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Sample records for accurate mathematical description

  1. The first accurate description of an aurora

    NASA Astrophysics Data System (ADS)

    Schröder, Wilfried

    2006-12-01

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

  2. A mathematical recursive model for accurate description of the phase behavior in the near-critical region by Generalized van der Waals Equation

    NASA Astrophysics Data System (ADS)

    Kim, Jibeom; Jeon, Joonhyeon

    2015-01-01

    Recently, related studies on Equation Of State (EOS) have reported that generalized van der Waals (GvdW) shows poor representations in the near critical region for non-polar and non-sphere molecules. Hence, there are still remains a problem of GvdW parameters to minimize loss in describing saturated vapor densities and vice versa. This paper describes a recursive model GvdW (rGvdW) for an accurate representation of pure fluid materials in the near critical region. For the performance evaluation of rGvdW in the near critical region, other EOS models are also applied together with two pure molecule group: alkane and amine. The comparison results show rGvdW provides much more accurate and reliable predictions of pressure than the others. The calculating model of EOS through this approach gives an additional insight into the physical significance of accurate prediction of pressure in the nearcritical region.

  3. Mathematical Description of Dendrimer Structure

    NASA Technical Reports Server (NTRS)

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

    2004-01-01

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

  4. Accurate description of calcium solvation in concentrated aqueous solutions.

    PubMed

    Kohagen, Miriam; Mason, Philip E; Jungwirth, Pavel

    2014-07-17

    Calcium is one of the biologically most important ions; however, its accurate description by classical molecular dynamics simulations is complicated by strong electrostatic and polarization interactions with surroundings due to its divalent nature. Here, we explore the recently suggested approach for effectively accounting for polarization effects via ionic charge rescaling and develop a new and accurate parametrization of the calcium dication. Comparison to neutron scattering and viscosity measurements demonstrates that our model allows for an accurate description of concentrated aqueous calcium chloride solutions. The present model should find broad use in efficient and accurate modeling of calcium in aqueous environments, such as those encountered in biological and technological applications.

  5. Development of a mechanism and an accurate and simple mathematical model for the description of drug release: Application to a relevant example of acetazolamide-controlled release from a bio-inspired elastin-based hydrogel.

    PubMed

    Fernández-Colino, A; Bermudez, J M; Arias, F J; Quinteros, D; Gonzo, E

    2016-04-01

    Transversality between mathematical modeling, pharmacology, and materials science is essential in order to achieve controlled-release systems with advanced properties. In this regard, the area of biomaterials provides a platform for the development of depots that are able to achieve controlled release of a drug, whereas pharmacology strives to find new therapeutic molecules and mathematical models have a connecting function, providing a rational understanding by modeling the parameters that influence the release observed. Herein we present a mechanism which, based on reasonable assumptions, explains the experimental data obtained very well. In addition, we have developed a simple and accurate “lumped” kinetics model to correctly fit the experimentally observed drug-release behavior. This lumped model allows us to have simple analytic solutions for the mass and rate of drug release as a function of time without limitations of time or mass of drug released, which represents an important step-forward in the area of in vitro drug delivery when compared to the current state of the art in mathematical modeling. As an example, we applied the mechanism and model to the release data for acetazolamide from a recombinant polymer. Both materials were selected because of a need to develop a suitable ophthalmic formulation for the treatment of glaucoma. The in vitro release model proposed herein provides a valuable predictive tool for ensuring product performance and batch-to-batch reproducibility, thus paving the way for the development of further pharmaceutical devices.

  6. Development of a mechanism and an accurate and simple mathematical model for the description of drug release: Application to a relevant example of acetazolamide-controlled release from a bio-inspired elastin-based hydrogel.

    PubMed

    Fernández-Colino, A; Bermudez, J M; Arias, F J; Quinteros, D; Gonzo, E

    2016-04-01

    Transversality between mathematical modeling, pharmacology, and materials science is essential in order to achieve controlled-release systems with advanced properties. In this regard, the area of biomaterials provides a platform for the development of depots that are able to achieve controlled release of a drug, whereas pharmacology strives to find new therapeutic molecules and mathematical models have a connecting function, providing a rational understanding by modeling the parameters that influence the release observed. Herein we present a mechanism which, based on reasonable assumptions, explains the experimental data obtained very well. In addition, we have developed a simple and accurate “lumped” kinetics model to correctly fit the experimentally observed drug-release behavior. This lumped model allows us to have simple analytic solutions for the mass and rate of drug release as a function of time without limitations of time or mass of drug released, which represents an important step-forward in the area of in vitro drug delivery when compared to the current state of the art in mathematical modeling. As an example, we applied the mechanism and model to the release data for acetazolamide from a recombinant polymer. Both materials were selected because of a need to develop a suitable ophthalmic formulation for the treatment of glaucoma. The in vitro release model proposed herein provides a valuable predictive tool for ensuring product performance and batch-to-batch reproducibility, thus paving the way for the development of further pharmaceutical devices. PMID:26838852

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

    ERIC Educational Resources Information Center

    Straehler-Pohl, Hauke; Gellert, Uwe

    2013-01-01

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

  8. Connecting Intonation Labels to Mathematical Descriptions of Fundamental Frequency

    ERIC Educational Resources Information Center

    Grabe, Esther; Kochanski, Greg; Coleman, John

    2007-01-01

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

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

    PubMed

    Gunawardena, Jeremy

    2014-01-01

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

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

    PubMed

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

    2014-09-30

    This methodology paper sets out a mathematical description of the Sheffield Alcohol Policy Model version 2.0, a model to evaluate public health strategies for alcohol harm reduction in the UK. Policies that can be appraised include a minimum price per unit of alcohol, restrictions on price discounting, and broader public health measures. The model estimates the impact on consumers, health services, crime, employers, retailers and government tax revenues. The synthesis of public and commercial data sources to inform the model structure is described. A detailed algebraic description of the model is provided. This involves quantifying baseline levels of alcohol purchasing and consumption by age and gender subgroups, estimating the impact of policies on consumption, for example, using evidence on price elasticities of demand for alcohol, quantification of risk functions relating alcohol consumption to harms including 47 health conditions, crimes, absenteeism and unemployment, and finally monetary valuation of the consequences. The results framework, shown for a minimum price per unit of alcohol, has been used to provide policy appraisals for the UK government policy-makers. In discussion and online appendix, we explore issues around valuation and scope, limitations of evidence/data, how the framework can be adapted to other countries and decisions, and ongoing plans for further development. © 2014 The Authors. Health Economics published by John Wiley & Sons Ltd. PMID:25270223

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

    PubMed

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

    2014-09-30

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

  12. A mathematical description of the inclusive fitness theory.

    PubMed

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

    2013-03-01

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

  13. Connecting intonation labels to mathematical descriptions of fundamental frequency.

    PubMed

    Grabe, Esther; Kochanski, Greg; Coleman, John

    2007-01-01

    The mathematical models of intonation used in speech technology are often inaccessible to linguists. By the same token, phonological descriptions of intonation are rarely used by speech technologists, as they cannot be implemented directly in applications. Consequently, these research communities do not benefit much from each other's insights. In this paper, we explore the interface between the disciplines, in search of bridges between intonational phonology and speech technology. In a corpus of speech data from seven dialects of English, we hand-labeled over 700 sentences and identified seven nuclear accent types. Then we fitted a third-order polynomial to the fundamental frequency (F0) contour in the region around the accent mark. The polynomial captures the local shape (time-dependence) of F0 in a few numbers, in our case, four coefficients. The coefficients were subjected to statistical analysis. Nineteen of the 21 pairs of accent types differed significantly in one or more coefficients. Our approach bridges the gap between intonational phonology and speech technology. It provides quantitative, empirically testable models of intonation labels that can be implemented in applications. PMID:17974321

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

    ERIC Educational Resources Information Center

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

    2004-01-01

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

  15. A Flexible Fringe Projection Vision System with Extended Mathematical Model for Accurate Three-Dimensional Measurement

    PubMed Central

    Xiao, Suzhi; Tao, Wei; Zhao, Hui

    2016-01-01

    In order to acquire an accurate three-dimensional (3D) measurement, the traditional fringe projection technique applies complex and laborious procedures to compensate for the errors that exist in the vision system. However, the error sources in the vision system are very complex, such as lens distortion, lens defocus, and fringe pattern nonsinusoidality. Some errors cannot even be explained or rendered with clear expressions and are difficult to compensate directly as a result. In this paper, an approach is proposed that avoids the complex and laborious compensation procedure for error sources but still promises accurate 3D measurement. It is realized by the mathematical model extension technique. The parameters of the extended mathematical model for the ’phase to 3D coordinates transformation’ are derived using the least-squares parameter estimation algorithm. In addition, a phase-coding method based on a frequency analysis is proposed for the absolute phase map retrieval to spatially isolated objects. The results demonstrate the validity and the accuracy of the proposed flexible fringe projection vision system on spatially continuous and discontinuous objects for 3D measurement. PMID:27136553

  16. A Flexible Fringe Projection Vision System with Extended Mathematical Model for Accurate Three-Dimensional Measurement.

    PubMed

    Xiao, Suzhi; Tao, Wei; Zhao, Hui

    2016-01-01

    In order to acquire an accurate three-dimensional (3D) measurement, the traditional fringe projection technique applies complex and laborious procedures to compensate for the errors that exist in the vision system. However, the error sources in the vision system are very complex, such as lens distortion, lens defocus, and fringe pattern nonsinusoidality. Some errors cannot even be explained or rendered with clear expressions and are difficult to compensate directly as a result. In this paper, an approach is proposed that avoids the complex and laborious compensation procedure for error sources but still promises accurate 3D measurement. It is realized by the mathematical model extension technique. The parameters of the extended mathematical model for the 'phase to 3D coordinates transformation' are derived using the least-squares parameter estimation algorithm. In addition, a phase-coding method based on a frequency analysis is proposed for the absolute phase map retrieval to spatially isolated objects. The results demonstrate the validity and the accuracy of the proposed flexible fringe projection vision system on spatially continuous and discontinuous objects for 3D measurement. PMID:27136553

  17. Accurate description of argon and water adsorption on surfaces of graphene-based carbon allotropes.

    PubMed

    Kysilka, Jiří; Rubeš, Miroslav; Grajciar, Lukáš; Nachtigall, Petr; Bludský, Ota

    2011-10-20

    Accurate interaction energies of nonpolar (argon) and polar (water) adsorbates with graphene-based carbon allotropes were calculated by means of a combined density functional theory (DFT)-ab initio computational scheme. The calculated interaction energy of argon with graphite (-9.7 kJ mol(-1)) is in excellent agreement with the available experimental data. The calculated interaction energy of water with graphene and graphite is -12.8 and -14.6 kJ mol(-1), respectively. The accuracy of combined DFT-ab initio methods is discussed in detail based on a comparison with the highly precise interaction energies of argon and water with coronene obtained at the coupled-cluster CCSD(T) level extrapolated to the complete basis set (CBS) limit. A new strategy for a reliable estimate of the CBS limit is proposed for systems where numerical instabilities occur owing to basis-set near-linear dependence. The most accurate estimate of the argon and water interaction with coronene (-8.1 and -14.0 kJ mol(-1), respectively) is compared with the results of other methods used for the accurate description of weak intermolecular interactions.

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

    NASA Astrophysics Data System (ADS)

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

    2016-05-01

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

  19. Educational Plan: Title I Elementary Mathematics Program. Description, Performance Objectives, and Tests. Revised.

    ERIC Educational Resources Information Center

    Des Moines Public Schools, IA.

    This three-part guide presents a brief program description along with lists of performance objectives and lists of test items for the Des Moines (Iowa) Public Schools Title I Elementary Mathematics Program. The program description provides background information on the Des Moines Public School District and describes the student selection/screening…

  20. Accurate electronic-structure description of Mn complexes: a GGA+U approach

    NASA Astrophysics Data System (ADS)

    Li, Elise Y.; Kulik, Heather; Marzari, Nicola

    2008-03-01

    Conventional density-functional approach often fail in offering an accurate description of the spin-resolved energetics in transition metals complexes. We will focus here on Mn complexes, where many aspects of the molecular structure and the reaction mechanisms are still unresolved - most notably in the oxygen-evolving complex (OEC) of photosystem II and the manganese catalase (MC). We apply a self-consistent GGA + U approach [1], originally designed within the DFT framework for the treatment of strongly correlated materials, to describe the geometry, the electronic and the magnetic properties of various manganese oxide complexes, finding very good agreement with higher-order ab-initio calculations. In particular, the different oxidation states of dinuclear systems containing the [Mn2O2]^n+ (n= 2, 3, 4) core are investigated, in order to mimic the basic face unit of the OEC complex. [1]. H. J. Kulik, M. Cococcioni, D. A. Scherlis, N. Marzari, Phys. Rev. Lett., 2006, 97, 103001

  1. Mathematical description of human body constitution and fatness.

    PubMed

    Sheikh-Zade, Yu R; Galenko-Yaroshevskii, P A; Cherednik, I L

    2014-02-01

    Using mathematical modeling of human body, we demonstrated logical drawbacks of body mass index (BMI1 = M/H(2); A. Quetelet, 1832) and proposed more precise body mass index (BMI2 = M/H(3)) as well as body constitution index (BCI = (M/H(3))(1/2)) and fatness index (FI = M/HC(2)), where M, H, and C are body weight, height, and wrist circumference of the individual. PMID:24771443

  2. Mathematical Description of an Asynchronous Motor with the Indirect Control of the Output Mechanical Variables

    NASA Astrophysics Data System (ADS)

    Glazachev, A. V.; Dementyev, Yu. N.; Negodin, K. N.; Umursakova, A. D.

    2016-02-01

    The article gives the mathematical description of an asynchronous motor with the indirect control of the output mechanical variables of an asynchronous motor in the electric drive. To determine the electromagnetic torque and angular velocity of the asynchronous motor in the electric drive the mathematical description is used in which the values are determined by the readings of the motor and easily measured values by means of known in practice devices. The proposed in the article the mathematical description for the indirect measuring the electromagnetic torque and angular velocity of the asynchronous motor in the electric drive does not contain the integral components that introduce the great error into the value of the controlled electromagnetic torque and angular velocity.

  3. Learning to write without writing: writing accurate descriptions of interactions after learning graph-printed description relations.

    PubMed

    Spear, Jack; Fields, Lanny

    2015-12-01

    Interpreting and describing complex information shown in graphs are essential skills to be mastered by students in many disciplines; both are skills that are difficult to learn. Thus, interventions that produce these outcomes are of great value. Previous research showed that conditional discrimination training that established stimulus control by some elements of graphs and their printed descriptions produced some improvement in the accuracy of students' written descriptions of graphs. In the present experiment, students wrote nearly perfect descriptions of the information conveyed in interaction-based graphs after the establishment of conditional relations between graphs and their printed descriptions. This outcome was achieved with the use of special conditional discrimination training procedures that required participants to attend to many of the key elements of the graphs and the phrases in the printed descriptions that corresponded to the elements in the graphs. Thus, students learned to write full descriptions of the information represented by complex graphs by an automated training procedure that did not involve the direct training of writing.

  4. a Mathematical Description of the Critical Point in Phase Transitions

    NASA Astrophysics Data System (ADS)

    Bilge, Ayse Humeyra; Pekcan, Onder

    2013-10-01

    Let y(x) be a smooth sigmoidal curve, y(n) be its nth derivative and {xm,i} and {xa,i}, i = 1,2,…, be the set of points where respectively the derivatives of odd and even order reach their extreme values. We argue that if the sigmoidal curve y(x) represents a phase transition, then the sequences {xm,i} and {xa,i} are both convergent and they have a common limit xc that we characterize as the critical point of the phase transition. In this study, we examine the logistic growth curve and the Susceptible-Infected-Removed (SIR) epidemic model as typical examples of symmetrical and asymmetrical transition curves. Numerical computations indicate that the critical point of the logistic growth curve that is symmetrical about the point (x0, y0) is always the point (x0, y0) but the critical point of the asymmetrical SIR model depends on the system parameters. We use the description of the sol-gel phase transition of polyacrylamide-sodium alginate (SA) composite (with low SA concentrations) in terms of the SIR epidemic model, to compare the location of the critical point as described above with the "gel point" determined by independent experiments. We show that the critical point tc is located in between the zero of the third derivative ta and the inflection point tm of the transition curve and as the strength of activation (measured by the parameter k/η of the SIR model) increases, the phase transition occurs earlier in time and the critical point, tc, moves toward ta.

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

    ERIC Educational Resources Information Center

    Friedman, Lee; Harvey, Robert J.

    1986-01-01

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

  6. A simple mathematical description of an off-grid hybrid solar-wind power generating system

    NASA Astrophysics Data System (ADS)

    Blasone, M.; Dell'Anno, F.; De Luca, R.; Torre, G.

    2013-05-01

    We give a detailed description of the energy balance equation for a stand-alone hybrid solar-wind power generating system. The dimensions of the power generator and the energy capacity of a buffer battery (used as an energy storage system) are chosen to suit a known consumer's profile. Future applications of the mathematical model developed and analogies with a similar hydrodynamic problem are discussed.

  7. Doubly hybrid density functional for accurate descriptions of nonbond interactions, thermochemistry, and thermochemical kinetics

    PubMed Central

    Zhang, Ying; Xu, Xin; Goddard, William A.

    2009-01-01

    We develop and validate a density functional, XYG3, based on the adiabatic connection formalism and the Görling–Levy coupling-constant perturbation expansion to the second order (PT2). XYG3 is a doubly hybrid functional, containing 3 mixing parameters. It has a nonlocal orbital-dependent component in the exchange term (exact exchange) plus information about the unoccupied Kohn–Sham orbitals in the correlation part (PT2 double excitation). XYG3 is remarkably accurate for thermochemistry, reaction barrier heights, and nonbond interactions of main group molecules. In addition, the accuracy remains nearly constant with system size. PMID:19276116

  8. Mathematical model accurately predicts protein release from an affinity-based delivery system.

    PubMed

    Vulic, Katarina; Pakulska, Malgosia M; Sonthalia, Rohit; Ramachandran, Arun; Shoichet, Molly S

    2015-01-10

    Affinity-based controlled release modulates the delivery of protein or small molecule therapeutics through transient dissociation/association. To understand which parameters can be used to tune release, we used a mathematical model based on simple binding kinetics. A comprehensive asymptotic analysis revealed three characteristic regimes for therapeutic release from affinity-based systems. These regimes can be controlled by diffusion or unbinding kinetics, and can exhibit release over either a single stage or two stages. This analysis fundamentally changes the way we think of controlling release from affinity-based systems and thereby explains some of the discrepancies in the literature on which parameters influence affinity-based release. The rate of protein release from affinity-based systems is determined by the balance of diffusion of the therapeutic agent through the hydrogel and the dissociation kinetics of the affinity pair. Equations for tuning protein release rate by altering the strength (KD) of the affinity interaction, the concentration of binding ligand in the system, the rate of dissociation (koff) of the complex, and the hydrogel size and geometry, are provided. We validated our model by collapsing the model simulations and the experimental data from a recently described affinity release system, to a single master curve. Importantly, this mathematical analysis can be applied to any single species affinity-based system to determine the parameters required for a desired release profile. PMID:25449806

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

    PubMed Central

    2014-01-01

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

  10. Accurate description of aqueous carbonate ions: an effective polarization model verified by neutron scattering.

    PubMed

    Mason, Philip E; Wernersson, Erik; Jungwirth, Pavel

    2012-07-19

    The carbonate ion plays a central role in the biochemical formation of the shells of aquatic life, which is an important path for carbon dioxide sequestration. Given the vital role of carbonate in this and other contexts, it is imperative to develop accurate models for such a high charge density ion. As a divalent ion, carbonate has a strong polarizing effect on surrounding water molecules. This raises the question whether it is possible to describe accurately such systems without including polarization. It has recently been suggested the lack of electronic polarization in nonpolarizable water models can be effectively compensated by introducing an electronic dielectric continuum, which is with respect to the forces between atoms equivalent to rescaling the ionic charges. Given how widely nonpolarizable models are used to model electrolyte solutions, establishing the experimental validity of this suggestion is imperative. Here, we examine a stringent test for such models: a comparison of the difference of the neutron scattering structure factors of K2CO3 vs KNO3 solutions and that predicted by molecular dynamics simulations for various models of the same systems. We compare standard nonpolarizable simulations in SPC/E water to analogous simulations with effective ion charges, as well as simulations in explicitly polarizable POL3 water (which, however, has only about half the experimental polarizability). It is found that the simulation with rescaled charges is in a very good agreement with the experimental data, which is significantly better than for the nonpolarizable simulation and even better than for the explicitly polarizable POL3 model.

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

    PubMed Central

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

    2014-01-01

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

  12. Accurate description of the optical response of a multilayered spherical system in the long wavelength approximation

    NASA Astrophysics Data System (ADS)

    Chung, H. Y.; Guo, G. Y.; Chiang, H.-P.; Tsai, D. P.; Leung, P. T.

    2010-10-01

    The optical response of a multilayered spherical system of unlimited number of layers (a “matryushka”) in the long wavelength limit can be accounted for from the knowledge of the static multipole polarizability of the system to first-order accuracy. However, for systems of ultrasmall dimensions or systems with sizes not-too-small compared to the wavelength, this ordinary quasistatic long wavelength approximation (LWA) becomes inaccurate. Here we introduce two significant modifications of the LWA for such a nanomatryushka in each of the two limits: the nonlocal optical response for ultrasmall systems (<10nm) , and the “finite-wavelength corrections” for systems ˜100nm . This is accomplished by employing the previous work for a single-layer shell, in combination with a certain effective-medium approach formulated recently in the literature. Numerical calculations for the extinction cross sections for such a system of different dimensions are provided as illustrations for these effects. This formulation thus provides significant improvements on the ordinary LWA, yielding enough accuracy for the description of the optical response of these nanoshell systems over an appreciable range of sizes, without resorting to more involved quantum mechanical or fully electrodynamic calculations.

  13. Electrostatics of proteins in dielectric solvent continua. I. An accurate and efficient reaction field description

    SciTech Connect

    Bauer, Sebastian; Mathias, Gerald; Tavan, Paul

    2014-03-14

    We present a reaction field (RF) method which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of an electrostatics calculation with polarizable molecular mechanics (MM) force fields. The method combines an approach originally suggested by Egwolf and Tavan [J. Chem. Phys. 118, 2039 (2003)] with concepts generalizing the Born solution [Z. Phys. 1, 45 (1920)] for a solvated ion. First, we derive an exact representation according to which the sources of the RF potential and energy are inducible atomic anti-polarization densities and atomic shielding charge distributions. Modeling these atomic densities by Gaussians leads to an approximate representation. Here, the strengths of the Gaussian shielding charge distributions are directly given in terms of the static partial charges as defined, e.g., by standard MM force fields for the various atom types, whereas the strengths of the Gaussian anti-polarization densities are calculated by a self-consistency iteration. The atomic volumes are also described by Gaussians. To account for covalently overlapping atoms, their effective volumes are calculated by another self-consistency procedure, which guarantees that the dielectric function ε(r) is close to one everywhere inside the protein. The Gaussian widths σ{sub i} of the atoms i are parameters of the RF approximation. The remarkable accuracy of the method is demonstrated by comparison with Kirkwood's analytical solution for a spherical protein [J. Chem. Phys. 2, 351 (1934)] and with computationally expensive grid-based numerical solutions for simple model systems in dielectric continua including a di-peptide (Ac-Ala-NHMe) as modeled by a standard MM force field. The latter example shows how weakly the RF conformational free energy landscape depends on the parameters σ{sub i}. A summarizing discussion highlights the achievements of the new theory and of its approximate solution

  14. Electrostatics of proteins in dielectric solvent continua. I. An accurate and efficient reaction field description.

    PubMed

    Bauer, Sebastian; Mathias, Gerald; Tavan, Paul

    2014-03-14

    We present a reaction field (RF) method which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of an electrostatics calculation with polarizable molecular mechanics (MM) force fields. The method combines an approach originally suggested by Egwolf and Tavan [J. Chem. Phys. 118, 2039 (2003)] with concepts generalizing the Born solution [Z. Phys. 1, 45 (1920)] for a solvated ion. First, we derive an exact representation according to which the sources of the RF potential and energy are inducible atomic anti-polarization densities and atomic shielding charge distributions. Modeling these atomic densities by Gaussians leads to an approximate representation. Here, the strengths of the Gaussian shielding charge distributions are directly given in terms of the static partial charges as defined, e.g., by standard MM force fields for the various atom types, whereas the strengths of the Gaussian anti-polarization densities are calculated by a self-consistency iteration. The atomic volumes are also described by Gaussians. To account for covalently overlapping atoms, their effective volumes are calculated by another self-consistency procedure, which guarantees that the dielectric function ε(r) is close to one everywhere inside the protein. The Gaussian widths σ(i) of the atoms i are parameters of the RF approximation. The remarkable accuracy of the method is demonstrated by comparison with Kirkwood's analytical solution for a spherical protein [J. Chem. Phys. 2, 351 (1934)] and with computationally expensive grid-based numerical solutions for simple model systems in dielectric continua including a di-peptide (Ac-Ala-NHMe) as modeled by a standard MM force field. The latter example shows how weakly the RF conformational free energy landscape depends on the parameters σ(i). A summarizing discussion highlights the achievements of the new theory and of its approximate solution particularly by

  15. Accurate description of van der Waals complexes by density functional theory including empirical corrections.

    PubMed

    Grimme, Stefan

    2004-09-01

    An empirical method to account for van der Waals interactions in practical calculations with the density functional theory (termed DFT-D) is tested for a wide variety of molecular complexes. As in previous schemes, the dispersive energy is described by damped interatomic potentials of the form C6R(-6). The use of pure, gradient-corrected density functionals (BLYP and PBE), together with the resolution-of-the-identity (RI) approximation for the Coulomb operator, allows very efficient computations for large systems. Opposed to previous work, extended AO basis sets of polarized TZV or QZV quality are employed, which reduces the basis set superposition error to a negligible extend. By using a global scaling factor for the atomic C6 coefficients, the functional dependence of the results could be strongly reduced. The "double counting" of correlation effects for strongly bound complexes is found to be insignificant if steep damping functions are employed. The method is applied to a total of 29 complexes of atoms and small molecules (Ne, CH4, NH3, H2O, CH3F, N2, F2, formic acid, ethene, and ethine) with each other and with benzene, to benzene, naphthalene, pyrene, and coronene dimers, the naphthalene trimer, coronene. H2O and four H-bonded and stacked DNA base pairs (AT and GC). In almost all cases, very good agreement with reliable theoretical or experimental results for binding energies and intermolecular distances is obtained. For stacked aromatic systems and the important base pairs, the DFT-D-BLYP model seems to be even superior to standard MP2 treatments that systematically overbind. The good results obtained suggest the approach as a practical tool to describe the properties of many important van der Waals systems in chemistry. Furthermore, the DFT-D data may either be used to calibrate much simpler (e.g., force-field) potentials or the optimized structures can be used as input for more accurate ab initio calculations of the interaction energies.

  16. Towards an accurate model of redshift-space distortions: a bivariate Gaussian description for the galaxy pairwise velocity distributions

    NASA Astrophysics Data System (ADS)

    Bianchi, Davide; Chiesa, Matteo; Guzzo, Luigi

    2016-10-01

    As a step towards a more accurate modelling of redshift-space distortions (RSD) in galaxy surveys, we develop a general description of the probability distribution function of galaxy pairwise velocities within the framework of the so-called streaming model. For a given galaxy separation , such function can be described as a superposition of virtually infinite local distributions. We characterize these in terms of their moments and then consider the specific case in which they are Gaussian functions, each with its own mean μ and variance σ2. Based on physical considerations, we make the further crucial assumption that these two parameters are in turn distributed according to a bivariate Gaussian, with its own mean and covariance matrix. Tests using numerical simulations explicitly show that with this compact description one can correctly model redshift-space distorsions on all scales, fully capturing the overall linear and nonlinear dynamics of the galaxy flow at different separations. In particular, we naturally obtain Gaussian/exponential, skewed/unskewed distribution functions, depending on separation as observed in simulations and data. Also, the recently proposed single-Gaussian description of redshift-space distortions is included in this model as a limiting case, when the bivariate Gaussian is collapsed to a two-dimensional Dirac delta function. More work is needed, but these results indicate a very promising path to make definitive progress in our program to improve RSD estimators.

  17. Mathematical analysis and algorithms for efficiently and accurately implementing stochastic simulations of short-term synaptic depression and facilitation.

    PubMed

    McDonnell, Mark D; Mohan, Ashutosh; Stricker, Christian

    2013-01-01

    The release of neurotransmitter vesicles after arrival of a pre-synaptic action potential (AP) at cortical synapses is known to be a stochastic process, as is the availability of vesicles for release. These processes are known to also depend on the recent history of AP arrivals, and this can be described in terms of time-varying probabilities of vesicle release. Mathematical models of such synaptic dynamics frequently are based only on the mean number of vesicles released by each pre-synaptic AP, since if it is assumed there are sufficiently many vesicle sites, then variance is small. However, it has been shown recently that variance across sites can be significant for neuron and network dynamics, and this suggests the potential importance of studying short-term plasticity using simulations that do generate trial-to-trial variability. Therefore, in this paper we study several well-known conceptual models for stochastic availability and release. We state explicitly the random variables that these models describe and propose efficient algorithms for accurately implementing stochastic simulations of these random variables in software or hardware. Our results are complemented by mathematical analysis and statement of pseudo-code algorithms.

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

    NASA Astrophysics Data System (ADS)

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

    2014-03-01

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

  19. Specificity of mathematical description of statistical and dynamical properties of CELSS

    NASA Astrophysics Data System (ADS)

    Bartsev, Sergey

    CELSS for long-term space missions has to be possessed high level of matter turnover closure. Designing, studying, and maintaining such kind of systems seems to be not possible without accounting their specificity -high closure. For measuring this specific property potentially universal coefficient of closure is suggested and disscussed. It can be shown standard statistical formulas are incorrect for estimating mean values of biomass of CELSS components. Account-ing closure as specific constraint of closed ecological systems allows obtaining correct formulas for calculating mean values of biomass and composition of chemical compounds of CELSS. Errors due to using standard statistical evaluations are discussed. Organisms composing bi-ological LSS consume and produce spectrum of different substances. Providing high level of closure -the absence of deadlocks -depends on accuracy of adjusting all organisms input and output to each other. This is practical objective of high importance. Adequate mathematical models ought to describe possibility of organisms to vary their consumption and production spectrum (stoichiometric ratio). Traditional ecological models describing dynamics of limiting element can not be adequately applied for describing CELSS dynamics over all possible oper-ating regimes. Possible use of adaptive metabolism models for providing correct description of CELSS dynamics is considered.

  20. A computerized method for mathematical description of three-dimensional root canal axis.

    PubMed

    Dobó-Nagy, C; Keszthelyi, G; Szabó, J; Sulyok, P; Ledeczky, G; Szabó, J

    2000-11-01

    Knowledge of the three-dimensional (3D) morphology of root canals is important for successful endodontic treatment. The objective of the present study was to determine the 3D root canal axis mathematically. Two views (mesiodistal and buccolingual) of digitized images were taken from extracted natural human teeth. Geometric reconstruction to standardize projection geometry was conducted on images. Because 90-degree turn-around image pairs are Monge images of a given root canal, these Monge images were positioned using photogrammetric methods. Each well-ordered axis pair of a given root canal was put into a common coordinate system resulting in 3D polynomial function of the actual root canal. On the basis of the results gained using 10 samples evaluated with the Friedman statistical test, this description seems to be reproducible. The 3D representation of the root canal may help the clinicians in choosing the optimal instruments and shaping techniques. The root canal axis that is described by the 3D function forms a basis for determination of curvature values and torsion values in each of the axis points. Evaluating these values may also yield a new type of classification. PMID:11469291

  1. The mathematical description of the gasification process of woody biomass in installations with a plasma heat source for producing synthesis gas

    NASA Astrophysics Data System (ADS)

    Sadrtdinov, A. R.; Safin, R. G.; Gerasimov, M. K.; Petrov, V. I.; Gilfanov, K. K.

