Reading the Principia

NASA Astrophysics Data System (ADS)

Guicciardini, Niccoló

2003-10-01

1. Purpose of this book; Part I. Newton's Methods: 2. Newton's methods of series and fluxions; 3. The mathematical methods of the Principia; Part II. Three Readers: 4. Newton: between tradition and innovation; 5. Huygens: the Principia and proportion theory; 6. Leibniz: not equivalent in practice; Part III. Two Schools: 7. Britain: in the wake of the Principia; 8. Basel: challenging the Principia; 9. Conclusion: Newtonians, Leibnizians and Eulerians; References.

Full nonlinear treatment of the global thermospheric wind system. Part 1: Mathematical method and analysis of forces

NASA Technical Reports Server (NTRS)

Blum, P. W.; Harris, I.

1973-01-01

The equations of horizontal motion of the neutral atmosphere between 120 and 500 km are integrated with the inclusion of all the nonlinear terms of the convective derivative and the viscous forces due to vertical and horizontal velocity gradients. Empirical models of the distribution of neutral and charged particles are assumed to be known. The model of velocities developed is a steady state model. In part 1 the mathematical method used in the integration of the Navier-Stokes equations is described and the various forces are analysed.

Students' Reflections on Mathematics Homework Feedback

ERIC Educational Resources Information Center

Landers, Mara; Reinholz, Daniel

2015-01-01

Homework is considered an important aspect of learning mathematics, but little research has considered how students utilize feedback as part of the homework process. This mixed methods, quasi-experimental study examines how community college students in a developmental intermediate algebra course participated in a feedback reflection activity…

The averaging method in applied problems

NASA Astrophysics Data System (ADS)

Grebenikov, E. A.

1986-04-01

The totality of methods, allowing to research complicated non-linear oscillating systems, named in the literature "averaging method" has been given. THe author is describing the constructive part of this method, or a concrete form and corresponding algorithms, on mathematical models, sufficiently general , but built on concrete problems. The style of the book is that the reader interested in the Technics and algorithms of the asymptotic theory of the ordinary differential equations, could solve individually such problems. For specialists in the area of applied mathematics and mechanics.

Functional Integration

NASA Astrophysics Data System (ADS)

Cartier, Pierre; DeWitt-Morette, Cecile

2006-11-01

Acknowledgements; List symbols, conventions, and formulary; Part I. The Physical and Mathematical Environment: 1. The physical and mathematical environment; Part II. Quantum Mechanics: 2. First lesson: gaussian integrals; 3. Selected examples; 4. Semiclassical expansion: WKB; 5. Semiclassical expansion: beyond WKB; 6. Quantum dynamics: path integrals and operator formalism; Part III. Methods from Differential Geometry: 7. Symmetries; 8. Homotopy; 9. Grassmann analysis: basics; 10. Grassmann analysis: applications; 11. Volume elements, divergences, gradients; Part IV. Non-Gaussian Applications: 12. Poisson processes in physics; 13. A mathematical theory of Poisson processes; 14. First exit time: energy problems; Part V. Problems in Quantum Field Theory: 15. Renormalization 1: an introduction; 16. Renormalization 2: scaling; 17. Renormalization 3: combinatorics; 18. Volume elements in quantum field theory Bryce DeWitt; Part VI. Projects: 19. Projects; Appendix A. Forward and backward integrals: spaces of pointed paths; Appendix B. Product integrals; Appendix C. A compendium of gaussian integrals; Appendix D. Wick calculus Alexander Wurm; Appendix E. The Jacobi operator; Appendix F. Change of variables of integration; Appendix G. Analytic properties of covariances; Appendix H. Feynman's checkerboard; Bibliography; Index.

Functional Integration

NASA Astrophysics Data System (ADS)

Cartier, Pierre; DeWitt-Morette, Cecile

2010-06-01

Acknowledgements; List symbols, conventions, and formulary; Part I. The Physical and Mathematical Environment: 1. The physical and mathematical environment; Part II. Quantum Mechanics: 2. First lesson: gaussian integrals; 3. Selected examples; 4. Semiclassical expansion: WKB; 5. Semiclassical expansion: beyond WKB; 6. Quantum dynamics: path integrals and operator formalism; Part III. Methods from Differential Geometry: 7. Symmetries; 8. Homotopy; 9. Grassmann analysis: basics; 10. Grassmann analysis: applications; 11. Volume elements, divergences, gradients; Part IV. Non-Gaussian Applications: 12. Poisson processes in physics; 13. A mathematical theory of Poisson processes; 14. First exit time: energy problems; Part V. Problems in Quantum Field Theory: 15. Renormalization 1: an introduction; 16. Renormalization 2: scaling; 17. Renormalization 3: combinatorics; 18. Volume elements in quantum field theory Bryce DeWitt; Part VI. Projects: 19. Projects; Appendix A. Forward and backward integrals: spaces of pointed paths; Appendix B. Product integrals; Appendix C. A compendium of gaussian integrals; Appendix D. Wick calculus Alexander Wurm; Appendix E. The Jacobi operator; Appendix F. Change of variables of integration; Appendix G. Analytic properties of covariances; Appendix H. Feynman's checkerboard; Bibliography; Index.

MATHEMATICAL METHODS IN MEDICAL IMAGE PROCESSING

PubMed Central

ANGENENT, SIGURD; PICHON, ERIC; TANNENBAUM, ALLEN

2013-01-01

In this paper, we describe some central mathematical problems in medical imaging. The subject has been undergoing rapid changes driven by better hardware and software. Much of the software is based on novel methods utilizing geometric partial differential equations in conjunction with standard signal/image processing techniques as well as computer graphics facilitating man/machine interactions. As part of this enterprise, researchers have been trying to base biomedical engineering principles on rigorous mathematical foundations for the development of software methods to be integrated into complete therapy delivery systems. These systems support the more effective delivery of many image-guided procedures such as radiation therapy, biopsy, and minimally invasive surgery. We will show how mathematics may impact some of the main problems in this area, including image enhancement, registration, and segmentation. PMID:23645963

Mathematical methods in medicine: neuroscience, cardiology and pathology

PubMed Central

Amigó, José M.

2017-01-01

The application of mathematics, natural sciences and engineering to medicine is gaining momentum as the mutual benefits of this collaboration become increasingly obvious. This theme issue is intended to highlight the trend in the case of mathematics. Specifically, the scope of this theme issue is to give a general view of the current research in the application of mathematical methods to medicine, as well as to show how mathematics can help in such important aspects as understanding, prediction, treatment and data processing. To this end, three representative specialties have been selected: neuroscience, cardiology and pathology. Concerning the topics, the 12 research papers and one review included in this issue cover biofluids, cardiac and virus dynamics, computational neuroscience, functional magnetic resonance imaging data processing, neural networks, optimization of treatment strategies, time-series analysis and tumour growth. In conclusion, this theme issue contains a collection of fine contributions at the intersection of mathematics and medicine, not as an exercise in applied mathematics but as a multidisciplinary research effort that interests both communities and our society in general. This article is part of the themed issue ‘Mathematical methods in medicine: neuroscience, cardiology and pathology’. PMID:28507240

Mathematical methods in medicine: neuroscience, cardiology and pathology.

PubMed

Amigó, José M; Small, Michael

2017-06-28

The application of mathematics, natural sciences and engineering to medicine is gaining momentum as the mutual benefits of this collaboration become increasingly obvious. This theme issue is intended to highlight the trend in the case of mathematics. Specifically, the scope of this theme issue is to give a general view of the current research in the application of mathematical methods to medicine, as well as to show how mathematics can help in such important aspects as understanding, prediction, treatment and data processing. To this end, three representative specialties have been selected: neuroscience, cardiology and pathology. Concerning the topics, the 12 research papers and one review included in this issue cover biofluids, cardiac and virus dynamics, computational neuroscience, functional magnetic resonance imaging data processing, neural networks, optimization of treatment strategies, time-series analysis and tumour growth. In conclusion, this theme issue contains a collection of fine contributions at the intersection of mathematics and medicine, not as an exercise in applied mathematics but as a multidisciplinary research effort that interests both communities and our society in general.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'. © 2017 The Author(s).

Sines and Cosines. Part 2 of 3

NASA Technical Reports Server (NTRS)

Apostol, Tom M. (Editor)

1993-01-01

The Law of Sines and the Law of Cosines are introduced and demonstrated in this 'Project Mathematics' series video using both film footage and computer animation. This video deals primarily with the mathematical field of Trigonometry and explains how these laws were developed and their applications. One significant use is geographical and geological surveying. This includes both the triangulation method and the spirit leveling method. With these methods, it is shown how the height of the tallest mountain in the world, Mt. Everest, was determined.

Rail-highway crossing accident prediction research results - FY80

DOT National Transportation Integrated Search

1981-01-01

This report presents the results of research performed at the : Transportation Systems Center (TSC) dealing with mathematical : methods of predicting accidents at rail-highway crossings. The : work consists of three parts : Part I - Revised DOT Accid...

Activities in Elementary Probability, Monograph No. 9.

ERIC Educational Resources Information Center

Fouch, Daniel J.

This monograph on elementary probability for middle school, junior high, or high school consumer mathematics students is divided into two parts. Part one emphasizes lessons which cover the fundamental counting principle, permutations, and combinations. The 5 lessons of part I indicate the objectives, examples, methods, application, and problems…

Critical perspectives of pedagogical approaches to reversing the order of integration in double integrals

NASA Astrophysics Data System (ADS)

Tisdell, Christopher C.

2017-11-01

This paper presents some critical perspectives regarding pedagogical approaches to the method of reversing the order of integration in double integrals from prevailing educational literature on multivariable calculus. First, we question the message found in popular textbooks that the traditional process of reversing the order of integration is necessary when solving well-known problems. Second, we illustrate that the method of integration by parts can be directly applied to many of the classic pedagogical problems in the literature concerning double integrals, without taking the well-worn steps associated with reversing the order of integration. Third, we examine the benefits and limitations of such a method. In our conclusion, we advocate for integration by parts to be a part of the pedagogical conversation in the learning and teaching of double integral methods; and call for more debate around its use in the learning and teaching of other areas of mathematics. Finally, we emphasize the need for critical approaches in the pedagogy of mathematics more broadly.

