathematical model was developed and a finite element analysis procedure was conducted for the lateral collapse behaviour of symmetric octagonal tubes. Lastly, the mathematical model was verified by using the finite element analysis simulation results. It was discovered that these tubes performed different deformation behaviour than the cylindrical tube. Symmetric octagonal tubes perform 2 phases of elastic - plastic deformation behaviour patterns. The mathematical model had managed to show the fundamental of the deformation behaviour of octagonal tubes. However, further studies need to be conducted in order to further improve on the proposed mathematical model.

Jones index, secret sharing and total quantum dimension

NASA Astrophysics Data System (ADS)

Fiedler, Leander; Naaijkens, Pieter; Osborne, Tobias J.

2017-02-01

We study the total quantum dimension in the thermodynamic limit of topologically ordered systems. In particular, using the anyons (or superselection sectors) of such models, we define a secret sharing scheme, storing information invisible to a malicious party, and argue that the total quantum dimension quantifies how well we can perform this task. We then argue that this can be made mathematically rigorous using the index theory of subfactors, originally due to Jones and later extended by Kosaki and Longo. This theory provides us with a ‘relative entropy’ of two von Neumann algebras and a quantum channel, and we argue how these can be used to quantify how much classical information two parties can hide form an adversary. We also review the total quantum dimension in finite systems, in particular how it relates to topological entanglement entropy. It is known that the latter also has an interpretation in terms of secret sharing schemes, although this is shown by completely different methods from ours. Our work provides a different and independent take on this, which at the same time is completely mathematically rigorous. This complementary point of view might be beneficial, for example, when studying the stability of the total quantum dimension when the system is perturbed.

"When Mathematical Activity Moves You": An Exploration of the Design and Use of Purposefully Embodied Mathematical Activities, Models, Contexts, and Environments

ERIC Educational Resources Information Center

Campbell, William James

2017-01-01

This dissertation describes a mathematics curriculum and instruction design experiment involving a series of embodied mathematical activities conducted in two Colorado elementary schools Activities designed for this experiment include multi-scalar number line models focused on supporting students' understanding of elementary mathematics. Realistic…

Mathematical Modeling Is Also Physics--Interdisciplinary Teaching between Mathematics and Physics in Danish Upper Secondary Education

ERIC Educational Resources Information Center

Michelsen, Claus

2015-01-01

Mathematics plays a crucial role in physics. This role is brought about predominantly through the building, employment, and assessment of mathematical models, and teachers and educators should capture this relationship in the classroom in an effort to improve students' achievement and attitude in both physics and mathematics. But although there…

Exploring Yellowstone National Park with Mathematical Modeling

ERIC Educational Resources Information Center

Wickstrom, Megan H.; Carr, Ruth; Lackey, Dacia

2017-01-01

Mathematical modeling, a practice standard in the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010), is a process by which students develop and use mathematics as a tool to make sense of the world around them. Students investigate a real-world situation by asking mathematical questions; along the way, they need to decide how to use…

"Model Your Genes the Mathematical Way"--A Mathematical Biology Workshop for Secondary School Teachers

ERIC Educational Resources Information Center

Martins, Ana Margarida; Vera-Licona, Paola; Laubenbacher, Reinhard

2008-01-01

This article describes a mathematical biology workshop given to secondary school teachers of the Danville area in Virginia, USA. The goal of the workshop was to enable teams of teachers with biology and mathematics expertise to incorporate lesson plans in mathematical modelling into the curriculum. The biological focus of the activities is the…

An Analysis of Pre-Service Mathematics Teachers' Performance in Modelling Tasks in Terms of Spatial Visualisation Ability

ERIC Educational Resources Information Center

Tasova, Halil Ibrahim; Delice, Ali

2012-01-01

Mathematical modelling involves mathematical constructions chosen to represent some real world situations and the relationships among them; it is the process of expressing a real world situation mathematically. Visualisation can play a significant role in the development of thinking or understanding mathematical concepts, and also makes abstract…

Cultivation of an L-lactate dehydrogenase mutant of Bacillus stearothermophilus in continuous culture with cell recycle

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

Martin, R.S.; Bushell, D.; Leak, D.J.