    2016-04-01

    The article presents the scheme of processing of plant biomass in the gasification installation with a plasma heat source to produce synthesis gas suitable for chemical industry. The analyzed physical picture of raw materials' recycling process underlies a mathematical description of the process set out in the form of the basic differential equations with boundary conditions. The received mathematical description allows calculating of the main parameters of equipment for biomass recycling and to determine the optimal modes of its operation.

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

    NASA Astrophysics Data System (ADS)

    Gurova, E. G.

    2016-08-01

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

  3. A Description of Fourth Grade Children's Problem-Solving in Mathematics

    ERIC Educational Resources Information Center

    Brennan, Martha K.; Rule, Ann M.; Walmsley, Angela L. E.; Swanson, Joy R.

    2010-01-01

    This preliminary study described fourth grade students verbally solving a mathematics problem using a think-aloud protocol. Comments in the think aloud were categorized according to type (e.g., paraphrases and elaborations) and facilitative nature (i.e., whether the comments facilitated correct solution of the problem). Amount of the students'…

  4. Mathematical description of polymerization using an organolithium catalyst in the presence of a donor

    SciTech Connect

    Zak, A.V.; Perlin, B.A.; Shpakov, P.P.; Drozdov, B.T.; Erenburg, E.G.; Ermakova, I.I.; Ryakhovskii, V.S.

    1986-10-20

    The authors present a mathematical representation of the polymerization of butadiene to rubber via a complex of lithium in the presence of the donor diethylene glycol dimethyl ether toward the end of increasing the efficiency of the process as well as the quality of the final product. The model demonstrates the dependence of the properties and composition of the polybutadiene on polymerization conditions.

  5. A Description and Characterization of Student Activity in an Open, Online, Mathematics Help Forum

    ERIC Educational Resources Information Center

    van de Sande, Carla

    2011-01-01

    Free, open, online, calculus forums are websites where students from around the world can post course-related queries that may be viewed and responded to by anonymous others. These sites are an emergent resource for students seeking help and have become a part of many students' mathematical experience. The purpose of this paper is to introduce and…

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

    NASA Astrophysics Data System (ADS)

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

    2016-09-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2016-07-01

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

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

    NASA Technical Reports Server (NTRS)

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

    1984-01-01

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

  9. Kinetic analysis of AUC-dependent saturable clearance of liposomes: mathematical description of AUC dependency.

    PubMed

    Harashima, H; Yamane, C; Kume, Y; Kiwada, H

    1993-06-01

    The objective of this study was to examine the AUC dependency of saturable hepatic clearance (CLh) of liposomes and to postulate a mathematical model to describe the characteristics. The AUC dependency of saturable CLh was examined under intravenous rapid administration at various doses. The CLh increased with increasing blood concentration but decreased with the increase of AUC at each dose. In addition, the relationship between AUC and CLh was consistent with that observed in previously reported infusion studies. These experimental data confirm the AUC dependency of saturable CLh of liposomes. A mathematical model was developed for this AUC dependency. The decrease of CLh was described by the uptake amount (X) as follows: CLh = CLm(1-X/Xm), where CLm and Xm represent the maximum uptake clearance and the maximum uptake amount, respectively. The rate equation for uptake was analytically solved as CLh = X/AUC = Xm/AUC(1-exp(CLm/XmAUC)). Uptake clearance can be described by CLm, Xm, and AUC, and so uptake clearance is constant if AUC is constant. These experimental analyses and theoretical considerations show the validity of the AUC-dependent saturable CLh of liposomes.

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

    NASA Astrophysics Data System (ADS)

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

    2011-09-01

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

  11. Mathematical description and measurement of refractive parameters of freeform spectacle lenses.

    PubMed

    Yu, Jing; Qiu, Zhongjun; Fang, Fengzhou

    2014-08-01

    Refractive parameters are the main design and evaluation parameters of freeform spectacle lenses. In this paper, the mathematical model of refractive parameters is established, and the refractive power distribution on the whole surface is drawn with a radial basis function. The measurement methods are analyzed, and typical freeform spectacle lenses are measured with a freeform verifier. The refractive power distribution on the whole surface, the cylinder view, and the refractive power curve along the progressive corridor are drawn up. There are no evident image changes on the whole surface. The refractive power smoothly varies along the progressive corridor. In comparing the results with the analysis, measurement results are in agreement with the calculation. PMID:25090322

  12. [Mathematical description of the three-dimensional axis of the root canal of human teeth].

    PubMed

    Dobó, Nagy Csaba; Keszthelyi, Gusztáv; Sulyok, Péter; Ledeczky, Gábor; Szabó, József

    2002-08-01

    The objective of the present study was to describe root canal axes of natural human teeth mathematically. Two views (clinical and proximal) radiographs were taken from extracted human teeth. Geometry defines the 90-degree turn-around image pairs as Monge images. These Monge images of the root canals were positioned using photogrammetric methods. Each well-ordered axis pair of a given root canal was put into a common coordinate system resulting in three-dimensional polynomial function of the actual root canal. Testing differences between determined and repeatedly determined axes of ten samples by statistical analysis did not show any significant differences. Evaluation of data gained on a large number of samples may also yield a new type of classification. PMID:12236090

  13. A theory of cerebral learning regulated by the reward system. I. Hypotheses and mathematical description.

    PubMed

    Nakamura, K

    1993-01-01

    Hypothetical mechanisms of the neocorticohippocampal system are presented. Neurophysiological and neuroanatomical findings concerning the system are integrated to demonstrate how animals associate sensory stimuli with rewarding actions: (1) cortical plasticity regulated by cholinergic/noradrenergic inputs from the hypothalamic reward system reinforces association connections between the most activated columns in the cortex; (2) the repetitive reinforcement forms association pathways connecting sensory cortical columns activated by the stimuli with motor cortical columns producing the rewarding actions; (3) after the pathways are formed, the cortex is capable of temporarily memorizing the stimuli by producing long-term potentiation through the cortico-hippocampal circuits; and (4) the memory allows the cortex to extend correct association pathways even in an environment where sensory stimuli rapidly change. A mathematical model of parts of the nervous system is presented to quantitatively examine the mechanisms. Membrane characteristics of single neurons are given by the Hodgkin-Huxley electric circuit. According to anatomical data, neural circuits of the neocortico-hippocampal system are composed by connecting populations of the model neurons. Computer simulation using physiological data concerning ion channels demonstrates how the mechanisms work and how to test the hypotheses presented.

  14. Spatial Mapping of Translational Diffusion Coefficients Using Diffusion Tensor Imaging: A Mathematical Description

    PubMed Central

    SHETTY, ANIL N.; CHIANG, SHARON; MALETIC-SAVATIC, MIRJANA; KASPRIAN, GREGOR; VANNUCCI, MARINA; LEE, WESLEY

    2016-01-01

    In this article, we discuss the theoretical background for diffusion weighted imaging and diffusion tensor imaging. Molecular diffusion is a random process involving thermal Brownian motion. In biological tissues, the underlying microstructures restrict the diffusion of water molecules, making diffusion directionally dependent. Water diffusion in tissue is mathematically characterized by the diffusion tensor, the elements of which contain information about the magnitude and direction of diffusion and is a function of the coordinate system. Thus, it is possible to generate contrast in tissue based primarily on diffusion effects. Expressing diffusion in terms of the measured diffusion coefficient (eigenvalue) in any one direction can lead to errors. Nowhere is this more evident than in white matter, due to the preferential orientation of myelin fibers. The directional dependency is removed by diagonalization of the diffusion tensor, which then yields a set of three eigenvalues and eigenvectors, representing the magnitude and direction of the three orthogonal axes of the diffusion ellipsoid, respectively. For example, the eigenvalue corresponding to the eigenvector along the long axis of the fiber corresponds qualitatively to diffusion with least restriction. Determination of the principal values of the diffusion tensor and various anisotropic indices provides structural information. We review the use of diffusion measurements using the modified Stejskal–Tanner diffusion equation. The anisotropy is analyzed by decomposing the diffusion tensor based on symmetrical properties describing the geometry of diffusion tensor. We further describe diffusion tensor properties in visualizing fiber tract organization of the human brain. PMID:27441031

  15. A particulate pulse-release system and mathematical description with the Maxwell-Stefan theory.

    PubMed

    Hartman Kok, P J; Vonk, P; Kossen, N W

    2000-05-15

    In this contribution both the development of a multi-particulate delayed release system with release properties dependent on the swelling of an UV crosslinked coating and a mathematical model to describe its release properties are presented. The formulation consists of a water-soluble core coated with a copolymer of methacrylic acid and ethyl acrylate. Incorporating a network of crosslinked pentaerythritol triacrylate decreases the water-solubility of the coating. After immersing the formulation in water the coating will take up water and subsequently swell in such a degree that the diffusion coefficient of water in the coating will increase. This makes the coating permeable to the dissolved components present in the core. The swelling kinetics of the coating are such that the formulation has a pulse-release profile, i.e. a fast release of the contents is obtained after a pre-determined lag-time. Both the coating thickness and the duration of the UV crosslinking time can be used to adjust the lag-time. The experimental results are used to estimate the Maxwell-Stefan diffusion coefficients of water in the coating. The relation between the Maxwell-Stefan diffusion coefficient and the mole fraction of water in the coating differs from results found in the literature. However, the prediction of the release time based on the presented model is in good agreement with the experimental findings.

  16. Mathematical Description of Complex Chemical Kinetics and Application to CFD Modeling Codes

    NASA Technical Reports Server (NTRS)

    Bittker, D. A.

    1993-01-01

    A major effort in combustion research at the present time is devoted to the theoretical modeling of practical combustion systems. These include turbojet and ramjet air-breathing engines as well as ground-based gas-turbine power generating systems. The ability to use computational modeling extensively in designing these products not only saves time and money, but also helps designers meet the quite rigorous environmental standards that have been imposed on all combustion devices. The goal is to combine the very complex solution of the Navier-Stokes flow equations with realistic turbulence and heat-release models into a single computer code. Such a computational fluid-dynamic (CFD) code simulates the coupling of fluid mechanics with the chemistry of combustion to describe the practical devices. This paper will focus on the task of developing a simplified chemical model which can predict realistic heat-release rates as well as species composition profiles, and is also computationally rapid. We first discuss the mathematical techniques used to describe a complex, multistep fuel oxidation chemical reaction and develop a detailed mechanism for the process. We then show how this mechanism may be reduced and simplified to give an approximate model which adequately predicts heat release rates and a limited number of species composition profiles, but is computationally much faster than the original one. Only such a model can be incorporated into a CFD code without adding significantly to long computation times. Finally, we present some of the recent advances in the development of these simplified chemical mechanisms.

  17. Mathematical description of complex chemical kinetics and application to CFD modeling codes

    NASA Technical Reports Server (NTRS)

    Bittker, D. A.

    1993-01-01

    A major effort in combustion research at the present time is devoted to the theoretical modeling of practical combustion systems. These include turbojet and ramjet air-breathing engines as well as ground-based gas-turbine power generating systems. The ability to use computational modeling extensively in designing these products not only saves time and money, but also helps designers meet the quite rigorous environmental standards that have been imposed on all combustion devices. The goal is to combine the very complex solution of the Navier-Stokes flow equations with realistic turbulence and heat-release models into a single computer code. Such a computational fluid-dynamic (CFD) code simulates the coupling of fluid mechanics with the chemistry of combustion to describe the practical devices. This paper will focus on the task of developing a simplified chemical model which can predict realistic heat-release rates as well as species composition profiles, and is also computationally rapid. We first discuss the mathematical techniques used to describe a complex, multistep fuel oxidation chemical reaction and develop a detailed mechanism for the process. We then show how this mechanism may be reduced and simplified to give an approximate model which adequately predicts heat release rates and a limited number of species composition profiles, but is computationally much faster than the original one. Only such a model can be incorporated into a CFD code without adding significantly to long computation times. Finally, we present some of the recent advances in the development of these simplified chemical mechanisms.

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

    ERIC Educational Resources Information Center

    Fowler, Crystal Nicole

    2013-01-01

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

  19. Mathematical description of nonstationary aerodynamic characteristics of a passenger aircraft model in longitudinal motion at large angles of attack

    NASA Astrophysics Data System (ADS)

    Petoshin, V. I.; Chasovnikov, E. A.

    2011-05-01

    Aerodynamic loads in problems of flight dynamics of passenger aircraft in stalled flow regimes are described using a mathematical model that includes an ordinary linear first-order differential equation. A procedure for determining the parameters of the mathematical model is proposed which is based on approximating experimental frequency characteristics with the frequency characteristics of the linearized mathematical model. The mathematical model was verified by tests of a modern passenger aircraft model in a wind tunnel.

  20. How Iron-Containing Proteins Control Dioxygen Chemistry: A Detailed Atomic Level Description Via Accurate Quantum Chemical and Mixed Quantum Mechanics/Molecular Mechanics Calculations.

    SciTech Connect

    Friesner, Richard A.; Baik, Mu-Hyun; Gherman, Benjamin F.; Guallar, Victor; Wirstam, Maria E.; Murphy, Robert B.; Lippard, Stephen J.

    2003-03-01

    Over the past several years, rapid advances in computational hardware, quantum chemical methods, and mixed quantum mechanics/molecular mechanics (QM/MM) techniques have made it possible to model accurately the interaction of ligands with metal-containing proteins at an atomic level of detail. In this paper, we describe the application of our computational methodology, based on density functional (DFT) quantum chemical methods, to two diiron-containing proteins that interact with dioxygen: methane monooxygenase (MMO) and hemerythrin (Hr). Although the active sites are structurally related, the biological function differs substantially. MMO is an enzyme found in methanotrophic bacteria and hydroxylates aliphatic C-H bonds, whereas Hr is a carrier protein for dioxygen used by a number of marine invertebrates. Quantitative descriptions of the structures and energetics of key intermediates and transition states involved in the reaction with dioxygen are provided, allowing their mechanisms to be compared and contrasted in detail. An in-depth understanding of how the chemical identity of the first ligand coordination shell, structural features, electrostatic and van der Waals interactions of more distant shells control ligand binding and reactive chemistry is provided, affording a systematic analysis of how iron-containing proteins process dioxygen. Extensive contact with experiment is made in both systems, and a remarkable degree of accuracy and robustness of the calculations is obtained from both a qualitative and quantitative perspective.

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

    PubMed

    Pagliaro, Claudia M; Kritzer, Karen L

    2013-04-01

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

  2. Multivariate and Descriptive Discriminant Analysis of Multidisciplinary Approaches to Integrating Mathematics, Science, and Technology Education in the High School.

    ERIC Educational Resources Information Center

    Wicklein, Robert C.; Schell, John W.

    A study examined the perceptions of participants in a multidisciplinary project regarding the degree to which the integration of technology, mathematics, and science had enabled advanced mental skills in technical thinking and problem solving. A literature review focused on advanced learning and thinking, ill-structured workplace problems,…

  3. Coupling geostatistics to detailed reservoir description allows better visualization and more accurate characterization/simulation of turbidite reservoirs: Elk Hills oil field, California

    SciTech Connect

    Allan, M.E.; Wilson, M.L.; Wightman, J. )

    1996-01-01

    The Elk Hills giant oilfield, located in the southern San Joaquin Valley of California, has produced 1.1 billion barrels of oil from Miocene and shallow Pliocene reservoirs. 65% of the current 64,000 BOPD production is from the pressure-supported, deeper Miocene turbidite sands. In the turbidite sands of the 31 S structure, large porosity permeability variations in the Main Body B and Western 31 S sands cause problems with the efficiency of the waterflooding. These variations have now been quantified and visualized using geostatistics. The end result is a more detailed reservoir characterization for simulation. Traditional reservoir descriptions based on marker correlations, cross-sections and mapping do not provide enough detail to capture the short-scale stratigraphic heterogeneity needed for adequate reservoir simulation. These deterministic descriptions are inadequate to tie with production data as the thinly bedded sand/shale sequences blur into a falsely homogenous picture. By studying the variability of the geologic petrophysical data vertically within each wellbore and spatially from well to well, a geostatistical reservoir description has been developed. It captures the natural variability of the sands and shales that was lacking from earlier work. These geostatistical studies allow the geologic and petrophysical characteristics to be considered in a probabilistic model. The end-product is a reservoir description that captures the variability of the reservoir sequences and can be used as a more realistic starting point for history matching and reservoir simulation.

  4. Coupling geostatistics to detailed reservoir description allows better visualization and more accurate characterization/simulation of turbidite reservoirs: Elk Hills oil field, California

    SciTech Connect

    Allan, M.E.; Wilson, M.L.; Wightman, J.

    1996-12-31

    The Elk Hills giant oilfield, located in the southern San Joaquin Valley of California, has produced 1.1 billion barrels of oil from Miocene and shallow Pliocene reservoirs. 65% of the current 64,000 BOPD production is from the pressure-supported, deeper Miocene turbidite sands. In the turbidite sands of the 31 S structure, large porosity & permeability variations in the Main Body B and Western 31 S sands cause problems with the efficiency of the waterflooding. These variations have now been quantified and visualized using geostatistics. The end result is a more detailed reservoir characterization for simulation. Traditional reservoir descriptions based on marker correlations, cross-sections and mapping do not provide enough detail to capture the short-scale stratigraphic heterogeneity needed for adequate reservoir simulation. These deterministic descriptions are inadequate to tie with production data as the thinly bedded sand/shale sequences blur into a falsely homogenous picture. By studying the variability of the geologic & petrophysical data vertically within each wellbore and spatially from well to well, a geostatistical reservoir description has been developed. It captures the natural variability of the sands and shales that was lacking from earlier work. These geostatistical studies allow the geologic and petrophysical characteristics to be considered in a probabilistic model. The end-product is a reservoir description that captures the variability of the reservoir sequences and can be used as a more realistic starting point for history matching and reservoir simulation.

  5. Mathematical description of the kinetics of the thermal degradation of coals over a wide range of rates of heating

    SciTech Connect

    Aksenov, L.N.; Bronshtein, A.P.; Zadorina, E.N.; Zagorets, A.M.; Makarov, G.N.; Polyakov, A.A.; Shlenskii, O.F.

    1981-01-01

    The determination of the most effective regimes for the thermal processing of solid fuels and the control of these processes requires a well-based selection of mathematical models for them. In the reported theoretical study, the question is considered of the possibility of using the traditional equations of chemical kinetics for describing the thermal degradation of the organic matter of coals. Various methods are proposed for the detemination of thermogravimetric curves. 14 refs.

  6. Mathematical and system level HW description DSP algorithms modeling investigation in an experimental 100G optical coherent system

    NASA Astrophysics Data System (ADS)

    Ribeiro, Vitor B.; Silva, Flávio A.; Oliveira, Julio C. R. F.; Franz, Lucas V.; Schneider, Eduardo O.; Moretti, Cleber; Ranzini, Stenio M.

    2013-01-01

    Today and next generation optical coherent systems rely more and more in DSP algorithms to improve capacity, spectral efficiency and fiber impairments mitigation. The amount of signal processing is remarkable, and because of that ASICs are preferable in order to comply with cost, power consumption and size, required in OIF 100G optical module standards. One important step in the ASIC development process is the validation of the DSP algorithms mathematical models in a high level language that consider HW characteristics and constrains. In this work we present, compare and evaluate in experimental data the mathematical model developed in Matlab and the SystemC model developed in C++. The DSP algorithms functionalities implemented were orthonormalization, CD equalizer, clock recovery, dynamic equalizer, frequency offset and phase estimation. The SystemC model considers clock signals, reset/enable structures, parallelization, finite fixed-point operations and structures that are closer to the ASIC HW implementation; due to these restrictions the performance is not as good as the mathematical modeling. The DSP algorithms models are evaluated in two 112 Gbit/s DP-QPSK experimental scenarios. In the first scenario the models are evaluated in back-to-back with ASE noise loading; in the second scenario the models are compared in a 226km optical fiber recirculation loop, with 80x112 Gbit/s DP-QPSK channels (8.96 Tbit/s). In the back-to-back experiment the OSNR penalty from the mathematical model to the SystemC model is only 1,0dB and in the recirculation loop the maximum reach is 2,600 km and 2,200 km for the Matlab and SystemC models respectively.

  7. On the Inclusion of the Interfacial Area Between Phases in the Physical and Mathematical Description of Subsurface Multiphase Flow

    SciTech Connect

    Gray, W.G.

    2001-01-25

    This project has contributed to the improved understanding and precise physical description of multiphase subsurface flow by combining theoretical derivation of equations, lattice Boltzmann modeling of hydrodynamics to identify characteristics and parameters, and simplification of field-scale equations to assess the advantages and disadvantages of the complete theory.

  8. A Mathematical Model for Vertical Attitude Takeoff and Landing (VATOL) Aircraft Simulation. Volume 1; Model Description Application

    NASA Technical Reports Server (NTRS)

    Fortenbaugh, R. L.

    1980-01-01

    A mathematical model of a high performance airplane capable of vertical attitude takeoff and landing (VATOL) was developed. An off line digital simulation program incorporating this model was developed to provide trim conditions and dynamic check runs for the piloted simulation studies and support dynamic analyses of proposed VATOL configuration and flight control concepts. Development details for the various simulation component models and the application of the off line simulation program, Vertical Attitude Take-Off and Landing Simulation (VATLAS), to develop a baseline control system for the Vought SF-121 VATOL airplane concept are described.

  9. Barely started and already left behind: a descriptive analysis of the mathematics ability demonstrated by young deaf children.

    PubMed

    Kritzer, Karen L

    2009-01-01

    This study examined young deaf children's early informal/formal mathematical knowledge as measured by the Test of Early Mathematics Ability (TEMA-3). Findings from this study suggest that prior to the onset of formal schooling, young deaf children might already demonstrate evidence of academic delays. Of these 28 participants (4-6 years of age), for whom data were analyzed, none received a score on the TEMA-3, indicating above-"average" ability according to normative ranking. More than half of participants received scores substantially below average with 11 participants receiving scores a year or more behind normative age-equivalent scores. Upon more focused analysis, specific areas of difficulty were found to include word/story problems, skip counting (i.e., counting by twos, threes, etc.), number comparisons, the reading/writing of two to three digit numbers, and addition/subtraction number facts. A qualitative analysis of the answers participants gave and the behaviors they demonstrated while answering the test items was conducted and revealed possible explanations for why specific test items may have been challenging. Implications of findings for parents, early interventionists, and teachers of young deaf children are discussed. PMID:19596725

  10. DEVELOPMENT OF AN ANNOTATION SCHEME FOR STANDARDIZED DESCRIPTION OF MATHEMATICAL MODELS IN THE FIELD OF PLANT PROTECTION.

    PubMed

    Günther, T; Büttner, C; Käsbohrer, A; Filter, M

    2015-01-01

    Mathematical models on properties and behavior of harmful organisms in the food chain are an increas- ingly relevant approach of the agriculture and food industry. As a consequence, there are many efforts to develop biological models in science, economics and risk assessment nowadays. However, there is a lack of international harmonized standards on model annotation and model formats, which would be neces- sary to set up efficient tools supporting broad model application and information exchange. There are some established standards in the field of systems biology, but there is currently no corresponding provi- sion in the area of plant protection. This work therefore aimed at the development of an annotation scheme using domain-specific metadata. The proposed scheme has been validated in a prototype implementation of a web-database model repository. This prototypic community resource currently contains models on aflatoxin secreting fungal Aspergillus flavus in maize, as these models have a high relevance to food safety and economic impact. Specifically, models describing biological processes of the fungus (growth, Aflatoxin secreting), as well as dose-response- and carry over models were included. Furthermore, phenological models for maize were integrated as well. The developed annotation scheme is based on the well-established data exchange format SBML, which is broadly applied in the field of systems biology. The identified example models were annotated according to the developed scheme and entered into a Web-table (Google Sheets), which was transferred to a web based demonstrator available at https://sites.google.com/site/test782726372685/. By implementation of a software demonstrator it became clear that the proposed annotation scheme can be applied to models on plant pathogens and that broad adoption within the domain could promote communication and application of mathematical models. PMID:27141756

  11. Petermann I and II spot size: Accurate semi analytical description involving Nelder-Mead method of nonlinear unconstrained optimization and three parameter fundamental modal field

    NASA Astrophysics Data System (ADS)

    Roy Choudhury, Raja; Roy Choudhury, Arundhati; Kanti Ghose, Mrinal

    2013-01-01

    A semi-analytical model with three optimizing parameters and a novel non-Gaussian function as the fundamental modal field solution has been proposed to arrive at an accurate solution to predict various propagation parameters of graded-index fibers with less computational burden than numerical methods. In our semi analytical formulation the optimization of core parameter U which is usually uncertain, noisy or even discontinuous, is being calculated by Nelder-Mead method of nonlinear unconstrained minimizations as it is an efficient and compact direct search method and does not need any derivative information. Three optimizing parameters are included in the formulation of fundamental modal field of an optical fiber to make it more flexible and accurate than other available approximations. Employing variational technique, Petermann I and II spot sizes have been evaluated for triangular and trapezoidal-index fibers with the proposed fundamental modal field. It has been demonstrated that, the results of the proposed solution identically match with the numerical results over a wide range of normalized frequencies. This approximation can also be used in the study of doped and nonlinear fiber amplifier.

  12. A name for the 'blueberry tetra', an aquarium trade popular species of Hyphessobrycon Durbin (Characiformes, Characidae), with comments on fish species descriptions lacking accurate type locality.

    PubMed

    Marinho, M M F; Dagosta, F C P; Camelier, P; Oyakawa, O T

    2016-07-01

    A new species of Hyphessobrycon is described from a tributary of the upper Rio Tapajós, Amazon basin, Mato Grosso, Brazil. Its exuberant colour in life, with blue to purple body and red fins, is appreciated in the aquarium trade. Characters to diagnose the new species from all congeners are the presence of a single humeral blotch, absence of a distinct caudal-peduncle blotch, absence of a well-defined dark mid-lateral stripe on body, the presence of 16-18 branched anal-fin rays, nine branched dorsal-fin rays and six branched pelvic-fin rays. A brief comment on fish species descriptions solely based on aquarium material and its consequence for conservation policies is provided.

  13. A name for the 'blueberry tetra', an aquarium trade popular species of Hyphessobrycon Durbin (Characiformes, Characidae), with comments on fish species descriptions lacking accurate type locality.

    PubMed

    Marinho, M M F; Dagosta, F C P; Camelier, P; Oyakawa, O T

    2016-07-01

    A new species of Hyphessobrycon is described from a tributary of the upper Rio Tapajós, Amazon basin, Mato Grosso, Brazil. Its exuberant colour in life, with blue to purple body and red fins, is appreciated in the aquarium trade. Characters to diagnose the new species from all congeners are the presence of a single humeral blotch, absence of a distinct caudal-peduncle blotch, absence of a well-defined dark mid-lateral stripe on body, the presence of 16-18 branched anal-fin rays, nine branched dorsal-fin rays and six branched pelvic-fin rays. A brief comment on fish species descriptions solely based on aquarium material and its consequence for conservation policies is provided. PMID:27245763

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

    PubMed

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

    2016-01-01

    In the literature we found many studies that confirmed our concerns about nursing students' poor maths skills that directly impact on their ability to correctly calculate drug dosages with very serious consequences for patient safety. The aim of our study was to explore where students had most difficulty and identify appropriate educational interventions to bridge their mathematical knowledge gaps. This was a quali-quantitative descriptive study that included a sample of 726 undergraduate nursing students. We identified exactly where students had most difficulty and identified appropriate educational interventions to bridge their mathematical knowledge gaps. We found that the undergraduate nursing students mainly had difficulty with basic maths principles. Specific learning interventions are needed to improve their basic maths skills and their dosage calculation skills. For this purpose, we identified safeMedicate and eDose (Authentic World Ltd.), only that they are only available in English. In the near future we hope to set up a partnership to work together on the Italian version of these tools. PMID:26347449

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

    PubMed

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

    2016-01-01

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

  16. Mathematical Description of the Hydrodynamic Regimes of an Asymptotic Model for Two-Phase Flow Arising in PFBC Boilers

    NASA Astrophysics Data System (ADS)

    de Vicente, S.; Galiano, G.; Velasco, J.; Aróstegui, J. M.

    Two-phase systems where a dense phase of small particles is fluidized with a gas flow appear in many industrial applications, among which the fluidized bed combustors are probably the most important. A homogenization technique allows us to formulate the mathematical model in form of the compressible Navier-Stokes system type with some particularities: 1) the volumetric fraction of the dense phase (analogous to the density in the Navier-Stokes equations) may vanish, 2) the constitutive viscosity law may depend in a nonlinear form on this density, 3) the source term is nonlinear and coupled with state equations involving drag forces and hydrodynamic pressure, and 4) the state equation for the collision pressure of dense phase blows up for finite values of the density. We develop a rigorous theory for a special kind of solutions we call stationary clouds. Such solutions exist only under restrictions on the geometry of combustor and on the boundary conditions that usually meet in engineering applications. In return, these solutions have a stationary one-dimensional structure very simple and, from them, it is possible to reconstruct much of the dynamics of the whole system, responding to most of the practical issues of interest. Finally, we study the linear stability for the trivial solutions corresponding to uniform fluidized states injecting plane wave perturbations in our equations. Depending on the parameters of the equations of state describing the collisions between solid particles, hydrodynamic pressure, and the values of blowing boundary condition, we can draw detailed abacus separating stable regions of unstable regions where bubbles appear. Then, we use the dispersion relations of this multidimensional linearized model, combined with the stationary phase theorem, to approach the profiles and the evolution of the bubbles appearing in unstable regimes, and verify that the obtained results adjust to the observations.

  17. Interactions between Activation and Repolarization Restitution Properties in the Intact Human Heart: In-Vivo Whole-Heart Data and Mathematical Description

    PubMed Central

    Taggart, Peter; Srinivasan, Neil; Hayward, Martin; Lambiase, Pier D.

    2016-01-01

    Background The restitution of the action potential duration (APDR) and conduction velocity (CVR) are mechanisms whereby cardiac excitation and repolarization adapt to changes in heart rate. They modulate the vulnerability to dangerous arrhythmia, but the mechanistic link between restitution and arrhythmogenesis remains only partially understood. Methods This paper provides an experimental and theoretical study of repolarization and excitation restitution properties and their interactions in the intact human epicardium. The interdependence between excitation and repolarization dynamic is studied in 8 patients (14 restitution protocols, 1722 restitution curves) undergoing global epicardial mapping with multi-electrode socks before open heart surgery. A mathematical description of the contribution of both repolarization and conduction dynamics to the steepness of the APDR slope is proposed. Results This study demonstrates that the APDR slope is a function of both activation and repolarization dynamics. At short cycle length, conduction delay significantly increases the APDR slope by interacting with the diastolic interval. As predicted by the proposed mathematical formulation, the APDR slope was more sensitive to activation time prolongation than to the simultaneous shortening of repolarization time. A steep APDR slope was frequently identified, with 61% of all cardiac sites exhibiting an APDR slope > 1, suggesting that a slope > 1 may not necessarily promote electrical instability in the human epicardium. APDR slope did not change for different activation or repolarization times, and it was not a function of local baseline APD. However, it was affected by the spatial organization of electrical excitation, suggesting that in tissue APDR is not a unique function of local electrophysiological properties. Spatial heterogeneity in both activation and repolarization restitution contributed to the increase in the modulated dispersion of repolarization, which for short cycle

  18. Rural Mathematics Educator, 2002.

    ERIC Educational Resources Information Center

    Rural Mathematics Educator, 2002

    2002-01-01

    This document contains the two issues of "Rural Mathematics Educator" published in 2002. This newsletter of the Appalachian Collaborative Center for Learning, Assessment, and Instruction in Mathematics (ACCLAIM) includes articles on rural mathematics education, as well as information and descriptions of professional development opportunities for…

  19. What Counts as Mathematical Discourse?

    ERIC Educational Resources Information Center

    Moschkovich, Judit

    2003-01-01

    In this paper I use situated and socio-cultural perspective (Gee, 1996 & 1999) to examine descriptions of mathematical discourse and an example of student talk in a mathematics classroom. Using this example, I discuss how the distinction between everyday and mathematical discourse can help or hinder us in hearing the mathematical content in…

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

    ERIC Educational Resources Information Center

    Locklear, Tonja Motley

    2012-01-01

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

  1. Improved Detection System Description and New Method for Accurate Calibration of Micro-Channel Plate Based Instruments and Its Use in the Fast Plasma Investigation on NASA's Magnetospheric MultiScale Mission

    NASA Technical Reports Server (NTRS)

    Gliese, U.; Avanov, L. A.; Barrie, A. C.; Kujawski, J. T.; Mariano, A. J.; Tucker, C. J.; Chornay, D. J.; Cao, N. T.; Gershman, D. J.; Dorelli, J. C.; Zeuch, M. A.; Pollock, C. J.; Jacques, A. D.