Celestial mechanics - Methods of the theory of motion of 'artificial' celestial bodies

NASA Astrophysics Data System (ADS)

Duboshin, G. N.

This book is concerned with the translational motion of 'artificial' celestial bodies. The difference between natural celestial bodies, which are ordinarily considered by celestial mechanics, and 'artificial' celestial bodies is discussed, taking into account hypothetical celestial bodies introduced in connection with mathematical developments and problems, invisible celestial bodies whose existence can be assumed on the basis of some plausible hypothesis, and man-made satellites of the earth. The book consists of two parts. The first part presents introductory material, and examines a number of general mathematical questions to provide a basis for the studies conducted in the second part. Subjects considered in the first part are related to basic problems, integration methods, and perturbation theory. In the second part, attention is given to the motion of artificial celestial bodies in the gravitational field of the basic planet, external perturbations regarding the motion of these bodies, the motion of the bodies in the earth-moon system, and periodic solutions.

Teaching Methods for Modelling Problems and Students' Task-Specific Enjoyment, Value, Interest and Self-Efficacy Expectations

ERIC Educational Resources Information Center

Schukajlow, Stanislaw; Leiss, Dominik; Pekrun, Reinhard; Blum, Werner; Muller, Marcel; Messner, Rudolf

2012-01-01

In this study which was part of the DISUM-project, 224 ninth graders from 14 German classes from middle track schools (Realschule) were asked about their enjoyment, interest, value and self-efficacy expectations concerning three types of mathematical problems: intra-mathematical problems, word problems and modelling problems. Enjoyment, interest,…

Mathematical model of an indirect action fuel flow controller for aircraft jet engines

NASA Astrophysics Data System (ADS)

Tudosie, Alexandru-Nicolae

2017-06-01

The paper deals with a fuel mass flow rate controller with indirect action for aircraft jet engines. The author has identified fuel controller's main parts and its operation mode, then, based on these observations, one has determined motion equations of each main part, which have built system's non-linear mathematical model. In order to realize a better study this model was linearised (using the finite differences method) and then adimensionalized. Based on this new form of the mathematical model, after applying Laplace transformation, the embedded system (controller+engine) was described by the block diagram with transfer functions. Some Simulink-Matlab simulations were performed, concerning system's time behavior for step input, which lead to some useful conclusions and extension possibilities.

Airflow and Particle Transport Through Human Airways: A Systematic Review

NASA Astrophysics Data System (ADS)

Kharat, S. B.; Deoghare, A. B.; Pandey, K. M.

2017-08-01

This paper describes review of the relevant literature about two phase analysis of air and particle flow through human airways. An emphasis of the review is placed on elaborating the steps involved in two phase analysis, which are Geometric modelling methods and Mathematical models. The first two parts describes various approaches that are followed for constructing an Airway model upon which analysis are conducted. Broad two categories of geometric modelling viz. Simplified modelling and Accurate modelling using medical scans are discussed briefly. Ease and limitations of simplified models, then examples of CT based models are discussed. In later part of the review different mathematical models implemented by researchers for analysis are briefed. Mathematical models used for Air and Particle phases are elaborated separately.

High-Resolution Wind Measurements for Offshore Wind Energy Development

NASA Technical Reports Server (NTRS)

Nghiem, Son V.; Neumann, Gregory

2011-01-01

A mathematical transform, called the Rosette Transform, together with a new method, called the Dense Sampling Method, have been developed. The Rosette Transform is invented to apply to both the mean part and the fluctuating part of a targeted radar signature using the Dense Sampling Method to construct the data in a high-resolution grid at 1-km posting for wind measurements over water surfaces such as oceans or lakes.

Mathematical Selfies: Students' Real-World Mathematics

ERIC Educational Resources Information Center

Jaqua, Kathy M. C.

2017-01-01

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

Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis

ERIC Educational Resources Information Center

Jeffrey, Alan

1971-01-01

The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)

Full non-linear treatment of the global thermospheric wind system. I - Mathematical method and analysis of forces. II - Results and comparison with observations

NASA Technical Reports Server (NTRS)

Blum, P. W.; Harris, I.

1975-01-01

The equations of horizontal motion of the neutral atmosphere between 120 and 500 km are integrated with the inclusion of all nonlinear terms of the convective derivative and the viscous forces due to vertical and horizontal velocity gradients. Empirical models of the distribution of neutral and charged particles are assumed to be known. The model of velocities developed is a steady state model. In Part I the mathematical method used in the integration of the Navier-Stokes equations is described and the various forces are analyzed. Results of the method given in Part I are presented with comparison with previous calculations and observations of upper atmospheric winds. Conclusions are that nonlinear effects are only significant in the equatorial region, especially at solstice conditions and that nonlinear effects do not produce any superrotation.

Mathematical modeling and hydrodynamics of Electrochemical deburring process

NASA Astrophysics Data System (ADS)

Prabhu, Satisha; Abhishek Kumar, K., Dr

2018-04-01

The electrochemical deburring (ECD) is a variation of electrochemical machining is considered as one of the efficient methods for deburring of intersecting features and internal parts. Since manual deburring costs are comparatively high one can potentially use this method in both batch production and flow production. The other advantage of this process is that time of deburring as is on the order of seconds as compared to other methods. In this paper, the mathematical modeling of Electrochemical deburring is analysed from its deburring time and base metal removal point of view. Simultaneously material removal rate is affected by electrolyte temperature and bubble formation. The mathematical model and hydrodynamics of the process throw limelight upon optimum velocity calculations which can be theoretically determined. The analysis can be the powerful tool for prediction of the above-mentioned parameters by experimentation.

Developments in School Mathematics Education around the World. University of Chicago School Mathematics Project. Volume Three. Proceedings of the UCSMP International Conference on Mathematics Education (3rd, October 30-November 1, 1991).

ERIC Educational Resources Information Center

Wirszup, Izaak, Ed.; Streit, Robert, Ed.

Papers from the International Conference on Mathematics Education are organized into four parts. Part 1, "The Goal of Mathematics for All," includes: "Will Everybody Ever Count?" (Steen); "Mathematics Education: An Industrial View" (McHenry); "The Popularization of Mathematics" (Kahane); "Is There a…

Math in Motion: Origami in the Classroom. A Hands-On Creative Approach to Teaching Mathematics. K-8.

ERIC Educational Resources Information Center

Pearl, Barbara

This perfect bound teacher's guide presents techniques and activities to teach mathematics using origami paper folding. Part 1 includes a history of origami, mathematics and origami, and careers using mathematics. Parts 2 and 3 introduce paper-folding concepts and teaching techniques and include suggestions for low-budget paper resources. Part 4…

A case study of pedagogy of mathematics support tutors without a background in mathematics education

NASA Astrophysics Data System (ADS)

Walsh, Richard

2017-01-01

This study investigates the pedagogical skills and knowledge of three tertiary-level mathematics support tutors in a large group classroom setting. This is achieved through the use of video analysis and a theoretical framework comprising Rowland's Knowledge Quartet and general pedagogical knowledge. The study reports on the findings in relation to these tutors' provision of mathematics support to first and second year undergraduate engineering students and second year undergraduate science students. It was found that tutors are lacking in various pedagogical skills which are needed for high-quality learning amongst service mathematics students (e.g. engineering/science/technology students), a demographic which have low levels of mathematics upon entering university. Tutors teach their support classes in a very fast didactic way with minimal opportunities for students to ask questions or to attempt problems. It was also found that this teaching method is even more so exaggerated in mandatory departmental mathematics tutorials that students take as part of their mathematics studies at tertiary level. The implications of the findings on mathematics tutor training at tertiary level are also discussed.

Mathematical Formulation used by MATLAB Code to Convert FTIR Interferograms to Calibrated Spectra

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

Armstrong, Derek Elswick

This report discusses the mathematical procedures used to convert raw interferograms from Fourier transform infrared (FTIR) sensors to calibrated spectra. The work discussed in this report was completed as part of the Helios project at Los Alamos National Laboratory. MATLAB code was developed to convert the raw interferograms to calibrated spectra. The report summarizes the developed MATLAB scripts and functions, along with a description of the mathematical methods used by the code. The first step in working with raw interferograms is to convert them to uncalibrated spectra by applying an apodization function to the raw data and then by performingmore » a Fourier transform. The developed MATLAB code also addresses phase error correction by applying the Mertz method. This report provides documentation for the MATLAB scripts.« less

Reorganizing Freshman Business Mathematics II: Authentic Assessment in Mathematics through Professional Memos

ERIC Educational Resources Information Center

Green, Kris; Emerson, Allen

2008-01-01

The first part of this two-part paper [see EJ787497] described the development of a new freshman business mathematics (FBM) course at our college. In this paper, we discuss our assessment tool, the business memo, as a venue for students to apply mathematical skills, via mathematical modelling, to realistic business problems. These memos have…

Can Mathematics be Justified by Natural Logic?

NASA Astrophysics Data System (ADS)

Schreiber, Lothar; Sommer, Hanns

2010-11-01

Charles Darwin claimed that the forms and the behaviour of living beings can be explained from their will to survive. But what are the consequences of this idea for humans knowledge, their theories of nature and their mathematics?. We discuss the view that even Plato's objective world of mathematical objects does not exist absolutely, without the intentions of mathematicians. Using Husserl's Phenomenological Method, cognition can be understood as a process by which meaning is deduced from empirical data relative to intentions. Thereby the essential structure of any cognition process can be detected and this structure is mirrored in logic. A natural logic becomes the direct result of cognition. Only in a second step, mathematics is obtained by abstraction from natural logic. In this way mathematics gains a well-defined foundation and is no longer part of a dubious 'a-priori knowledge' (Kant). This access to mathematics offers a new look on many old problems, e.g. the Petersburg problem and the problem 'P = NP?'. We demonstrate that this new justification of mathematics has also important applications in Artificial Intelligence. Our method provides a procedure to construct an adequate logic to solve most efficiently the problems of a given problem class. Thus, heuristics can be tailor-made for the necessities of applications.