1994-06-05

Continuous fermentation with cell recycle proved very effective in increasing the ethanol volumetric productivity of the thermophilic facultative anaerobe, Bacillus stearothermophilus strain LLD-15, on sucrose at 70 C. When complete cell recycle was used, cell viability decreased after a few residence times and sucrose consumption was reduced. Operation using a constant bleed rate resulted in greater stability and higher ethanol volumetric productivities. A mathematical model based on maintenance energy requirements provided an adequate description of the system.

An infinitely-stiff elastic system via a tuned negative-stiffness component stabilized by rotation-produced gyroscopic forces

NASA Astrophysics Data System (ADS)

Kochmann, D. M.; Drugan, W. J.

2016-06-01

An elastic system containing a negative-stiffness element tuned to produce positive-infinite system stiffness, although statically unstable as is any such elastic system if unconstrained, is proved to be stabilized by rotation-produced gyroscopic forces at sufficiently high rotation rates. This is accomplished in possibly the simplest model of a composite structure (or solid) containing a negative-stiffness component that exhibits all these features, facilitating a conceptually and mathematically transparent, completely closed-form analysis.

Video-Based Intervention in Teaching Fraction Problem-Solving to Students with Autism Spectrum Disorder.

PubMed

Yakubova, Gulnoza; Hughes, Elizabeth M; Hornberger, Erin

2015-09-01

The purpose of this study was to determine the effectiveness of a point-of-view video modeling intervention to teach mathematics problem-solving when working on word problems involving subtracting mixed fractions with uncommon denominators. Using a multiple-probe across students design of single-case methodology, three high school students with ASD completed the study. All three students demonstrated greater accuracy in solving fraction word problems and maintained accuracy levels at a 1-week follow-up.

Bridging the Gap Between Theory and Practice: Structure and Randomization in Large Scale Combinatorial Search

DTIC Science & Technology

2012-01-17

PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION...world problems. Our work brings together techniques from constraint programming, mathematical programming, and satisfiability in a symbiotic way to...power-­‐law  search  tree  model  for  complete  or  exact  methods     (See [9] for a detailed description of this work and

Heat storage capability of a rolling cylinder using Glauber's salt

NASA Technical Reports Server (NTRS)

Herrick, C. S.; Zarnoch, K. P.

1980-01-01

The rolling cylinder phase change heat storage concept was developed to the point where a prototype design is completed and a cost analysis is prepared. A series of experimental and analytical tasks are defined to establish the thermal, mechanical, and materials behavior of rolling cylinder devices. These tasks include: analyses of internal and external heat transfer; performance and lifetime testing of the phase change materials; corrosion evaluation; development of a mathematical model; and design of a prototype and associated test equipment.

Components of Mathematics Anxiety: Factor Modeling of the MARS30-Brief

PubMed Central

Pletzer, Belinda; Wood, Guilherme; Scherndl, Thomas; Kerschbaum, Hubert H.; Nuerk, Hans-Christoph

2016-01-01

Mathematics anxiety involves feelings of tension, discomfort, high arousal, and physiological reactivity interfering with number manipulation and mathematical problem solving. Several factor analytic models indicate that mathematics anxiety is rather a multidimensional than unique construct. However, the factor structure of mathematics anxiety has not been fully clarified by now. This issue shall be addressed in the current study. The Mathematics Anxiety Rating Scale (MARS) is a reliable measure of mathematics anxiety (Richardson and Suinn, 1972), for which several reduced forms have been developed. Most recently, a shortened version of the MARS (MARS30-brief) with comparable reliability was published. Different studies suggest that mathematics anxiety involves up to seven different factors. Here we examined the factor structure of the MARS30-brief by means of confirmatory factor analysis. The best model fit was obtained by a six-factor model, dismembering the known two general factors “Mathematical Test Anxiety” (MTA) and “Numerical Anxiety” (NA) in three factors each. However, a more parsimonious 5-factor model with two sub-factors for MTA and three for NA fitted the data comparably well. Factors were differentially susceptible to sex differences and differences between majors. Measurement invariance for sex was established. PMID:26924996

Components of Mathematics Anxiety: Factor Modeling of the MARS30-Brief.