    2015-01-01

    system calibration method that enables accurate and repeatable measurement and calibration of MCP gain, MCP efficiency, signal loss due to variation in gain and efficiency, crosstalk from effects both above and below the MCP, noise margin, and stability margin in one single measurement. More precise calibration is highly desirable as the instruments will produce higher quality raw data that will require less post-acquisition data correction using results from in-flight pitch angle distribution measurements and ground calibration measurements. The detection system description and the fundamental concepts of this new calibration method, named threshold scan, will be presented. It will be shown how to derive all the individual detection system parameters and how to choose the optimum detection system operating point. This new method has been successfully applied to achieve a highly accurate calibration of the DESs and DISs of the MMS mission. The practical application of the method will be presented together with the achieved calibration results and their significance. Finally, it will be shown that, with further detailed modeling, this method can be extended for use in flight to achieve and maintain a highly accurate detection system calibration across a large number of instruments during the mission.

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

    NASA Technical Reports Server (NTRS)

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

    1982-01-01

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

  3. Constrained Mathematics for Calculating Logical Safety and Reliability Probabilities with Uncertain Inputs

    SciTech Connect

    Cooper, D.K.; Cooper, J.A.; Ferson, S.

    1999-01-21

    Calculating safety and reliability probabilities with functions of uncertain variables can yield incorrect or misleading results if some precautions are not taken. One important consideration is the application of constrained mathematics for calculating probabilities for functions that contain repeated variables. This paper includes a description of the problem and develops a methodology for obtaining an accurate solution.

  4. NNLOPS accurate associated HW production

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

  5. The Nature of Mathematics Anxiety.

    ERIC Educational Resources Information Center

    Cemen, Pamala Byrd

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

  6. A description of a system of programs for mathematically processing on unified series (YeS) computers photographic images of the Earth taken from spacecraft

    NASA Technical Reports Server (NTRS)

    Zolotukhin, V. G.; Kolosov, B. I.; Usikov, D. A.; Borisenko, V. I.; Mosin, S. T.; Gorokhov, V. N.

    1980-01-01

    A description of a batch of programs for the YeS-1040 computer combined into an automated system for processing photo (and video) images of the Earth's surface, taken from spacecraft, is presented. Individual programs with the detailed discussion of the algorithmic and programmatic facilities needed by the user are presented. The basic principles for assembling the system, and the control programs are included. The exchange format within whose framework the cataloging of any programs recommended for the system of processing will be activated in the future is displayed.

  7. On the inclusion of the interfacial area between phases in the physical and mathematical description of subsurface multiphase flow. 1998 annual progress report

    SciTech Connect

    Gray, W.G.; Tompson, A.; Soll, W.E.

    1998-06-01

    'Improved capabilities for modeling multiphase flow in the subsurface requires that several aspects of the system which impact the flow and transport processes be more properly accounted for. A distinguishing feature of multiphase flow in comparison to single phase flow is the existence of interfaces between fluids. At the microscopic (pore) scale, these interfaces are known to influence system behavior by supporting non-zero stresses such that the pressures in adjacent phases are not equal. In problems of interphase transport at the macroscopic (core) scale, knowledge of the total amount of interfacial area in the system provides a clue to the effectiveness of the communication between phases. Although interfacial processes are central to multiphase flow physics, their treatment in traditional porous-media theories has been implicit rather than explicit; and no attempts have been made to systematically account for the evolution of the interfacial area in dynamic systems or to include the dependence of constitutive functions, such as capillary pressure, on the interfacial area. This project implements a three-pronged approach to assessing the importance of various features of multiphase flow to its description. The research contributes to the improved understanding and precise physical description of multiphase subsurface flow by combining: (1) theoretical derivation of equations, (2) lattice Boltzmann modeling of hydrodynamics to identify characteristics and parameters, and (3) solution of the field-scale equations using a discrete numerical method to assess the advantages and disadvantages of the complete theory. This approach includes both fundamental scientific inquiry and a path for inclusion of the scientific results obtained in a technical tool that will improve assessment capabilities for multiphase flow situations that have arisen due to the introduction of organic materials in the natural environment. This report summarizes work after 1.5 years of a 3

  8. Mathematics Underground

    ERIC Educational Resources Information Center

    Luther, Kenneth H.

    2012-01-01

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

  9. A mathematical approach to human pterygium shape

    PubMed Central

    Pajic, Bojan; Vastardis, Iraklis; Rajkovic, Predrag; Pajic-Eggspuehler, Brigitte; Aebersold, Daniel M; Cvejic, Zeljka

    2016-01-01

    Purpose Pterygium is a common lesion affecting the population in countries with high levels of ultraviolet exposure. The final shape of a pterygium is the result of a growth pattern, which remains poorly understood. This manuscript provides a mathematical analysis as a tool to determine the shape of human pterygia. Materials and methods Eighteen patients, all affected by nasal unilateral pterygia, were randomly selected from our patient database independently of sex, origin, or race. We included all primary or recurrent pterygia with signs of proliferation, dry eye, and induction of astigmatism. Pseudopterygia were excluded from this study. Pterygia were outlined and analyzed mathematically using a Cartesian coordinate system with two axes (X, Y) and five accurate landmarks of the pterygium. Results In 13 patients (72%), the shape of the pterygia was hyperbolic and in five patients (28%), the shape was rather elliptical. Conclusion This analysis gives a highly accurate mathematical description of the shape of human pterygia. This might help to better assess the clinical results and outcome of the great variety of therapeutic approaches concerning these lesions. PMID:27555741

  10. Computation and graphics in mathematical research

    SciTech Connect

    Hoffman, D.A.; Spruck, J.

    1992-08-13

    This report discusses: The description of the GANG Project and results for prior research; the center for geometry, analysis, numerics and graphics; description of GANG Laboratory; software development at GANG; and mathematical and scientific research activities.

  11. Mathematical epidemiology is not an oxymoron

    PubMed Central

    2009-01-01

    A brief description of the importance of communicable diseases in history and the development of mathematical modelling of disease transmission is given. This includes reasons for mathematical modelling, the history of mathematical modelling from the foundations laid in the late nineteenth century to the present, some of the accomplishments of mathematical modelling, and some challenges for the future. Our purpose is to demonstrate the importance of mathematical modelling for the understanding and management of infectious disease transmission. PMID:19922686

  12. The Mathematics of Global Change

    ERIC Educational Resources Information Center

    Kreith, Kurt

    2011-01-01

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

  13. Fostering Creativity Through Mathematics.

    ERIC Educational Resources Information Center

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

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

  14. Mathematics, Anyone?

    ERIC Educational Resources Information Center

    Reys, Robert; Reys, Rustin

    2011-01-01

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

  15. CARE 3 phase 2 report - mathematical description

    NASA Technical Reports Server (NTRS)

    Stiffler, J. J.; Bryant, L. A.

    1982-01-01

    CARE III (Computer-Aided Reliability Estimation, version three) a computer program designed to help estimate the reliability of complex, redundant systems is described. Although the program can model a wide variety of redundant structures, it was developed specifically for fault tolerant avionics systems. CARE III generalizes the class of system structures that can be modeled and greatly expands the coverage model to take into account such effects as intermittent and transient faults, latent faults, and error propagation.

  16. Mathematical Geology.

    ERIC Educational Resources Information Center

    Jones, Thomas A.

    1983-01-01

    Mathematical techniques used to solve geological problems are briefly discussed (including comments on use of geostatistics). Highlights of conferences/meetings and conference papers in mathematical geology are also provided. (JN)

  17. Mathematics anxiety and mathematics achievement

    NASA Astrophysics Data System (ADS)

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

    2003-09-01

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

  18. Rainforest Mathematics

    ERIC Educational Resources Information Center

    Kilpatrick, Jeremy

    2014-01-01

    This paper addresses the contested way that ethnomathematics has sometimes been received by mathematicians and others and what that disagreement might suggest about issues in mathematics education; namely, (a) the relation of ethnomathematics to academic mathematics; (b) recent efforts to reform secondary school mathematics so that it prepares…

  19. Beauty as Fit: A Metaphor in Mathematics?

    ERIC Educational Resources Information Center

    Raman, Manya; Öhman, Lars-Daniel

    2013-01-01

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

  20. Mathematics Placement Tests and Gender Bias.

    ERIC Educational Resources Information Center

    Dorner, Celine D'Souza; Hutton, Ivan

    2002-01-01

    Examined whether a mathematics placement system accurately predicted success in university mathematics classes for both genders. The placement system used four variables to predict grades a student would receive if placed in various freshman mathematics classes. Found that the multiple predictors added to the gender bias of the Scholastic…

  1. Drought description

    USGS Publications Warehouse

    Matalas, N.C.

    1991-01-01

    What constitutes a comprehensive description of drought, a description forming a basis for answering why a drought occurred is outlined. The description entails two aspects that are "naturally" coupled, named physical and economic, and treats the set of hydrologic measures of droughts in terms of their multivariate distribution, rather than in terms of a collection of the marginal distributions. ?? 1991 Springer-Verlag.

  2. 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…

  3. Self-Efficacy Beliefs of Prospective Primary Mathematics Teachers about Mathematical Literacy

    ERIC Educational Resources Information Center

    Yavuz, Gunes; Gunhan, Berna Canturk; Ersoy, Esen; Narli, Serkan

    2013-01-01

    The aim of this study was to examine the self-efficacy beliefs about mathematical literacy among teachers of primary school mathematics and the relationship between the self-efficacy beliefs and attitudes towards mathematics. To that end, a descriptive research study was conducted with 550 prospective teachers studying primary school mathematics…

  4. Mathematics Education.

    ERIC Educational Resources Information Center

    Langbort, Carol, Ed.; Curtis, Deborah, Ed.

    2000-01-01

    The focus of this special issue is mathematics education. All articles were written by graduates of the new masters Degree program in which students earn a Master of Arts degree in Education with a concentration in Mathematics Education at San Francisco State University. Articles include: (1) "Developing Teacher-Leaders in a Masters Degree Program…

  5. Making Mathematics.

    ERIC Educational Resources Information Center

    Huckstep, Peter

    2002-01-01

    Contends teachers must resist the temptation to suggest that, while children can create stories and melodies, they cannot create mathematics. Quotes mathematician G. H. Hardy: "A mathematician, like a painter or poet, is a 'maker' of patterns." Considers mathematics should be able to stand up for itself. (BT)

  6. Technical Mathematics.

    ERIC Educational Resources Information Center

    Flannery, Carol A.

    This manuscript provides information and problems for teaching mathematics to vocational education students. Problems reflect applications of mathematical concepts to specific technical areas. The materials are organized into six chapters. Chapter 1 covers basic arithmetic, including fractions, decimals, ratio and proportions, percentages, and…

  7. Mathematics Scrapbook

    ERIC Educational Resources Information Center

    Prochazka, Helen

    2004-01-01

    One section of this "scrapbook" section describes Pythagoras' belief in the connections between music and mathematics -- that everything in the universe was a series of harmonies and regulated by music. Another section explains why Phythagoras felt it important for women to be encouraged to learn mathematics. At least 28 women were involved in his…

  8. Developmental Kindergarten: Definition and Description.

    ERIC Educational Resources Information Center

    Virginia State Dept. of Education, Richmond.

    This paper sets forth a definition and operational description of a developmental program that should be of use as a guide, especially to Virginia's teachers and administrators. Also included in the paper are kindergarten curriculum objectives in the areas of language arts, mathematics, science, art, social studies, family life, health, mental…

  9. Accurate monotone cubic interpolation

    NASA Technical Reports Server (NTRS)

    Huynh, Hung T.

    1991-01-01

    Monotone piecewise cubic interpolants are simple and effective. They are generally third-order accurate, except near strict local extrema where accuracy degenerates to second-order due to the monotonicity constraint. Algorithms for piecewise cubic interpolants, which preserve monotonicity as well as uniform third and fourth-order accuracy are presented. The gain of accuracy is obtained by relaxing the monotonicity constraint in a geometric framework in which the median function plays a crucial role.

  10. Accurate Finite Difference Algorithms

    NASA Technical Reports Server (NTRS)

    Goodrich, John W.

    1996-01-01

    Two families of finite difference algorithms for computational aeroacoustics are presented and compared. All of the algorithms are single step explicit methods, they have the same order of accuracy in both space and time, with examples up to eleventh order, and they have multidimensional extensions. One of the algorithm families has spectral like high resolution. Propagation with high order and high resolution algorithms can produce accurate results after O(10(exp 6)) periods of propagation with eight grid points per wavelength.

  11. Remedial Mathematics in the College: A Bibliography

    ERIC Educational Resources Information Center

    Akst, Geoffrey

    1978-01-01

    References dealing specifically with college remedial mathematics programs fall into several categories: descriptions of programs at individual colleges, regional surveys, and comparative studies on the relative effectiveness of various modes of instruction. (MN)

  12. Mathematical modeling of radio systems and devices

    NASA Astrophysics Data System (ADS)

    Borisov, Iu. P.; Tsvetnov, V. V.

    Methods for developing mathematical models of radio systems and devices are presented with emphasis on the functional approach to the modeling of radio systems. In particular, attention is given to the formal description of radio systems, computer-aided modeling of radio systems, a classification of methods of radio system modeling, and methods of mathematical description of signals and noise. Specific methods discussed include the carrier method, the complex envelope method, the method of statistical equivalents, and the information parameter method.

  13. Mathematical Geology.

    ERIC Educational Resources Information Center

    McCammon, Richard B.

    1979-01-01

    The year 1978 marked a continued trend toward practical applications in mathematical geology. Developments included work in interactive computer graphics, factor analysis, the vanishing tons problem, universal kriging, and resource estimating. (BB)

  14. Mathematical Games

    ERIC Educational Resources Information Center

    Gardner, Martin

    1978-01-01

    Describes the life and work of Charles Peirce, U.S. mathematician and philosopher. His accomplishments include contributions to logic, the foundations of mathematics and scientific method, and decision theory and probability theory. (MA)

  15. Computer-Game-Based Tutoring of Mathematics

    ERIC Educational Resources Information Center

    Ke, Fengfeng

    2013-01-01

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

  16. On the Role of Mathematics in Physics

    ERIC Educational Resources Information Center

    Quale, Andreas

    2011-01-01

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

  17. Mathematics Teachers' Criteria of Dimension

    ERIC Educational Resources Information Center

    Ural, Alattin

    2014-01-01

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

  18. Dynamic Boolean Mathematics

    ERIC Educational Resources Information Center

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

    2016-01-01

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

  19. Mathematical wit and mathematical cognition.

    PubMed

    Aberdein, Andrew

    2013-04-01

    The published works of scientists often conceal the cognitive processes that led to their results. Scholars of mathematical practice must therefore seek out less obvious sources. This article analyzes a widely circulated mathematical joke, comprising a list of spurious proof types. An account is proposed in terms of argumentation schemes: stereotypical patterns of reasoning, which may be accompanied by critical questions itemizing possible lines of defeat. It is argued that humor is associated with risky forms of inference, which are essential to creative mathematics. The components of the joke are explicated by argumentation schemes devised for application to topic-neutral reasoning. These in turn are classified under seven headings: retroduction, citation, intuition, meta-argument, closure, generalization, and definition. Finally, the wider significance of this account for the cognitive science of mathematics is discussed. PMID:23512504

  20. Mathematical Perspectives

    SciTech Connect

    Glimm, J.

    2009-10-14

    Progress for the past decade or so has been extraordinary. The solution of Fermat's Last Theorem [11] and of the Poincare Conjecture [1] have resolved two of the most outstanding challenges to mathematics. For both cases, deep and advanced theories and whole subfields of mathematics came into play and were developed further as part of the solutions. And still the future is wide open. Six of the original seven problems from the Clay Foundation challenge remain open, the 23 DARPA challenge problems are open. Entire new branches of mathematics have been developed, including financial mathematics and the connection between geometry and string theory, proposed to solve the problems of quantized gravity. New solutions of the Einstein equations, inspired by shock wave theory, suggest a cosmology model which fits accelerating expansion of the universe possibly eliminating assumptions of 'dark matter'. Intellectual challenges and opportunities for mathematics are greater than ever. The role of mathematics in society continues to grow; with this growth comes new opportunities and some growing pains; each will be analyzed here. We see a broadening of the intellectual and professional opportunities and responsibilities for mathematicians. These trends are also occuring across all of science. The response can be at the level of the professional societies, which can work to deepen their interactions, not only within the mathematical sciences, but also with other scientific societies. At a deeper level, the choices to be made will come from individual mathematicians. Here, of course, the individual choices will be varied, and we argue for respect and support for this diversity of responses. In such a manner, we hope to preserve the best of the present while welcoming the best of the new.

  1. Accurate quantum chemical calculations

    NASA Technical Reports Server (NTRS)

    Bauschlicher, Charles W., Jr.; Langhoff, Stephen R.; Taylor, Peter R.

    1989-01-01

    An important goal of quantum chemical calculations is to provide an understanding of chemical bonding and molecular electronic structure. A second goal, the prediction of energy differences to chemical accuracy, has been much harder to attain. First, the computational resources required to achieve such accuracy are very large, and second, it is not straightforward to demonstrate that an apparently accurate result, in terms of agreement with experiment, does not result from a cancellation of errors. Recent advances in electronic structure methodology, coupled with the power of vector supercomputers, have made it possible to solve a number of electronic structure problems exactly using the full configuration interaction (FCI) method within a subspace of the complete Hilbert space. These exact results can be used to benchmark approximate techniques that are applicable to a wider range of chemical and physical problems. The methodology of many-electron quantum chemistry is reviewed. Methods are considered in detail for performing FCI calculations. The application of FCI methods to several three-electron problems in molecular physics are discussed. A number of benchmark applications of FCI wave functions are described. Atomic basis sets and the development of improved methods for handling very large basis sets are discussed: these are then applied to a number of chemical and spectroscopic problems; to transition metals; and to problems involving potential energy surfaces. Although the experiences described give considerable grounds for optimism about the general ability to perform accurate calculations, there are several problems that have proved less tractable, at least with current computer resources, and these and possible solutions are discussed.

  2. Enhancing Mathematical Communication: "Bag of Tricks" Game

    ERIC Educational Resources Information Center

    Patahuddin, Sitti Maesuri; Ramful, Ajay; Greenlees, Jane

    2015-01-01

    An engaging activity which prompts students to listen, talk, reason and write about geometrical properties. The "Bag of Tricks" encourages students to clarify their thoughts and communicate precisely using accurate mathematical language.

  3. Applied mathematical problems in modern electromagnetics

    NASA Astrophysics Data System (ADS)

    Kriegsman, Gregory

    1994-05-01

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

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

    NASA Astrophysics Data System (ADS)

    Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

    2011-04-01

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

  5. Elementary Statistics I--Mathematics 274 Course Syllabus, Fall 2001.

    ERIC Educational Resources Information Center

    Clark, Deborah L.

    This document features the syllabus for a course in Elementary Statistics/Mathematics at Southern University in Baton Rouge, LA. The course textbook, a course description, readings, goals, and course requirements are presented. Basic descriptive analysis and mathematical concepts commonly used in statistics are emphasized in the course. Topics…

  6. Anaphoric Descriptions

    ERIC Educational Resources Information Center

    Beller, Charley

    2013-01-01

    The study of definite descriptions has been a central part of research in linguistics and philosophy of language since Russell's seminal work "On Denoting" (Russell 1905). In that work Russell quickly dispatches analyses of denoting expressions with forms like "no man," "some man," "a man," and "every…

  7. The Definition of Mathematics: Philosophical and Pedagogical Aspects

    ERIC Educational Resources Information Center

    Khait, Alexander

    2005-01-01

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

  8. Accurate Optical Reference Catalogs

    NASA Astrophysics Data System (ADS)

    Zacharias, N.

    2006-08-01

    Current and near future all-sky astrometric catalogs on the ICRF are reviewed with the emphasis on reference star data at optical wavelengths for user applications. The standard error of a Hipparcos Catalogue star position is now about 15 mas per coordinate. For the Tycho-2 data it is typically 20 to 100 mas, depending on magnitude. The USNO CCD Astrograph Catalog (UCAC) observing program was completed in 2004 and reductions toward the final UCAC3 release are in progress. This all-sky reference catalogue will have positional errors of 15 to 70 mas for stars in the 10 to 16 mag range, with a high degree of completeness. Proper motions for the about 60 million UCAC stars will be derived by combining UCAC astrometry with available early epoch data, including yet unpublished scans of the complete set of AGK2, Hamburg Zone astrograph and USNO Black Birch programs. Accurate positional and proper motion data are combined in the Naval Observatory Merged Astrometric Dataset (NOMAD) which includes Hipparcos, Tycho-2, UCAC2, USNO-B1, NPM+SPM plate scan data for astrometry, and is supplemented by multi-band optical photometry as well as 2MASS near infrared photometry. The Milli-Arcsecond Pathfinder Survey (MAPS) mission is currently being planned at USNO. This is a micro-satellite to obtain 1 mas positions, parallaxes, and 1 mas/yr proper motions for all bright stars down to about 15th magnitude. This program will be supplemented by a ground-based program to reach 18th magnitude on the 5 mas level.

  9. Mathematical Visualization

    ERIC Educational Resources Information Center

    Rogness, Jonathan

    2011-01-01

    Advances in computer graphics have provided mathematicians with the ability to create stunning visualizations, both to gain insight and to help demonstrate the beauty of mathematics to others. As educators these tools can be particularly important as we search for ways to work with students raised with constant visual stimulation, from video games…

  10. Underground Mathematics

    ERIC Educational Resources Information Center

    Hadlock, Charles R

    2013-01-01

    The movement of groundwater in underground aquifers is an ideal physical example of many important themes in mathematical modeling, ranging from general principles (like Occam's Razor) to specific techniques (such as geometry, linear equations, and the calculus). This article gives a self-contained introduction to groundwater modeling with…

  11. Relevant Mathematics.

    ERIC Educational Resources Information Center

    Catterton, Gene; And Others

    This material was developed to be used with the non college-bound student in the senior high school. It provides the student with everyday problems and experiences in which practical mathematical applications are made. The package includes worksheets pertaining to letterhead invoices, sales slips, payroll sheets, inventory sheets, carpentry and…

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

    ERIC Educational Resources Information Center

    Eisenberg, Michael

    2007-01-01

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

  13. Symmetry in Mathematics and Art: An Exploration of an Art Venue for Mathematics Learning

    ERIC Educational Resources Information Center

    Stylianou, Despina A.; Grzegorczyk, Ivona

    2005-01-01

    Symmetry is an aspect of mathematics that is strongly linked to art and design. We chose to explore this connection in the context of a liberal arts mathematics course. Here we present a brief description of this course, including an outline of the curriculum and specific features of the course. We subsequently present the results of a study we…

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

    ERIC Educational Resources Information Center

    Gafoor, Kunnathodi Abdul; Sarabi, M. K.

    2015-01-01

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

  15. A mathematical model for dynamic simulation of anaerobic digestion of complex substrates: Focusing on ammonia inhibition

    SciTech Connect

    Angelidaki, I.; Ellegaard, L.; Ahring, B.K. )

    1993-06-20

    A mathematical model for anaerobic degradation of complex organic material, such as manure, has been developed. The model includes an enzymatic hydrolytic step and four bacterial steps and involves 12 chemical compounds. The model focuses on ammonia inhibition and includes a detailed description of pH and temperature characteristics in order to accurately simulate free ammonia concentration. Free ammonia and acetate constitute the primary modulating factors in the model. The model has been applied for the simulation of digestion of cattle manure in continuously stirred tank reactors (CSTRs), and results compare favorably with experimental data.

  16. Mathematics Curriculum Guide. Mathematics IV.

    ERIC Educational Resources Information Center

    Gary City Public School System, IN.

    GRADES OR AGES: Grade 12. SUBJECT MATTER: Mathematics. ORGANIZATION AND PHYSICAL APPEARANCE: The subject matter is presented in four columns: major areas, significant outcomes, observations and suggestions, and films and references. The topics include: sets-relations-functions, circular functions, graphs of circular functions, inverses of circular…

  17. Constructing Meanings of Mathematical Registers Using Metaphorical Reasoning and Models

    ERIC Educational Resources Information Center

    Lai, Mun Yee

    2013-01-01

    Current debates about successful mathematics pedagogy suggest that mathematical learning and problem solving can be enhanced by using metaphors as they provide students with a tool for thinking. But assisting pre-service teachers to understand the importance of careful and accurate explanations for mathematical concepts remains an issue. This…

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

    NASA Technical Reports Server (NTRS)

    Gottlieb, D. M.

    1979-01-01

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

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

    NASA Astrophysics Data System (ADS)

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

    2008-02-01

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

  20. Accurate calculation of diffraction-limited encircled and ensquared energy.

    PubMed

    Andersen, Torben B

    2015-09-01

    Mathematical properties of the encircled and ensquared energy functions for the diffraction-limited point-spread function (PSF) are presented. These include power series and a set of linear differential equations that facilitate the accurate calculation of these functions. Asymptotic expressions are derived that provide very accurate estimates for the relative amount of energy in the diffraction PSF that fall outside a square or rectangular large detector. Tables with accurate values of the encircled and ensquared energy functions are also presented. PMID:26368873

  1. Accurate modeling of parallel scientific computations

    NASA Technical Reports Server (NTRS)

    Nicol, David M.; Townsend, James C.

    1988-01-01

    Scientific codes are usually parallelized by partitioning a grid among processors. To achieve top performance it is necessary to partition the grid so as to balance workload and minimize communication/synchronization costs. This problem is particularly acute when the grid is irregular, changes over the course of the computation, and is not known until load time. Critical mapping and remapping decisions rest on the ability to accurately predict performance, given a description of a grid and its partition. This paper discusses one approach to this problem, and illustrates its use on a one-dimensional fluids code. The models constructed are shown to be accurate, and are used to find optimal remapping schedules.

  2. Dilemma in Teaching Mathematics

    ERIC Educational Resources Information Center

    Md Kamaruddin, Nafisah Kamariah; Md Amin, Zulkarnain

    2012-01-01

    The challenge in mathematics education is finding the best way to teach mathematics. When students learn the reasoning and proving in mathematics, they will be proficient in mathematics. Students must know mathematics before they can apply it. Symbolism and logic is the key to both the learning of mathematics and its effective application to…

  3. Mathematical Models of Gene Regulation

    NASA Astrophysics Data System (ADS)

    Mackey, Michael C.

    2004-03-01

    This talk will focus on examples of mathematical models for the regulation of repressible operons (e.g. the tryptophan operon), inducible operons (e.g. the lactose operon), and the lysis/lysogeny switch in phage λ. These ``simple" gene regulatory elements can display characteristics experimentally of rapid response to perturbations and bistability, and biologically accurate mathematical models capture these aspects of the dynamics. The models, if realistic, are always nonlinear and contain significant time delays due to transcriptional and translational delays that pose substantial problems for the analysis of the possible ranges of dynamics.

  4. Three essays in mathematical finance

    NASA Astrophysics Data System (ADS)

    Wang, Ruming

    This dissertation uses mathematical techniques to solve three problems in mathematical finance. The first two problems are on model-independent pricing and hedging of financial derivatives. We use asymptotic expansions to express derivative prices and implied volatilities. Then just by using the first few terms in the expansions, we get simple and accurate formulas, which can also help us find connections between different products. The last problem is on optimal trading strategies in a limit order book. Under a very general setup, we solve explicitly for a dynamic decision problem involving choosing between limit order and market order.

  5. 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…

  6. Mathematizing Darwin.

    PubMed

    Edwards, A W F

    2011-03-01

    Ernst Mayr called the first part of the evolutionary synthesis the 'Fisherian synthesis' on account of the dominant role played by R.A. Fisher in forging a mathematical theory of natural selection together with J.B.S. Haldane and Sewall Wright in the decade 1922-1932. It is here argued that Fisher's contribution relied on a close reading of Darwin's work to a much greater extent than did the contributions of Haldane and Wright, that it was synthetic in contrast to their analytic approach and that it was greatly influenced by his friendship with the Darwin family, particularly with Charles's son Leonard. PMID:21423339

  7. A Multifaceted Mathematical Approach for Complex Systems

    SciTech Connect

    Alexander, F.; Anitescu, M.; Bell, J.; Brown, D.; Ferris, M.; Luskin, M.; Mehrotra, S.; Moser, B.; Pinar, A.; Tartakovsky, A.; Willcox, K.; Wright, S.; Zavala, V.

    2012-03-07

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

  8. Descriptive thermodynamics

    NASA Astrophysics Data System (ADS)

    Ford, David; Huntsman, Steven

    2006-06-01

    Thermodynamics (in concert with its sister discipline, statistical physics) can be regarded as a data reduction scheme based on partitioning a total system into a subsystem and a bath that weakly interact with each other. Whereas conventionally, the systems investigated require this form of data reduction in order to facilitate prediction, a different problem also occurs, in the context of communication networks, markets, etc. Such “empirically accessible” systems typically overwhelm observers with the sort of information that in the case of (say) a gas is effectively unobtainable. What is required for such complex interacting systems is not prediction (this may be impossible when humans besides the observer are responsible for the interactions) but rather, description as a route to understanding. Still, the need for a thermodynamical data reduction scheme remains. In this paper, we show how an empirical temperature can be computed for finite, empirically accessible systems, and further outline how this construction allows the age-old science of thermodynamics to be fruitfully applied to them.

  9. Authenticity of Mathematical Modeling

    ERIC Educational Resources Information Center

    Tran, Dung; Dougherty, Barbara J.

    2014-01-01

    Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…

  10. Computation and graphics in mathematical research. Progress report, June 1, 1991--May 31, 1992

    SciTech Connect

    Hoffman, D.A.; Spruck, J.

    1992-08-13

    This report discusses: The description of the GANG Project and results for prior research; the center for geometry, analysis, numerics and graphics; description of GANG Laboratory; software development at GANG; and mathematical and scientific research activities.

  11. The reasonable effectiveness of mathematics in the natural sciences

    NASA Astrophysics Data System (ADS)

    Harvey, Alex

    2011-12-01

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

  12. Mathematical Language and Advanced Mathematics Learning

    ERIC Educational Resources Information Center

    Ferrari, Pier Luigi

    2004-01-01

    This paper is concerned with the role of language in mathematics learning at college level. Its main aim is to provide a perspective on mathematical language appropriate to effectively interpret students' linguistic behaviors in mathematics and to suggest new teaching ideas. Examples are given to show that the explanation of students' behaviors…

  13. Mathematical Story: A Metaphor for Mathematics Curriculum

    ERIC Educational Resources Information Center

    Dietiker, Leslie

    2015-01-01

    This paper proposes a theoretical framework for interpreting the content found in mathematics curriculum in order to offer teachers and other mathematics educators comprehensive conceptual tools with which to make curricular decisions. More specifically, it describes a metaphor of "mathematics curriculum as story" and defines and…

  14. Mathematics for Life: Sustainable Mathematics Education

    ERIC Educational Resources Information Center

    Renert, Moshe

    2011-01-01

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

  15. 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…

  16. Mathematics Anxiety and Attitudes toward Mathematics.

    ERIC Educational Resources Information Center

    Rounds, James B., Jr.; Hendel, Darwin D.