Human behaviours in evacuation crowd dynamics: From modelling to "big data" toward crisis management

NASA Astrophysics Data System (ADS)

Bellomo, N.; Clarke, D.; Gibelli, L.; Townsend, P.; Vreugdenhil, B. J.

2016-09-01

This paper proposes an essay concerning the understanding of human behaviours and crisis management of crowds in extreme situations, such as evacuation through complex venues. The first part focuses on the understanding of the main features of the crowd viewed as a living, hence complex system. The main concepts are subsequently addressed, in the second part, to a critical analysis of mathematical models suitable to capture them, as far as it is possible. Then, the third part focuses on the use, toward safety problems, of a model derived by the methods of the mathematical kinetic theory and theoretical tools of evolutionary game theory. It is shown how this model can depict critical situations and how these can be managed with the aim of minimizing the risk of catastrophic events.

Nonlinear versus Ordinary Adaptive Control of Continuous Stirred-Tank Reactor

PubMed Central

Dostal, Petr

2015-01-01

Unfortunately, the major group of the systems in industry has nonlinear behavior and control of such processes with conventional control approaches with fixed parameters causes problems and suboptimal or unstable control results. An adaptive control is one way to how we can cope with nonlinearity of the system. This contribution compares classic adaptive control and its modification with Wiener system. This configuration divides nonlinear controller into the dynamic linear part and the static nonlinear part. The dynamic linear part is constructed with the use of polynomial synthesis together with the pole-placement method and the spectral factorization. The static nonlinear part uses static analysis of the controlled plant for introducing the mathematical nonlinear description of the relation between the controlled output and the change of the control input. Proposed controller is tested by the simulations on the mathematical model of the continuous stirred-tank reactor with cooling in the jacket as a typical nonlinear system. PMID:26346878

Computational Methods for Structural Mechanics and Dynamics, part 1

NASA Technical Reports Server (NTRS)

Stroud, W. Jefferson (Editor); Housner, Jerrold M. (Editor); Tanner, John A. (Editor); Hayduk, Robert J. (Editor)

1989-01-01

The structural analysis methods research has several goals. One goal is to develop analysis methods that are general. This goal of generality leads naturally to finite-element methods, but the research will also include other structural analysis methods. Another goal is that the methods be amenable to error analysis; that is, given a physical problem and a mathematical model of that problem, an analyst would like to know the probable error in predicting a given response quantity. The ultimate objective is to specify the error tolerances and to use automated logic to adjust the mathematical model or solution strategy to obtain that accuracy. A third goal is to develop structural analysis methods that can exploit parallel processing computers. The structural analysis methods research will focus initially on three types of problems: local/global nonlinear stress analysis, nonlinear transient dynamics, and tire modeling.

Teaching Bayesian Statistics in a Health Research Methodology Program

ERIC Educational Resources Information Center

Pullenayegum, Eleanor M.; Thabane, Lehana

2009-01-01

Despite the appeal of Bayesian methods in health research, they are not widely used. This is partly due to a lack of courses in Bayesian methods at an appropriate level for non-statisticians in health research. Teaching such a course can be challenging because most statisticians have been taught Bayesian methods using a mathematical approach, and…

General Mathematics; Part 1. Mathematics Curriculum Guide (Career Oriented).

ERIC Educational Resources Information Center

Nuschler, Alexandra; And Others

The curriculum guide for secondary level, career-oriented General Mathematics Part 1, correlates performance objectives in basic mathematics with career-oriented concepts and activities. The material is designed to lead the student in a systematic development that provides for continuous progress. The guide is in outline format, providing a…

Analyzing the reliability of mechanical parts in 10 kV aerial transmission lines under ice-coating and wind effects in view of their design features

NASA Astrophysics Data System (ADS)

Doletskaya, L. I.; Solopov, R. V.; Kavchenkov, V. P.; Andreenkov, E. S.

2017-12-01

The physical features of the damage of aerial lines with a voltage of 10 kV under ice and wind loads are examined, mathematical models for estimating the reliability the mechanical part in aerial lines with the application of analytical theoretical methods and corresponding mathematical models taking into account the probabilistic nature of ice and wind loads are described, calculation results on reliability, specific damage and average time for restoration in case of emergency outages of 10 kV high-voltage transmission aerial lines with the use of uninsulated and protected wires are presented.

Methods in Symbolic Computation and p-Adic Valuations of Polynomials

NASA Astrophysics Data System (ADS)

Guan, Xiao

Symbolic computation has widely appear in many mathematical fields such as combinatorics, number theory and stochastic processes. The techniques created in the area of experimental mathematics provide us efficient ways of symbolic computing and verification of complicated relations. Part I consists of three problems. The first one focuses on a unimodal sequence derived from a quartic integral. Many of its properties are explored with the help of hypergeometric representations and automatic proofs. The second problem tackles the generating function of the reciprocal of Catalan number. It springs from the closed form given by Mathematica. Furthermore, three methods in special functions are used to justify this result. The third issue addresses the closed form solutions for the moments of products of generalized elliptic integrals , which combines the experimental mathematics and classical analysis. Part II concentrates on the p-adic valuations of polynomials from the perspective of trees. For a given polynomial f( n) indexed in positive integers, the package developed in Mathematica will create certain tree structure following a couple of rules. The evolution of such trees are studied both rigorously and experimentally from the view of field extension, nonparametric statistics and random matrix.

Adaptation of abbreviated mathematics anxiety rating scale for engineering students

NASA Astrophysics Data System (ADS)

Nordin, Sayed Kushairi Sayed; Samat, Khairul Fadzli; Sultan, Al Amin Mohamed; Halim, Bushra Abdul; Ismail, Siti Fatimah; Mafazi, Nurul Wirdah

2015-05-01

Mathematics is an essential and fundamental tool used by engineers to analyse and solve problems in their field. Due to this, most engineering education programs involve a concentration of study in mathematics courses whereby engineering students have to take mathematics courses such as numerical methods, differential equations and calculus in the first two years and continue to do so until the completion of the sequence. However, the students struggled and had difficulties in learning courses that require mathematical abilities. Hence, this study presents the factors that caused mathematics anxiety among engineering students using Abbreviated Mathematics Anxiety Rating Scale (AMARS) through 95 students of Universiti Teknikal Malaysia Melaka (UTeM). From 25 items in AMARS, principal component analysis (PCA) suggested that there are four mathematics anxiety factors, namely experiences of learning mathematics, cognitive skills, mathematics evaluation anxiety and students' perception on mathematics. Minitab 16 software was used to analyse the nonparametric statistics. Kruskal-Wallis Test indicated that there is a significant difference in the experience of learning mathematics and mathematics evaluation anxiety among races. The Chi-Square Test of Independence revealed that the experience of learning mathematics, cognitive skills and mathematics evaluation anxiety depend on the results of their SPM additional mathematics. Based on this study, it is recommended to address the anxiety problems among engineering students at the early stage of studying in the university. Thus, lecturers should play their part by ensuring a positive classroom environment which encourages students to study mathematics without fear.

Fundamentals of digital filtering with applications in geophysical prospecting for oil

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

Mesko, A.

This book is a comprehensive work bringing together the important mathematical foundations and computing techniques for numerical filtering methods. The first two parts of the book introduce the techniques, fundamental theory and applications, while the third part treats specific applications in geophysical prospecting. Discussion is limited to linear filters, but takes in related fields such as correlational and spectral analysis.

An Examination of the Statistical Problem-Solving Process as a Potential Means for Developing an Understanding of Argumentation

ERIC Educational Resources Information Center

Smith Baum, Brittany Deshae

2017-01-01

As part of the recent history of the mathematics curriculum, reasoning and argument have been emphasized throughout mathematics curriculum standards. Specifically, as part of the Common Core State Standards for Mathematics, the Standards for Mathematical Practice were presented, which included the expectation that students develop arguments and…

Comparison of using different bridge prosthetic designs for partial defect restoration through mathematical modeling.

PubMed

Styranivska, Oksana; Kliuchkovska, Nataliia; Mykyyevych, Nataliya

2017-01-01

To analyze the stress-strain states of bone and abutment teeth during the use of different prosthetic designs of fixed partial dentures with the use of relevant mathematical modeling principles. The use of Comsol Multiphysics 3.5 (Comsol AB, Sweden) software during the mathematical modeling of stress-strain states provided numerical data for analytical interpretation in three different clinical scenarios with fixed dentures and different abutment teeth and demountable prosthetic denture with the saddle-shaped intermediate part. Microsoft Excel Software (Microsoft Office 2017) helped to evaluate absolute mistakes of stress and strain parameters of each abutment tooth during three modeled scenarios and normal condition and to summarize data into the forms of tables. In comparison with the fixed prosthetic denture supported by the canine, first premolar, and third molar, stresses at the same abutment teeth with the use of demountable denture with the saddle-shaped intermediate part decreased: at the mesial abutment tooth by 2.8 times, at distal crown by 6.1 times, and at the intermediate part by 11.1 times, respectively, the deformation level decreased by 3.1, 1.9, and 1.4 times at each area. The methods of mathematical modeling proved that complications during the use of fixed partial dentures based on the overload effect of the abutment teeth and caused by the deformation process inside the intermediate section of prosthetic construction.

Mathematics on the Move: Using Mobile Technologies to Support Student Learning (Part 2)

ERIC Educational Resources Information Center

Attard, Catherine; Northcote, Maria

2012-01-01

Continuing the series of articles on teaching mathematics with technology, this article furthers the authors' exploration of the use of a range of mobile technologies to enhance teachers' practices in the primary mathematics classroom. In Part 1 of this article, the authors explored the use of the iPod Touch and iPad. In Part 2, they explore…

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Research on cutting path optimization of sheet metal parts based on ant colony algorithm

NASA Astrophysics Data System (ADS)

Wu, Z. Y.; Ling, H.; Li, L.; Wu, L. H.; Liu, N. B.