PubMed

Pletzer, Belinda; Wood, Guilherme; Scherndl, Thomas; Kerschbaum, Hubert H; Nuerk, Hans-Christoph

2016-01-01

Mathematics anxiety involves feelings of tension, discomfort, high arousal, and physiological reactivity interfering with number manipulation and mathematical problem solving. Several factor analytic models indicate that mathematics anxiety is rather a multidimensional than unique construct. However, the factor structure of mathematics anxiety has not been fully clarified by now. This issue shall be addressed in the current study. The Mathematics Anxiety Rating Scale (MARS) is a reliable measure of mathematics anxiety (Richardson and Suinn, 1972), for which several reduced forms have been developed. Most recently, a shortened version of the MARS (MARS30-brief) with comparable reliability was published. Different studies suggest that mathematics anxiety involves up to seven different factors. Here we examined the factor structure of the MARS30-brief by means of confirmatory factor analysis. The best model fit was obtained by a six-factor model, dismembering the known two general factors "Mathematical Test Anxiety" (MTA) and "Numerical Anxiety" (NA) in three factors each. However, a more parsimonious 5-factor model with two sub-factors for MTA and three for NA fitted the data comparably well. Factors were differentially susceptible to sex differences and differences between majors. Measurement invariance for sex was established.

Control of Crazyflie nano quadcopter using Simulink

NASA Astrophysics Data System (ADS)

Gopabhat Madhusudhan, Meghana

This thesis focuses on developing a mathematical model in Simulink to Crazyflie, an open source platform. Attitude, altitude and position controllers of a Crazyflie are designed in the mathematical model. The mathematical model is developed based on the quadcopter system dynamics using a non-linear approach. The parameters of translational and rotational dynamics of the quadcopter system are linearized and tuned individually. The tuned attitude and altitude controllers from the mathematical model are implemented on real time Crazyflie Simulink model to achieve autonomous and controlled flight.

Computational modeling of the cell-autonomous mammalian circadian oscillator.

PubMed

Podkolodnaya, Olga A; Tverdokhleb, Natalya N; Podkolodnyy, Nikolay L

2017-02-24

This review summarizes various mathematical models of cell-autonomous mammalian circadian clock. We present the basics necessary for understanding of the cell-autonomous mammalian circadian oscillator, modern experimental data essential for its reconstruction and some special problems related to the validation of mathematical circadian oscillator models. This work compares existing mathematical models of circadian oscillator and the results of the computational studies of the oscillating systems. Finally, we discuss applications of the mathematical models of mammalian circadian oscillator for solving specific problems in circadian rhythm biology.

Students’ errors in solving combinatorics problems observed from the characteristics of RME modeling

NASA Astrophysics Data System (ADS)

Meika, I.; Suryadi, D.; Darhim

2018-01-01

This article was written based on the learning evaluation results of students’ errors in solving combinatorics problems observed from the characteristics of Realistic Mathematics Education (RME); that is modeling. Descriptive method was employed by involving 55 students from two international-based pilot state senior high schools in Banten. The findings of the study suggested that the students still committed errors in simplifying the problem as much 46%; errors in making mathematical model (horizontal mathematization) as much 60%; errors in finishing mathematical model (vertical mathematization) as much 65%; and errors in interpretation as well as validation as much 66%.

Dynamics and forecast in a simple model of sustainable development for rural populations.

PubMed

Angulo, David; Angulo, Fabiola; Olivar, Gerard

2015-02-01

Society is becoming more conscious on the need to preserve the environment. Sustainable development schemes have grown rapidly as a tool for managing, predicting and improving the growth path in different regions and economy sectors. We introduce a novel and simple mathematical model of ordinary differential equations (ODEs) in order to obtain a dynamical description for each one of the sustainability components (economy, social development and environment conservation), together with their dependence with demographic dynamics. The main part in the modeling task is inspired by the works by Cobb, Douglas, Brander and Taylor. This is completed through some new insights by the authors. A model application is presented for three specific geographical rural regions in Caldas (Colombia).