    1980-01-01

    Results indicate that the Mathematics Anxiety Rating Scale and the Math Anxiety Scale measure similar components of mathematics-anxiety domain. Mathematics-anxiety scales and Fennema-Sherman scales of Confidence and Effectance Motivation measure similar affective domains and are approximately equal predictors of arithmetic performance. (Author)

  17. Number Sense in the Elementary School Mathematics Classroom.

    ERIC Educational Resources Information Center

    McBride, John W.; Lamb, Charles E.

    1986-01-01

    The number sense program in Texas was developed to help motivate students to learn mathematics and to literally develop "number sense." A description of the program, a 70-item exercise (with answers), and teaching tips are provided. (JN)

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

    NASA Astrophysics Data System (ADS)

    Limbaco, K. S. A.

    2015-03-01

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

  19. Bridging the Gap Between Common Sense and Mathematical Models

    ERIC Educational Resources Information Center

    Press, Laurence

    1975-01-01

    Describes a four-phase method of helping students who are mathematically unsophisticated and have difficulty relating their common sense, English-language understanding of a system to an abstract, mathematical description. The approach uses interactive simulation models. (Author/IRT)

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

    ERIC Educational Resources Information Center

    Cambridge Conference on School Mathematics, Newton, MA.

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

  1. The Necessary Teaching Competences for Mathematics Teachers in Middle Schools

    ERIC Educational Resources Information Center

    Alnoor, A. G.; xiang, G. Y.

    2007-01-01

    The professional competences of middle school mathematics teachers has been identified, also the significance extent of such competences for chinese and yemenies mathematics teachers has been studied. The researcher used descriptive research approach. The study data collected from Specialist educators and teachers experts to determine the…

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

    ERIC Educational Resources Information Center

    Lewis, Gareth

    2015-01-01

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

  3. [Representation and mathematical analysis of human corneal surface].

    PubMed

    Tălu, Stefan; Tălu, Mihai; Giovanzana, Stefano

    2011-01-01

    In the description and analysis of human corneal surface are used various mathematical models based on parametric representations, used in biomechanical studies and 3D solid modeling of the cornea. Mathematical models are important into the biomechanics of the cornea to model the corneal behavior. Corneal biomechanics also has the potential to improve outcomes in refractive surgery. The objective of this paper is to present the most representative mathematical models currently used for modeling of human corneal in optics and biomechanics fields.

  4. Projects in Higher Education Science, Mathematics, Engineering.

    ERIC Educational Resources Information Center

    National Science Foundation, Washington, DC.

    Presented are brief descriptions of the activities of the directors of projects related to new courses, curricula, teaching hardware, and other mechanisms designed to provide more and better learning experiences for students in areas of science, mathematics, and engineering in higher education. The publication provides information about these…

  5. Mathematical and Statistical Software Index. Final Report.

    ERIC Educational Resources Information Center

    Black, Doris E., Comp.

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

  6. Teaching Mathematics from a Chemist's Viewpoint.

    ERIC Educational Resources Information Center

    DeLorenzo, Ronald A.

    This paper describes a chemistry professor's approach to teaching mathematics in the college classroom. Based on the assumption that the four main goals of the educational process in general are to teach students to communicate clearly, study regularly, master basic math skills, and think logically, a description is provided of the manner in which…

  7. Classroom Instruction and Students' Attitudes Towards Mathematics

    ERIC Educational Resources Information Center

    Tessema, Taddesse G.

    2010-01-01

    This quantitative study examined the association between classroom instruction and students' attitudes towards mathematics at the secondary level. Data were collected through a Likert-type survey of Hope High School students and then analyzed for statistical significance by utilizing descriptive statistics, tests of significance, and correlation…

  8. Students as Mathematics Consultants

    ERIC Educational Resources Information Center

    Jensen, Jennifer L.

    2013-01-01

    If students are going to develop reasoning and thinking skills, use their mathematical knowledge, and recognize the relevance of mathematics in their lives, they need to experience mathematics in meaningful ways. Only then will their mathematical skills be transferrable to all other parts of their lives. To promote such flexible mathematical…

  9. Transforming Primary Mathematics

    ERIC Educational Resources Information Center

    Askew, Mike

    2011-01-01

    What is good mathematics teaching? What is mathematics teaching good for? Who is mathematics teaching for? These are just some of the questions addressed in "Transforming Primary Mathematics", a highly timely new resource for teachers which accessibly sets out the key theories and latest research in primary maths today. Under-pinned by findings…

  10. Mathematics for Real Life.

    ERIC Educational Resources Information Center

    Morsy, Zaghloul, Ed.; Draxler, Alexandra, Ed.

    1979-01-01

    A set of articles with the theme "Mathematics for Real Life" is presented. These article titles are: (1) Teaching Mathematics as a Tool for Problem Solving; (2) New Math or New Education; (3) Hand Calculators and Math in Primary School; (4) Mass Media in the Mathematical Training of Polish Primary Teachers; (5) The Goals of Mathematics Teaching in…

  11. Mathematical Epistemologies at Work.

    ERIC Educational Resources Information Center

    Noss, Richard

    2002-01-01

    Investigates young people's expression of mathematical ideas with a computer, the nature of mathematical practices, and the problem of mathematical meaning from cognitive and socio-cultural perspectives. Describes a mathematical activity system designed for learning and the role of digital technologies in helping to understand and reshape the…

  12. Functioning Mathematically: 1

    ERIC Educational Resources Information Center

    Cain, David

    2007-01-01

    This article presents the first part of the closing address given by the author to the 2007 Association of Teachers of Mathematics (ATM) Easter conference at Loughborough. In his closing address, the author focuses on functioning mathematically as opposed to functional mathematics. His view of functional mathematics is that the focus is on someone…

  13. Mathematics Lessons without ...

    ERIC Educational Resources Information Center

    Cross, Kath; Hibbs, John

    2006-01-01

    In the Association of Teachers of Mathematics (ATM) Easter conference, 2006, the authors presented a list of important aspects of mathematics lessons, recommended for students to have a positive attitude to mathematics and for teachers to acquire effective teaching. The following are discussed in detail: (1) Mathematics lessons without good…

  14. Accurate basis set truncation for wavefunction embedding

    NASA Astrophysics Data System (ADS)

    Barnes, Taylor A.; Goodpaster, Jason D.; Manby, Frederick R.; Miller, Thomas F.

    2013-07-01

    Density functional theory (DFT) provides a formally exact framework for performing embedded subsystem electronic structure calculations, including DFT-in-DFT and wavefunction theory-in-DFT descriptions. In the interest of efficiency, it is desirable to truncate the atomic orbital basis set in which the subsystem calculation is performed, thus avoiding high-order scaling with respect to the size of the MO virtual space. In this study, we extend a recently introduced projection-based embedding method [F. R. Manby, M. Stella, J. D. Goodpaster, and T. F. Miller III, J. Chem. Theory Comput. 8, 2564 (2012)], 10.1021/ct300544e to allow for the systematic and accurate truncation of the embedded subsystem basis set. The approach is applied to both covalently and non-covalently bound test cases, including water clusters and polypeptide chains, and it is demonstrated that errors associated with basis set truncation are controllable to well within chemical accuracy. Furthermore, we show that this approach allows for switching between accurate projection-based embedding and DFT embedding with approximate kinetic energy (KE) functionals; in this sense, the approach provides a means of systematically improving upon the use of approximate KE functionals in DFT embedding.

  15. Cardiovascular response to dynamic aerobic exercise: a mathematical model.

    PubMed

    Magosso, E; Ursino, M

    2002-11-01

    An original mathematical model of the cardiovascular response to dynamic exercise is presented. It includes the pulsating heart, the pulmonary and systemic circulation, a separate description of the vascular bed in active tissues, the local metabolic vasodilation in these tissues and the mechanical effects of muscular contractions on venous return. Moreover, the model provides a description of the ventilatory response to exercise and various neural regulatory mechanisms working on cardiovascular parameters. These mechanisms embrace the so-called central command, the arterial baroreflex and the lung inflation reflex. All parameters in the model have been given in accordance with physiological data from the literature. In this work, the model has been used to simulate the steady-state value of the main cardiorespiratory quantities at different levels of aerobic exercise and the temporal pattern in the transient phase from rest to moderate exercise. Results suggest that, with suitable parameter values the model is able accurately to simulate the cardiorespiratory response in the overall range of aerobic exercise. This response is characterised by a moderate hypertension (10-30%) and by a conspicuous increase in systemic conductance (80-130%), heart rate (64-150%) and cardiac output (100-200%). The transient pattern exhibits three distinct phases (lasting approximately 5s, 15s and 2 min), that reflect the temporal heterogeneity of the mechanisms involved. The model may be useful to improve understanding of exercise physiology and as an educational tool to analyse the complexity of cardiovascular and respiratory regulation.

  16. Cardiovascular response to dynamic aerobic exercise: a mathematical model.

    PubMed

    Magosso, E; Ursino, M

    2002-11-01

    An original mathematical model of the cardiovascular response to dynamic exercise is presented. It includes the pulsating heart, the pulmonary and systemic circulation, a separate description of the vascular bed in active tissues, the local metabolic vasodilation in these tissues and the mechanical effects of muscular contractions on venous return. Moreover, the model provides a description of the ventilatory response to exercise and various neural regulatory mechanisms working on cardiovascular parameters. These mechanisms embrace the so-called central command, the arterial baroreflex and the lung inflation reflex. All parameters in the model have been given in accordance with physiological data from the literature. In this work, the model has been used to simulate the steady-state value of the main cardiorespiratory quantities at different levels of aerobic exercise and the temporal pattern in the transient phase from rest to moderate exercise. Results suggest that, with suitable parameter values the model is able accurately to simulate the cardiorespiratory response in the overall range of aerobic exercise. This response is characterised by a moderate hypertension (10-30%) and by a conspicuous increase in systemic conductance (80-130%), heart rate (64-150%) and cardiac output (100-200%). The transient pattern exhibits three distinct phases (lasting approximately 5s, 15s and 2 min), that reflect the temporal heterogeneity of the mechanisms involved. The model may be useful to improve understanding of exercise physiology and as an educational tool to analyse the complexity of cardiovascular and respiratory regulation. PMID:12507317

  17. Mapping Pedagogical Opportunities Provided by Mathematics Analysis Software

    ERIC Educational Resources Information Center

    Pierce, Robyn; Stacey, Kaye

    2010-01-01

    This paper proposes a taxonomy of the pedagogical opportunities that are offered by mathematics analysis software such as computer algebra systems, graphics calculators, dynamic geometry or statistical packages. Mathematics analysis software is software for purposes such as calculating, drawing graphs and making accurate diagrams. However, its…

  18. Classroom Aids for Mathematics, Volume 1: Polynomials.

    ERIC Educational Resources Information Center

    Holden, Herbert L.

    The goal of this pamphlet is to provide instructors of various scientific disciplines with mathematically accurate graphs of elementary polynomial functions. The figures in this pamphlet are intended to provide suitable material for the preparation of classroom handouts and overhead transparencies. In addition, sample sets of exercises are…

  19. Mathematics of Information Processing and the Internet

    ERIC Educational Resources Information Center

    Hart, Eric W.

    2010-01-01

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

  20. Profitable capitation requires accurate costing.

    PubMed

    West, D A; Hicks, L L; Balas, E A; West, T D

    1996-01-01

    In the name of costing accuracy, nurses are asked to track inventory use on per treatment basis when more significant costs, such as general overhead and nursing salaries, are usually allocated to patients or treatments on an average cost basis. Accurate treatment costing and financial viability require analysis of all resources actually consumed in treatment delivery, including nursing services and inventory. More precise costing information enables more profitable decisions as is demonstrated by comparing the ratio-of-cost-to-treatment method (aggregate costing) with alternative activity-based costing methods (ABC). Nurses must participate in this costing process to assure that capitation bids are based upon accurate costs rather than simple averages. PMID:8788799

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

    ERIC Educational Resources Information Center

    Silver, Edward A.; Lane, Suzanne

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

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

    ERIC Educational Resources Information Center

    Wasserman, Nicholas H.

    2015-01-01

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

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

    ERIC Educational Resources Information Center

    Salani, End

    2013-01-01

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

  4. Mathematical Modelling: A New Approach to Teaching Applied Mathematics.

    ERIC Educational Resources Information Center

    Burghes, D. N.; Borrie, M. S.

    1979-01-01

    Describes the advantages of mathematical modeling approach in teaching applied mathematics and gives many suggestions for suitable material which illustrates the links between real problems and mathematics. (GA)

  5. Mathematics and Sports. Mathematical World. Volume 3.

    ERIC Educational Resources Information Center

    Sadovskii, L. E.; Sadovskii, A. L.

    This volume contains some examples of mathematical applications in sports. Sports discussed include tennis, figure skating, gymnastics, track and field, soccer, skiing, hockey, and swimming. Problems and situations are posed and answers with thorough explanations are provided. Chapters include: (1) Mathematics and Sports; (2) What Is Applied…

  6. Mathematics Coursework Regulates Growth in Mathematics Achievement

    ERIC Educational Resources Information Center

    Ma, Xin; Wilkins, Jesse L. M.

    2007-01-01

    Using data from the Longitudinal Study of American Youth (LSAY), we examined the extent to which students' mathematics coursework regulates (influences) the rate of growth in mathematics achievement during middle and high school. Graphical analysis showed that students who started middle school with higher achievement took individual mathematics…

  7. Mathematics for Language, Language for Mathematics

    ERIC Educational Resources Information Center

    Prochazkova, Lenka Tejkalova

    2013-01-01

    The author discusses the balance and mutual influence of the language of instruction and mathematics in the context of CLIL, Content and Language Integrated Learning. Different aspects of the relationship of language and Mathematics teaching and learning are discussed: the benefits of using a foreign language of instruction, as well as the…

  8. Negotiation of Mathematical Meaning and Learning Mathematics.

    ERIC Educational Resources Information Center

    Voigt, Jorg

    1994-01-01

    Presents a case study of a first-grade class and their teacher who were observed as they ascribed mathematical meanings of numbers and of numerical operations to empirical phenomena. Differences in ascriptions led to negotiation of meanings. Discusses some indirect relations between social interaction and mathematics learning. (Contains 60…

  9. Accurate documentation and wound measurement.

    PubMed

    Hampton, Sylvie

    This article, part 4 in a series on wound management, addresses the sometimes routine yet crucial task of documentation. Clear and accurate records of a wound enable its progress to be determined so the appropriate treatment can be applied. Thorough records mean any practitioner picking up a patient's notes will know when the wound was last checked, how it looked and what dressing and/or treatment was applied, ensuring continuity of care. Documenting every assessment also has legal implications, demonstrating due consideration and care of the patient and the rationale for any treatment carried out. Part 5 in the series discusses wound dressing characteristics and selection.

  10. Perspectives from Mathematics Education.

    ERIC Educational Resources Information Center

    Sowder, Judith Threadgill

    1998-01-01

    Explores possible reasons for the gender differences in mathematics problem-solving strategies found in primary-grade students in the study by E. Fennema and others and considers implications of the findings for mathematics instruction. (SLD)

  11. Mathematical and statistical analysis

    NASA Technical Reports Server (NTRS)

    Houston, A. Glen

    1988-01-01

    The goal of the mathematical and statistical analysis component of RICIS is to research, develop, and evaluate mathematical and statistical techniques for aerospace technology applications. Specific research areas of interest include modeling, simulation, experiment design, reliability assessment, and numerical analysis.

  12. Developing My Mathematics Identity

    ERIC Educational Resources Information Center

    Gonzalez, Lidia

    2016-01-01

    Assuming the role of storyteller, the author uses her experiences as a graduate student and beginning teacher to reflect critically on issues related to mathematics, mathematics education, gender, and diversity.

  13. Mental Mathematics Moves Ahead.

    ERIC Educational Resources Information Center

    Jones, Pamela

    1988-01-01

    The author suggests that the efficient use of mathematics in everyday life means translating situations into mathematical contexts, using a calculator and mental methods of calculation. Suggestions for teaching these concepts are included. (PK)

  14. Soft Biometrics; Human Identification Using Comparative Descriptions.

    PubMed

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

    2014-06-01

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

  15. Soft Biometrics; Human Identification Using Comparative Descriptions.

    PubMed

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

    2014-06-01

    Soft biometrics are a new form of biometric identification which use physical or behavioral traits that can be naturally described by humans. Unlike other biometric approaches, this allows identification based solely on verbal descriptions, bridging the semantic gap between biometrics and human description. To permit soft biometric identification the description must be accurate, yet conventional human descriptions comprising of absolute labels and estimations are often unreliable. A novel method of obtaining human descriptions will be introduced which utilizes comparative categorical labels to describe differences between subjects. This innovative approach has been shown to address many problems associated with absolute categorical labels-most critically, the descriptions contain more objective information and have increased discriminatory capabilities. Relative measurements of the subjects' traits can be inferred from comparative human descriptions using the Elo rating system. The resulting soft biometric signatures have been demonstrated to be robust and allow accurate recognition of subjects. Relative measurements can also be obtained from other forms of human representation. This is demonstrated using a support vector machine to determine relative measurements from gait biometric signatures-allowing retrieval of subjects from video footage by using human comparisons, bridging the semantic gap. PMID:26353282

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

    ERIC Educational Resources Information Center

    Barwell, Richard

    2013-01-01

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

  17. Mathematics for Electronics.

    ERIC Educational Resources Information Center

    Clary, Joseph R.; Nery, Karen P.

    This set of 20 modules was designed for use primarily to help teach and reinforce the basic mathematics skills in electronics classes. The modules are based on electronics competencies that require mathematics skills, as determined by a panel of high school electronics and mathematics teachers. Each module consists of one or two pages of basic…

  18. Making Mathematics Phenomenal

    ERIC Educational Resources Information Center

    Pratt, Dave

    2012-01-01

    Mathematics is often portrayed as an "abstract" cerebral subject, beyond the reach of many. In response, research with digital technology has led to innovative design in which mathematics can be experienced much like everyday phenomena. This lecture examines how careful design can "phenomenalise" mathematics and support not only engagement but…

  19. Translations toward Connected Mathematics

    ERIC Educational Resources Information Center

    Applebaum, Mark; Leikin, Roza

    2010-01-01

    The translation principle allows students to solve problems in different branches of mathematics and thus to develop connectedness in their mathematical knowledge. Successful application of the translation principle depends on the classroom mathematical norms for the development of discussions and the comparison of different solutions to one…

  20. Mathematics and Comprehensive Ideals

    ERIC Educational Resources Information Center

    Watson, Anne

    2011-01-01

    This article revisits methods and debates about teaching mathematics that were common in the 1980s and early 1990s, and then moves up to date with the findings from three mathematics departments that set out to make a difference for their lowest attaining students. The methods they used were distinctly focused on core mathematical ideas, and how…

  1. Winning Women into Mathematics.

    ERIC Educational Resources Information Center

    Kenschaft, Patricia Clark, Ed.; Keith, Sandra Zaroodny, Ed.

    Mathematics is an auspicious discipline for young people of both sexes and all ethnic groups. This booklet aims to help members of the Mathematical Association of America (MAA) and others to increase future participation of women in mathematics, to better understand their present roles, and to develop a vision of a world with greater equal…

  2. Mathematics Teaching Today

    ERIC Educational Resources Information Center

    Martin, Tami S.; Speer, William R.

    2009-01-01

    This article describes features, consistent messages, and new components of "Mathematics Teaching Today: Improving Practice, Improving Student Learning" (NCTM 2007), an updated edition of "Professional Standards for Teaching Mathematics" (NCTM 1991). The new book describes aspects of high-quality mathematics teaching; offers a model for observing,…

  3. Revisiting Mathematics Manipulative Materials

    ERIC Educational Resources Information Center

    Swan, Paul; Marshall, Linda

    2010-01-01

    It is over 12 years since "APMC" published Bob Perry and Peter Howard's research on the use of mathematics manipulative materials in primary mathematics classrooms. Since then the availability of virtual manipulatives and associated access to computers and interactive whiteboards have caused educators to rethink the use of mathematics manipulative…

  4. Mathematics and Global Survival.

    ERIC Educational Resources Information Center

    Schwartz, Richard H.

    This resource was written to provide students with an awareness of critical issues facing the world today. In courses for college students, it can motivate their study of mathematics, teach them how to solve mathematical problems related to current global issues, provide coherence to mathematical studies through a focus on issues of human…

  5. Who Can Know Mathematics?

    ERIC Educational Resources Information Center

    Walshaw, Margaret

    2014-01-01

    This paper explores contemporary thinking about learning mathematics, and within that, social justice within mathematics education. The discussion first looks at mechanisms offered by conventional explanations on the emancipatory project and then moves towards more recent insights developed within mathematics education. Synergies are drawn between…

  6. Making Mathematics Culturally Relevant.

    ERIC Educational Resources Information Center

    Moyer, Patricia

    2001-01-01

    Examines three strands of elementary mathematics--numerals and counting, recording and calculating, and mathematics exploration and play--and provides ways to integrate culture and mathematics experiences in each area. Specific topics include Egyptian methods for multiplication, the abacus, and the words for the numbers 1-10 in seven different…

  7. Mathematical Epistemologies at Work.

    ERIC Educational Resources Information Center

    Noss, Richard

    In this paper, I draw together a corpus of findings derived from two sources: studies of students using computers to learn mathematics, and research into the use of mathematics in professional practice. Using this as a basis, I map some elements of a theoretical framework for understanding the nature of mathematical knowledge in use, and how it is…

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

    ERIC Educational Resources Information Center

    Darlington, Ellie

    2014-01-01

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

  9. Mathematics and Sports

    ERIC Educational Resources Information Center

    Gallian, Joseph A., Ed.

    2010-01-01

    "Mathematics and Sports", edited by Joseph A. Gallian, gathers 25 articles that illuminate the power and role of mathematics in the worlds of professional and recreational play. Divided into sections by the kind of sports, the book offers source materials for classroom use and student projects. Readers will encounter mathematical ideas from an…

  10. A "Mathematics Background Check"

    ERIC Educational Resources Information Center

    Hubisz, John

    2009-01-01

    Early in my career someone else reported that the best indicator of success in calculus-based physics (CBP) at our school was whether students had taken mathematics in a certain region of New Brunswick. I sat down with a very longtime mathematics teacher and asked him what he thought students should know in mathematics after high school to succeed…

  11. Topics in Mathematics.

    ERIC Educational Resources Information Center

    Posey, Johnsie Jo, Ed.; And Others

    This manual is a collection of materials and teaching strategies to motivate the development of mathematical ideas in secondary school mathematics programs or in beginning college mathematics programs. The unit is written for the instructor with step-by-step procedures including lists of needed materials. The exercises in this unit also appear in…

  12. Mathematics and Mobile Learning

    ERIC Educational Resources Information Center

    Sayed, Fayez

    2015-01-01

    The wide range of Mathematical Apps targeting different mathematical concepts and the various types of mobile devices available present a demanding and challenging problem to the teaching and learning in the field of mathematics. In an attempt to address this issue, a few Apps were selected, implemented and tested in this work. [For complete…

  13. Latinos and Mathematics.

    ERIC Educational Resources Information Center

    Ortiz-Franco, Luis

    An historical perspective reveals that sophisticated mathematical activity has been going on in the Latino culture for thousands of years. This paper provides a general definition of the area of mathematics education that deals with issues of culture and mathematics (ethnomathematics) and defines what is meant by the term Latino in this essay.…

  14. Mathenger Hunt: Mathematics Matters.

    ERIC Educational Resources Information Center

    Falba, Christy J.; Weiss, Maria J.

    1991-01-01

    Presented is an activity which shows how mathematics is used in real life and helps to establish a need for mathematics in students' futures. Adapted from a scavenger-hunt idea, this activity helps students to discover that almost every career makes use of mathematics. (KR)

  15. Mathematics. [SITE 2001 Section].

    ERIC Educational Resources Information Center

    Connell, Michael L., Ed.; Lowery, Norene Vail, Ed.; Harnisch, Delwyn L., Ed.

    This document contains the following papers on mathematics from the SITE (Society for Information Technology & Teacher Education) 2001 conference: "Secondary Mathematics Methods Course with Technology Units: Encouraging Pre-Service Teachers To Use Technology" (Rajee Amarasinghe); "Competency Exams in College Mathematics" (Kathy R. Autrey and Leigh…

  16. Applying Mathematical Processes (AMP)

    ERIC Educational Resources Information Center

    Kathotia, Vinay

    2011-01-01

    This article provides insights into the "Applying Mathematical Processes" resources, developed by the Nuffield Foundation. It features Nuffield AMP activities--and related ones from Bowland Maths--that were designed to support the teaching and assessment of key processes in mathematics--representing a situation mathematically, analysing,…

  17. Mathematics and mysticism.

    PubMed

    Abraham, Ralph

    2015-12-01

    Is there a world of mathematics above and beyond ordinary reality, as Plato proposed? Or is mathematics a cultural construct? In this short article we speculate on the place of mathematical reality from the perspective of the mystical cosmologies of the ancient traditions of meditation, psychedelics, and divination.

  18. Creating Words in Mathematics

    ERIC Educational Resources Information Center

    Galligan, Linda

    2016-01-01

    A "National Numeracy Report" and the Australian Curriculum (2014) have recognised the importance of language in mathematics. The general capabilities contained within the "Australian Curriculum: Mathematics" (2014) highlight literacy as an important tool in the teaching and learning of mathematics, from the interpretation of…

  19. SPLASH: Accurate OH maser positions

    NASA Astrophysics Data System (ADS)

    Walsh, Andrew; Gomez, Jose F.; Jones, Paul; Cunningham, Maria; Green, James; Dawson, Joanne; Ellingsen, Simon; Breen, Shari; Imai, Hiroshi; Lowe, Vicki; Jones, Courtney

    2013-10-01

    The hydroxyl (OH) 18 cm lines are powerful and versatile probes of diffuse molecular gas, that may trace a largely unstudied component of the Galactic ISM. SPLASH (the Southern Parkes Large Area Survey in Hydroxyl) is a large, unbiased and fully-sampled survey of OH emission, absorption and masers in the Galactic Plane that will achieve sensitivities an order of magnitude better than previous work. In this proposal, we request ATCA time to follow up OH maser candidates. This will give us accurate (~10") positions of the masers, which can be compared to other maser positions from HOPS, MMB and MALT-45 and will provide full polarisation measurements towards a sample of OH masers that have not been observed in MAGMO.

  20. Accurate thickness measurement of graphene

    NASA Astrophysics Data System (ADS)

    Shearer, Cameron J.; Slattery, Ashley D.; Stapleton, Andrew J.; Shapter, Joseph G.; Gibson, Christopher T.

    2016-03-01

    Graphene has emerged as a material with a vast variety of applications. The electronic, optical and mechanical properties of graphene are strongly influenced by the number of layers present in a sample. As a result, the dimensional characterization of graphene films is crucial, especially with the continued development of new synthesis methods and applications. A number of techniques exist to determine the thickness of graphene films including optical contrast, Raman scattering and scanning probe microscopy techniques. Atomic force microscopy (AFM), in particular, is used extensively since it provides three-dimensional images that enable the measurement of the lateral dimensions of graphene films as well as the thickness, and by extension the number of layers present. However, in the literature AFM has proven to be inaccurate with a wide range of measured values for single layer graphene thickness reported (between 0.4 and 1.7 nm). This discrepancy has been attributed to tip-surface interactions, image feedback settings and surface chemistry. In this work, we use standard and carbon nanotube modified AFM probes and a relatively new AFM imaging mode known as PeakForce tapping mode to establish a protocol that will allow users to accurately determine the thickness of graphene films. In particular, the error in measuring the first layer is reduced from 0.1-1.3 nm to 0.1-0.3 nm. Furthermore, in the process we establish that the graphene-substrate adsorbate layer and imaging force, in particular the pressure the tip exerts on the surface, are crucial components in the accurate measurement of graphene using AFM. These findings can be applied to other 2D materials.

  1. Accurate thickness measurement of graphene.

    PubMed

    Shearer, Cameron J; Slattery, Ashley D; Stapleton, Andrew J; Shapter, Joseph G; Gibson, Christopher T

    2016-03-29

    Graphene has emerged as a material with a vast variety of applications. The electronic, optical and mechanical properties of graphene are strongly influenced by the number of layers present in a sample. As a result, the dimensional characterization of graphene films is crucial, especially with the continued development of new synthesis methods and applications. A number of techniques exist to determine the thickness of graphene films including optical contrast, Raman scattering and scanning probe microscopy techniques. Atomic force microscopy (AFM), in particular, is used extensively since it provides three-dimensional images that enable the measurement of the lateral dimensions of graphene films as well as the thickness, and by extension the number of layers present. However, in the literature AFM has proven to be inaccurate with a wide range of measured values for single layer graphene thickness reported (between 0.4 and 1.7 nm). This discrepancy has been attributed to tip-surface interactions, image feedback settings and surface chemistry. In this work, we use standard and carbon nanotube modified AFM probes and a relatively new AFM imaging mode known as PeakForce tapping mode to establish a protocol that will allow users to accurately determine the thickness of graphene films. In particular, the error in measuring the first layer is reduced from 0.1-1.3 nm to 0.1-0.3 nm. Furthermore, in the process we establish that the graphene-substrate adsorbate layer and imaging force, in particular the pressure the tip exerts on the surface, are crucial components in the accurate measurement of graphene using AFM. These findings can be applied to other 2D materials.

  2. Scaffolding students' opportunities to learn mathematics through social interactions

    NASA Astrophysics Data System (ADS)

    Bell, Clare V.; Pape, Stephen J.

    2012-12-01

    In this study, we take a sociocultural perspective on teaching and learning to examine how teachers in an urban Algebra 1 classroom constructed opportunities to learn. Drawing on analyses of discourse practices, including videotaped classroom lessons as well as other classroom artifacts and telephone interviews, we describe ways that two teachers and their students interacted to develop mathematical understanding. Through descriptive narrative, we highlight practices that positioned students as competent mathematical thinkers and provided evidence of students' mathematical agency. This study suggests that critical awareness of discourse practices in conjunction with teacher mediation of other affordances for learning within the classroom environment might engage students in mathematical practices such as problem solving, explaining mathematical ideas, arguing for or against specific solutions to problems, and justifying mathematical thinking.

  3. The History of Mathematics and Mathematical Education

    ERIC Educational Resources Information Center

    Grattan-Guinness, I.

    1977-01-01

    Answers to questions which were asked after the author's various lectures in Australia are gathered here. Topics touched upon include "new" mathematics, unknown constants and free variables, propositional functions, linear algebra, arithmetic and geometry, and student assessment. (MN)

  4. Acquisition of teleological descriptions

    NASA Astrophysics Data System (ADS)

    Franke, David W.

    1992-03-01

    Teleology descriptions capture the purpose of an entity, mechanism, or activity with which they are associated. These descriptions can be used in explanation, diagnosis, and design reuse. We describe a technique for acquiring teleological descriptions expressed in the teleology language TeD. Acquisition occurs during design by observing design modifications and design verification. We demonstrate the acquisition technique in an electronic circuit design.

  5. Writing job descriptions.

    PubMed

    Schaffner, M

    1990-01-01

    The skill of writing job descriptions begins with an understanding of the advantages, as well as the basic elements, of a well written description. The end result should be approved and updated as needed. Having a better understanding of this process makes writing the job description a challenge rather than a chore.