2017-09-01

In view of the disadvantages of the current cutting path optimization methods of sheet metal parts, a new method based on ant colony algorithm was proposed in this paper. The cutting path optimization problem of sheet metal parts was taken as the research object. The essence and optimization goal of the optimization problem were presented. The traditional serial cutting constraint rule was improved. The cutting constraint rule with cross cutting was proposed. The contour lines of parts were discretized and the mathematical model of cutting path optimization was established. Thus the problem was converted into the selection problem of contour lines of parts. Ant colony algorithm was used to solve the problem. The principle and steps of the algorithm were analyzed.

Features of control systems analysis with discrete control devices using mathematical packages

NASA Astrophysics Data System (ADS)

Yakovleva, E. M.; Faerman, V. A.

2017-02-01

The article contains presentation of basic provisions of the theory of automatic pulse control systems as well as methods of analysis of such systems using the mathematical software widespread in the academic environment. The pulse systems under research are considered as analogues systems interacting among themselves, including sensors, amplifiers, controlled objects, and discrete parts. To describe such systems, one uses a mathematical apparatus of difference equations as well as discrete transfer functions. To obtain a transfer function of the open-loop system, being important from the point of view of the analysis of control systems, one uses mathematical packages Mathcad and Matlab. Despite identity of the obtained result, the way of its achievement from the point of view of user’s action is various for the specified means. In particular, Matlab uses a structural model of the control system while Mathcad allows only execution of a chain of operator transforms. It is worth noting that distinctions taking place allow considering transformation of signals during interaction of the linear and continuous parts of the control system from different sides. The latter can be used in an educational process for the best assimilation of the course of the control system theory by students.

The Effect of a Modified Moore Method on Attitudes and Beliefs in Precalculus

ERIC Educational Resources Information Center

Bailey, Brad; Cooper, Thomas E.; Briggs, Karen S.

2012-01-01

As part of a study on the effects of teaching with a Modified Moore Method (MMM), a survey containing 20 items from Schoenfeld's (1989) investigation of attitudes and beliefs about mathematics was administered to students in undergraduate precalculus classes. The study included one section of precalculus taught with an MMM, a student-centered and…

Administrator Observation and Feedback: Does It Lead toward Improvement in Inquiry-Oriented Math Instruction?

ERIC Educational Resources Information Center

Rigby, Jessica G.; Larbi-Cherif, Adrian; Rosenquist, Brooks A.; Sharpe, Charlotte J.; Cobb, Paul; Smith, Thomas

2017-01-01

Purpose: This study examines the content and efficacy of instructional leaders' expectations and feedback (press) in relation to the improvement of middle school mathematics teachers' instruction in the context of coherent systems of supports. Research Method/Approach: This mixed methods study is a part of a larger, 8-year longitudinal study in…

Optimization methods of laws control of electric propulsion spacecraft in the restricted three-body task

NASA Astrophysics Data System (ADS)

Starinova, Olga L.

2014-12-01

This paper outlines the optimization methods of the control law of the low thrust spacecraft for the restrict problem of three-body. The conditions for fragmentation trajectory on the specific parts of trajectory are formulated. The mathematical statement and methods to solve the optimal control problem on these parts are stated. Results of the decision of applied problems for various classes of spacecrafts which are carrying out maneuvers with low thrust are presented. In particular, the non-coplanar maneuvers of the low thrust spacecraft in the Earth-Moon system are viewed.

Talking about the Weather, Part II.

ERIC Educational Resources Information Center

Gibb, Allan A.

1984-01-01

This second part of a two-part article highlights some mathematics involved in the study of meteorology. Examples are given of the application of mathematics to the study of the atmosphere, with three problems discussed. (MNS)

Computing the stability of steady-state solutions of mathematical models of the electrical activity in the heart.

PubMed

Tveito, Aslak; Skavhaug, Ola; Lines, Glenn T; Artebrant, Robert

2011-08-01

Instabilities in the electro-chemical resting state of the heart can generate ectopic waves that in turn can initiate arrhythmias. We derive methods for computing the resting state for mathematical models of the electro-chemical process underpinning a heartbeat, and we estimate the stability of the resting state by invoking the largest real part of the eigenvalues of a linearized model. The implementation of the methods is described and a number of numerical experiments illustrate the feasibility of the methods. In particular, we test the methods for problems where we can compare the solutions with analytical results, and problems where we have solutions computed by independent software. The software is also tested for a fairly realistic 3D model. Copyright © 2011 Elsevier Ltd. All rights reserved.

Survey of meshless and generalized finite element methods: A unified approach

NASA Astrophysics Data System (ADS)

Babuška, Ivo; Banerjee, Uday; Osborn, John E.

In the past few years meshless methods for numerically solving partial differential equations have come into the focus of interest, especially in the engineering community. This class of methods was essentially stimulated by difficulties related to mesh generation. Mesh generation is delicate in many situations, for instance, when the domain has complicated geometry; when the mesh changes with time, as in crack propagation, and remeshing is required at each time step; when a Lagrangian formulation is employed, especially with nonlinear PDEs. In addition, the need for flexibility in the selection of approximating functions (e.g., the flexibility to use non-polynomial approximating functions), has played a significant role in the development of meshless methods. There are many recent papers, and two books, on meshless methods; most of them are of an engineering character, without any mathematical analysis.In this paper we address meshless methods and the closely related generalized finite element methods for solving linear elliptic equations, using variational principles. We give a unified mathematical theory with proofs, briefly address implementational aspects, present illustrative numerical examples, and provide a list of references to the current literature.The aim of the paper is to provide a survey of a part of this new field, with emphasis on mathematics. We present proofs of essential theorems because we feel these proofs are essential for the understanding of the mathematical aspects of meshless methods, which has approximation theory as a major ingredient. As always, any new field is stimulated by and related to older ideas. This will be visible in our paper.

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

NASA Astrophysics Data System (ADS)

Priatna, Nanang

2017-08-01

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

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

NASA Astrophysics Data System (ADS)

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

2013-07-01

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

Aspects of Mathematical Modelling of Pressure Retarded Osmosis

PubMed Central

Anissimov, Yuri G.

2016-01-01

In power generating terms, a pressure retarded osmosis (PRO) energy generating plant, on a river entering a sea or ocean, is equivalent to a hydroelectric dam with a height of about 60 meters. Therefore, PRO can add significantly to existing renewable power generation capacity if economical constrains of the method are resolved. PRO energy generation relies on a semipermeable membrane that is permeable to water and impermeable to salt. Mathematical modelling plays an important part in understanding flows of water and salt near and across semipermeable membranes and helps to optimize PRO energy generation. Therefore, the modelling can help realizing PRO energy generation potential. In this work, a few aspects of mathematical modelling of the PRO process are reviewed and discussed. PMID:26848696

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

NASA Technical Reports Server (NTRS)

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

2005-01-01

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

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

NASA Technical Reports Server (NTRS)

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

2003-01-01

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

Purpose and Education: The Case of Mathematics

ERIC Educational Resources Information Center

Harouni, Houman

2015-01-01

Why do schools teach mathematics, and why do they teach the mathematics that they do? In this three-part dissertation, I argue that the justifications offered by national education systems are not convincing, and that students are tested on content whose purpose neither they nor their teachers clearly understand. In the first part of the…

The Carnegie Initiative on the Doctorate: The Case of Mathematics. Carnegie Essays on the Doctorate: Mathematics.

ERIC Educational Resources Information Center

Bass, Hyman

The Carnegie Foundation commissioned a collection of essays as part of the Carnegie Initiative on the Doctorate (CID). Essays and essayists represent six disciplines that are part of the CID: chemistry, education, English, history, mathematics, and neuroscience. Intended to engender conversation about the conceptual foundation of doctoral…

The Mathematics Doctorate: A Time for Change? Carnegie Essays on the Doctorate: Mathematics.

ERIC Educational Resources Information Center

Chan, Tony F.

The Carnegie Foundation commissioned a collection of essays as part of the Carnegie Initiative on the Doctorate (CID). Essays and essayists represent six disciplines that are part of the CID: chemistry, education, English, history, mathematics, and neuroscience. Intended to engender conversation about the conceptual foundation of doctoral…

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

ERIC Educational Resources Information Center

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

2013-01-01

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

Applied Mathematics Should Be Taught Mixed.

ERIC Educational Resources Information Center

Brown, Gary I.

1994-01-01

Discusses the differences between applied and pure mathematics and provides extensive history of mixed mathematics. Argues that applied mathematics should be taught allowing for speculative mathematics, which involves breaking down a given problem into simpler parts until one arrives at first principles. (ASK)

Doing Mathematics with Purpose: Mathematical Text Types

ERIC Educational Resources Information Center

Dostal, Hannah M.; Robinson, Richard

2018-01-01

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

Quantitative characterization of genetic parts and circuits for plant synthetic biology.

PubMed

Schaumberg, Katherine A; Antunes, Mauricio S; Kassaw, Tessema K; Xu, Wenlong; Zalewski, Christopher S; Medford, June I; Prasad, Ashok

2016-01-01

Plant synthetic biology promises immense technological benefits, including the potential development of a sustainable bio-based economy through the predictive design of synthetic gene circuits. Such circuits are built from quantitatively characterized genetic parts; however, this characterization is a significant obstacle in work with plants because of the time required for stable transformation. We describe a method for rapid quantitative characterization of genetic plant parts using transient expression in protoplasts and dual luciferase outputs. We observed experimental variability in transient-expression assays and developed a mathematical model to describe, as well as statistical normalization methods to account for, this variability, which allowed us to extract quantitative parameters. We characterized >120 synthetic parts in Arabidopsis and validated our method by comparing transient expression with expression in stably transformed plants. We also tested >100 synthetic parts in sorghum (Sorghum bicolor) protoplasts, and the results showed that our method works in diverse plant groups. Our approach enables the construction of tunable gene circuits in complex eukaryotic organisms.