An Activity to Encourage Writing in Mathematics

ERIC Educational Resources Information Center

Van Dyke, Frances; Malloy, Elizabeth J.; Stallings, Virginia

2014-01-01

This article discusses an activity designed to encourage writing to learn in mathematics. There were three stages of data collection. An assessment, requiring basic algebra only, was completed by 118 undergraduates from statistics and calculus courses. Students were given summaries of all participant responses, along with the correct answers.…

Reconsidering Approaches to Aboriginal Science and Mathematics Education

ERIC Educational Resources Information Center

Sterenberg, Gladys; Hogue, Michelle

2011-01-01

In Canada, Aboriginal postsecondary enrollment and completion rates are significantly lower than those of non-Aboriginal students. This is most evident in studies involving science and mathematics. The investigation of this issue was informed by focus group discussions with eight participants representing a Blackfoot community. Themes emerging in…

International Teachers' Judgment of Gifted Mathematics Student Characteristics

ERIC Educational Resources Information Center

Ficici, Abdullah; Siegle, Del

2008-01-01

Teachers play a key role in the identification and training of talented mathematicians, and their attitudes are important in improving math instruction for gifted students. We surveyed secondary mathematics teachers from South Korea, Turkey, and the United States. These teachers completed a survey instrument called the Teachers' Judgments of…

The Relationship between Mathematical Induction, Proposition Functions, and Implication Functions

ERIC Educational Resources Information Center

Andrew, Lane

2010-01-01

In this study, I explored the relationship between mathematical induction ability and proposition and implication functions through a mixed methods approach. Students from three universities (N = 78) and 6 classrooms completed a written assessment testing their conceptual and procedural capabilities with induction and functions. In addition, I…

Beyond the Given: Stretching Mathematical Thinking through Journaling

ERIC Educational Resources Information Center

Hamdan, May

2017-01-01

This paper reflects on a teaching experiment and presents details of a pedagogical technique where students periodically write down their clearest interpretation of the conditions imposed on various discrete mathematical subjects they are learning in class. Through iterations, students generate a more complete understanding of the material, one…

The Relationship between Big Data and Mathematical Modeling: A Discussion in a Mathematical Education Scenario

ERIC Educational Resources Information Center

Dalla Vecchia, Rodrigo

2015-01-01

This study discusses aspects of the association between Mathematical Modeling (MM) and Big Data in the scope of mathematical education. We present an example of an activity to discuss two ontological factors that involve MM. The first is linked to the modeling stages. The second involves the idea of pedagogical objectives. The main findings…

On a Mathematical Model with Noncompact Boundary Conditions Describing Bacterial Population

NASA Astrophysics Data System (ADS)

Boulanouar, Mohamed

2013-04-01

In this work, we are concerned with the well-posedness of a mathematical model describing a maturation-velocity structured bacterial population. Each bacterium is distinguished by its degree of maturity and its maturation velocity. The bacterial mitosis is mathematically described by noncompact boundary conditions. We show that the mathematical model is governed by a positive strongly continuous semigroup.

What’s about Peer Tutoring Learning Model?

NASA Astrophysics Data System (ADS)

Muthma'innah, M.

2017-09-01

Mathematics learning outcomes in Indonesia in general is still far from satisfactory. One effort that could be expected to solve the problem is to apply the model of peer tutoring learning in mathematics. This study aims to determine whether the results of students’ mathematics learning can be enhanced through peer tutoring learning models. This type of research is the study of literature, so that the method used is to summarize and analyze the results of relevant research that has been done. Peer tutoring learning model is a model of learning in which students learn in small groups that are grouped with different ability levels, all group members to work together and help each other to understand the material. By paying attention to the syntax of the learning, then learning will be invaluable peer tutoring for students who served as teachers and students are taught. In mathematics, the implementation of this learning model can make students understand each other mathematical concepts and help students in solving mathematical problems that are poorly understood, due to the interaction between students in learning. Then it will be able to improve learning outcomes in mathematics. The impact, it can be applied in mathematics learning.

The semantic system is involved in mathematical problem solving.