  6. Experimental and Mathematical-Modeling Characterization of Trypanosoma cruzi Epimastigote Motility.

    PubMed

    Sosa-Hernández, Eduardo; Ballesteros-Rodea, Gilberto; Arias-Del-Angel, Jorge A; Dévora-Canales, Diego; Manning-Cela, Rebeca G; Santana-Solano, Jesús; Santillán, Moisés

    2015-01-01

    The present work is aimed at characterizing the motility of parasite T. cruzi in its epimastigote form. To that end, we recorded the trajectories of two strains of this parasite (a wild-type strain and a stable transfected strain, which contains an ectopic copy of LYT1 gene and whose motility is known to be affected). We further extracted parasite trajectories from the recorded videos, and statistically analysed the following trajectory-step features: step length, angular change of direction, longitudinal and transverse displacements with respect to the previous step, and mean square displacement. Based on the resulting observations, we developed a mathematical model to simulate parasite trajectories. The fact that the model predictions closely match most of the experimentally observed parasite-trajectory characteristics, allows us to conclude that the model is an accurate description of T. cruzi motility. PMID:26544863

  7. Experimental and Mathematical-Modeling Characterization of Trypanosoma cruzi Epimastigote Motility

    PubMed Central

    Arias-del-Angel, Jorge A.; Dévora-Canales, Diego; Manning-Cela, Rebeca G.; Santana-Solano, Jesús; Santillán, Moisés

    2015-01-01

    The present work is aimed at characterizing the motility of parasite T. cruzi in its epimastigote form. To that end, we recorded the trajectories of two strains of this parasite (a wild-type strain and a stable transfected strain, which contains an ectopic copy of LYT1 gene and whose motility is known to be affected). We further extracted parasite trajectories from the recorded videos, and statistically analysed the following trajectory-step features: step length, angular change of direction, longitudinal and transverse displacements with respect to the previous step, and mean square displacement. Based on the resulting observations, we developed a mathematical model to simulate parasite trajectories. The fact that the model predictions closely match most of the experimentally observed parasite-trajectory characteristics, allows us to conclude that the model is an accurate description of T. cruzi motility. PMID:26544863

  8. Conceptions of mathematics and student identity: implications for engineering education

    NASA Astrophysics Data System (ADS)

    Craig, Tracy S.

    2013-10-01

    Lecturers of first-year mathematics often have reason to believe that students enter university studies with naïve conceptions of mathematics and that more mature conceptions need to be developed in the classroom. Students' conceptions of the nature and role of mathematics in current and future studies as well as future career are pedagogically important as they can impact on student learning and have the potential to influence how and what we teach. As part of ongoing longitudinal research into the experience of a cohort of students registered at the author's institution, students' conceptions of mathematics were determined using a coding scheme developed elsewhere. In this article, I discuss how the cohort of students choosing to study engineering exhibits a view of mathematics as conceptual skill and as problem-solving, coherent with an accurate understanding of the role of mathematics in engineering. Parallel investigation shows, however, that the students do not embody designated identities as engineers.

  9. Joint Control and the Selection of Stimuli from Their Description

    ERIC Educational Resources Information Center

    Lowenkron, Barry

    2006-01-01

    This research examined the role the two constituents of joint control, the tact and the echoic, play in producing accurate selections of novel stimuli in response to their spoken descriptions. Experiment 1 examined the role of tacts. In response to unfamiliar spoken descriptions, children learned to select from among six successively presented…

  10. Early childhood mathematics intervention.

    PubMed

    Clements, Douglas H; Sarama, Julie

    2011-08-19

    Preschool and primary grade children have the capacity to learn substantial mathematics, but many children lack opportunities to do so. Too many children not only start behind their more advantaged peers, but also begin a negative trajectory in mathematics. Interventions designed to facilitate their mathematical learning during ages 3 to 5 years have a strong positive effect on these children's lives for many years thereafter.

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

    PubMed

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

    2014-01-01

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

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

    PubMed Central

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

    2014-01-01

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

  13. Mathematical Ties That Bind.

    ERIC Educational Resources Information Center

    House, Peggy A.

    1994-01-01

    Describes some mathematical investigations of the necktie which includes applications of geometry, statistics, data analysis, sampling, probability, symmetry, proportion, problem solving, and business. (MKR)

  14. The emerging and emergent present: a view on the indeterminate nature of mathematics lessons

    NASA Astrophysics Data System (ADS)

    Roth, Wolff-Michael; Maheux, Jean-François

    2014-06-01

    The notion of emergence has considerable currency in mathematics education. However, the notion tends to be used in a descriptive way rather than being theorized and developed as a phenomenon sui generis. The purpose of this article is to contribute to building a theory of emergence. After providing an exemplifying description and analysis of an episode from a second-grade mathematics classroom studying three-dimensional geometry, we discuss implications for theoretical and classroom praxis in mathematics education, especially for the curriculum planning and the preparation, training, and enhancement of teachers of mathematics.

  15. Mathematical modelling of microtumour infiltration based on in vitro experiments.

    PubMed

    Luján, Emmanuel; Guerra, Liliana N; Soba, Alejandro; Visacovsky, Nicolás; Gandía, Daniel; Calvo, Juan C; Suárez, Cecilia

    2016-08-01

    The present mathematical models of microtumours consider, in general, volumetric growth and spherical tumour invasion shapes. Nevertheless in many cases, such as in gliomas, a need for more accurate delineation of tumour infiltration areas in a patient-specific manner has arisen. The objective of this study was to build a mathematical model able to describe in a case-specific way as well as to predict in a probabilistic way the growth and the real invasion pattern of multicellular tumour spheroids (in vitro model of an avascular microtumour) immersed in a collagen matrix. The two-dimensional theoretical model was represented by a reaction-convection-diffusion equation that considers logistic proliferation, volumetric growth, a rim with proliferative cells at the tumour surface and invasion with diffusive and convective components. Population parameter values of the model were extracted from the experimental dataset and a shape function that describes the invasion area was derived from each experimental case by image processing. New possible and aleatory shape functions were generated by data mining and Monte Carlo tools by means of a satellite EGARCH model, which were fed with all the shape functions of the dataset. Then the main model is used in two different ways: to reproduce the growth and invasion of a given experimental tumour in a case-specific manner when fed with the corresponding shape function (descriptive simulations) or to generate new possible tumour cases that respond to the general population pattern when fed with an aleatory-generated shape function (predictive simulations). Both types of simulations are in good agreement with empirical data, as it was revealed by area quantification and Bland-Altman analysis. This kind of experimental-numerical interaction has wide application potential in designing new strategies able to predict as much as possible the invasive behaviour of a tumour based on its particular characteristics and microenvironment

  16. Mathematical modelling of microtumour infiltration based on in vitro experiments.

    PubMed

    Luján, Emmanuel; Guerra, Liliana N; Soba, Alejandro; Visacovsky, Nicolás; Gandía, Daniel; Calvo, Juan C; Suárez, Cecilia

    2016-08-01

    The present mathematical models of microtumours consider, in general, volumetric growth and spherical tumour invasion shapes. Nevertheless in many cases, such as in gliomas, a need for more accurate delineation of tumour infiltration areas in a patient-specific manner has arisen. The objective of this study was to build a mathematical model able to describe in a case-specific way as well as to predict in a probabilistic way the growth and the real invasion pattern of multicellular tumour spheroids (in vitro model of an avascular microtumour) immersed in a collagen matrix. The two-dimensional theoretical model was represented by a reaction-convection-diffusion equation that considers logistic proliferation, volumetric growth, a rim with proliferative cells at the tumour surface and invasion with diffusive and convective components. Population parameter values of the model were extracted from the experimental dataset and a shape function that describes the invasion area was derived from each experimental case by image processing. New possible and aleatory shape functions were generated by data mining and Monte Carlo tools by means of a satellite EGARCH model, which were fed with all the shape functions of the dataset. Then the main model is used in two different ways: to reproduce the growth and invasion of a given experimental tumour in a case-specific manner when fed with the corresponding shape function (descriptive simulations) or to generate new possible tumour cases that respond to the general population pattern when fed with an aleatory-generated shape function (predictive simulations). Both types of simulations are in good agreement with empirical data, as it was revealed by area quantification and Bland-Altman analysis. This kind of experimental-numerical interaction has wide application potential in designing new strategies able to predict as much as possible the invasive behaviour of a tumour based on its particular characteristics and microenvironment.

  17. Towards Accurate Application Characterization for Exascale (APEX)

    SciTech Connect

    Hammond, Simon David

    2015-09-01

    Sandia National Laboratories has been engaged in hardware and software codesign activities for a number of years, indeed, it might be argued that prototyping of clusters as far back as the CPLANT machines and many large capability resources including ASCI Red and RedStorm were examples of codesigned solutions. As the research supporting our codesign activities has moved closer to investigating on-node runtime behavior a nature hunger has grown for detailed analysis of both hardware and algorithm performance from the perspective of low-level operations. The Application Characterization for Exascale (APEX) LDRD was a project concieved of addressing some of these concerns. Primarily the research was to intended to focus on generating accurate and reproducible low-level performance metrics using tools that could scale to production-class code bases. Along side this research was an advocacy and analysis role associated with evaluating tools for production use, working with leading industry vendors to develop and refine solutions required by our code teams and to directly engage with production code developers to form a context for the application analysis and a bridge to the research community within Sandia. On each of these accounts significant progress has been made, particularly, as this report will cover, in the low-level analysis of operations for important classes of algorithms. This report summarizes the development of a collection of tools under the APEX research program and leaves to other SAND and L2 milestone reports the description of codesign progress with Sandia’s production users/developers.

  18. Mathematics for Teaching: A Form of Applied Mathematics

    ERIC Educational Resources Information Center

    Stylianides, Gabriel J.; Stylianides, Andreas J.

    2010-01-01

    In this article we elaborate a conceptualisation of "mathematics for teaching" as a form of applied mathematics (using Bass's idea of characterising mathematics education as a form of applied mathematics) and we examine implications of this conceptualisation for the mathematical preparation of teachers. Specifically, we focus on issues of design…

  19. Using Mathematics Literature with Prospective Secondary Mathematics Teachers

    ERIC Educational Resources Information Center

    Jett, Christopher C.

    2014-01-01

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

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

    ERIC Educational Resources Information Center

    Johnson, Marvin L.

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

  1. Exploring Differential Effects of Mathematics Courses on Mathematics Achievement

    ERIC Educational Resources Information Center

    Ma, Xin; McIntyre, Laureen J.

    2005-01-01

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

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

    ERIC Educational Resources Information Center

    Wang, Youjun

    2009-01-01

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

  3. A Capstone Mathematics Course for Prospective Secondary Mathematics Teachers

    ERIC Educational Resources Information Center

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

    2012-01-01

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

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

    NASA Astrophysics Data System (ADS)

    Fuentes Sepúlveda, J.; Ferres, L.

    2012-09-01

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

  5. Multimedia content description framework

    NASA Technical Reports Server (NTRS)

    Bergman, Lawrence David (Inventor); Kim, Michelle Yoonk Yung (Inventor); Li, Chung-Sheng (Inventor); Mohan, Rakesh (Inventor); Smith, John Richard (Inventor)

    2003-01-01

    A framework is provided for describing multimedia content and a system in which a plurality of multimedia storage devices employing the content description methods of the present invention can interoperate. In accordance with one form of the present invention, the content description framework is a description scheme (DS) for describing streams or aggregations of multimedia objects, which may comprise audio, images, video, text, time series, and various other modalities. This description scheme can accommodate an essentially limitless number of descriptors in terms of features, semantics or metadata, and facilitate content-based search, index, and retrieval, among other capabilities, for both streamed or aggregated multimedia objects.

  6. Remedial Mathematics for Quantum Chemistry

    ERIC Educational Resources Information Center

    Koopman, Lodewijk; Brouwer, Natasa; Heck, Andre; Buma, Wybren Jan

    2008-01-01

    Proper mathematical skills are important for every science course and mathematics-intensive chemistry courses rely on a sound mathematical pre-knowledge. In the first-year quantum chemistry course at this university, it was noticed that many students lack basic mathematical knowledge. To tackle the mathematics problem, a remedial mathematics…

  7. Combinatorics, geometry, and mathematical physics

    SciTech Connect

    Chen, W.Y.C.; Louck, J.D.

    1998-11-01

    This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). Combinatorics and geometry have been among the most active areas of mathematics over the past few years because of newly discovered inter-relations between them and their potential for applications. In this project, the authors set out to identify problems in physics, chemistry, and biology where these methods could impact significantly. In particular, the experience suggested that the areas of unitary symmetry and discrete dynamical systems could be brought more strongly under the purview of combinatorial methods. Unitary symmetry deals with the detailed description of the quantum mechanics of many-particle systems, and discrete dynamical systems with chaotic systems. The depth and complexity of the mathematics in these physical areas of research suggested that not only could significant advances be made in these areas, but also that here would be a fertile feedback of concept and structure to enrich combinatorics itself by setting new directions. During the three years of this project, the goals have been realized beyond expectation, and in this report the authors set forth these advancements and justify their optimism.

  8. Mathematical models of diabetes progression.

    PubMed

    De Gaetano, Andrea; Hardy, Thomas; Beck, Benoit; Abu-Raddad, Eyas; Palumbo, Pasquale; Bue-Valleskey, Juliana; Pørksen, Niels

    2008-12-01

    Few attempts have been made to model mathematically the progression of type 2 diabetes. A realistic representation of the long-term physiological adaptation to developing insulin resistance is necessary for effectively designing clinical trials and evaluating diabetes prevention or disease modification therapies. Writing a good model for diabetes progression is difficult because the long time span of the disease makes experimental verification of modeling hypotheses extremely awkward. In this context, it is of primary importance that the assumptions underlying the model equations properly reflect established physiology and that the mathematical formulation of the model give rise only to physically plausible behavior of the solutions. In the present work, a model of the pancreatic islet compensation is formulated, its physiological assumptions are presented, some fundamental qualitative characteristics of its solutions are established, the numerical values assigned to its parameters are extensively discussed (also with reference to available cross-sectional epidemiologic data), and its performance over the span of a lifetime is simulated under various conditions, including worsening insulin resistance and primary replication defects. The differences with respect to two previously proposed models of diabetes progression are highlighted, and therefore, the model is proposed as a realistic, robust description of the evolution of the compensation of the glucose-insulin system in healthy and diabetic individuals. Model simulations can be run from the authors' web page.

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

    ERIC Educational Resources Information Center

    Dede, Yuksel

    2013-01-01

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

  10. Solving Common Mathematical Problems

    NASA Technical Reports Server (NTRS)

    Luz, Paul L.

    2005-01-01

    Mathematical Solutions Toolset is a collection of five software programs that rapidly solve some common mathematical problems. The programs consist of a set of Microsoft Excel worksheets. The programs provide for entry of input data and display of output data in a user-friendly, menu-driven format, and for automatic execution once the input data has been entered.

  11. Issues in Teaching Mathematics

    ERIC Educational Resources Information Center

    Ediger, Marlow

    2013-01-01

    In this article, the author states that there are selected issues in mathematics instruction that educators should be well aware of when planning lessons and units of study. These issues provide a basis for thought and discussion when assisting pupils to attain more optimally. Purposeful studying of issues guides mathematics teachers in…

  12. Mathematics: The Universal Language?

    ERIC Educational Resources Information Center

    Hoffert, Sharon B.

    2009-01-01

    Mathematics is considered the universal language, but students who speak languages other than English have difficulty doing mathematics in English. For instance, because of a lack of familiarity with the problem's context, many have trouble understanding exactly what operations to perform. In the United States, approximately one in seven students…

  13. Mathematical techniques: A compilation

    NASA Technical Reports Server (NTRS)

    1975-01-01

    Articles on theoretical and applied mathematics are introduced. The articles cover information that might be of interest to workers in statistics and information theory, computational aids that could be used by scientists and engineers, and mathematical techniques for design and control.

  14. Modularizing Remedial Mathematics

    ERIC Educational Resources Information Center

    Wong, Aaron

    2013-01-01

    As remedial mathematics education has become an increasingly important topic of conversation in higher education. Mathematics departments have been put under increased pressure to change their programs to increase the student success rate. A number of models have been introduced over the last decade that represent a wide range of new ideas and…

  15. Dyslexia, Dyspraxia and Mathematics.

    ERIC Educational Resources Information Center

    Yeo, Dorian

    This book explores how primary school children with dyslexia or dyspraxia and difficulty in math can learn math and provides practical support and detailed teaching suggestions. It considers cognitive features that underlie difficulty with mathematics generally or with specific aspects of mathematics. It outlines the ways in which children usually…

  16. Developing Mathematically Promising Students.

    ERIC Educational Resources Information Center

    Sheffield, Linda Jensen, Ed.

    This book, written on the recommendation of the Task Force on Mathematically Promising Students, investigates issues involving the development of promising mathematics students. Recommendations are made concerning topics such as the definition of promising students; the identification of such students; appropriate curriculum, instruction, and…

  17. 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…

  18. Experimenting with Mathematical Biology

    ERIC Educational Resources Information Center

    Sanft, Rebecca; Walter, Anne

    2016-01-01

    St. Olaf College recently added a Mathematical Biology concentration to its curriculum. The core course, Mathematics of Biology, was redesigned to include a wet laboratory. The lab classes required students to collect data and implement the essential modeling techniques of formulation, implementation, validation, and analysis. The four labs…

  19. What Is Discrete Mathematics?

    ERIC Educational Resources Information Center

    Sharp, Karen Tobey

    This paper cites information received from a number of sources, e.g., mathematics teachers in two-year colleges, publishers, and convention speakers, about the nature of discrete mathematics and about what topics a course in this subject should contain. Note is taken of the book edited by Ralston and Young which discusses the future of college…

  20. Consumer Mathematics Curriculum Guide.

    ERIC Educational Resources Information Center

    Louisiana State Dept. of Education, Baton Rouge.

    This guide for high school consumer mathematics (one in a set of curriculum guides developed by Louisiana statewide mathematics curriculum committees) contains a course outline, performance objectives, and coordinated activities designed to teach skills that students will need as citizens and consumers. Background on the development,…

  1. Business Mathematics Curriculum.

    ERIC Educational Resources Information Center

    EASTCONN Regional Educational Services Center, North Windham, CT.

    This curriculum guide for teaching business mathematics in the Connecticut Vocational-Technical School System is based on the latest thinking of instructors in the field, suggestions from mathematics authorities, and current instructional approaches in education. The curriculum guide consists of six sections: (1) career relationships and…

  2. Astronomy and Mathematics Education

    NASA Astrophysics Data System (ADS)

    Ros, Rosa M.

    There are many European countries where Astronomy does not appear as a specific course on the secondary school. In these cases Astronomy content can be introduced by means of other subjects. There are some astronomical topics within the subject of Physics but this talk concerns introducing Astronomy in Mathematics classes. Teaching Astronomy through Mathematics would result in more exposure than through Physics as Mathematics is more prevalent in the curriculum. Generally it is not easy to motivate students in Mathematics but they are motivated to find out more about the universe and Astronomy current events than appears in the media. This situation can be an excellent introduction to several mathematics topics. The teachers in secondary and high school can use this idea in order to present more attractive mathematics courses. In particular some different examples will be offered regarding * Angles and spherical coordinates considering star traces * Logarithms and visual magnitudes * Plane trigonometry related orbital movements * Spherical trigonometry in connection with ecliptic obliquity * Conic curves related to sundial at several latitudes Some students do not enjoy studying Mathematics but they can be attracted by practical situations using Applied Mathematics: Astronomy is always very attractive to teenagers.

  3. Quality Teaching in Mathematics

    ERIC Educational Resources Information Center

    Ediger, Marlow

    2012-01-01

    The best teaching possible needs to accrue in the mathematics curriculum. Pupils also need to become proficient in using mathematics in every day situations in life. Individuals buy goods and services. They pay for these in different ways, including cash. Here, persons need to be able to compute the total cost of items purchased and then pay for…

  4. Learning Mathematics while Black

    ERIC Educational Resources Information Center

    Martin, Danny Bernard

    2012-01-01

    While research by scholars has contributed greatly to an emerging knowledge base on Black children and mathematics, there continues to be a dire need for insightful research that de-centers longstanding accounts that have contributed to the construction of Black children as mathematically illiterate and as less than ideal learners relative to…

  5. Intermediate Mathematics Study Guide.

    ERIC Educational Resources Information Center

    Stanford Univ., CA. School Mathematics Study Group.

    This SMSG study guide is intended to provide teachers who use "Intermediate Mathematics," as a textbook with references to materials which will help them to gain a better understanding of the mathematics contained in the text. For each chapter of the text a brief resume of its content is followed by a list of annotated references which are…

  6. Mathematics in History.

    ERIC Educational Resources Information Center

    Hallenberg, Harvey

    1995-01-01

    Presents ideas for creating mathematical classroom activities associated with the history of mathematics: calculating sums and products the way ancient Greeks did it, using an abacus or moving stones on a sanded floor, and engaging elementary students through role playing specific mathematicians. Suggests that through such techniques, mathematics…

  7. Designing Assessment for Mathematics

    ERIC Educational Resources Information Center

    Depka, Eileen

    2007-01-01

    Teaching mathematics in today's world requires practices and procedures integrated with performance tasks that actively involve students. In this second edition of Designing Rubrics for Mathematics, Eileen Depka clarifies the purpose of rubrics in math instruction and illustrates the relationship between assessment, rubrics, and the National…

  8. Mathematical Graphic Organizers

    ERIC Educational Resources Information Center

    Zollman, Alan

    2009-01-01

    As part of a math-science partnership, a university mathematics educator and ten elementary school teachers developed a novel approach to mathematical problem solving derived from research on reading and writing pedagogy. Specifically, research indicates that students who use graphic organizers to arrange their ideas improve their comprehension…

  9. Mathematics. [SITE 2002 Section].

    ERIC Educational Resources Information Center

    Connell, Michael L., Ed.; Lowery, Norene Vail, Ed.; Harnisch, Delwyn L., Ed.

    This document contains the following papers on mathematics from the SITE (Society for Information Technology & Teacher Education) 2002 conference: (1) "Teachers' Learning of Mathematics in the Presence of Technology: Participatory Cognitive Apprenticeship" (Mara Alagic); (2) "A Fractal Is a Pattern in Your Neighborhood" (Craig N. Bach); (3)…

  10. See a Different Mathematics

    ERIC Educational Resources Information Center

    Stallings, L. Lynn

    2007-01-01

    This article proposes four strategies for posing mathematics problems that raise the cognitive demands of the tasks given to students. Each strategy is illustrated with three common middle school mathematics examples: finding the greatest common factor, finding area or perimeter, and finding the equation of a line. Posing these types of problems…

  11. The Impossible in Mathematics.

    ERIC Educational Resources Information Center

    Adler, Irving

    The material in this reprint, with minor editorial changes, is from the chapter "Doing the Impossible" in MONKEY BUSINESS by Irving Adler. This 25-page booklet contains brief accounts of historical attempts to prove impossible problems in mathematics. The mathematical recreations in this booklet of geometric constructions include the trisection…

  12. Strengthen Your Mathematical Muscles

    ERIC Educational Resources Information Center

    Wohlhuter, Kay A.; Breyfogle, M. Lynn; McDuffie, Amy Roth

    2010-01-01

    Developing deep knowledge and understanding of mathematics is a lifelong process, and building the foundation for teachers' development must begin in preservice preparation and continue throughout one's professional life. While teaching mathematics content courses and methods courses, the authors have found that preservice elementary school…

  13. Mathematics: Content and Pedagogy

    ERIC Educational Resources Information Center

    Ediger, Marlow

    2009-01-01

    The debate has gone on for some time in terms of which is more salient for the teacher to be well versed in, mathematical content versus methods and approaches in teaching. Both are salient. They cannot be separated from each other. The mathematics teacher must indeed have broad, in-depth knowledge of subject matter as well as in teaching and…

  14. Mathematics Education in Argentina

    ERIC Educational Resources Information Center

    Varsavsky, Cristina; Anaya, Marta

    2009-01-01

    This article gives an overview of the state of mathematics education in Argentina across all levels, in the regional and world contexts. Statistics are drawn from Mercosur and UNESCO data bases, World Education Indicators and various national time-series government reports. Mathematics results in national testing programmes, Programme for…

  15. [Collected Papers on Mathematics.

    ERIC Educational Resources Information Center

    Connell, Michael L., Ed.

    This document contains the following papers on issues related to mathematics in technology and teacher education: "A Case for Strong Conceptualization in Technology Enhanced Mathematics Instruction" (Michael L. Connell and Delwyn L. Harnisch); "Faculty/Student Collaboration in Education and Math--Using the Web To Improve Student Learning and…

  16. Discrete Mathematics Re "Tooled."

    ERIC Educational Resources Information Center

    Grassl, Richard M.; Mingus, Tabitha T. Y.

    1999-01-01

    Indicates the importance of teaching discrete mathematics. Describes how the use of technology can enhance the teaching and learning of discrete mathematics. Explorations using Excel, Derive, and the TI-92 proved how preservice and inservice teachers experienced a new dimension in problem solving and discovery. (ASK)

  17. Mathematics and Gender.

    ERIC Educational Resources Information Center

    Fennema, Elizabeth, Ed.; Leder, Gilah C., Ed.

    This book reports on various studies that have increased our understanding of why females and males learn different kinds and amounts of mathematics. In particular, this book explicates the Autonomous Learning Behavior model, proposed by Fennema and Peterson, which is a possible explanation of the development of gender differences in mathematics.…

  18. Mathematics Knowledge for Teaching

    ERIC Educational Resources Information Center

    Mohr, Margaret

    2006-01-01

    Research indicates that U. S. teachers' mathematical knowledge continues to be weak, and there is an inherent difference between the mathematical knowledge needed to be an effective teacher and that needed by a mathematician. In this article, the author discusses pedagogical content knowledge. According to Schulman (1987), pedagogical content…

  19. Attitudes and Mathematics.

    ERIC Educational Resources Information Center

    Iben, Miriam F.

    1991-01-01

    Examines seventh and eighth grade students in Australia, Japan, and the United States for attitudes related to mathematics, and the relationship these attitudes have to students' development of abstract mathematical thought and spatial relations. Study uses the Iowa Algebra Aptitude Test, Differential Aptitude Test-Spatial Relations, and the…

  20. Developing Mathematical Vocabulary.

    ERIC Educational Resources Information Center

    Monroe, Eula Ewing; Orme, Michelle P.

    2002-01-01

    This article discusses the importance of mathematical vocabulary, difficulties students encounter in learning this vocabulary, and some instructional strategies. Two general methods for teaching vocabulary are discussed: context and explicit vocabulary instruction. The methods are summarized as they apply to mathematical vocabulary instruction and…

  1. Mathematics and Art

    ERIC Educational Resources Information Center

    Sharp, John

    2012-01-01

    This relationship is omnipresent to those who appreciate the shared attributes of these two areas of creativity. The dynamic nature of media, and further study, enable mathematicians and artists to present new and exciting manifestations of the "mathematics in art", and the "art in mathematics". The illustrative images of the relationship--that…

  2. Why physics needs mathematics

    NASA Astrophysics Data System (ADS)

    Rohrlich, Fritz

    2011-12-01

    Classical and the quantum mechanical sciences are in essential need of mathematics. Only thus can the laws of nature be formulated quantitatively permitting quantitative predictions. Mathematics also facilitates extrapolations. But classical and quantum sciences differ in essential ways: they follow different laws of logic, Aristotelian and non-Aristotelian logics, respectively. These are explicated.

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

    SciTech Connect

    Concus, P.; Zabihi, F. California Univ., Berkeley, CA . Dept. of Mathematics); Finn, R. . Dept. of Mathematics)

    1992-07-01

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

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

    SciTech Connect

    Concus, P.; Zabihi, F. |; Finn, R.

    1992-07-01

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

  5. 38 CFR 4.46 - Accurate measurement.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 38 Pensions, Bonuses, and Veterans' Relief 1 2010-07-01 2010-07-01 false Accurate measurement. 4... RATING DISABILITIES Disability Ratings The Musculoskeletal System § 4.46 Accurate measurement. Accurate measurement of the length of stumps, excursion of joints, dimensions and location of scars with respect...

  6. 38 CFR 4.46 - Accurate measurement.

    Code of Federal Regulations, 2013 CFR

    2013-07-01

    ... 38 Pensions, Bonuses, and Veterans' Relief 1 2013-07-01 2013-07-01 false Accurate measurement. 4... RATING DISABILITIES Disability Ratings The Musculoskeletal System § 4.46 Accurate measurement. Accurate measurement of the length of stumps, excursion of joints, dimensions and location of scars with respect...

  7. 38 CFR 4.46 - Accurate measurement.

    Code of Federal Regulations, 2011 CFR

    2011-07-01

    ... 38 Pensions, Bonuses, and Veterans' Relief 1 2011-07-01 2011-07-01 false Accurate measurement. 4... RATING DISABILITIES Disability Ratings The Musculoskeletal System § 4.46 Accurate measurement. Accurate measurement of the length of stumps, excursion of joints, dimensions and location of scars with respect...

  8. 38 CFR 4.46 - Accurate measurement.

    Code of Federal Regulations, 2014 CFR

    2014-07-01

    ... 38 Pensions, Bonuses, and Veterans' Relief 1 2014-07-01 2014-07-01 false Accurate measurement. 4... RATING DISABILITIES Disability Ratings The Musculoskeletal System § 4.46 Accurate measurement. Accurate measurement of the length of stumps, excursion of joints, dimensions and location of scars with respect...

  9. 38 CFR 4.46 - Accurate measurement.

    Code of Federal Regulations, 2012 CFR

    2012-07-01

    ... 38 Pensions, Bonuses, and Veterans' Relief 1 2012-07-01 2012-07-01 false Accurate measurement. 4... RATING DISABILITIES Disability Ratings The Musculoskeletal System § 4.46 Accurate measurement. Accurate measurement of the length of stumps, excursion of joints, dimensions and location of scars with respect...

  10. Two pre-Willan descriptions of psoriasis.

    PubMed

    De Bersaques, Jean

    2012-01-01

    Accurate descriptions of skin lesions, and in particular of those of what we now call osiriasis vulgaris, are rare before the book of Willan's On Cutaneous Diseases at the very beginning of the 19th century. Here we present two instances in which such clinical descriptions are given. Benjamin Franklin wrote about his own skin lesions and their evolution. Dr. Willam Falconer, physician in Bath, England, presents the clinical symptoms and his results with 83 patients with 'lepra graecorum' (the name used at that time) treated between 1772 and 1775. One can wonder why such a now frequent, obvious and distinctive disease had not attracted more attention. PMID:22902228

  11. The Definition of Mathematics: Philosophical and Pedagogical Aspects

    NASA Astrophysics Data System (ADS)

    Khait, Alexander

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

  12. Business Mathematics. Mathematics Curriculum Guide (Career Oriented).

    ERIC Educational Resources Information Center

    Nuschler, Alexandra; And Others

    The curriculum guide correlates concepts in business mathematics with career-oriented concepts and activities. The curriculum outline format gives the concepts to be taught, matched with related career-oriented performance objectives, concepts, and suggested instructional activities in facing page layouts. The outline is divided into the major…

  13. Technical Mathematics: Restructure of Technical Mathematics.

    ERIC Educational Resources Information Center

    Flannery, Carol A.