Liter - Metric Volume.

ERIC Educational Resources Information Center

Sisk, Diane

This autoinstructional program, developed as part of a general science course, is offered for students in the middle schools. Mathematics of fractions and decimals is considered to be prerequisite knowledge. The behavioral objectives are directed toward mastery of determining volumes of solid objects using the water displacement method as well as…

Effectiveness of the Incentive Loan Program for Mathematics and Science Teachers--Washington State 1983-1986. Part III: Report to Washington State Legislature Incentive Loan Program for Mathematics and Science Teachers.

ERIC Educational Resources Information Center

Harder, Annie K.; And Others

The effectiveness of a loan program in providing an incentive for students to prepare for mathematics and/or science teaching in Washington State is described in this report. It is the third of a three part report to the Washington State Legislature regarding the Teacher Incentive Loan Program for Mathematics and Science. Recipients of forgiveness…

A consistent modelling methodology for secondary settling tanks in wastewater treatment.

PubMed

Bürger, Raimund; Diehl, Stefan; Nopens, Ingmar

2011-03-01

The aim of this contribution is partly to build consensus on a consistent modelling methodology (CMM) of complex real processes in wastewater treatment by combining classical concepts with results from applied mathematics, and partly to apply it to the clarification-thickening process in the secondary settling tank. In the CMM, the real process should be approximated by a mathematical model (process model; ordinary or partial differential equation (ODE or PDE)), which in turn is approximated by a simulation model (numerical method) implemented on a computer. These steps have often not been carried out in a correct way. The secondary settling tank was chosen as a case since this is one of the most complex processes in a wastewater treatment plant and simulation models developed decades ago have no guarantee of satisfying fundamental mathematical and physical properties. Nevertheless, such methods are still used in commercial tools to date. This particularly becomes of interest as the state-of-the-art practice is moving towards plant-wide modelling. Then all submodels interact and errors propagate through the model and severely hamper any calibration effort and, hence, the predictive purpose of the model. The CMM is described by applying it first to a simple conversion process in the biological reactor yielding an ODE solver, and then to the solid-liquid separation in the secondary settling tank, yielding a PDE solver. Time has come to incorporate established mathematical techniques into environmental engineering, and wastewater treatment modelling in particular, and to use proven reliable and consistent simulation models. Copyright © 2011 Elsevier Ltd. All rights reserved.

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…

Progress in Mathematical Modeling of Gastrointestinal Slow Wave Abnormalities

PubMed Central

Du, Peng; Calder, Stefan; Angeli, Timothy R.; Sathar, Shameer; Paskaranandavadivel, Niranchan; O'Grady, Gregory; Cheng, Leo K.

2018-01-01

Gastrointestinal (GI) motility is regulated in part by electrophysiological events called slow waves, which are generated by the interstitial cells of Cajal (ICC). Slow waves propagate by a process of “entrainment,” which occurs over a decreasing gradient of intrinsic frequencies in the antegrade direction across much of the GI tract. Abnormal initiation and conduction of slow waves have been demonstrated in, and linked to, a number of GI motility disorders. A range of mathematical models have been developed to study abnormal slow waves and applied to propose novel methods for non-invasive detection and therapy. This review provides a general outline of GI slow wave abnormalities and their recent classification using multi-electrode (high-resolution) mapping methods, with a particular emphasis on the spatial patterns of these abnormal activities. The recently-developed mathematical models are introduced in order of their biophysical scale from cellular to whole-organ levels. The modeling techniques, main findings from the simulations, and potential future directions arising from notable studies are discussed. PMID:29379448

What Makes a Problem Mathematically Interesting? Inviting Prospective Teachers to Pose Better Problems

ERIC Educational Resources Information Center

Crespo, Sandra; Sinclair, Nathalie

2008-01-01

School students of all ages, including those who subsequently become teachers, have limited experience posing their own mathematical problems. Yet problem posing, both as an act of mathematical inquiry and of mathematics teaching, is part of the mathematics education reform vision that seeks to promote mathematics as an worthy intellectual…

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…

A stochastic method to characterize model uncertainty for a Nutrient TMDL

USDA-ARS?s Scientific Manuscript database

The U.S. EPA’s Total Maximum Daily Load (TMDL) program has encountered resistances in its implementation partly because of its strong dependence on mathematical models to set limitations on the release of impairing substances. The uncertainty associated with predictions of such models is often not s...

A Stochastic Method to Develop Nutrient TMDLs Using SWAT

USDA-ARS?s Scientific Manuscript database

The U.S. EPA’s Total Maximum Daily Load (TMDL) program has encountered hindrances in its implementation partly because of its strong dependence on mathematical models to set limitations on the release of impairing substances. The uncertainty associated with predictions of such models is often not fo...

Teaching Reductive Thinking

ERIC Educational Resources Information Center

Armoni, Michal; Gal-Ezer, Judith

2005-01-01

When dealing with a complex problem, solving it by reduction to simpler problems, or problems for which the solution is already known, is a common method in mathematics and other scientific disciplines, as in computer science and, specifically, in the field of computability. However, when teaching computational models (as part of computability)…

Analytical solutions for sequentially coupled one-dimensional reactive transport problems Part I: Mathematical derivations

NASA Astrophysics Data System (ADS)

Srinivasan, V.; Clement, T. P.

2008-02-01

Multi-species reactive transport equations coupled through sorption and sequential first-order reactions are commonly used to model sites contaminated with radioactive wastes, chlorinated solvents and nitrogenous species. Although researchers have been attempting to solve various forms of these reactive transport equations for over 50 years, a general closed-form analytical solution to this problem is not available in the published literature. In Part I of this two-part article, we derive a closed-form analytical solution to this problem for spatially-varying initial conditions. The proposed solution procedure employs a combination of Laplace and linear transform methods to uncouple and solve the system of partial differential equations. Two distinct solutions are derived for Dirichlet and Cauchy boundary conditions each with Bateman-type source terms. We organize and present the final solutions in a common format that represents the solutions to both boundary conditions. In addition, we provide the mathematical concepts for deriving the solution within a generic framework that can be used for solving similar transport problems.

Developing Mathematical Knowledge and Skills through the Awareness Approach of Teaching and Learning

ERIC Educational Resources Information Center

Cherif, Abour H.; Gialamas, Stefanos; Stamati, Angeliki

2017-01-01

Every object we think of or encounter, whether a natural or human-made, has a regular or irregular shape. In its own intrinsic conceptual design, it has elements of mathematics, science, engineering, and arts, etc., which are part of the object's geometric shape, form and structure. Geometry is not only an important part of mathematics, but it is…

Mathematics Through Science, Part III: An Experimental Approach to Functions. Teacher's Commentary. Revised Edition.

ERIC Educational Resources Information Center

Bolduc, Elroy J., Jr.; And Others

The purpose of this project is to teach learning and understanding of mathematics at the ninth grade level through the use of science experiments. This part of the program contains significant amounts of material normally found in a beginning algebra class. The material should be found useful for classes in general mathematics as a preparation for…

Engaging Pre-Service Middle-School Teacher-Education Students in Mathematical Problem Posing: Development of an Active Learning Framework

ERIC Educational Resources Information Center

Ellerton, Nerida F.

2013-01-01

Although official curriculum documents make cursory mention of the need for problem posing in school mathematics, problem posing rarely becomes part of the implemented or assessed curriculum. This paper provides examples of how problem posing can be made an integral part of mathematics teacher education programs. It is argued that such programs…

Making Basic Math Skills Work for You in Marketing. Student Manual and Laboratory Guide.

ERIC Educational Resources Information Center

Klewer, Edwin D.

This student manual and workbook is the second part of a mathematics series for use with high school students. The manual is to be used to apply the mathematics skills that students have learned in a first part called "Developing Basic Math Skills for Marketing." The manual presents conceptual instruction in mathematics in a competency based…

Professional Opportunities in the Mathematical Sciences. Eleventh Edition. A Report for Undergraduate Students of Mathematics.

ERIC Educational Resources Information Center

Mathematical Association of America, Washington, DC.

This report is intended to give an indication of the variety of careers available to persons with interest and preparation in the mathematical sciences. Each part focuses on a particular class of professions, with necessary training as well as the character of the work and general conditions of employment described. Parts I through V deal with…

Do girls really experience more anxiety in mathematics?

PubMed

Goetz, Thomas; Bieg, Madeleine; Lüdtke, Oliver; Pekrun, Reinhard; Hall, Nathan C

2013-10-01

Two studies were conducted to examine gender differences in trait (habitual) versus state (momentary) mathematics anxiety in a sample of students (Study 1: N = 584; Study 2: N = 111). For trait math anxiety, the findings of both studies replicated previous research showing that female students report higher levels of anxiety than do male students. However, no gender differences were observed for state anxiety, as assessed using experience-sampling methods while students took a math test (Study 1) and attended math classes (Study 2). The discrepant findings for trait versus state math anxiety were partly accounted for by students' beliefs about their competence in mathematics, with female students reporting lower perceived competence than male students despite having the same average grades in math. Implications for educational practices and the assessment of anxiety are discussed.

Forest Fires, Oil Spills, and Fractal Geometry: An Investigation in Two Parts. Part 2: Using Fractal Complexity to Analyze Mathematical Models.

ERIC Educational Resources Information Center

Biehl, L. Charles

1999-01-01

Presents an activity that utilizes the mathematical models of forest fires and oil spills that were generated (in the first part of this activity, published in the November 1998 issue) by students using probability and cellular automata. (ASK)

Upgrading geometry conceptual understanding and strategic competence through implementing rigorous mathematical thinking (RMT)

NASA Astrophysics Data System (ADS)

Nugraheni, Z.; Budiyono, B.; Slamet, I.