PubMed

Zhou, Xinlin; Li, Mengyi; Li, Leinian; Zhang, Yiyun; Cui, Jiaxin; Liu, Jie; Chen, Chuansheng

2018-02-01

Numerous studies have shown that the brain regions around bilateral intraparietal cortex are critical for number processing and arithmetical computation. However, the neural circuits for more advanced mathematics such as mathematical problem solving (with little routine arithmetical computation) remain unclear. Using functional magnetic resonance imaging (fMRI), this study (N = 24 undergraduate students) compared neural bases of mathematical problem solving (i.e., number series completion, mathematical word problem solving, and geometric problem solving) and arithmetical computation. Direct subject- and item-wise comparisons revealed that mathematical problem solving typically had greater activation than arithmetical computation in all 7 regions of the semantic system (which was based on a meta-analysis of 120 functional neuroimaging studies on semantic processing). Arithmetical computation typically had greater activation in the supplementary motor area and left precentral gyrus. The results suggest that the semantic system in the brain supports mathematical problem solving. Copyright © 2017 Elsevier Inc. All rights reserved.

Current problems in applied mathematics and mathematical modeling

NASA Astrophysics Data System (ADS)

Alekseev, A. S.

Papers are presented on mathematical modeling noting applications to such fields as geophysics, chemistry, atmospheric optics, and immunology. Attention is also given to models of ocean current fluxes, atmospheric and marine interactions, and atmospheric pollution. The articles include studies of catalytic reactors, models of global climate phenomena, and computer-assisted atmospheric models.

Mathematical modeling of urea transport in the kidney.

PubMed

Layton, Anita T

2014-01-01

Mathematical modeling techniques have been useful in providing insights into biological systems, including the kidney. This article considers some of the mathematical models that concern urea transport in the kidney. Modeling simulations have been conducted to investigate, in the context of urea cycling and urine concentration, the effects of hypothetical active urea secretion into pars recta. Simulation results suggest that active urea secretion induces a "urea-selective" improvement in urine concentrating ability. Mathematical models have also been built to study the implications of the highly structured organization of tubules and vessels in the renal medulla on urea sequestration and cycling. The goal of this article is to show how physiological problems can be formulated and studied mathematically, and how such models may provide insights into renal functions.

The Effects of Mathematical Modeling on Creative Production Ability and Self-Directed Learning Attitude

ERIC Educational Resources Information Center

Kim, Sun Hee; Kim, Soojin

2010-01-01

What should we do to educate the mathematically gifted and how should we do it? In this research, to satisfy diverse mathematical and cognitive demands of the gifted who have excellent learning ability and task tenacity in mathematics, we sought to apply mathematical modeling. One of the objectives of the gifted education in Korea is cultivating…

A Mathematical Diet Model

ERIC Educational Resources Information Center

Toumasis, Charalampos

2004-01-01

Emphasis on problem solving and mathematical modeling has gained considerable attention in the last few years. Connecting mathematics to other subjects and to the real world outside the classroom has received increased attention in mathematics programs. This article describes an application of simple differential equations in the field of…

Mathematical study on robust tissue pattern formation in growing epididymal tubule.

PubMed

Hirashima, Tsuyoshi

2016-10-21

Tissue pattern formation during development is a reproducible morphogenetic process organized by a series of kinetic cellular activities, leading to the building of functional and stable organs. Recent studies focusing on mechanical aspects have revealed physical mechanisms on how the cellular activities contribute to the formation of reproducible tissue patterns; however, the understanding for what factors achieve the reproducibility of such patterning and how it occurs is far from complete. Here, I focus on a tube pattern formation during murine epididymal development, and show that two factors influencing physical design for the patterning, the proliferative zone within the tubule and the viscosity of tissues surrounding to the tubule, control the reproducibility of epididymal tubule pattern, using a mathematical model based on experimental data. Extensive numerical simulation of the simple mathematical model revealed that a spatially localized proliferative zone within the tubule, observed in experiments, results in more reproducible tubule pattern. Moreover, I found that the viscosity of tissues surrounding to the tubule imposes a trade-off regarding pattern reproducibility and spatial accuracy relating to the region where the tubule pattern is formed. This indicates an existence of optimality in material properties of tissues for the robust patterning of epididymal tubule. The results obtained by numerical analysis based on experimental observations provide a general insight on how physical design realizes robust tissue pattern formation. Copyright © 2016 Elsevier Ltd. All rights reserved.