    Designed to accompany a series of videotapes, this textbook provides information, examples, problems, and solutions relating to mathematics and its applications in technical fields. Chapter I deals with basic arithmetic, providing information on fractions, decimals, ratios, proportions, percentages, and order of operations. Chapter II focuses on…

  14. The FLUKA Code: An Accurate Simulation Tool for Particle Therapy

    PubMed Central

    Battistoni, Giuseppe; Bauer, Julia; Boehlen, Till T.; Cerutti, Francesco; Chin, Mary P. W.; Dos Santos Augusto, Ricardo; Ferrari, Alfredo; Ortega, Pablo G.; Kozłowska, Wioletta; Magro, Giuseppe; Mairani, Andrea; Parodi, Katia; Sala, Paola R.; Schoofs, Philippe; Tessonnier, Thomas; Vlachoudis, Vasilis

    2016-01-01

    Monte Carlo (MC) codes are increasingly spreading in the hadrontherapy community due to their detailed description of radiation transport and interaction with matter. The suitability of a MC code for application to hadrontherapy demands accurate and reliable physical models capable of handling all components of the expected radiation field. This becomes extremely important for correctly performing not only physical but also biologically based dose calculations, especially in cases where ions heavier than protons are involved. In addition, accurate prediction of emerging secondary radiation is of utmost importance in innovative areas of research aiming at in vivo treatment verification. This contribution will address the recent developments of the FLUKA MC code and its practical applications in this field. Refinements of the FLUKA nuclear models in the therapeutic energy interval lead to an improved description of the mixed radiation field as shown in the presented benchmarks against experimental data with both 4He and 12C ion beams. Accurate description of ionization energy losses and of particle scattering and interactions lead to the excellent agreement of calculated depth–dose profiles with those measured at leading European hadron therapy centers, both with proton and ion beams. In order to support the application of FLUKA in hospital-based environments, Flair, the FLUKA graphical interface, has been enhanced with the capability of translating CT DICOM images into voxel-based computational phantoms in a fast and well-structured way. The interface is capable of importing also radiotherapy treatment data described in DICOM RT standard. In addition, the interface is equipped with an intuitive PET scanner geometry generator and automatic recording of coincidence events. Clinically, similar cases will be presented both in terms of absorbed dose and biological dose calculations describing the various available features. PMID:27242956

  15. The FLUKA Code: An Accurate Simulation Tool for Particle Therapy.

    PubMed

    Battistoni, Giuseppe; Bauer, Julia; Boehlen, Till T; Cerutti, Francesco; Chin, Mary P W; Dos Santos Augusto, Ricardo; Ferrari, Alfredo; Ortega, Pablo G; Kozłowska, Wioletta; Magro, Giuseppe; Mairani, Andrea; Parodi, Katia; Sala, Paola R; Schoofs, Philippe; Tessonnier, Thomas; Vlachoudis, Vasilis

    2016-01-01

    Monte Carlo (MC) codes are increasingly spreading in the hadrontherapy community due to their detailed description of radiation transport and interaction with matter. The suitability of a MC code for application to hadrontherapy demands accurate and reliable physical models capable of handling all components of the expected radiation field. This becomes extremely important for correctly performing not only physical but also biologically based dose calculations, especially in cases where ions heavier than protons are involved. In addition, accurate prediction of emerging secondary radiation is of utmost importance in innovative areas of research aiming at in vivo treatment verification. This contribution will address the recent developments of the FLUKA MC code and its practical applications in this field. Refinements of the FLUKA nuclear models in the therapeutic energy interval lead to an improved description of the mixed radiation field as shown in the presented benchmarks against experimental data with both (4)He and (12)C ion beams. Accurate description of ionization energy losses and of particle scattering and interactions lead to the excellent agreement of calculated depth-dose profiles with those measured at leading European hadron therapy centers, both with proton and ion beams. In order to support the application of FLUKA in hospital-based environments, Flair, the FLUKA graphical interface, has been enhanced with the capability of translating CT DICOM images into voxel-based computational phantoms in a fast and well-structured way. The interface is capable of importing also radiotherapy treatment data described in DICOM RT standard. In addition, the interface is equipped with an intuitive PET scanner geometry generator and automatic recording of coincidence events. Clinically, similar cases will be presented both in terms of absorbed dose and biological dose calculations describing the various available features. PMID:27242956

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

    ERIC Educational Resources Information Center

    Hebert, Michael A.; Powell, Sarah R.

    2016-01-01

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

  17. Mathematical model for gyroscope effects

    NASA Astrophysics Data System (ADS)

    Usubamatov, Ryspek

    2015-05-01

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

  18. Mathematical algorithms for approximate reasoning

    NASA Technical Reports Server (NTRS)

    Murphy, John H.; Chay, Seung C.; Downs, Mary M.

    1988-01-01

    Most state of the art expert system environments contain a single and often ad hoc strategy for approximate reasoning. Some environments provide facilities to program the approximate reasoning algorithms. However, the next generation of expert systems should have an environment which contain a choice of several mathematical algorithms for approximate reasoning. To meet the need for validatable and verifiable coding, the expert system environment must no longer depend upon ad hoc reasoning techniques but instead must include mathematically rigorous techniques for approximate reasoning. Popular approximate reasoning techniques are reviewed, including: certainty factors, belief measures, Bayesian probabilities, fuzzy logic, and Shafer-Dempster techniques for reasoning. A group of mathematically rigorous algorithms for approximate reasoning are focused on that could form the basis of a next generation expert system environment. These algorithms are based upon the axioms of set theory and probability theory. To separate these algorithms for approximate reasoning various conditions of mutual exclusivity and independence are imposed upon the assertions. Approximate reasoning algorithms presented include: reasoning with statistically independent assertions, reasoning with mutually exclusive assertions, reasoning with assertions that exhibit minimum overlay within the state space, reasoning with assertions that exhibit maximum overlay within the state space (i.e. fuzzy logic), pessimistic reasoning (i.e. worst case analysis), optimistic reasoning (i.e. best case analysis), and reasoning with assertions with absolutely no knowledge of the possible dependency among the assertions. A robust environment for expert system construction should include the two modes of inference: modus ponens and modus tollens. Modus ponens inference is based upon reasoning towards the conclusion in a statement of logical implication, whereas modus tollens inference is based upon reasoning away

  19. Math Description Engine Software Development Kit

    NASA Technical Reports Server (NTRS)

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

    2010-01-01

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

  20. Provocative Opinion: Descriptive Chemistry.

    ERIC Educational Resources Information Center

    Bent, Henry A.; Bent, Brian E.

    1987-01-01

    Discusses many of the distinctions that chemists draw between theoretical chemistry and descriptive chemistry, along with the tendency for chemical educators to adopt the type of chemistry they feel is most important to teach. Uses examples to argue that theoretical chemistry and descriptive chemistry are, at the bottom line, the same. (TW)

  1. A Descriptive Experiment.

    ERIC Educational Resources Information Center

    Brand, Josef

    1979-01-01

    In this experiment in description, students in a high school honors English class were asked to select a surrealistic painting and capture it in writing. Their compositions were given to art students who tried to reproduce the paintings from the written descriptions. (SJL)

  2. Physics 3204. Course Description.

    ERIC Educational Resources Information Center

    Newfoundland and Labrador Dept. of Education.

    A description of the physics 3204 course in Newfoundland and Labrador is provided. The description includes: (1) statement of purpose, including general objectives of science education; (2) a list of six course objectives; (3) course content for units on sound, light, optical instruments, electrostatics, current electricity, Michael Faraday and…

  3. Job descriptions made easy.

    PubMed

    Miller, Larry

    2014-01-01

    The act of writing a job description can be a daunting and difficult task for many managers. This article focuses on the key concepts of What, How, and Measureable Results as they relate to an employee's job duties. When the answers to these three elements are articulated, they define the core responsibilities of any job that form the basis for an effective job description.

  4. Assessing Students Beliefs about Mathematics.

    ERIC Educational Resources Information Center

    Spangler, Denise A.

    1992-01-01

    Presents 11 open-ended questions that can be presented to students and teachers at all educational levels in various formats to assess mathematical beliefs. Questions investigate beliefs toward mathematics, the problem-solving process, mathematicians, and mathematical applications. (MDH)

  5. Mathematics as verbal behavior.

    PubMed

    Marr, M Jackson

    2015-04-01

    "Behavior which is effective only through the mediation of other persons has so many distinguishing dynamic and topographical properties that a special treatment is justified and indeed demanded" (Skinner, 1957, p. 2). Skinner's demand for a special treatment of verbal behavior can be extended within that field to domains such as music, poetry, drama, and the topic of this paper: mathematics. For centuries, mathematics has been of special concern to philosophers who have continually argued to the present day about what some deem its "special nature." Two interrelated principal questions have been: (1) Are the subjects of mathematical interest pre-existing in some transcendental realm and thus are "discovered" as one might discover a new planet; and (2) Why is mathematics so effective in the practices of science and engineering even though originally such mathematics was "pure" with applications neither contemplated or even desired? I argue that considering the actual practice of mathematics in its history and in the context of acquired verbal behavior one can address at least some of its apparent mysteries. To this end, I discuss some of the structural and functional features of mathematics including verbal operants, rule-and contingency-modulated behavior, relational frames, the shaping of abstraction, and the development of intuition. How is it possible to understand Nature by properly talking about it? Essentially, it is because nature taught us how to talk. PMID:25595115

  6. Mathematics as verbal behavior.

    PubMed

    Marr, M Jackson

    2015-04-01

    "Behavior which is effective only through the mediation of other persons has so many distinguishing dynamic and topographical properties that a special treatment is justified and indeed demanded" (Skinner, 1957, p. 2). Skinner's demand for a special treatment of verbal behavior can be extended within that field to domains such as music, poetry, drama, and the topic of this paper: mathematics. For centuries, mathematics has been of special concern to philosophers who have continually argued to the present day about what some deem its "special nature." Two interrelated principal questions have been: (1) Are the subjects of mathematical interest pre-existing in some transcendental realm and thus are "discovered" as one might discover a new planet; and (2) Why is mathematics so effective in the practices of science and engineering even though originally such mathematics was "pure" with applications neither contemplated or even desired? I argue that considering the actual practice of mathematics in its history and in the context of acquired verbal behavior one can address at least some of its apparent mysteries. To this end, I discuss some of the structural and functional features of mathematics including verbal operants, rule-and contingency-modulated behavior, relational frames, the shaping of abstraction, and the development of intuition. How is it possible to understand Nature by properly talking about it? Essentially, it is because nature taught us how to talk.

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

    NASA Astrophysics Data System (ADS)

    Sheryn, Louise; Ell, Fiona

    2014-08-01

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

  8. Mathematics and Measurement

    PubMed Central

    Boisvert, Ronald F.; Donahue, Michael J.; Lozier, Daniel W.; McMichael, Robert; Rust, Bert W.

    2001-01-01

    In this paper we describe the role that mathematics plays in measurement science at NIST. We first survey the history behind NIST’s current work in this area, starting with the NBS Math Tables project of the 1930s. We then provide examples of more recent efforts in the application of mathematics to measurement science, including the solution of ill-posed inverse problems, characterization of the accuracy of software for micromagnetic modeling, and in the development and dissemination of mathematical reference data. Finally, we comment on emerging issues in measurement science to which mathematicians will devote their energies in coming years. PMID:27500024

  9. The Greatest Mathematical Discovery?

    SciTech Connect

    Bailey, David H.; Borwein, Jonathan M.

    2010-05-12

    What mathematical discovery more than 1500 years ago: (1) Is one of the greatest, if not the greatest, single discovery in the field of mathematics? (2) Involved three subtle ideas that eluded the greatest minds of antiquity, even geniuses such as Archimedes? (3) Was fiercely resisted in Europe for hundreds of years after its discovery? (4) Even today, in historical treatments of mathematics, is often dismissed with scant mention, or else is ascribed to the wrong source? Answer: Our modern system of positional decimal notation with zero, together with the basic arithmetic computational schemes, which were discovered in India about 500 CE.

  10. Mathematization in introductory physics

    NASA Astrophysics Data System (ADS)

    Brahmia, Suzanne M.

    Mathematization is central to STEM disciplines as a cornerstone of the quantitative reasoning that characterizes these fields. Introductory physics is required for most STEM majors in part so that students develop expert-like mathematization. This dissertation describes coordinated research and curriculum development for strengthening mathematization in introductory physics; it blends scholarship in physics and mathematics education in the form of three papers. The first paper explores mathematization in the context of physics, and makes an original contribution to the measurement of physics students' struggle to mathematize. Instructors naturally assume students have a conceptual mastery of algebra before embarking on a college physics course because these students are enrolled in math courses beyond algebra. This paper provides evidence that refutes the validity of this assumption and categorizes some of the barriers students commonly encounter with quantification and representing ideas symbolically. The second paper develops a model of instruction that can help students progress from their starting points to their instructor's desired endpoints. Instructors recognize that the introductory physics course introduces new ideas at an astonishing rate. More than most physicists realize, however, the way that mathematics is used in the course is foreign to a large portion of class. This paper puts forth an instructional model that can move all students toward better quantitative and physical reasoning, despite the substantial variability of those students' initial states. The third paper describes the design and testing of curricular materials that foster mathematical creativity to prepare students to better understand physics reasoning. Few students enter introductory physics with experience generating equations in response to specific challenges involving unfamiliar quantities and units, yet this generative use of mathematics is typical of the thinking involved in

  11. Accurate polarimeter with multicapture fitting for plastic lens evaluation

    NASA Astrophysics Data System (ADS)

    Domínguez, Noemí; Mayershofer, Daniel; Garcia, Cristina; Arasa, Josep

    2016-02-01

    Due to their manufacturing process, plastic injection molded lenses do not achieve a constant density throughout their volume. This change of density introduces tensions in the material, inducing local birefringence, which in turn is translated into a variation of the ordinary and extraordinary refractive indices that can be expressed as a retardation phase plane using the Jones matrix notation. The detection and measurement of the value of the retardation of the phase plane are therefore very useful ways to evaluate the quality of plastic lenses. We introduce a polariscopic device to obtain two-dimensional maps of the tension distribution in the bulk of a lens, based on detection of the local birefringence. In addition to a description of the device and the mathematical approach used, a set of initial measurements is presented that confirms the validity of the developed system for the testing of the uniformity of plastic lenses.

  12. Physical vs. Mathematical Models in Rock Mechanics

    NASA Astrophysics Data System (ADS)

    Morozov, I. B.; Deng, W.

    2013-12-01

    One of the less noted challenges in understanding the mechanical behavior of rocks at both in situ and lab conditions is the character of theoretical approaches being used. Currently, the emphasis is made on spatial averaging theories (homogenization and numerical models of microstructure), empirical models for temporal behavior (material memory, compliance functions and complex moduli), and mathematical transforms (Laplace and Fourier) used to infer the Q-factors and 'relaxation mechanisms'. In geophysical applications, we have to rely on such approaches for very broad spatial and temporal scales which are not available in experiments. However, the above models often make insufficient use of physics and utilize, for example, the simplified 'correspondence principle' instead of the laws of viscosity and friction. As a result, the commonly-used time- and frequency dependent (visco)elastic moduli represent apparent properties related to the measurement procedures and not necessarily to material properties. Predictions made from such models may therefore be inaccurate or incorrect when extrapolated beyond the lab scales. To overcome the above challenge, we need to utilize the methods of micro- and macroscopic mechanics and thermodynamics known in theoretical physics. This description is rigorous and accurate, uses only partial differential equations, and allows straightforward numerical implementations. One important observation from the physical approach is that the analysis should always be done for the specific geometry and parameters of the experiment. Here, we illustrate these methods on axial deformations of a cylindrical rock sample in the lab. A uniform, isotropic elastic rock with a thermoelastic effect is considered in four types of experiments: 1) axial extension with free transverse boundary, 2) pure axial extension with constrained transverse boundary, 3) pure bulk expansion, and 4) axial loading harmonically varying with time. In each of these cases, an

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

    PubMed Central

    Janssen, Paddy K.C.

    2016-01-01

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

  14. On the Role of Mathematics in Physics

    NASA Astrophysics Data System (ADS)

    Quale, Andreas

    2011-03-01

    I examine the association between the observable physical world and the mathematical models of theoretical physics. These models will exhibit many entities that have no counterpart in the physical world, but which are still necessary for the mathematical description of physical systems. Moreover, when the model is applied to the analysis of a physical system, it will sometimes produce solutions that are unphysical—i.e. describe a physical system that simply cannot exist in the real world. It is argued that this poses a problem for the epistemic position of realism in physics: a mathematical theory that professes to give a correct description of physical reality should not contain such unrealistic objects. Some concrete examples are examined, and their implications for physics are discussed from a relativist epistemic perspective. I argue that the appearance of the unphysical entities and solutions also has significance for the teaching of physics. It is recommended that the students be exposed from the start to a relativist ontology, as advocated by the theory of radical constructivism; here the unphysical objects do not pose an epistemic problem.

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

    NASA Astrophysics Data System (ADS)

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

    2014-05-01

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

  16. Benjamin Banneker's Mathematical Puzzles.

    ERIC Educational Resources Information Center

    Mahoney, John F.

    2003-01-01

    Benjamin Banneker, a self-taught African American mathematician, kept a journal containing a number of mathematical puzzles. Explores four of these puzzles, 200 years later, with the aid of 21st century technology. (Author/NB)

  17. Mathematics Case Methods Project.

    ERIC Educational Resources Information Center

    Barnett, Carne S.

    1998-01-01

    Presents an overview and analysis of the Mathematics Case Methods Project, which uses cases in order to examine and reflect upon teaching. Focuses on a special kind of teacher knowledge, coined pedagogical-content knowledge. (ASK)

  18. Standards in Mathematics Teaching.

    ERIC Educational Resources Information Center

    Brookes, Bill

    1978-01-01

    This article is based on a lecture given at the 1978 Easter Course at Padgate College of Higher Education. The lecture is an analysis of the complexity of mathematics teaching and the setting of teaching standards. (MN)

  19. The use of experimental bending tests to more accurate numerical description of TBC damage process

    NASA Astrophysics Data System (ADS)

    Sadowski, T.; Golewski, P.

    2016-04-01

    Thermal barrier coatings (TBCs) have been extensively used in aircraft engines to protect critical engine parts such as blades and combustion chambers, which are exposed to high temperatures and corrosive environment. The blades of turbine engines are additionally exposed to high mechanical loads. These loads are created by the high rotational speed of the rotor (30 000 rot/min), causing the tensile and bending stresses. Therefore, experimental testing of coated samples is necessary in order to determine strength properties of TBCs. Beam samples with dimensions 50×10×2 mm were used in those studies. The TBC system consisted of 150 μm thick bond coat (NiCoCrAlY) and 300 μm thick top coat (YSZ) made by APS (air plasma spray) process. Samples were tested by three-point bending test with various loads. After bending tests, the samples were subjected to microscopic observation to determine the quantity of cracks and their depth. The above mentioned results were used to build numerical model and calibrate material data in Abaqus program. Brittle cracking damage model was applied for the TBC layer, which allows to remove elements after reaching criterion. Surface based cohesive behavior was used to model the delamination which may occur at the boundary between bond coat and top coat.

  20. Toward an Accurate Density-Functional Tight-Binding Description of Zinc-Containing Compounds.

    PubMed

    Moreira, Ney H; Dolgonos, Grygoriy; Aradi, Bálint; da Rosa, Andreia L; Frauenheim, Thomas

    2009-03-10

    An extended self-consistent charge density-functional tight-binding (SCC-DFTB) parametrization for Zn-X (X = H, C, N, O, S, and Zn) interactions has been derived. The performance of this new parametrization has been validated by calculating the structural and energetic properties of zinc solid phases such as bulk Zn, ZnO, and ZnS; ZnO surfaces and nanostructures; adsorption of small species (H, CO2, and NH3) on ZnO surfaces; and zinc-containing complexes mimicking the biological environment. Our results show that the derived parameters are universal and fully transferable, describing all the above-mentioned systems with accuracies comparable to those of first-principles DFT results. PMID:26610226

  1. Reciprocal Relationships between Attitude toward Mathematics and Achievement in Mathematics.

    ERIC Educational Resources Information Center

    Ma, Xin

    1997-01-01

    This study examined reciprocal relationships between attitude toward mathematics and mathematics achievement. High school seniors from the Dominican Republic completed mathematics achievement tests and a questionnaire on mathematics attitudes. Results indicated that reciprocal relationships existed, suggesting that the reciprocal nature between…

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

    ERIC Educational Resources Information Center

    Lyon, Steve

    2014-01-01

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

  3. Applications of Secondary School Mathematics: Readings from the "Mathematics Teacher."

    ERIC Educational Resources Information Center

    Austin, Joe Dan, Ed.

    This book provides applications for use in the secondary school mathematics curriculum by selecting related articles appearing in the "Mathematics Teacher" during the last 15 years. The articles are grouped into chapters that reflect the main secondary school mathematics courses and categorized by the highest level of mathematics needed for…

  4. Promoting Critical Mathematics Literacy in Secondary Mathematics Teacher Education

    ERIC Educational Resources Information Center

    Fish, Michael Charles

    2012-01-01

    This study examines how critical mathematical literacy teachers conceptualize their practices and how those practices were demonstrated in the classroom. Practices were considered from an ontology of mathematics education, specific to critical mathematical literacy, in which classroom interactions question what it means to do mathematics as an…

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

    ERIC Educational Resources Information Center

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

    2007-01-01

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

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

    ERIC Educational Resources Information Center

    Kaya, Defne; Aydin, Hasan

    2016-01-01

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

  7. 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…

  8. A mathematical process model for cadmium precipitation by sulfate-reducing bacterial biofilms.

    PubMed

    White, Christopher; Dennis, John S; Gadd, Geoffrey M

    2003-04-01

    Sulfate-reducing bacterial (SRB) biofilms were grown in a flowcell in which the biofilm was grown on a fixed area of support which was supplied with recirculating medium of defined composition, volume and circulation rate. Utilization rates for substrates, production rates for products and material mass-balances for substrates and Cd were determined and a mathematical model constructed based on theoretical considerations and experimental data. The rate of sulfate reduction was zero-order with respect to sulfate concentration and unaffected by the presence of 250 microM Cd. However, Cd reacted with the sulfide produced by the SRB to produce solid CdS, removing sulfide from solution. A significant fraction of colloidal CdS was formed which flocculated relatively slowly, limiting the overall rate of Cd bioprecipitation. Experiments using chemically-synthesised colloidal CdS indicated that the biofilm did not influence colloidal Cd flocculation but stimulated sedimentation of the CdS precipitate once flocculated. A mathematical model of bioprecipitation was developed in which the CdS formation rate was determined by two steps: sulfide production by the biofilm and colloidal CdS flocculation. This model accurately predicted the behaviour of further experimental runs which indicated the adequacy of the overall process description. The model also indicated that the rate of sulfate reduction and the rate of flocculation were the key variables in optimising the biofilm system for metal removal.

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

    ERIC Educational Resources Information Center

    Simon, Martin A.; Tzur, Ron

    2004-01-01

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

  10. An Investigation of Pre-Service Mathematics Teachers' Skills in the Development of Activities

    ERIC Educational Resources Information Center

    Özgen, Kemal; Alkan, Hu¨seyin

    2014-01-01

    The purpose of this research is to determine pre-service mathematics teachers' skills in the development of activities. The research was carried out using the case study which is descriptive method. For the collection of data, 57 pre-service mathematics teachers' in their final year secondary math teachers' education department…

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

    ERIC Educational Resources Information Center

    Gerdes, Paulus

    1988-01-01

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

  12. Ten Equations That Changed Biology: Mathematics in Problem-Solving Biology Curricula.

    ERIC Educational Resources Information Center

    Jungck, John R.

    1997-01-01

    Mathematics plays an exceptionally important role in biological education and the history of biology. Ten equations and descriptions of their historical importance are presented to draw students' and faculty's attention to mathematical models that have been intrinsic to many of the significant discoveries in biology in the 20th century. Each…

  13. Opinions of Mathematics Teacher Candidates towards Applying 7E Instructional Model on Computer Aided Instruction Environments

    ERIC Educational Resources Information Center

    Yenilmez, Kursat; Ersoy, Mehmet

    2008-01-01

    The purpose of this study was to determine opinions of mathematics teacher candidates towards applying 7E instructional model on computer aided instruction environments. The descriptive case study model was used in this study. The sample of the study consists of 52 mathematics teacher candidates which were selected randomly from Eskisehir…

  14. Hardware description languages

    NASA Technical Reports Server (NTRS)

    Tucker, Jerry H.

    1994-01-01

    Hardware description languages are special purpose programming languages. They are primarily used to specify the behavior of digital systems and are rapidly replacing traditional digital system design techniques. This is because they allow the designer to concentrate on how the system should operate rather than on implementation details. Hardware description languages allow a digital system to be described with a wide range of abstraction, and they support top down design techniques. A key feature of any hardware description language environment is its ability to simulate the modeled system. The two most important hardware description languages are Verilog and VHDL. Verilog has been the dominant language for the design of application specific integrated circuits (ASIC's). However, VHDL is rapidly gaining in popularity.

  15. Description scheme for video editing work

    NASA Astrophysics Data System (ADS)

    Ruiloba, Rosa I.; Joly, Philippe

    2001-03-01

    This article presents a Description Scheme (DS) to describe the audio-visual documents from the video editing work point of view. This DS is based on edition techniques used in the video edition domain. The main objective of this DS is to provide a complete, modular and extensible description of the structure of the video documents based on editing process. This VideoEditing DS is generic in the sense that it may be used in a large number of applications such as video document indexing and analysis, description of Edit Decision List and elaboration of editing patterns. It is based on accurate and complete definitions of shots and transition effects required for video document analysis applications. The VideoEditing DS allows three levels of description : analytic, synthetic and semantic. In the DS, the higher (resp. the lower) is the element of description, the more analytic (resp. synthetic) is the information. %Phil This DS allows describing the editing work made by editing boards, using more detailed descriptors of Shots and Transition DSs. These elements are provided to define editing patterns that allow several possible reconstructions of movies depending on, for example, the target audience. A part of the video description made with this DS may be automatically produced by the video to shots segmentation algorithms (analytic DSs ) or by editing software, at the same time the edition work is made. This DS gives an answer to the needs related to the exchange of editing work descriptions between editing softwares. At the same time, the same DS provide an analytic description of editing work which is complementary to existing standards for Edit Decision Lists like SMPTE or AAF.

  16. Change and Calculations: MINNEMAST Coordinated Mathematics - Science Series, Unit 24.

    ERIC Educational Resources Information Center

    Adams, Patricia A., Ed.; Nyberg, Luanne, Ed.

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

  17. Eliciting Students' Beliefs about Who Is Good at Mathematics

    ERIC Educational Resources Information Center

    Morge, Shelby P.

    2007-01-01

    This article highlights a series of activities designed to elicit students' mathematics-related beliefs, particularly those related to gender. As a result of the activities, females in upper-level classes rated themselves as having less confidence than males, and viewing a movie clip was sufficient for some students to modify their descriptions of…

  18. Using Our Senses: MINNEMAST Coordinated Mathematics - Science Series, Unit 4.

    ERIC Educational Resources Information Center

    Page, Laura M.; Reed, Elizabeth W.

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

  19. Harmony between Turkish Early Childhood and Primary Mathematics Education Standards

    ERIC Educational Resources Information Center

    Caliskan Dedeoglu, Nuray; Alat, Zeynep

    2012-01-01

    The aim of this study was to explore the spiral relation and the congruency between mathematics standards listed in the Early Childhood and First Grade curricula in Turkey. A descriptive content analysis was conducted on Early Child Education Curriculum (OOEP) for 36-72 months old children and Math Curriculum for the Grades 1-5 (IMOP), both…

  20. In the Beginning: The Study of Mathematically Precocious Youth (SMPY).

    ERIC Educational Resources Information Center

    Stanley, Julian C.

    This paper contains a brief description of the founding and early years of the Study of Mathematically Precocious Youth (SMPY) from 1968 to the present. Several of the guiding principles behind SMPY are discussed. SMPY led to the formation of strong regional, state, and local centers that now blanket the United States with annual talent searches…

  1. Conditions Affecting Life: MINNEMAST Coordinated Mathematics - Science Series, Unit 23.

    ERIC Educational Resources Information Center

    Vogt, Elaine E., Ed.

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

  2. Investigating Systems: MINNEMAST Coordinated Mathematics - Science Series, Unit 15.

    ERIC Educational Resources Information Center

    David, Edith, Ed.

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

  3. 101 Environmental Education Activities. Booklet 3--Mathematics Activities.

    ERIC Educational Resources Information Center

    Schaljo, Roger, Comp.

    Each of the 14 environment-related mathematics activities included in this publication by the Upper Mississippi River ECO-Center includes objectives, materials needed, preparation, and activity description. Occasionally, variations and helpful hints are added. Because the student can gain experience to help him with the practical application of…

  4. Using Larger Numbers: MINNEMAST Coordinated Mathematics - Science Series, Unit 20.

    ERIC Educational Resources Information Center

    Ihrig, Elizabeth A., Ed.

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

  5. Watching and Wondering: MINNEMAST Coordinated Mathematics - Science Series, Unit 1.

    ERIC Educational Resources Information Center

    Page, Laura M.; Reed, Elizabeth W.

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

  6. Mathematics Education Is Not an Enigma--Part 2

    ERIC Educational Resources Information Center

    Williams, Doug

    2012-01-01

    Doug Williams presented the opening address at Conference 2012 on the theme of "Enigmas". Here he continues storytelling about the learning and teaching of mathematics at its best. The descriptions are of real classrooms with real teachers, and real learners. As with many good stories this is the narrative of a journey. A journey that seeks to…

  7. Mathematics Education Is Not an Enigma--Part 1

    ERIC Educational Resources Information Center

    Williams, Doug

    2012-01-01

    Doug Williams presented the opening address at Conference 2012 on the theme of "Enigmas". This is storytelling about the learning and teaching of mathematics at its best. The descriptions are of real classrooms with real teachers, and real learners. As with many good stories this is the narrative of a journey. A journey that seeks to change…

  8. Engaging Students in Mathematical Modeling through Service-Learning

    ERIC Educational Resources Information Center

    Carducci, Olivia M.

    2014-01-01

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

  9. Operating Procedures for HP Mathematics Drill and Practice Program.

    ERIC Educational Resources Information Center

    Hewlett Packard Co., Cupertino, CA.

    This book is one of a series of five providing a description of the Hewlett-Packard Mathematics Drill and Practice Program for the computer. Complete operating procedures for the program are given. Contents include: (1) introduction; (2) things to know before operating the system; (3) creating records and files; (4) daily tasks; (5) occasional…

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

    ERIC Educational Resources Information Center

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

    2013-01-01

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

  11. Brain Hemisphericity and Mathematics Achievement of High School Students

    ERIC Educational Resources Information Center

    Fernandez, Sanny F.

    2011-01-01

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

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

    ERIC Educational Resources Information Center

    Bakke, Jeannette; And Others

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

  13. Cultural Issues in the Communication of Research on Mathematics Education

    ERIC Educational Resources Information Center

    Bartolini Bussi, Maria G.; Martignone, Francesca

    2013-01-01

    It might be trite to observe that every research study is framed within a cultural background. In this paper we argue that the description of the cultural background is important for discussing, evaluating and exploiting internationally the findings of local educational studies. This issue is fundamental in every study in mathematics education…

  14. A Generalized Instructional System for Elementary Mathematical Logic.

    ERIC Educational Resources Information Center

    Goldberg, Adele

    A computer-based instructional system for teaching the notion of mathematical proof is described. The system is capable of handling formalizations of the full predicate calculus with identity and, with minor work, definite description. Designed as an instructional device, the program is also the basis for a number of research projects involving…

  15. Developing Interactive Learning Objects for a Computing Mathematics Module

    ERIC Educational Resources Information Center

    Lim, Cher Ping; Lee, Siew Lie; Richards, Cameron

    2006-01-01

    Based on a case study of the online component of a Computing Mathematics module at a local polytechnic in Singapore, this article provides a descriptive account of the development and employment of interactive learning objects to enhance the learning experiences of the students in the course. The experimented learning objects were branded as…

  16. Characterization of high school mathematics and physics language genres

    NASA Astrophysics Data System (ADS)

    Wallace, Michelle L.

    Research indicates that language factors play a critical role in the learning of school mathematics and science. Symbols and language-forms have been created to represent and discuss mathematical ideas. Understanding language factors, therefore, is critical in improving the teaching and learning of school mathematics and science. The specific goal of this research was to characterize language genres found in secondary school mathematics and physics classrooms. The research presented here was conducted in two secondary school classrooms---one algebra and one physics---taught by the same teacher. The focus was on the discourse between the teacher and her students. In both mathematics and physics, the teacher attended to the meaning of mathematical concepts and processes, but the talk differed. Physics talk focused on developing meaning for the physics concepts through activities and discussion, which were accompanied by mathematical calculations and analyses. Algebra talk, on the other hand, was procedural and narrative in nature. Thus physics talk was more descriptive of individual concepts and situation, and was more explanatory and exploratory than algebra talk. All discourse inevitably reflects one's thinking and beliefs about the content of that discourse. Thus talking algebra and talking physics, as observed in this study, both represented the teacher's beliefs about teaching and learning and the nature of the school curriculum. Even for a teacher with a strong academic background in both mathematics and science, integrating across the curriculum can be hindered by the approved school curriculum and by the reality of the particular classroom context. Providing professional development and implementing one of several available integrated curricula would be needed if more integration were to be implemented. This study presents a literature-based description of the conceptual notion of language genre. It additionally presents a conceptualization of mathematics and

  17. A robust and accurate formulation of molecular and colloidal electrostatics

    NASA Astrophysics Data System (ADS)

    Sun, Qiang; Klaseboer, Evert; Chan, Derek Y. C.