2018-03-01

To reach higher order thinking skill, needed to be mastered the conceptual understanding and strategic competence as they are two basic parts of high order thinking skill (HOTS). RMT is a unique realization of the cognitive conceptual construction approach based on Feurstein with his theory of Mediated Learning Experience (MLE) and Vygotsky’s sociocultural theory. This was quasi-experimental research which compared the experimental class that was given Rigorous Mathematical Thinking (RMT) as learning method and the control class that was given Direct Learning (DL) as the conventional learning activity. This study examined whether there was different effect of two learning model toward conceptual understanding and strategic competence of Junior High School Students. The data was analyzed by using Multivariate Analysis of Variance (MANOVA) and obtained a significant difference between experimental and control class when considered jointly on the mathematics conceptual understanding and strategic competence (shown by Wilk’s Λ = 0.84). Further, by independent t-test is known that there was significant difference between two classes both on mathematical conceptual understanding and strategic competence. By this result is known that Rigorous Mathematical Thinking (RMT) had positive impact toward Mathematics conceptual understanding and strategic competence.

Mathematic simulation of soil-vegetation condition and land use structure applying basin approach

NASA Astrophysics Data System (ADS)

Mishchenko, Natalia; Shirkin, Leonid; Krasnoshchekov, Alexey

2016-04-01

Ecosystems anthropogenic transformation is basically connected to the changes of land use structure and human impact on soil fertility. The Research objective is to simulate the stationary state of river basins ecosystems. Materials and Methods. Basin approach has been applied in the research. Small rivers basins of the Klyazma river have been chosen as our research objects. They are situated in the central part of the Russian plain. The analysis is carried out applying integrated characteristics of ecosystems functioning and mathematic simulation methods. To design mathematic simulator functional simulation methods and principles on the basis of regression, correlation and factor analysis have been applied in the research. Results. Mathematic simulation resulted in defining possible permanent conditions of "phytocenosis-soil" system in coordinates of phytomass, phytoproductivity, humus percentage in soil. Ecosystem productivity is determined not only by vegetation photosynthesis activity but also by the area ratio of forest and meadow phytocenosis. Local maximums attached to certain phytomass areas and humus content in soil have been defined on the basin phytoproductivity distribution diagram. We explain the local maximum by synergetic effect. It appears with the definite ratio of forest and meadow phytocenosis. In this case, utmost values of phytomass for the whole area are higher than just a sum of utmost values of phytomass for the forest and meadow phytocenosis. Efficient correlation of natural forest and meadow phytocenosis has been defined for the Klyazma river. Conclusion. Mathematic simulation methods assist in forecasting the ecosystem conditions under various changes of land use structure. Nowadays overgrowing of the abandoned agricultural lands is very actual for the Russian Federation. Simulation results demonstrate that natural ratio of forest and meadow phytocenosis for the area will restore during agricultural overgrowing.

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…

Students Upgrading Mathematical Achievement Project SUMA--1989. Evaluation Section Report.

ERIC Educational Resources Information Center

Berney, Tomi D.; Barrera, Marbella

Students Upgrading Mathematical Achievement (SUMA) is a part of the Bilingual Mathematics and Science Achievement project for Spanish-speaking Limited English Proficient (LEP) students. Its objective is to provide both remedial tutoring to students lacking mathematics skills and enrichment to students who are potentially gifted in mathematics.…

Matematica Para La Escuela Secundaria: Geometria (Parte 1). Traduccion Preliminar de la Edicion Inglesa Revisada. (Mathematics for High School: Geometry, Part 1. Preliminary Translation of the Revised English Edition).

ERIC Educational Resources Information Center

Allen, Frank B.; And Others

This is part one of a two-part SMSG mathematics text for high school students. Topics include plane geometry, real numbers, triangles and angles, congruence, construction, parallel lines, perpendicular lines, and parallelograms. The text is written in Spanish. (RH)

Complexity analysis and mathematical tools towards the modelling of living systems.

PubMed

Bellomo, N; Bianca, C; Delitala, M

2009-09-01

This paper is a review and critical analysis of the mathematical kinetic theory of active particles applied to the modelling of large living systems made up of interacting entities. The first part of the paper is focused on a general presentation of the mathematical tools of the kinetic theory of active particles. The second part provides a review of a variety of mathematical models in life sciences, namely complex social systems, opinion formation, evolution of epidemics with virus mutations, and vehicular traffic, crowds and swarms. All the applications are technically related to the mathematical structures reviewed in the first part of the paper. The overall contents are based on the concept that living systems, unlike the inert matter, have the ability to develop behaviour geared towards their survival, or simply to improve the quality of their life. In some cases, the behaviour evolves in time and generates destructive and/or proliferative events.

Mathematics Through Science, Part II: Graphing, Equations and Linear Functions. Student Text. Revised Edition.

ERIC Educational Resources Information Center

Bolduc, Elroy J., Jr.; And Others

The purpose of this text is to teach learning and understanding of mathematics at grades seven through nine through the use of science experiments. Previous knowledge of science on the part of students or teachers is not necessary. The text is designed to be usable with any mathematics textbook in common use. The material can be covered in four…

Mathematics for Junior High School, Volume II (Part 2).

ERIC Educational Resources Information Center

Anderson, R. D.; And Others

This is part two of a two-part SMSG mathematics text for junior high school students. Key ideas emphasized are structure of arithmetic from an algebraic viewpoint, the real number system as a progressing development, and metric and non-metric relations in geometry. Chapter topics include real numbers, similar triangles, variation, non-metric…

Scoring Points: Goals for Real World Problem Solving

ERIC Educational Resources Information Center

Galbraith, Peter

2012-01-01

This paper is presented in two parts. Through an example the first part takes up the issue of applying mathematics to situations that form part of the life context of students--the priority expressed in three curriculum statements presented. Then, noting the particular point in time--development of a National Curriculum for Mathematics--the second…

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

ERIC Educational Resources Information Center

Sophian, Catherine

2013-01-01

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

Computer Mathematics: An Introduction. Part II.

ERIC Educational Resources Information Center

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

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

Are Disadvantaged Students Given Equal Opportunities to Learn Mathematics? PISA in Focus. No. 63

ERIC Educational Resources Information Center

OECD Publishing, 2016

2016-01-01

Socio-economically advantaged and disadvantaged students are not equally exposed to mathematics problems and concepts at school. Exposure to mathematics at school has an impact on performance, and disadvantaged students' relative lack of familiarity with mathematics partly explains their lower performance. Widening access to mathematics content…

Mathematical Aspects of Educating Architecture Designers: A College Study

ERIC Educational Resources Information Center

Verner, I. M.; Maor, S.

2005-01-01

This paper considers a second-year Mathematical Aspects in Architectural Design course, which relies on a first-year mathematics course and offers mathematical learning as part of hands-on practice in architecture design studio. The 16-hour course consisted of seminar presentations of mathematics concepts, their application to covering the plane…

EVALUATION OF ROOSEVELT SUMMER DEMONSTRATION PROGRAM, 1967.

ERIC Educational Resources Information Center

RICHARDSON, JOY B.

THE FIRST PART OF THIS REPORT OF A SENATE BILL 28 DEMONSTRATION PROJECT DESCRIBES THE SUMMER JUNIOR HIGH SCHOOL PROGRAM IN WHICH STUDENTS WERE OFFERED (1) LANGUAGE INSTRUCTION TO IMPROVE THEIR READING ACHIEVEMENT, (2) AN INNOVATIVE MATHEMATICS COURSE CONDUCTED BY THE "DISCOVERY METHOD," AND (3) SPANISH-ENGLISH LANGUAGE CLASSES TO ENABLE PUPILS OF…

Quantifying Aluminum Crystal Size Part 2: The Model-Development Sequence

ERIC Educational Resources Information Center

Hjalmarson, Margret; Diefes-Dux, Heidi A.; Bowman, Keith; Zawojewski, Judith S.

2006-01-01

We have designed model-development sequences using a common context to provide authentic problem-solving experiences for first-year students. The model-development sequence takes a model-eliciting activity a step further by engaging students in the exploration and adaptation of a mathematical model (e.g., procedure, algorithm, method) for solving…

Young Children's Photographs of Measurement in the Home

ERIC Educational Resources Information Center

MacDonald, Amy

2012-01-01

This article explores the use of children's photography as a method for conducting mathematics education research with young children. Collected as part of a study focusing on the experiences with measurement children have at the start of schooling, the photographs presented here were taken by children aged five and six years, from two Australian…

Materials and Fabrication Methods II. A Study Guide of the Science and Engineering Technician Curriculum.

ERIC Educational Resources Information Center

Lindberg, Andrew; Bay, Robert

This study guide is part of a program of studies entitled Science and Engineering Technician (SET) Curriculum. The SET Curriculum integrates elements from the disciplines of chemistry, physics, mathematics, mechanical technology, and electronic technology with the objective of training technicians in the use of electronic instruments and their…

Materials and Fabrication Methods I. A Study Guide of the Science and Engineering Technician Curriculum.

ERIC Educational Resources Information Center

Lindberg, Andrew; And Others

This study guide is part of a curriculum entitled Science and Engineering Technician (SET) Curriculum, a program of studies which integrates elements from the disciplines of chemistry, physics, mathematics, mechanical technology, and electronic technology. The purpose of this national curriculum development project was to provide a framework for…

Pre-Service Teachers' Mental Constructions of Concepts in Matrix Algebra

ERIC Educational Resources Information Center

Ndlovu, Zanele; Brijlall, Deonarain

2015-01-01

This study is part of ongoing research in undergraduate mathematics education. The study was guided by the belief that understanding the mental constructions the pre-service teachers make when learning matrix algebra concepts leads to improved instructional methods. In this preliminary study the data was collected from 85 pre-service teachers…

Custodial Staffing Guidelines for Educational Facilities, Second Edition.

ERIC Educational Resources Information Center

APPA: Association of Higher Education Facilities Officers, Alexandria, VA.