Computational control of flexible aerospace systems

NASA Technical Reports Server (NTRS)

Sharpe, Lonnie, Jr.; Shen, Ji Yao

1994-01-01

The main objective of this project is to establish a distributed parameter modeling technique for structural analysis, parameter estimation, vibration suppression and control synthesis of large flexible aerospace structures. This report concentrates on the research outputs produced in the last two years. The main accomplishments can be summarized as follows. A new version of the PDEMOD Code had been completed based on several incomplete versions. The verification of the code had been conducted by comparing the results with those examples for which the exact theoretical solutions can be obtained. The theoretical background of the package and the verification examples has been reported in a technical paper submitted to the Joint Applied Mechanics & Material Conference, ASME. A brief USER'S MANUAL had been compiled, which includes three parts: (1) Input data preparation; (2) Explanation of the Subroutines; and (3) Specification of control variables. Meanwhile, a theoretical investigation of the NASA MSFC two-dimensional ground-based manipulator facility by using distributed parameter modeling technique has been conducted. A new mathematical treatment for dynamic analysis and control of large flexible manipulator systems has been conceived, which may provide an embryonic form of a more sophisticated mathematical model for future modified versions of the PDEMOD Codes.

Vibration analysis on compact car shock absorber

NASA Astrophysics Data System (ADS)

Tan, W. H.; Cheah, J. X.; Lam, C. K.; Lim, E. A.; Chuah, H. G.; Khor, C. Y.

2017-10-01

Shock absorber is a part of the suspension system which provides comfort experience while driving. Resonance, a phenomenon where forced frequency is coinciding with the natural frequency has significant effect on the shock absorber itself. Thus, in this study, natural frequencies of the shock absorber in a 2 degree-of-freedom system were investigated using Wolfram Mathematica 11, CATIA, and ANSYS. Both theoretical and simulation study how will the resonance affect the car shock absorber. The parametric study on the performance of shock absorber also had been conducted. It is found that the failure tends to occur on coil sprung of the shock absorber before the body of the shock absorber is fail. From mathematical modelling, it can also be seen that higher vibration level occurred on un-sprung mass compare to spring mass. This is due to the weight of sprung mass which could stabilize as compared with the weight of un-sprung mass. Besides that, two natural frequencies had been obtained which are 1.0 Hz and 9.1 Hz for sprung mass and un-sprung mass respectively where the acceleration is recorded as maximum. In conclusion, ANSYS can be used to validate with theoretical results with complete model in order to match with mathematical modelling.

Exploration of cellular reaction systems.

PubMed

Kirkilionis, Markus

2010-01-01

We discuss and review different ways to map cellular components and their temporal interaction with other such components to different non-spatially explicit mathematical models. The essential choices made in the literature are between discrete and continuous state spaces, between rule and event-based state updates and between deterministic and stochastic series of such updates. The temporal modelling of cellular regulatory networks (dynamic network theory) is compared with static network approaches in two first introductory sections on general network modelling. We concentrate next on deterministic rate-based dynamic regulatory networks and their derivation. In the derivation, we include methods from multiscale analysis and also look at structured large particles, here called macromolecular machines. It is clear that mass-action systems and their derivatives, i.e. networks based on enzyme kinetics, play the most dominant role in the literature. The tools to analyse cellular reaction networks are without doubt most complete for mass-action systems. We devote a long section at the end of the review to make a comprehensive review of related tools and mathematical methods. The emphasis is to show how cellular reaction networks can be analysed with the help of different associated graphs and the dissection into modules, i.e. sub-networks.

Near Identifiability of Dynamical Systems

NASA Technical Reports Server (NTRS)

Hadaegh, F. Y.; Bekey, G. A.