    2016-08-01

    This paper presents a re-formulation of the boundary integral method for the Debye-Hückel model of molecular and colloidal electrostatics that removes the mathematical singularities that have to date been accepted as an intrinsic part of the conventional boundary integral equation method. The essence of the present boundary regularized integral equation formulation consists of subtracting a known solution from the conventional boundary integral method in such a way as to cancel out the singularities associated with the Green's function. This approach better reflects the non-singular physical behavior of the systems on boundaries with the benefits of the following: (i) the surface integrals can be evaluated accurately using quadrature without any need to devise special numerical integration procedures, (ii) being able to use quadratic or spline function surface elements to represent the surface more accurately and the variation of the functions within each element is represented to a consistent level of precision by appropriate interpolation functions, (iii) being able to calculate electric fields, even at boundaries, accurately and directly from the potential without having to solve hypersingular integral equations and this imparts high precision in calculating the Maxwell stress tensor and consequently, intermolecular or colloidal forces, (iv) a reliable way to handle geometric configurations in which different parts of the boundary can be very close together without being affected by numerical instabilities, therefore potentials, fields, and forces between surfaces can be found accurately at surface separations down to near contact, and (v) having the simplicity of a formulation that does not require complex algorithms to handle singularities will result in significant savings in coding effort and in the reduction of opportunities for coding errors. These advantages are illustrated using examples drawn from molecular and colloidal electrostatics.

  18. A robust and accurate formulation of molecular and colloidal electrostatics.

    PubMed

    Sun, Qiang; Klaseboer, Evert; Chan, Derek Y C

    2016-08-01

    This paper presents a re-formulation of the boundary integral method for the Debye-Hückel model of molecular and colloidal electrostatics that removes the mathematical singularities that have to date been accepted as an intrinsic part of the conventional boundary integral equation method. The essence of the present boundary regularized integral equation formulation consists of subtracting a known solution from the conventional boundary integral method in such a way as to cancel out the singularities associated with the Green's function. This approach better reflects the non-singular physical behavior of the systems on boundaries with the benefits of the following: (i) the surface integrals can be evaluated accurately using quadrature without any need to devise special numerical integration procedures, (ii) being able to use quadratic or spline function surface elements to represent the surface more accurately and the variation of the functions within each element is represented to a consistent level of precision by appropriate interpolation functions, (iii) being able to calculate electric fields, even at boundaries, accurately and directly from the potential without having to solve hypersingular integral equations and this imparts high precision in calculating the Maxwell stress tensor and consequently, intermolecular or colloidal forces, (iv) a reliable way to handle geometric configurations in which different parts of the boundary can be very close together without being affected by numerical instabilities, therefore potentials, fields, and forces between surfaces can be found accurately at surface separations down to near contact, and (v) having the simplicity of a formulation that does not require complex algorithms to handle singularities will result in significant savings in coding effort and in the reduction of opportunities for coding errors. These advantages are illustrated using examples drawn from molecular and colloidal electrostatics. PMID:27497538

  19. The Applied Mathematics for Power Systems (AMPS)

    SciTech Connect

    Chertkov, Michael

    2012-07-24

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

  20. Reaching All Students with Mathematics.

    ERIC Educational Resources Information Center

    Cuevas, Gilbert, Ed.; Driscoll, Mark, Ed.

    The National Council of Teachers of Mathematics'"Curriculum and Evaluation Standards for School Mathematics" and "Professional Standards for Teaching Mathematics" reflect the belief that all students can learn a significant core of high-quality mathematics. Recognizing the magnitude of the task of reaching all students, this book was put together…

  1. A Mathematics Software Database Update.

    ERIC Educational Resources Information Center

    Cunningham, R. S.; Smith, David A.

    1987-01-01

    Contains an update of an earlier listing of software for mathematics instruction at the college level. Topics are: advanced mathematics, algebra, calculus, differential equations, discrete mathematics, equation solving, general mathematics, geometry, linear and matrix algebra, logic, statistics and probability, and trigonometry. (PK)

  2. Perceptions of Mathematics and Gender

    ERIC Educational Resources Information Center

    Kloosterman, Peter; Tassel, Janet; Ponniah, Ann G.; Esses, N. Kathryn

    2008-01-01

    This study examined students' perceptions about gender and the subject of mathematics, as well as gender and mathematics learning. Secondary school students and pre-service elementary teachers were surveyed using the Mathematics as a Gendered Domain and Who and Mathematics instruments developed by Leder and Forgasz (Leder, 2001). The data indicate…

  3. 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…

  4. Truth & Beauty: Mathematics in Literature

    ERIC Educational Resources Information Center

    Cohen, Marion D.

    2013-01-01

    Today there are many categories of mathematics literature, including fiction and poetry. Mathematics fiction appears in such anthologies as "Fantasia Mathematica" (Fadiman 1958, 1997) and "The Mathematical Magpie" (Fadiman 1962, 1997). In addition, mathematics fiction is featured at http://kasmana.people.cofc.edu/MATHFICT.…

  5. Semantic Processing of Mathematical Gestures

    ERIC Educational Resources Information Center

    Lim, Vanessa K.; Wilson, Anna J.; Hamm, Jeff P.; Phillips, Nicola; Iwabuchi, Sarina J.; Corballis, Michael C.; Arzarello, Ferdinando; Thomas, Michael O. J.

    2009-01-01

    Objective: To examine whether or not university mathematics students semantically process gestures depicting mathematical functions (mathematical gestures) similarly to the way they process action gestures and sentences. Semantic processing was indexed by the N400 effect. Results: The N400 effect elicited by words primed with mathematical gestures…

  6. On correct mathematical models of ecological LSS of high closure

    NASA Astrophysics Data System (ADS)

    Bartsev, S. I.

    Usually mathematical models of natural ecological systems are implicitly based on the assumption of stoichiometrically rigid metabolism In most cases such assumption is applicable but in the case of ecological systems of high closure it can cause errors of forecast For completely closed ecological system the assumption of rigid metabolism results in completely incorrect forecast Since CELSS for long-duration missions have to be of high closure then using adequate mathematical description is of great importance for successfulness of a space mission Possible variants of non-rigid metabolism applicable to different type of biological components of CELSS are considered in the paper It is shown non-rigid models of metabolism not only eliminate incorrectness of mathematical description but as well allow to obtain more adequate estimation of stability of closed ecological systems

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

    ERIC Educational Resources Information Center

    LoPresto, Michael C.

    2016-01-01

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

  8. Automatic TLI recognition system, general description

    SciTech Connect

    Lassahn, G.D.

    1997-02-01

    This report is a general description of an automatic target recognition system developed at the Idaho National Engineering Laboratory for the Department of Energy. A user`s manual is a separate volume, Automatic TLI Recognition System, User`s Guide, and a programmer`s manual is Automatic TLI Recognition System, Programmer`s Guide. This system was designed as an automatic target recognition system for fast screening of large amounts of multi-sensor image data, based on low-cost parallel processors. This system naturally incorporates image data fusion, and it gives uncertainty estimates. It is relatively low cost, compact, and transportable. The software is easily enhanced to expand the system`s capabilities, and the hardware is easily expandable to increase the system`s speed. In addition to its primary function as a trainable target recognition system, this is also a versatile, general-purpose tool for image manipulation and analysis, which can be either keyboard-driven or script-driven. This report includes descriptions of three variants of the computer hardware, a description of the mathematical basis if the training process, and a description with examples of the system capabilities.

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

    SciTech Connect

    Nakhleh, Luay

    2014-03-12

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

  10. Accurate thermoelastic tensor and acoustic velocities of NaCl

    NASA Astrophysics Data System (ADS)

    Marcondes, Michel L.; Shukla, Gaurav; da Silveira, Pedro; Wentzcovitch, Renata M.

    2015-12-01

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

  11. Accurate thermoelastic tensor and acoustic velocities of NaCl

    SciTech Connect

    Marcondes, Michel L.; Shukla, Gaurav; Silveira, Pedro da; Wentzcovitch, Renata M.

    2015-12-15

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

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

    ERIC Educational Resources Information Center

    Goodson, Joshua E.

    2012-01-01

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

  13. High School Mathematics Teachers' Perspectives on the Purposes of Mathematical Proof in School Mathematics

    ERIC Educational Resources Information Center

    Dickerson, David S.; Doerr, Helen M.

    2014-01-01

    Proof serves many purposes in mathematics. In this qualitative study of 17 high school mathematics teachers, we found that these teachers perceived that two of the most important purposes for proof in school mathematics were (a) to enhance students' mathematical understanding and (b) to develop generalized thinking skills that were…

  14. Attitudes toward Mathematics: Relationships to Mathematics Achievement, Gender, Mathematics Course-taking Plans, and Career Interests.

    ERIC Educational Resources Information Center

    Thorndike-Christ, Tracy

    The relationship of attitudes toward mathematics to mathematics performance, gender, mathematics course-taking plans, and career interests were investigated. Students enrolled in public middle and high school mathematics courses (722 male, 794 female) served as subjects. The Fennema-Sherman Math Attitude scales were used to measure attitudes…

  15. Basic mathematical cognition.

    PubMed

    Gaber, David; Schlimm, Dirk

    2015-01-01

    Mathematics is a powerful tool for describing and developing our knowledge of the physical world. It informs our understanding of subjects as diverse as music, games, science, economics, communications protocols, and visual arts. Mathematical thinking has its roots in the adaptive behavior of living creatures: animals must employ judgments about quantities and magnitudes in the assessment of both threats (how many foes) and opportunities (how much food) in order to make effective decisions, and use geometric information in the environment for recognizing landmarks and navigating environments. Correspondingly, cognitive systems that are dedicated to the processing of distinctly mathematical information have developed. In particular, there is evidence that certain core systems for understanding different aspects of arithmetic as well as geometry are employed by humans and many other animals. They become active early in life and, particularly in the case of humans, develop through maturation. Although these core systems individually appear to be quite limited in application, in combination they allow for the recognition of mathematical properties and the formation of appropriate inferences based upon those properties. In this overview, the core systems, their roles, their limitations, and their interaction with external representations are discussed, as well as possibilities for how they can be employed together to allow us to reason about more complex mathematical domains. PMID:26263425

  16. Mathematical and computational models of plasma flows

    NASA Astrophysics Data System (ADS)

    Brushlinsky, K. V.

    Investigations of plasma flows are of interest, firstly, due to numerous applications, and secondly, because of their general principles, which form a special branch of physics: the plasma dynamics. Numerical simulation and computation, together with theoretic and experimental methods, play an important part in these investigations. Speaking on flows, a relatively dense plasma is mentioned, so its mathematical models appertain to the fluid mechanics, i.e., they are based on the magnetohydrodynamic description of plasma. Time dependent two dimensional models of plasma flows of two wide-spread types are considered: the flows across the magnetic field and those in the magnetic field plane.

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

    ERIC Educational Resources Information Center

    Taber, Mary R.

    2013-01-01

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

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

    ERIC Educational Resources Information Center

    Roth, Wolff-Michael; Maheux, Jean-François

    2014-01-01

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

  19. The Provision, Use, Study Time and Effectiveness of Media: A Mathematical Model

    ERIC Educational Resources Information Center

    Burt, Gordon; Lloyd, David

    2005-01-01

    Many institutions regularly conduct surveys of students. In some cases these provide descriptive statistics about students' actual use of course components and the descriptive statistics are discussed using ordinary language. A number of refinements to these surveys are proposed. It is argued that mathematical modeling as used in the discipline of…

  20. CRAC2 model description

    SciTech Connect

    Ritchie, L.T.; Alpert, D.J.; Burke, R.P.; Johnson, J.D.; Ostmeyer, R.M.; Aldrich, D.C.; Blond, R.M.

    1984-03-01

    The CRAC2 computer code is a revised version of CRAC (Calculation of Reactor Accident Consequences) which was developed for the Reactor Safety Study. This document provides an overview of the CRAC2 code and a description of each of the models used. Significant improvements incorporated into CRAC2 include an improved weather sequence sampling technique, a new evacuation model, and new output capabilities. In addition, refinements have been made to the atmospheric transport and deposition model. Details of the modeling differences between CRAC2 and CRAC are emphasized in the model descriptions.

  1. Perception determinants in learning mathematics

    NASA Astrophysics Data System (ADS)

    Mokhtar, Siti Fairus; Ali, Noor Rasidah; Rashid, Nurazlina Abdul

    2015-05-01

    This article described a statistical study of students' perception in mathematics. The objective of this study is to identify factors related to perception about learning mathematics among non mathematics' student. This study also determined the relationship between of these factors among non mathematics' student. 43 items questionnaires were distributed to one hundred students in UiTM Kedah who enrolled in the Business Mathematics course. These items were measured by using a semantic scale with the following anchors: 1 = strongly disagree to 7 = strongly agree. A factor analysis of respondents were identified into five factors that influencing the students' perception in mathematics. In my study, factors identified were attitude, interest, role of the teacher, role of peers and usefulness of mathematics that may relate to the perception about learning mathematics among non mathematics' student.

  2. Mathematical Astronomy in India

    NASA Astrophysics Data System (ADS)

    Plofker, Kim

    Astronomy in South Asia's Sanskrit tradition, apparently originating in simple calendric computations regulating the timing of ancient ritual practices, expanded over the course of two or three millennia to include detailed spherical models, an endless variety of astrological systems, and academic mathematics in general. Assimilating various technical models, methods, and genres from the astronomy of neighboring cultures, Indian astronomers created new forms that were in turn borrowed by their foreign counterparts. Always recognizably related to the main themes of Eurasian geocentric mathematical astronomy, Indian astral science nonetheless maintained its culturally distinct character until Keplerian heliocentrism and Newtonian mechanics replaced it in colonial South Asia's academic mainstream.

  3. Mathematics in modern immunology

    PubMed Central

    Castro, Mario; Lythe, Grant; Molina-París, Carmen; Ribeiro, Ruy M.

    2016-01-01

    Mathematical and statistical methods enable multidisciplinary approaches that catalyse discovery. Together with experimental methods, they identify key hypotheses, define measurable observables and reconcile disparate results. We collect a representative sample of studies in T-cell biology that illustrate the benefits of modelling–experimental collaborations and that have proven valuable or even groundbreaking. We conclude that it is possible to find excellent examples of synergy between mathematical modelling and experiment in immunology, which have brought significant insight that would not be available without these collaborations, but that much remains to be discovered. PMID:27051512

  4. Mathematics in modern immunology.

    PubMed

    Castro, Mario; Lythe, Grant; Molina-París, Carmen; Ribeiro, Ruy M

    2016-04-01

    Mathematical and statistical methods enable multidisciplinary approaches that catalyse discovery. Together with experimental methods, they identify key hypotheses, define measurable observables and reconcile disparate results. We collect a representative sample of studies in T-cell biology that illustrate the benefits of modelling-experimental collaborations and that have proven valuable or even groundbreaking. We conclude that it is possible to find excellent examples of synergy between mathematical modelling and experiment in immunology, which have brought significant insight that would not be available without these collaborations, but that much remains to be discovered.

  5. Mathematical challenges from theoretical/computational chemistry

    SciTech Connect

    1995-12-31

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

  6. Transitioning into Mathematics Curriculum Leadership: A Study of How a Graduate Degree Program Influenced Leaders' Views, Actions, and Responses

    ERIC Educational Resources Information Center

    Cummings, Liza

    2011-01-01

    The purpose of this "intrinsic multi-descriptive" case study was to explore how a mathematics curriculum leadership graduate degree program influenced seven participants' views and actions as they transitioned into new mathematics curriculum leadership roles. The mathematics curriculum leadership graduate degree program was a joint…

  7. Mill profiler machines soft materials accurately

    NASA Technical Reports Server (NTRS)

    Rauschl, J. A.

    1966-01-01

    Mill profiler machines bevels, slots, and grooves in soft materials, such as styrofoam phenolic-filled cores, to any desired thickness. A single operator can accurately control cutting depths in contour or straight line work.

  8. Teaching Descriptive Style.

    ERIC Educational Resources Information Center

    Brashers, H. C.

    1968-01-01

    As the inexperienced writer becomes aware of the issues involved in the composition of effective descriptive prose, he also develops a consistent control over his materials. The persona he chooses, if coherently thought out, can function as an index of many choices, helping him to manipulate the tone, intent, and mood of this style; to regulate…

  9. Computer programs: Operational and mathematical, a compilation

    NASA Technical Reports Server (NTRS)

    1973-01-01

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

  10. Elementary School Mathematics Priorities

    ERIC Educational Resources Information Center

    Wilson, W. Stephen

    2009-01-01

    This article first describes some of the basic skills and knowledge that a solid elementary school mathematics foundation requires. It then elaborates on several points germane to these practices. These are then followed with a discussion and conclude with final comments and suggestions for future research. The article sets out the five…

  11. The Constructivist Mathematics Classroom

    ERIC Educational Resources Information Center

    Jones, Karrie; Jones, Jennifer L.; Vermette, Paul J.

    2010-01-01

    By examining how people learn, the educational theories of Dewey, Piaget, Vygotsky and Bruner can be synthesized to give this set of core Constructivist principles. Principles of effective mathematics teaching: (1) allows learning that is "active" and "reflective". Students are required to transfer key concepts to new situations; (2) allows…

  12. The Amazing Mathematical Race

    ERIC Educational Resources Information Center

    Noblitt, Bethany A.; Buckley, Brooke E.

    2011-01-01

    Teams, pit stops, clues, time limits, fast forwards, challenges, and prizes are all components of the CBS hit show "The Amazing Race." They were also elements of the Amazing Mathematical Race sponsored by the Math and Stats Club at Northern Kentucky University in April 2009. Held in recognition of Math Awareness Month, which is advocated by the…

  13. Mathematics in Vocational Education.

    ERIC Educational Resources Information Center

    Oregon State Univ., Corvallis. Vocational-Technical Education Dept.

    This handbook was developed to help the vocational teacher aid students in solving mathematical problems in vocational education classes. Most of the examples in the handbook were derived from metal-working and industrial mechanics classes; however, the procedures explained through them will work in any vocational class. The handbook is divided…

  14. Navajo Area Mathematics Guidelines.

    ERIC Educational Resources Information Center

    Bureau of Indian Affairs (Dept. of Interior), Window Rock, AZ.

    Heavy emphasis is placed on development of understanding of arithmetic in this mathematics curriculum prepared specifically for Navajo children and intended for use in reservation schools. Materials are presented so that only when a given concept is understood are skills associated with it and a written format introduced. Learning activities…

  15. Supporting Mathematical Thinking

    ERIC Educational Resources Information Center

    Houssart, Jenny; Roaf, Caroline; Watson, Anne

    2005-01-01

    This book looks at how practitioners have focused on the fully educational application of intellect to the problem of developing mathematical thinking among one's pupils. Each chapter demonstrates reflective minds at work, relying on close observation, willingness to understand the student's thinking processes and patient commitment to students…

  16. Mathematics Guide, K-12.

    ERIC Educational Resources Information Center

    Portales Public Schools, NM.

    This curriculum guide provides aid in organizing and planning for the mathematical needs of the individual classroom. It is recommended that: (1) each teacher study the entire curriculum to become familiar with the concepts that interlock and blend all the grades together, and (2) all students with average ability master 70% of the skills. The…

  17. Exploratory Problems in Mathematics.

    ERIC Educational Resources Information Center

    Stevenson, Frederick W.

    This book attempts to introduce students to the creative aspects of mathematics through exploratory problems. The introduction presents the criteria for the selection of the problems in the book. Criteria indicate that problems should: be immediately attractive, require data to be generated or gathered, appeal to students from junior high school…

  18. Making Music with Mathematics.

    ERIC Educational Resources Information Center

    Fernandez, Maria L.

    1999-01-01

    Presents examples of students' work when they are engaged in problem solving and reasoning tasks as they determine how to fill bottles with water to create musical notes by blowing across the tops of the bottles, and as they create mathematical models that represent these notes. (ASK)

  19. Mathematics as Problem Solving.

    ERIC Educational Resources Information Center

    Soifer, Alexander

    This book contains about 200 problems. It is suggested that it be used by students, teachers or anyone interested in exploring mathematics. In addition to a general discussion on problem solving, there are problems concerned with number theory, algebra, geometry, and combinatorics. (PK)

  20. Mathematics for Drafting.

    ERIC Educational Resources Information Center

    Clary, Joseph R.; Nery, Karen P.

    This set of three modules was designed for use primarily to help teach and reinforce the basic mathematics skills in drafting classes. The modules are based on the needs of drafting students in beginning courses as determined by a survey of teachers across North Carolina. Each module consists of basic information and examples and problem sheets…

  1. Corner Reflector Mathematics

    ERIC Educational Resources Information Center

    Popelka, Susan R.

    2011-01-01

    Tiny prisms in reflective road signs and safety vests have interesting geometrical properties that can be discussed at any level of high school mathematics. At the beginning of the school year, the author teaches a unit on these reflective materials in her precalculus class so that students can review and strengthen their geometry and trigonometry…

  2. Correlating Mathematics and Science

    ERIC Educational Resources Information Center

    Mireles, Selena Vasquez

    2009-01-01

    The change from students learning all subjects together in a one-room schoolhouse to learning in classes separated by subject and grade resulted in distinct disciplines such as social studies, mathematics, science, and English. What was lost was the unified, holistic curriculum that a one-room setting required. Since students move from…

  3. Investigating Children's Mathematics Readiness

    ERIC Educational Resources Information Center

    Lee, Joohi; Autry, Mary Murray; Fox, Jill; Williams, Cynthia

    2008-01-01

    A sample of 244 children (average age: 61 months) and their parents from the Dallas and Fort Worth (DFW) metroplex area in Texas were surveyed to investigate children's mathematics readiness. This study was conducted as part of a project funded by a local child care council, composed of business, civic, and education leaders in the community. The…

  4. Mathematics in Baseball.

    ERIC Educational Resources Information Center

    Battista, Michael T.

    1993-01-01

    Presents a series of 13 activities to explore the mathematics of baseball. Activities examine the numerical measures of player statistics and team standings and the geometry of baseball. Discusses the use of computer spreadsheets and LOGO computer simulations to study the concepts embodied in the activities. (MDH)

  5. Oral and Mental Mathematics

    ERIC Educational Resources Information Center

    Davis, Sue

    2009-01-01

    The Williams Review (Dept. for Children, Schools and Families, 2008) is significantly important to all early years and primary educationalists, including those who are involved in teaching mathematics to the next generation of primary school teachers. The report, compiled as a result of this review, sets out the ways that children in primary…

  6. Symmetry in Mathematics Learning.

    ERIC Educational Resources Information Center

    Dreyfus, Tommy; Eisenberg, Theodore

    1989-01-01

    Discusses the creed in symmetry and the omnipresence of symmetrical relationships in mathematics and nature, discusses mathematicians' attraction toward looking for symmetrical relationships as an unstated problem-solving heuristic, and shows how symmetry can be used as a didactical tool. (Author/MKR)

  7. Consumer Mathematics. Teaching Units.

    ERIC Educational Resources Information Center

    North Carolina State Dept. of Public Instruction, Raleigh.

    GRADES OR AGES: Secondary school. SUBJECT MATTER: Consumer mathematics including--money management, transportation, probability, swindles and gyps, insurance, housing, taxes, consumer credit, banks, savings, and investments. ORGANIZATION AND PHYSICAL APPEARANCE: The guide is divided into ten parallel units, one for each of the above areas, which…

  8. Every Day Is Mathematical

    ERIC Educational Resources Information Center

    Barger, Rita H.; Jarrah, Adeeb M.

    2012-01-01

    March 14 is special because it is Pi Day. Mathematics is celebrated on that day because the date, 3-14, replicates the first three digits of pi. Pi-related songs, websites, trivia facts, and more are at the fingertips of interested teachers and students. Less celebrated, but still fairly well known, is National Metric Day, which falls on October…

  9. Mathematics Unipac. Computers.

    ERIC Educational Resources Information Center

    Parma City School District, OH.

    Five activities are presented in this student workbook designed for exploration of a career in computers, and the mathematics related to that career. Included are activities on basic computer language, flow charts, and basic computer programming. Each activity includes the objective, materials needed, and information for completing the activity.…

  10. Mathematical Pattern Hunters

    ERIC Educational Resources Information Center

    Whitin, Phyllis; Whitin, David J.

    2011-01-01

    The habit of looking for patterns, the skills to find them, and the expectation that patterns have explanations is an essential mathematical habit of mind for young children (Goldenberg, Shteingold, & Feurzeig 2003, 23). Work with patterns leads to the ability to form generalizations, the bedrock of algebraic thinking, and teachers must nurture…

  11. Mathematical Intrusions in Literatures

    ERIC Educational Resources Information Center

    Modica, Erasmo

    2011-01-01

    This article describes an activity that can be carried out in one of the final classes of Italian secondary schools. The aim of the activity is to stimulate pupil curiosity, demonstrating that Mathematics is not a barren subject and allowing the students, according to an interdisciplinary point of view, to investigate some literary works and the…

  12. Audiovisual Materials in Mathematics.

    ERIC Educational Resources Information Center

    Raab, Joseph A.

    This pamphlet lists five thousand current, readily available audiovisual materials in mathematics. These are grouped under eighteen subject areas: Advanced Calculus, Algebra, Arithmetic, Business, Calculus, Charts, Computers, Geometry, Limits, Logarithms, Logic, Number Theory, Probability, Soild Geometry, Slide Rule, Statistics, Topology, and…

  13. Mathematics for the Baker.

    ERIC Educational Resources Information Center

    Bogdany, Melvin

    The curriculum guide offers a course of training in the fundamentals of mathematics as applied to baking. Problems specifically related to the baking trade are included to maintain a practical orientation. The course is designed to help the student develop proficiency in the basic computation of whole numbers, fractions, decimals, percentage,…

  14. Formal Definitions in Mathematics

    ERIC Educational Resources Information Center

    Shield, Mal

    2004-01-01

    The definition is an important language form in the register of mathematics. Students need to understand the structure of a definition so that they can make sense of the definitions they encounter and so that they can construct their own definitions as part of organising their thoughts about the concepts they have explored. This article suggests…

  15. New Technologies in Mathematics.

    ERIC Educational Resources Information Center

    Sarmiento, Jorge

    An understanding of past technological advancements can help educators understand the influence of new technologies in education. Inventions such as the abacus, logarithms, the slide rule, the calculating machine, computers, and electronic calculators have all found their place in mathematics education. While new technologies can be very useful,…

  16. Mathematics and Mobile Learning

    ERIC Educational Resources Information Center

    White, Tobin; Martin, Lee

    2014-01-01

    This paper argues for an approach to mobile learning that leverages students' informal digital practices as resources for designing mathematics classrooms activities. We briefly describe two exploratory designs along these lines, one featuring the use of photos taken by students outside class and the other centered on their recording and…

  17. Mathematics, Vol. 2.

    ERIC Educational Resources Information Center

    Bureau of Naval Personnel, Washington, DC.

    The second of three volumes of a mathematics training course for Navy personnel, this document contains material primarily found at the college level. Beginning with logarithms and trigonometry, the text moves into vectors and static equilibrium (physics). Coordinate geometry, conic sections, and the tangents, normals, and slopes of curves follow.…

  18. Using and Applying Mathematics

    ERIC Educational Resources Information Center

    Knight, Rupert

    2011-01-01

    The Nobel prize winning physicist Richard Feynman (2007) famously enthused about "the pleasure of finding things out". In day-to-day classroom life, however, it is easy to lose and undervalue this pleasure in the process, as opposed to products, of mathematics. Finding things out involves a journey and is often where the learning takes place.…

  19. Designing for Mathematical Abstraction

    ERIC Educational Resources Information Center

    Pratt, Dave; Noss, Richard

    2010-01-01

    Our focus is on the design of systems (pedagogical, technical, social) that encourage mathematical abstraction, a process we refer to as "designing for abstraction." In this paper, we draw on detailed design experiments from our research on children's understanding about chance and distribution to re-present this work as a case study in designing…

  20. A Classroom Mathematics Utility.

    ERIC Educational Resources Information Center

    Williams, Michael

    1984-01-01

    Reviews CATUSPLOT, a mathematics utility aimed at high school algebra through college-level calculus. Basic program capabilities include plotting, tabulating, integrating, and locating of intersections of functions composed of combinations of polynomial, trigonometric, and exponential functions. Rated excellent on all areas examined…

  1. Designing a Mathematics Curriculum

    ERIC Educational Resources Information Center

    Yee, Lee Peng

    2010-01-01

    A decade of PMRI saw the changes in the classroom in some of the primary schools in Indonesia. Based on observation, we can say that though the mathematics syllabus in Indonesia did not change, its curriculum has changed under the movement of PMRI. In this article, we put in writing some of the experience gained through the involvement in…

  2. Storytelling + Origami = Storigami Mathematics

    ERIC Educational Resources Information Center

    Mastin, Marla

    2007-01-01

    This article presents a way to engage students in mathematics learning by using the innovative instructional method of storigami. The author shares reactions from teachers who have used her storigami techniques in their classes and provides an example of storigami using the Norwegian fable "The Dog and the Mountain." (Contains 6 figures.)

  3. The Language of Mathematics

    ERIC Educational Resources Information Center

    Bruun, Faye; Diaz, Joan M.; Dykes, Valerie J.

    2015-01-01

    Students may excel in computation, but their ability to apply their skills will suffer if they do not understand the math vocabulary used in instructions and story problems. This action research project examines two methods for strengthening students' ability to communicate mathematically: (1) Journal writing and peer discussion; and (2) The…

  4. The Making of Mathematics.

    ERIC Educational Resources Information Center

    Thornton, Steve

    2000-01-01

    Describes the most enduring link between Napoleon and mathematics as the geometric result known as Napoleon's Theorem, which states that if equilateral triangles are drawn on the three sides of any triangle, the line segments joining the centers of these equilateral triangles will themselves form an equilateral triangle. (ASK)

  5. Learning Mathematics through Games

    ERIC Educational Resources Information Center

    Gough, John

    2015-01-01

    When considering the use of games for teaching mathematics, educators should distinguish between an "activity" and a "game". Gough (1999) states that "A 'game' needs to have two or more players, who take turns, each competing to achieve a 'winning' situation of some kind, each able to exercise some choice about how to move…

  6. Teaching Vocational Mathematics.

    ERIC Educational Resources Information Center

    Thiering, Jeannette; And Others

    This Australian document is a guide to teaching mathematics as it relates to specific work situations. After a brief introduction, chapter 1 looks at problem solving, advises teachers to lower the reading level and thus raise the understandability of written math problems, and describes a four-step problem-solving process. Chapter 2 outlines a…

  7. Comprehension Tests in Mathematics.

    ERIC Educational Resources Information Center

    Conradie, Jurie; Frith, John

    2000-01-01

    Presents an alternative way for testing a student's understanding of theory in a tertiary mathematics course. Provides two sample questions and discusses the advantages and disadvantages of the method. Argues that the method is an acceptable and flexible means of testing students and can be adapted to use in other contexts as well. (Author/ASK)

  8. Celebrate Mathematical Curiosity

    ERIC Educational Resources Information Center

    Redford, Christine

    2011-01-01

    Children's mathematical questions are often based in real-world experiences, as they instinctively make connections to the world around them. In teaching math methods courses, this author recently started to emphasize the importance of fostering curiosity in, and activating the thinking of, the students. In this article, she describes how to tap…

  9. Mathematics in the Middle.

    ERIC Educational Resources Information Center

    Leutzinger, Larry, Ed.

    This book contains articles that help to further the process of reform in the middle grades, recognizing that the knowledge acquired during these years greatly affects how well the secondary school curriculum will attain its goals. Critical issues facing middle grade classes in particular and all mathematics classrooms in general are discussed.…

  10. Mathematics Through Paper Folding.

    ERIC Educational Resources Information Center

    Olson, Alton T.