The 20 chapters of this guide to custodial staffing in educational facilities are grouped into five parts addressing: (1) staffing, (2) evaluation, (3) special considerations, (4) staff development tools, and (5) case studies. The five chapters on staffing are all by Jack C. Dudley and are titled: "General Methods"; "The Mathematics of Change";…

Introduction to Probability, Part 1 - Basic Concepts. Student Text. Revised Edition.

ERIC Educational Resources Information Center

Blakeslee, David W.; And Others

This book is designed to introduce the reader to some fundamental ideas about probability. The mathematical theory of probability plays an increasingly important role in science, government, industry, business, and economics. An understanding of the basic concepts of probability is essential for the study of statistical methods that are widely…

Optimization Techniques for Design Problems in Selected Areas in WSNs: A Tutorial

PubMed Central

Ibrahim, Ahmed; Alfa, Attahiru

2017-01-01

This paper is intended to serve as an overview of, and mostly a tutorial to illustrate, the optimization techniques used in several different key design aspects that have been considered in the literature of wireless sensor networks (WSNs). It targets the researchers who are new to the mathematical optimization tool, and wish to apply it to WSN design problems. We hence divide the paper into two main parts. One part is dedicated to introduce optimization theory and an overview on some of its techniques that could be helpful in design problem in WSNs. In the second part, we present a number of design aspects that we came across in the WSN literature in which mathematical optimization methods have been used in the design. For each design aspect, a key paper is selected, and for each we explain the formulation techniques and the solution methods implemented. We also provide in-depth analyses and assessments of the problem formulations, the corresponding solution techniques and experimental procedures in some of these papers. The analyses and assessments, which are provided in the form of comments, are meant to reflect the points that we believe should be taken into account when using optimization as a tool for design purposes. PMID:28763039

Optimization Techniques for Design Problems in Selected Areas in WSNs: A Tutorial.

PubMed

Ibrahim, Ahmed; Alfa, Attahiru

2017-08-01

This paper is intended to serve as an overview of, and mostly a tutorial to illustrate, the optimization techniques used in several different key design aspects that have been considered in the literature of wireless sensor networks (WSNs). It targets the researchers who are new to the mathematical optimization tool, and wish to apply it to WSN design problems. We hence divide the paper into two main parts. One part is dedicated to introduce optimization theory and an overview on some of its techniques that could be helpful in design problem in WSNs. In the second part, we present a number of design aspects that we came across in the WSN literature in which mathematical optimization methods have been used in the design. For each design aspect, a key paper is selected, and for each we explain the formulation techniques and the solution methods implemented. We also provide in-depth analyses and assessments of the problem formulations, the corresponding solution techniques and experimental procedures in some of these papers. The analyses and assessments, which are provided in the form of comments, are meant to reflect the points that we believe should be taken into account when using optimization as a tool for design purposes.

Collaborative Emission Reduction Model Based on Multi-Objective Optimization for Greenhouse Gases and Air Pollutants.

PubMed

Meng, Qing-chun; Rong, Xiao-xia; Zhang, Yi-min; Wan, Xiao-le; Liu, Yuan-yuan; Wang, Yu-zhi

2016-01-01

CO2 emission influences not only global climate change but also international economic and political situations. Thus, reducing the emission of CO2, a major greenhouse gas, has become a major issue in China and around the world as regards preserving the environmental ecology. Energy consumption from coal, oil, and natural gas is primarily responsible for the production of greenhouse gases and air pollutants such as SO2 and NOX, which are the main air pollutants in China. In this study, a mathematical multi-objective optimization method was adopted to analyze the collaborative emission reduction of three kinds of gases on the basis of their common restraints in different ways of energy consumption to develop an economic, clean, and efficient scheme for energy distribution. The first part introduces the background research, the collaborative emission reduction for three kinds of gases, the multi-objective optimization, the main mathematical modeling, and the optimization method. The second part discusses the four mathematical tools utilized in this study, which include the Granger causality test to analyze the causality between air quality and pollutant emission, a function analysis to determine the quantitative relation between energy consumption and pollutant emission, a multi-objective optimization to set up the collaborative optimization model that considers energy consumption, and an optimality condition analysis for the multi-objective optimization model to design the optimal-pole algorithm and obtain an efficient collaborative reduction scheme. In the empirical analysis, the data of pollutant emission and final consumption of energies of Tianjin in 1996-2012 was employed to verify the effectiveness of the model and analyze the efficient solution and the corresponding dominant set. In the last part, several suggestions for collaborative reduction are recommended and the drawn conclusions are stated.

Collaborative Emission Reduction Model Based on Multi-Objective Optimization for Greenhouse Gases and Air Pollutants

PubMed Central

Zhang, Yi-min; Wan, Xiao-le; Liu, Yuan-yuan; Wang, Yu-zhi

2016-01-01

CO2 emission influences not only global climate change but also international economic and political situations. Thus, reducing the emission of CO2, a major greenhouse gas, has become a major issue in China and around the world as regards preserving the environmental ecology. Energy consumption from coal, oil, and natural gas is primarily responsible for the production of greenhouse gases and air pollutants such as SO2 and NOX, which are the main air pollutants in China. In this study, a mathematical multi-objective optimization method was adopted to analyze the collaborative emission reduction of three kinds of gases on the basis of their common restraints in different ways of energy consumption to develop an economic, clean, and efficient scheme for energy distribution. The first part introduces the background research, the collaborative emission reduction for three kinds of gases, the multi-objective optimization, the main mathematical modeling, and the optimization method. The second part discusses the four mathematical tools utilized in this study, which include the Granger causality test to analyze the causality between air quality and pollutant emission, a function analysis to determine the quantitative relation between energy consumption and pollutant emission, a multi-objective optimization to set up the collaborative optimization model that considers energy consumption, and an optimality condition analysis for the multi-objective optimization model to design the optimal-pole algorithm and obtain an efficient collaborative reduction scheme. In the empirical analysis, the data of pollutant emission and final consumption of energies of Tianjin in 1996–2012 was employed to verify the effectiveness of the model and analyze the efficient solution and the corresponding dominant set. In the last part, several suggestions for collaborative reduction are recommended and the drawn conclusions are stated. PMID:27010658

A Window into Mathematical Support: How Parents' Perceptions Change Following Observations of Mathematics Tutoring

ERIC Educational Resources Information Center

Westenskow, Arla; Boyer-Thurgood, Jennifer; Moyer-Packenham, Patricia S.

2015-01-01

This research study examined the perceptions of 24 parents of rising 5th-grade students with mathematics learning difficulties as part of a 10-week summer mathematics tutoring experience. During the summer tutoring program, parents observed their children participating in mathematics learning experiences during one-to-one tutoring sessions. At the…

A Machine Learning Approach to Investigating the Effects of Mathematics Dispositions on Mathematical Literacy

ERIC Educational Resources Information Center

Gabriel, Florence; Signolet, Jason; Westwell, Martin

2018-01-01

Mathematics competency is fast becoming an essential requirement in ever greater parts of day-to-day work and life. Thus, creating strategies for improving mathematics learning in students is a major goal of education research. However, doing so requires an ability to look at many aspects of mathematics learning, such as demographics and…

Addressing the Needs of a Developing Nation: Electronic Maps of Mathematical Learning Resources Accessible via the Internet

ERIC Educational Resources Information Center

Fathurrohman, Maman; Porter, Anne

2012-01-01

Teaching and learning of mathematics are integral parts of societies throughout the world. The fundamental or core nature of mathematics, its compulsory acquisition, requires high quality mathematics learning experiences. Moreover it is highly desirable that the emergence of new technology positively influences learning experiences in mathematics.…

Matematicas Para La Escuela Primaria, Grado 4 (Parte 2), Comentario. Traduccion Preliminar de la Edicion en Ingles Revisada. (Mathematics for the Elementary School, Grade 4, Part 2, Teacher's Commentary. Preliminary Translation of the Revised English Edition).

ERIC Educational Resources Information Center

Beatty, Leslie; And Others

This is Part 2 of the teacher's commentary for the grade 4 mathematics program. Part 2 includes the commentary for chapters 6 through 10. Topics covered include addition and subtraction, multiplication and division, geometrical figures, lines and lineal measurement, and fractions. (RH)

Applying mathematical concepts with hands-on, food-based science curriculum.

PubMed

Roseno, Ashley T; Carraway-Stage, Virginia G; Hoerdeman, Callan; Díaz, Sebastián R; Eugene, Geist; Duffrin, Melani W

2015-01-01

This article addresses the current state of the mathematics education system in the United States and provides a possible solution to the contributing issues. As a result of lower performance in primary mathematics, American students are not acquiring the necessary quantitative literacy skills to become successful adults. This study analyzed the impact of the FoodMASTER Intermediate curriculum on fourth-grade student's mathematics knowledge. The curriculum is a part of the FoodMASTER Initiative, which is a compilation of programs utilizing food, a familiar and necessary part of everyday life, as a tool to teach mathematics and science. Students exposed to the curriculum completed a 20-item researcher-developed mathematics knowledge exam (Intervention n=288; Control n=194). Overall, the results showed a significant increase in mathematics knowledge from pre- to post-test. These findings suggest that students engaged in food-based science activities provided them with the context in which to apply mathematical concepts to an everyday experience. Therefore, the FoodMASTER approach was successful at improving students' mathematics knowledge while building a foundation for becoming quantitatively literate adults.

Applying mathematical concepts with hands-on, food-based science curriculum

PubMed Central

Roseno, Ashley T.; Carraway-Stage, Virginia G.; Hoerdeman, Callan; Díaz, Sebastián R.; Eugene, Geist; Duffrin, Melani W.