1987-01-01

Concepts regarding approximate mathematical models treated rigorously. Paper presents new results in analysis of structural identifiability, equivalence, and near equivalence between mathematical models and physical processes they represent. Helps establish rigorous mathematical basis for concepts related to structural identifiability and equivalence revealing fundamental requirements, tacit assumptions, and sources of error. "Structural identifiability," as used by workers in this field, loosely translates as meaning ability to specify unique mathematical model and set of model parameters that accurately predict behavior of corresponding physical system.

QMRA for Drinking Water: 1. Revisiting the Mathematical Structure of Single-Hit Dose-Response Models.

PubMed

Nilsen, Vegard; Wyller, John

2016-01-01

Dose-response models are essential to quantitative microbial risk assessment (QMRA), providing a link between levels of human exposure to pathogens and the probability of negative health outcomes. In drinking water studies, the class of semi-mechanistic models known as single-hit models, such as the exponential and the exact beta-Poisson, has seen widespread use. In this work, an attempt is made to carefully develop the general mathematical single-hit framework while explicitly accounting for variation in (1) host susceptibility and (2) pathogen infectivity. This allows a precise interpretation of the so-called single-hit probability and precise identification of a set of statistical independence assumptions that are sufficient to arrive at single-hit models. Further analysis of the model framework is facilitated by formulating the single-hit models compactly using probability generating and moment generating functions. Among the more practically relevant conclusions drawn are: (1) for any dose distribution, variation in host susceptibility always reduces the single-hit risk compared to a constant host susceptibility (assuming equal mean susceptibilities), (2) the model-consistent representation of complete host immunity is formally demonstrated to be a simple scaling of the response, (3) the model-consistent expression for the total risk from repeated exposures deviates (gives lower risk) from the conventional expression used in applications, and (4) a model-consistent expression for the mean per-exposure dose that produces the correct total risk from repeated exposures is developed. © 2016 Society for Risk Analysis.

How to Develop Teachers' Mathematical Molding Teaching Skills

ERIC Educational Resources Information Center

Mrayyan, Salwa

2016-01-01

This study aimed at developing some of the mathematical modelling skills necessary for the student teachers in mathematics education College. Modeling involves making genuine choices, modeling problems have many possible justifiable answers, modeling problems matter to the end-user who needs to understand something or make a decision. Modeling…

Developing Understanding of Mathematical Modeling in Secondary Teacher Preparation

ERIC Educational Resources Information Center

Anhalt, Cynthia Oropesa; Cortez, Ricardo

2016-01-01

This study examines the evolution of 11 prospective teachers' understanding of mathematical modeling through the implementation of a modeling module within a curriculum course in a secondary teacher preparation program. While the prospective teachers had not previously taken a course on mathematical modeling, they will be expected to include…

Model Eliciting Activities: Fostering 21st Century Learners

ERIC Educational Resources Information Center

Stohlmann, Micah

2013-01-01

Real world mathematical modeling activities can develop needed and valuable 21st century skills. The knowledge and skills to become adept at mathematical modeling need to develop over time and students in the elementary grades should have experiences with mathematical modeling. For this to occur elementary teachers need to have positive…

Some Reflections on the Teaching of Mathematical Modeling

ERIC Educational Resources Information Center

Warwick, Jon

2007-01-01

This paper offers some reflections on the difficulties of teaching mathematical modeling to students taking higher education courses in which modeling plays a significant role. In the author's experience, other aspects of the model development process often cause problems rather than the use of mathematics. Since these other aspects involve…

Group investigation with scientific approach in mathematics learning

NASA Astrophysics Data System (ADS)

Indarti, D.; Mardiyana; Pramudya, I.

2018-03-01

The aim of this research is to find out the effect of learning model toward mathematics achievement. This research is quasi-experimental research. The population of research is all VII grade students of Karanganyar regency in the academic year of 2016/2017. The sample of this research was taken using stratified cluster random sampling technique. Data collection was done based on mathematics achievement test. The data analysis technique used one-way ANOVA following the normality test with liliefors method and homogeneity test with Bartlett method. The results of this research is the mathematics learning using Group Investigation learning model with scientific approach produces the better mathematics learning achievement than learning with conventional model on material of quadrilateral. Group Investigation learning model with scientific approach can be used by the teachers in mathematics learning, especially in the material of quadrilateral, which is can improve the mathematics achievement.