    This booklet is a revised edition of Donovan Johnson's "Paper Folding for the Mathematics Class" (ED 077 711). It begins with directions for folding basic constructions such as as a straight line, the line perpendicular to a given line passing through a given point, and the bisector of an angle. Subsequent chapters cover concepts related to…

  11. Flipping Freshman Mathematics

    ERIC Educational Resources Information Center

    Zack, Laurie; Fuselier, Jenny; Graham-Squire, Adam; Lamb, Ron; O'Hara, Karen

    2015-01-01

    Our study compared a flipped class with a standard lecture class in four introductory courses: finite mathematics, precalculus, business calculus, and calculus 1. The flipped sections watched video lectures outside of class and spent time in class actively working on problems. The traditional sections had lectures in class and did homework outside…

  12. Functioning Mathematically: 2

    ERIC Educational Resources Information Center

    Cain, David

    2007-01-01

    In this article, the author looks at ways of creating conditions to bring about learning. If one is to "arrange conditions to bring about learning," one needs written guidance and support systems. Two books that discusses how to arrange these conditions are: "Thinking Mathematically" by John Mason with Leone Burton and Kaye Stacey and "Starting…

  13. Urban Mathematics Teacher Retention

    ERIC Educational Resources Information Center

    Hamdan, Kamal

    2010-01-01

    Mathematics teachers are both more difficult to attract and more difficult to retain than social sciences teachers. This fact is not unique to the United States; it is reported as being a problem in Europe as well (Howson, 2002). In the United States, however, the problem is particularly preoccupying. Because of the chronic teacher shortages and…

  14. NEEDLE TRADES, MATHEMATICS - I.

    ERIC Educational Resources Information Center

    COLICCHIO, ANTOINETTE J.

    THE NEEDLE TRADES INDUSTRY CONSISTS OF THREE TYPES OF ESTABLISHMENTS -- THE REGULAR MANUFACTURERS, THE APPAREL JOBBERS, AND THE CONTRACTORS. THE FUNCTIONS INCLUDED COVER A WIDE SCOPE FROM BUYING OF RAW MATERIAL TO SELLING OF THE FINISHED APPAREL. THE PURPOSE OF THIS STUDY GUIDE IS TO FURNISH BASIC KNOWLEDGE IN MATHEMATICS AND DEVELOP SKILL IN…

  15. COMMERCIAL FOODS, MATHEMATICS - I.

    ERIC Educational Resources Information Center

    DORNFIELD, BLANCHE E.

    THE UNDERSTANDING AND MASTERY OF FUNDAMENTAL MATHEMATICS IS A NECESSARY PART OF COMMERCIAL FOODS WORK. THIS STUDENT HANDBOOK WAS DESIGNED TO ACCOMPANY A COMMERCIAL FOODS COURSE AT THE HIGH SCHOOL LEVEL FOR STUDENTS WITH APPROPRIATE APTITUDES AND COMMERCIAL FOOD SERVICE GOALS. THE MATERIAL, TESTED IN VARIOUS INTERESTED CLASSROOMS, WAS PREPARED BY…

  16. Computers in Fundamental Mathematics.

    ERIC Educational Resources Information Center

    New York City Board of Education, Brooklyn, NY. Div. of Computer Information Services.

    This manual provides a resource for mathematics teachers who wish to take advantage of the extensive library of computer software materials available to expand and strengthen classroom instruction. Classroom management procedures, software duplication guidelines, copying procedures of diskettes for MS DOS and Apple II computers, and methods for…

  17. Middle School Mathematics Students' Perspectives on the Study of Mathematics

    ERIC Educational Resources Information Center

    Vaughn, Christy H.

    2012-01-01

    This qualitative study addressed the perceptions toward the study of mathematics by middle school students who had formerly been in a remedial mathematics program. The purpose of the study was to explore the past experiences of nine students in order to determine what is needed for them to feel successful in mathematics. The conceptual framework…

  18. Between the Academic Mathematics and the Mathematics Education Worlds.

    ERIC Educational Resources Information Center

    Moreira, Candida Queiroz

    1997-01-01

    Investigated stresses confronted by Portuguese secondary mathematics teachers during the first semester in a master's course, Perspectives on Mathematics Education, noting how they negatively affected teachers' self-confidence and morale and discussing fundamental issues teachers addressed in bridging the academic mathematics and mathematics…

  19. Mathematics Teacher Candidates' Metaphors about the Concept of "Mathematics"

    ERIC Educational Resources Information Center

    Erdogan, Ahmet; Yazlik, Derya Ozlem; Erdik, Cengiz

    2014-01-01

    The main purpose of this study was to research mathematics teacher candidates' perceptions about the concept of "mathematics" through the use of metaphors. The research is conducted during 2012-2013 academic year, on a group of 111 mathematics teacher candidates at the Education Faculty of a University in Turkey. To collect the research…

  20. History of Modern Applied Mathematics in Mathematics Education

    ERIC Educational Resources Information Center

    Jankvist, Uffe Thomas

    2009-01-01

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

  1. 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…

  2. 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…

  3. Multicultural Mathematics: A More Inclusive Mathematics. ERIC Digest.

    ERIC Educational Resources Information Center

    Strutchens, Marilyn

    Until recently there have not been many links to students' culture in the mathematics classroom. This may be one of the major barriers to achievement of many groups historically underrepresented in mathematics, for these students may see mathematics as a subject that has very little meaning or value for their current or future lives. This digest…

  4. Racial Differences in Mathematics Test Scores for Advanced Mathematics Students

    ERIC Educational Resources Information Center

    Minor, Elizabeth Covay

    2016-01-01

    Research on achievement gaps has found that achievement gaps are larger for students who take advanced mathematics courses compared to students who do not. Focusing on the advanced mathematics student achievement gap, this study found that African American advanced mathematics students have significantly lower test scores and are less likely to be…

  5. Mathematic coupling of data: a common source of error.

    PubMed Central

    Archie, J P

    1981-01-01

    The relationship between two variables may be mathematically coupled if either one or both variables are derived and/or calculated, and this can lead to erroneous results and invalid conclusions. The purpose of this report is to identify four types of mathematic coupling of data. Type 1 coupling involves directional changes in two variables which are mathematically coupled. Type 2 coupling is the functional relationship between two calculated variables which have one or more common component variables. Type 3, the most common type of mathematic coupling, is direct algebraic coupling between two variables, when one or more of the variables is derived and/or calculated. Type 4 is indirect coupling or physiologic coupling. The common problem in each type of mathematic coupling is that one variable either directly or indirectly contains the whole or components of the second variable. Statistical techniques, when properly applied to the relationship between the two variables, further obscure the underlying mathematic coupling, and tend to support the erroneous results. Recognition of mathematic coupling is imperative for correct data analysis and accurate interpretation. PMID:7212790

  6. Integrating Mathematics and Social Issues

    ERIC Educational Resources Information Center

    Harrell, Gregory K.

    2007-01-01

    This article illustrates how to integrate mathematics with social issues. Social issues discussed in the newspaper provide a rich context for connecting mathematical activities to the real world. The sample activities focus on measurement concepts. (Contains 2 figures.)

  7. Integrating Mathematics and Composition Instruction.

    ERIC Educational Resources Information Center

    Kirtland, Joseph; Hoh, Pau-San

    2002-01-01

    Describes the development of an integrated approach for teaching mathematics and writing to freshmen. The goals are to strengthen mathematical skills, develop writing competencies, and foster interdisciplinary awareness. (Author/MM)

  8. Overview of Mathematical Social Sciences.

    ERIC Educational Resources Information Center

    Kim, K. H.; And Others

    1992-01-01

    Provides a survey of models that use mathematics in a variety of fields of social science. Discusses specifically mathematical applications in demography, economics, management, political science, psychology, sociology, and other areas. Proposes four unsolved problems. (20 references) (MDH)

  9. Ambiguity and Paradox in Mathematics

    ERIC Educational Resources Information Center

    Byers, William

    2007-01-01

    Many people believe that mathematics provides a model of what thinking is, or should be. They imagine that mathematical thinking always proceeds in a logically rigorous, step-by-step fashion from one truth to another, like a formal proof or a computer program. In fact, insights in mathematics -- whether they are the scholar's breakthroughs or the…

  10. New Jersey Mathematics Curriculum Framework.

    ERIC Educational Resources Information Center

    Rosenstein, Joseph G.; And Others

    The New Jersey Mathematics Curriculum Framework is based on the "Mathematics Standards" adopted by the New Jersey State Board of Education on May 1, 1996, and is intended to provide guidance to teachers, administrators, and districts that will help them translate a vision of exemplary mathematics education into reality. It includes information and…

  11. Ethical Dimensions of Mathematics Education

    ERIC Educational Resources Information Center

    Boylan, Mark

    2016-01-01

    The relationships between mathematics, mathematics education and issues such as social justice and equity have been addressed by the sociopolitical tradition in mathematics education. Others have introduced explicit discussion of ethics, advocating for its centrality. However, this is an area that is still under developed. There is a need for an…

  12. Infants and Toddlers Exploring Mathematics.

    ERIC Educational Resources Information Center

    Geist, Eugene

    2003-01-01

    Offers examples of what infants and toddlers might do in early childhood settings, how these behaviors are related to mathematics, and what teachers can do to encourage the natural mathematical interests of this age group. Asserts that teachers' interactions with children are vitally important to children's understanding of early mathematics. (KB)

  13. The Emergence of Mathematical Structures

    ERIC Educational Resources Information Center

    Hegedus, Stephen John; Moreno-Armella, Luis

    2011-01-01

    We present epistemological ruptures that have occurred in mathematical history and in the transformation of using technology in mathematics education in the twenty-first century. We describe how such changes establish a new form of digital semiotics that challenges learning paradigms and mathematical inquiry for learners today. We focus on drawing…

  14. Students' Mathematical Noticing

    ERIC Educational Resources Information Center

    Lobato, Joanne; Hohensee, Charles; Rhodehamel, Bohdan

    2013-01-01

    Even in simple mathematical situations, there is an array of different mathematical features that students can attend to or notice. What students notice mathematically has consequences for their subsequent reasoning. By adapting work from both cognitive science and applied linguistics anthropology, we present a focusing framework, which treats…

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

    ERIC Educational Resources Information Center

    Sriraman, Bharath, Ed.

    2012-01-01

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

  16. 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…

  17. Resisting Reductionism in Mathematics Pedagogy

    ERIC Educational Resources Information Center

    Foster, Colin

    2013-01-01

    Although breaking down a mathematical problem into smaller parts can often be an effective solution strategy, when the same reductionist approach is applied to mathematics pedagogy the effects are far from beneficial for students. Mathematics pedagogy in UK schools is gaining an increasingly reductionist flavour, as seen in an excessive focus on…

  18. Learning to Write about Mathematics

    ERIC Educational Resources Information Center

    Parker, Renee; Breyfogle, M. Lynn

    2011-01-01

    Beginning in third grade, Pennsylvania students are required to take the Pennsylvania State Standardized Assessment (PSSA), which presents multiple-choice mathematics questions and open-ended mathematics problems. Consistent with the Communication Standard of the National Council of Teachers of Mathematics, while solving the open-ended problems,…

  19. The Psychological Foundations of Mathematics.

    ERIC Educational Resources Information Center

    Suppes, Patrick

    1967-01-01

    This paper outlines problems which are central to the psychological foundations of mathematics. Discussed are the relations that exist between psychological and classical foundations of mathematics. It is shown how the inadequacies of current learning theories which account for complex mathematics learning may be made explicit for appropriate…

  20. Toddlers' Opportunities to Learn Mathematics

    ERIC Educational Resources Information Center

    Bjorklund, Camilla

    2008-01-01

    Mathematical knowledge has developed from human activities through thousands of years and is bound to the world and cultures that men and women experience. One can say that mathematics is rooted in humans' everyday life, an environment where people reach agreement regarding principles in mathematics. Through interaction with worldly phenomena and…

  1. Mathematics in the Early Years.

    ERIC Educational Resources Information Center

    Copley, Juanita V., Ed.

    Noting that young children are capable of surprisingly complex forms of mathematical thinking and learning, this book presents a collection of articles depicting children discovering mathematical ideas, teachers fostering students' informal mathematical knowledge, adults asking questions and listening to answers, and researchers examining…

  2. Investigating Teachers' Images of Mathematics

    ERIC Educational Resources Information Center

    Sterenberg, Gladys

    2008-01-01

    Research suggests that understanding new images of mathematics is very challenging and can contribute to teacher resistance. An explicit exploration of personal views of mathematics may be necessary for pedagogical change. One possible way for exploring these images is through mathematical metaphors. As metaphors focus on similarities, they can be…

  3. Creativity: The Essence of Mathematics

    ERIC Educational Resources Information Center

    Mann, Eric L.

    2006-01-01

    For the gifted mathematics student, early mastery of concepts and skills in the mathematics curriculum usually results in getting more of the same work and/or moving through the curriculum at a faster pace. Testing, grades, and pacing overshadow the essential role of creativity involved in doing mathematics. Talent development requires creative…

  4. Unlocking Mathematics Teaching. Second Edition

    ERIC Educational Resources Information Center

    Koshy, Valsa, Ed.; Murray, Jean, Ed.

    2011-01-01

    Now in a fully updated second edition, "Unlocking Mathematics Teaching" is a comprehensive guide to teaching mathematics in the primary school. Combining theory and practice, selected experts outline the current context of mathematics education. They suggest strategies, activities and examples to help develop readers understanding and confidence…

  5. Assessment and Learning of Mathematics.

    ERIC Educational Resources Information Center

    Leder, Gilah C., Ed.

    This book addresses the link between student learning of mathematics, the teaching method adopted in the mathematics classroom, and the assessment procedures used to determine and measure student knowledge. Fifteen chapters address issues that include a review of different models of mathematics learning and assessment practices, three contrasting…

  6. Mathematics Unit Plans. PACE '94.

    ERIC Educational Resources Information Center

    Wiles, Clyde A., Ed.; Schoon, Kenneth J., Ed.

    This booklet contains mathematics unit plans for Algebra 1, Geometry, Math for Technology, Mathematical Problem Solving, and Pre-Algebra developed by PACE (Promoting Academic Excellence In Mathematics, Science & Technology for Workers of the 21st Century). Each unit plan contains suggested timing, objectives, skills to be acquired, workplace…

  7. Professional Development of Mathematics Teachers.

    ERIC Educational Resources Information Center

    Wu, Hung-Hsi

    1999-01-01

    This essay discusses inservice professional development and suggests that any improvement in mathematics education must begin with teachers already in the classroom. It includes three examples of mathematical presentations in professional development made in Californian schools relating to discrete mathematics, connections, and technology. (MM)

  8. STEM Gives Meaning to Mathematics

    ERIC Educational Resources Information Center

    Hefty, Lukas J.

    2015-01-01

    The National Council of Teachers of Mathematics' (NCTM's) "Principles and Standards for School Mathematics" (2000) outlines fi ve Process Standards that are essential for developing deep understanding of mathematics: (1) Problem Solving; (2) Reasoning and Proof; (3) Communication; (4) Connections; and (5) Representation. The Common Core…

  9. Mathematical Giftedness: A Creative Scenario

    ERIC Educational Resources Information Center

    Sharma, Yogesh

    2013-01-01

    Identification and development of giftedness is a major task of mathematics teachers worldwide. An early identification of gifted children in mathematics can have a number of benefits, like, providing opportunities for the nourishment of their talent, saving them from burnout, and proper utilisation of mathematical talent in future. As creativity…

  10. Putting Mathematical Tasks into Context

    ERIC Educational Resources Information Center

    Nagle, Courtney R.; Styers, Jodie L.

    2015-01-01

    Although many factors affect students' mathematical activity during a lesson, the teacher's selection and implementation of tasks is arguably the most influential in determining the level of student engagement. Mathematical tasks are intended to focus students' attention on a particular mathematical concept and it is the careful developing and…

  11. Mathematical Modelling in European Education

    ERIC Educational Resources Information Center

    Ferri, Rita Borromeo

    2013-01-01

    Teaching and learning of mathematical modelling has become a key competence within school curricula and educational standards in many countries of the world. The term mathematical modelling, its meaning, and how it can be implemented in mathematics lessons have been intensively discussed during several Conferences of the European Society for…

  12. Elementary Mathematics: Not so Elementary

    ERIC Educational Resources Information Center

    Scillieri, Elissa Mains

    2012-01-01

    International tests indicate that United States students have been outscored by other countries in the area of mathematics. Researchers warn that elementary mathematics curricula and instruction in this country is not designed around helping students achieve mathematics proficiency. Much of this could also be attributed to the weak development and…

  13. Mathematical History, Philosophy and Education

    ERIC Educational Resources Information Center

    Otte, Michael

    2007-01-01

    History of mathematics occupies itself describing processes of growth and development, whereas philosophy of mathematics is concerned with questions of justification. Both play an essential role within the educational context. But there is a problem because genuine historical studies necessitate ever greater particularity whereas mathematics and…

  14. Early Mathematics Fluency with CCSSM

    ERIC Educational Resources Information Center

    Matney, Gabriel T.

    2014-01-01

    To develop second-grade students' confidence and ease, this author presents examples of learning tasks (Number of the Day, Word Problem Solving, and Modeling New Mathematical Ideas) that align with Common Core State Standards for Mathematics and that build mathematical fluency to promote students' creative expression of mathematical…

  15. 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…

  16. Experimental Mathematics and Computational Statistics

    SciTech Connect

    Bailey, David H.; Borwein, Jonathan M.

    2009-04-30

    The field of statistics has long been noted for techniques to detect patterns and regularities in numerical data. In this article we explore connections between statistics and the emerging field of 'experimental mathematics'. These includes both applications of experimental mathematics in statistics, as well as statistical methods applied to computational mathematics.

  17. Redundancy management of electrohydraulic servoactuators by mathematical model referencing

    NASA Technical Reports Server (NTRS)

    Campbell, R. A.

    1971-01-01

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

  18. Chern-Simons terms and cocycles in physics and mathematics

    SciTech Connect

    Jackiw, R.

    1984-12-01

    Contemporary topological research in Yang-Mills theory is reviewed, emphasizing the Chern-Simons terms and their relatives. Three applications of the Chern-Simons terms in physical theory are described: to help understanding gauge theories in even dimensional space-time; gauge field dynamics in odd dimensional space-time; and mathematically coherent description of even-dimensional gauge theories with chiral fermions that are apparently inconsistent due to chiral anomalies. Discussion of these applications is preceded by explanation of the mathematical preliminaries and examples in simple quantum mechanical settings. 24 refs. (LEW)

  19. Spacelab J experiment descriptions

    SciTech Connect

    Miller, T.Y.

    1993-08-01

    Brief descriptions of the experiment investigations for the Spacelab J Mission which was launched from the Kennedy Space Center aboard the Endeavour in Sept. 1992 are presented. Experiments cover the following: semiconductor crystals; single crystals; superconducting composite materials; crystal growth; bubble behavior in weightlessness; microgravity environment; health monitoring of Payload Specialists; cultured plant cells; effect of low gravity on calcium metabolism and bone formation; and circadian rhythm. Separate abstracts have been prepared for articles from this report.

  20. Spacelab J experiment descriptions

    NASA Technical Reports Server (NTRS)

    Miller, Teresa Y. (Editor)

    1993-01-01

    Brief descriptions of the experiment investigations for the Spacelab J Mission which was launched from the Kennedy Space Center aboard the Endeavour in Sept. 1992 are presented. Experiments cover the following: semiconductor crystals; single crystals; superconducting composite materials; crystal growth; bubble behavior in weightlessness; microgravity environment; health monitoring of Payload Specialists; cultured plant cells; effect of low gravity on calcium metabolism and bone formation; and circadian rhythm.

  1. Management control system description

    SciTech Connect

    Bence, P. J.

    1990-10-01

    This Management Control System (MCS) description describes the processes used to manage the cost and schedule of work performed by Westinghouse Hanford Company (Westinghouse Hanford) for the US Department of Energy, Richland Operations Office (DOE-RL), Richland, Washington. Westinghouse Hanford will maintain and use formal cost and schedule management control systems, as presented in this document, in performing work for the DOE-RL. This MCS description is a controlled document and will be modified or updated as required. This document must be approved by the DOE-RL; thereafter, any significant change will require DOE-RL concurrence. Westinghouse Hanford is the DOE-RL operations and engineering contractor at the Hanford Site. Activities associated with this contract (DE-AC06-87RL10930) include operating existing plant facilities, managing defined projects and programs, and planning future enhancements. This document is designed to comply with Section I-13 of the contract by providing a description of Westinghouse Hanford's cost and schedule control systems used in managing the above activities. 5 refs., 22 figs., 1 tab.

  2. Modified chemiluminescent NO analyzer accurately measures NOX

    NASA Technical Reports Server (NTRS)

    Summers, R. L.

    1978-01-01

    Installation of molybdenum nitric oxide (NO)-to-higher oxides of nitrogen (NOx) converter in chemiluminescent gas analyzer and use of air purge allow accurate measurements of NOx in exhaust gases containing as much as thirty percent carbon monoxide (CO). Measurements using conventional analyzer are highly inaccurate for NOx if as little as five percent CO is present. In modified analyzer, molybdenum has high tolerance to CO, and air purge substantially quenches NOx destruction. In test, modified chemiluminescent analyzer accurately measured NO and NOx concentrations for over 4 months with no denegration in performance.

  3. Kepler's mathematization of Cosmology

    NASA Astrophysics Data System (ADS)

    Field, Judith V.

    The paper concerns with mathematical knowledge of Johannes Kepler. A part of the paper describes the mathematical education of Kepler which includes the Euclidean geometry and texts by Ptolemy. The first He knew from the Proclus' Commentary which was published in 1533. The author is pointing out that Kepler's epistemology was close to Plato's. The "polyhedral archetype" is discussed in detail. The greatest error was in the case of Mercury (~20%) Kepler's reaction was otherwise absolutely what one would exopect of a theoretician in the twentieth century: he suggested that better observations would imoprouve matter. The author make an analogy with modern discussions on metal abundances in the outer layers of old stars. The author is mentioning also that the Kepler's version of Copernicus' system is noticeably different from Copernicus' original one, including important improvements.

  4. Statistical Content in Middle Grades Mathematics Textbooks

    ERIC Educational Resources Information Center

    Pickle, Maria Consuelo Capiral

    2012-01-01

    This study analyzed the treatment and scope of statistical concepts in four, widely-used, contemporary, middle grades mathematics textbook series: "Glencoe Math Connects," "Prentice Hall Mathematics," "Connected Mathematics Project," and "University of Chicago School Mathematics Project." There were three…

  5. Mathematical Methods for Physicists

    NASA Astrophysics Data System (ADS)

    Chow, Tai L.

    2000-07-01

    Preface; 1. Vector and tensor analysis; 2. Ordinary differential equations; 3. Matrix algebra; 4. Fourier series and integrals; 5. Linear vector spaces; 6. Functions of a complex variable; 7. Special functions of mathematical physics; 8. The calculus of variations; 9. The Laplace transformation; 10. Partial differential equations; 11. Simple linear integral equations; 12. Elements of group theory; 13. Numerical methods; 14. Introduction to probability theory; Appendices; Further reading; Index.

  6. Wronski's Foundations of Mathematics.

    PubMed

    Wagner, Roi

    2016-09-01

    Argument This paper reconstructs Wronski's philosophical foundations of mathematics. It uses his critique of Lagrange's algebraic analysis as a vignette to introduce the problems that he raised, and argues that these problems have not been properly appreciated by his contemporaries and subsequent commentators. The paper goes on to reconstruct Wronski's mathematical law of creation and his notions of theory and techne, in order to put his objections to Lagrange in their philosophical context. Finally, Wronski's proof of his universal law (the expansion of a given function by any series of functions) is reviewed in terms of the above reconstruction. I argue that Wronski's philosophical approach poses an alternative to the views of his contemporary mainstream mathematicians, which brings up the contingency of their choices, and bridges the foundational concerns of early modernity with those of the twentieth-century foundations crisis. I also argue that Wronski's views may be useful to contemporary philosophy of mathematical practice, if they are read against their metaphysical grain. PMID:27573997

  7. Mathematical models of hysteresis

    SciTech Connect

    1998-08-01

    The ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach. Their research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. During the past four years, the study has been by and large centered around the following topics: (1) further development of Scalar and vector Preisach-type models of hysteresis; (2) experimental testing of Preisach-type models of hysteresis; (3) development of new models for viscosity (aftereffect) in hysteretic systems; (4) development of mathematical models for superconducting hysteresis in the case of gradual resistive transitions; (5) software implementation of Preisach-type models of hysteresis; and (6) development of new ideas which have emerged in the course of the research work. The author briefly describes the main scientific results obtained in the areas outlined above.

  8. Cultural horizons for mathematics

    NASA Astrophysics Data System (ADS)

    Owens, Kay; Paraides, Patricia; Jannok Nutti, Ylva; Johansson, Gunilla; Bennet, Maria; Doolan, Pat; Peckham, Ray; Hill, John; Doolan, Frank; O'Sullivan, Dominic; Murray, Libbey; Logan, Patricia; McNair, Melissa; Sunnari, Vappu; Murray, Beatrice; Miller, Alissa; Nolan, John; Simpson, Alca; Ohrin, Christine; Doolan, Terry; Doolan, Michelle; Taylor, Paul

    2011-06-01

    As a result of a number of government reports, there have been numerous systemic changes in Indigenous education in Australia revolving around the importance of partnerships with the community. A forum with our local Dubbo community established the importance of working together and developed a model which placed the child in an ecological perspective that particularly noted the role of Elders and the place of the child in the family. However, there was also the issue of curriculum and mathematics education to be addressed. It was recognised that a colonised curriculum reduces the vision of what might be the potential for Indigenous mathematics education. This paper reports on the sharing that developed between our local community and some researchers and teachers from Sweden, Papua New Guinea and New Zealand. It has implications for recognising the impact of testing regimes, the teaching space, understanding the ways children learn, the curriculum, and teacher education. As a result of these discussions, a critical pedagogy that considers culture and place is presented as an ecocultural perspective on mathematics education. This perspective was seen as critical for the curriculum and learning experiences of Indigenous children.

  9. Mathematical foundations of biomechanics.

    PubMed

    Niederer, Peter F

    2010-01-01

    The aim of biomechanics is the analysis of the structure and function of humans, animals, and plants by means of the methods of mechanics. Its foundations are in particular embedded in mathematics, physics, and informatics. Due to the inherent multidisciplinary character deriving from its aim, biomechanics has numerous connections and overlapping areas with biology, biochemistry, physiology, and pathophysiology, along with clinical medicine, so its range is enormously wide. This treatise is mainly meant to serve as an introduction and overview for readers and students who intend to acquire a basic understanding of the mathematical principles and mechanics that constitute the foundation of biomechanics; accordingly, its contents are limited to basic theoretical principles of general validity and long-range significance. Selected examples are included that are representative for the problems treated in biomechanics. Although ultimate mathematical generality is not in the foreground, an attempt is made to derive the theory from basic principles. A concise and systematic formulation is thereby intended with the aim that the reader is provided with a working knowledge. It is assumed that he or she is familiar with the principles of calculus, vector analysis, and linear algebra. PMID:21303323

  10. On Mathematical Proving

    NASA Astrophysics Data System (ADS)

    Stefaneas, Petros; Vandoulakis, Ioannis M.

    2015-12-01

    This paper outlines a logical representation of certain aspects of the process of mathematical proving that are important from the point of view of Artificial Intelligence. Our starting-point is the concept of proof-event or proving, introduced by Goguen, instead of the traditional concept of mathematical proof. The reason behind this choice is that in contrast to the traditional static concept of mathematical proof, proof-events are understood as processes, which enables their use in Artificial Intelligence in such contexts, in which problem-solving procedures and strategies are studied. We represent proof-events as problem-centered spatio-temporal processes by means of the language of the calculus of events, which captures adequately certain temporal aspects of proof-events (i.e. that they have history and form sequences of proof-events evolving in time). Further, we suggest a "loose" semantics for the proof-events, by means of Kolmogorov's calculus of problems. Finally, we expose the intented interpretations for our logical model from the fields of automated theorem-proving and Web-based collective proving.

  11. Mathematics for understanding disease.

    PubMed

    Bies, R R; Gastonguay, M R; Schwartz, S L

    2008-06-01

    The application of mathematical models to reflect the organization and activity of biological systems can be viewed as a continuum of purpose. The far left of the continuum is solely the prediction of biological parameter values, wherein an understanding of the underlying biological processes is irrelevant to the purpose. At the far right of the continuum are mathematical models, the purposes of which are a precise understanding of those biological processes. No models in present use fall at either end of the continuum. Without question, however, the emphasis in regards to purpose has been on prediction, e.g., clinical trial simulation and empirical disease progression modeling. Clearly the model that ultimately incorporates a universal understanding of biological organization will also precisely predict biological events, giving the continuum the logical form of a tautology. Currently that goal lies at an immeasurable distance. Nonetheless, the motive here is to urge movement in the direction of that goal. The distance traveled toward understanding naturally depends upon the nature of the scientific question posed with respect to comprehending and/or predicting a particular disease process. A move toward mathematical models implies a move away from static empirical modeling and toward models that focus on systems biology, wherein modeling entails the systematic study of the complex pattern of organization inherent in biological systems.

  12. Wronski's Foundations of Mathematics.

    PubMed

    Wagner, Roi

    2016-09-01

    Argument This paper reconstructs Wronski's philosophical foundations of mathematics. It uses his critique of Lagrange's algebraic analysis as a vignette to introduce the problems that he raised, and argues that these problems have not been properly appreciated by his contemporaries and subsequent commentators. The paper goes on to reconstruct Wronski's mathematical law of creation and his notions of theory and techne, in order to put his objections to Lagrange in their philosophical context. Finally, Wronski's proof of his universal law (the expansion of a given function by any series of functions) is reviewed in terms of the above reconstruction. I argue that Wronski's philosophical approach poses an alternative to the views of his contemporary mainstream mathematicians, which brings up the contingency of their choices, and bridges the foundational concerns of early modernity with those of the twentieth-century foundations crisis. I also argue that Wronski's views may be useful to contemporary philosophy of mathematical practice, if they are read against their metaphysical grain.

  13. a Contextualist Interpretation of Mathematics

    NASA Astrophysics Data System (ADS)

    Liu, Jie

    2014-03-01

    The nature of mathematics has been the subject of heated debate among mathematicians and philosophers throughout the ages. The realist and anti-realist positions have had longstanding debate over this problem, but some of the most important recent development has focused on the interpretations; each of the above positions has its own interpretation of the nature of mathematics. I argue in this paper a contextualist interpretation of mathematics, it elucidates the essential features of mathematical context. That is, being integral and having concrete structure, mathematical context is a recontextualizational process with determinate boundary.

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

    ERIC Educational Resources Information Center

    Ernest, Paul, Ed.

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

  15. 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…

  16. 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…

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

    ERIC Educational Resources Information Center

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

    2016-01-01

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

  18. Can Appraisers Rate Work Performance Accurately?

    ERIC Educational Resources Information Center

    Hedge, Jerry W.; Laue, Frances J.

    The ability of individuals to make accurate judgments about others is examined and literature on this subject is reviewed. A wide variety of situational factors affects the appraisal of performance. It is generally accepted that the purpose of the appraisal influences the accuracy of the appraiser. The instrumentation, or tools, available to the…

  19. Accurate pointing of tungsten welding electrodes

    NASA Technical Reports Server (NTRS)

    Ziegelmeier, P.

    1971-01-01

    Thoriated-tungsten is pointed accurately and quickly by using sodium nitrite. Point produced is smooth and no effort is necessary to hold the tungsten rod concentric. The chemically produced point can be used several times longer than ground points. This method reduces time and cost of preparing tungsten electrodes.

  20. Measuring Joint Stimulus Control by Complex Graph/Description Correspondences

    ERIC Educational Resources Information Center

    Fields, Lanny; Spear, Jack

    2012-01-01

    Joint stimulus control occurs when responding is determined by the correspondence of elements of a complex sample and a complex comparison stimulus. In academic settings, joint stimulus control of behavior would be evidenced by the selection of an accurate description of a complex graph in which each element of a graph corresponded to particular…