2015-01-01

This article addresses the current state of the mathematics education system in the United States and provides a possible solution to the contributing issues. As a result of lower performance in primary mathematics, American students are not acquiring the necessary quantitative literacy skills to become successful adults. This study analyzed the impact of the FoodMASTER Intermediate curriculum on fourth-grade student’s mathematics knowledge. The curriculum is a part of the FoodMASTER Initiative, which is a compilation of programs utilizing food, a familiar and necessary part of everyday life, as a tool to teach mathematics and science. Students exposed to the curriculum completed a 20-item researcher-developed mathematics knowledge exam (Intervention n=288; Control n=194). Overall, the results showed a significant increase in mathematics knowledge from pre- to post-test. These findings suggest that students engaged in food-based science activities provided them with the context in which to apply mathematical concepts to an everyday experience. Therefore, the FoodMASTER approach was successful at improving students’ mathematics knowledge while building a foundation for becoming quantitatively literate adults. PMID:26494927

Transforming Ethnomathematical Ideas in Western Mathematics Curriculum Texts

ERIC Educational Resources Information Center

Dickenson-Jones, Amelia

2008-01-01

When ethnomathematical ideas, that is, the mathematical ideas of different cultural groups, are included in mathematics curriculum texts they can become part of the learning experience in various ways. Once included in western classroom mathematics texts, the ethnomathematical ideas become transformed. The transformations involve changes in form…

[Mathematics - astronomy - astrology special library].

PubMed

Gluch, Sibylle

2011-01-01

About 1560 Elector August of Saxony created an unusual library--one distinguished within its period by both its specialization and location. Situated within the Kunstkammer this library was mostly dedicated to the mathematical sciences and related disciplines. It contained works by the most important authors on mathematics, astronomy, and astrology from the classical, medieval, and early modern periods. This essay traces the formation and composition of August's library, and examines its function: What kind of relationship existed between the library and the Kunstkammer? In what way did the library mirror the interests of the Elector, and to what extend does it permit inferences regarding the Elector's knowledge of mathematics? From the analysis August emerges not as a specialist with a deep understanding of mathematics, but as a particular aficionado of mathematical applications. As a practitioner and general follower of the mathematical arts he took part in a far-reaching intellectual network the center of which lay in the University of Wittenberg. Here, Melanchthon had effectively strengthened the importance of the mathematical disciplines within the university curriculum. He regarded mathematics as the foremost science, arguing that before all other disciplines its method enabled man to recognize the harmonic order of the world, and to discern divine providence. Thus, mathematics offered consoling stability and support in an often seemingly chaotic world torn by religious controversies. This kind of esteem for the mathematical sciences did not presuppose expert knowledge. Hence, the fact that August does not appear to have read the mathematical books he collected does not come as a contradiction. On the contrary, for August it sufficed to recognize the potential of the mathematical sciences, which he brought into life through the creation of a specialized library that developed a rhetoric of its own. The collection of his Kunstkammer library spoke of a harmonically ordered world while at the same time memorializing August as a lover of mathematics and an important figure within the group of mathematical experts and enthusiasts.

Symbolic Drawings Reveal Changes in Preservice Teacher Mathematics Attitudes after a Mathematics Methods Course

ERIC Educational Resources Information Center

Rule, Audrey C.; Harrell, Mary H.

2006-01-01

A new method of analyzing mathematics attitudes through symbolic drawings, situated within the field of Jungian-oriented analytical psychology, was applied to 52 preservice elementary teachers before and after a mathematics methods course. In this triangulation mixed methods design study, pretest images related to past mathematics experiences…

Student Assistance General Provisions; Federal Pell Grant Program; Academic Competitiveness Grant Program; and National Science and Mathematics Access to Retain Talent Grant Program. Final Rule. Federal Register, Part IV, Department of Education, 34 CFR Parts 668, 690, and 691

ERIC Educational Resources Information Center

National Archives and Records Administration, 2006

2006-01-01

The Secretary is adopting as final, with changes, interim final regulations in: 34 CFR part 691 for the Academic Competitiveness Grant (ACG) and National Science and Mathematics Access to Retain Talent Grant (National SMART Grant) programs; 34 CFR part 668 (Student Assistance General Provisions); and 34 CFR part 690 (Federal Pell Grant Program).…

Conceptualisations of infinity by primary pre-service teachers

NASA Astrophysics Data System (ADS)

Date-Huxtable, Elizabeth; Cavanagh, Michael; Coady, Carmel; Easey, Michael

2018-05-01

As part of the Opening Real Science: Authentic Mathematics and Science Education for Australia project, an online mathematics learning module embedding conceptual thinking about infinity in science-based contexts, was designed and trialled with a cohort of 22 pre-service teachers during 1 week of intensive study. This research addressed the question: "How do pre-service teachers conceptualise infinity mathematically?" Participants argued the existence of infinity in a summative reflective task, using mathematical and empirical arguments that were coded according to five themes: definition, examples, application, philosophy and teaching; and 17 codes. Participants' reflections were differentiated as to whether infinity was referred to as an abstract (A) or a real (R) concept or whether both (B) codes were used. Principal component analysis of the reflections, using frequency of codings, revealed that A and R codes occurred at different frequencies in three groups of reflections. Distinct methods of argument were associated with each group of reflections: mathematical numerical examples and empirical measurement comparisons characterised arguments for infinity as an abstract concept, geometric and empirical dynamic examples and belief statements characterised arguments for infinity as a real concept and empirical measurement and mathematical examples and belief statements characterised arguments for infinity as both an abstract and a real concept. An implication of the results is that connections between mathematical and empirical applications of infinity may assist pre-service teachers to contrast finite with infinite models of the world.

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…

Enhancing Mathematics (STEM) Teacher Education in Regional Australia: Pedagogical Interactions and Affect

ERIC Educational Resources Information Center

Woolcott, Geoff; Yeigh, Tony

2015-01-01

This article reports on initial findings, including the mathematics components, of a multi-institutional Science, Technology, Engineering, and Mathematics (STEM) project, "It's part of my life: Engaging university and community to enhance science and mathematics education." This project is focussed on improving the scientific and…

Re-"Conceptualizing" Procedural Knowledge in Mathematics.

ERIC Educational Resources Information Center

Star, Jon R.

Many mathematics educators have lost sight of the critical importance of the mathematical understanding which underlies procedural competence, in part because we do not have a language to refer to this kind of understanding. The modal way of categorizing mathematical knowledge--conceptual and procedural knowledge--is limited in that: (a) it is…

Mathematical Communication in the Classroom: A Teacher Makes a Difference

ERIC Educational Resources Information Center

Cooke, Bessie Davis; Buchholz, Dilek

2005-01-01

The National Council of Teachers of Mathematics (NCTM) states that "Communication is an essential part of mathematics and mathematics education" (2000, p. 60). In fact, communication is one of the five process standards emphasized by NCTM. The communication standard highlights the importance of young children communicating their mathematical…

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

ERIC Educational Resources Information Center

Battista, Michael T.

1986-01-01

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

[HUGO STEINHAUS--CO-FOUNDER OF THE LWÓW SCHOOL OF MATHEMATICS].

PubMed

Wócik, Wiesław

2014-01-01

The paper is dedicated to the presentation of professor Hugo Steinhaus--co-founder of the Lwów School of Mathematics. It is indicated that had it not been for the scholar, the founding and development of the Lwów School of Mathematics would have been almost impossible. The analyses focus on his undertakings during the Lvov period in the early 1920s and those events that preceded the founding of the school (namely Steinhaus's education at the Göttingen University, various meetings and gatherings, discussions, first fascinations and mathematical dissertations). This paper, however, does not look into the scientific output of Steinhaus, only presents his method of scientific work and highlights the strategy that he chose in order to create the scientific community. An attempt has been also made to justify the effectiveness of the adopted strategy by describing the scientific atmosphere of Lvov and intellectual potential of the students of the school. Steinhaus's activities in the 1930s will be only marginally presented with an impact on particularly interesting cooperation with the alumni of the Lwów School of Mathematics--Marek Kac, Stefan Kaczmarz, Paweł Nikliborec and scholars from other fields of science (as part of the process of the application of mathematics).

A Short History of the Science and Mathematics Education Centre at Curtin University

ERIC Educational Resources Information Center

Treagust, David F.

2011-01-01

This article is presented in four parts. In the first part, I describe the foundation of the Science and Mathematics Education Centre (SMEC) at Curtin University. In the second part, I explain the development of SMEC's teaching and research capacity under its three directors. In the third section, I describe how federal government support of SMEC…

Young Children's Learning Performance and Efficiency When Using Virtual Manipulative Mathematics iPad Apps

ERIC Educational Resources Information Center

Moyer-Packenham, Patricia S.; Shumway, Jessica F.; Bullock, Emma; Tucker, Stephen I.; Anderson-Pence, Katie L.; Westenskow, Arla; Boyer-Thurgood, Jennifer; Maahs-Fladung, Cathy; Symanzik, Juergen; Mahamane, Salif; MacDonald, Beth; Jordan, Kerry

2015-01-01

Part of a larger initiation mixed methods study (Greene, Caracelli, & Graham, 1989), this paper discusses the changes in young children's learning performance and efficiency (one element of the quantitative portion of the larger study) during clinical interviews in which each child interacted with a variety of virtual manipulative…

Trigonometry with Year 8: Part 1

ERIC Educational Resources Information Center

Steer, Jessica; de Vila, Maria Antioneta; Eaton, James

2009-01-01

The authors explore the teaching of trigonometry using a method developed by Jeremy Burke of Kings College. A series of lessons was planned using an approach which looks at moving from a mathematical description of the topic, to a sequence plan, to a set of activities, which students can use to help them come to understand the topic. This is…

Simulation-Visualization and Self-Assessment Modules' Capabilities in Structural Analysis Course Including Survey Analysis Results

ERIC Educational Resources Information Center

Kadiam, Subhash Chandra Bose S. V.; Mohammed, Ahmed Ali; Nguyen, Duc T.

2010-01-01

In this paper, we describe an approach to analyze 2D truss/Frame/Beam structures under Flash-based environment. Stiffness Matrix Method (SMM) module was developed as part of ongoing projects on a broad topic "Students' Learning Improvements in Science, Technology, Engineering and Mathematics (STEM) Related Areas" at Old Dominion…

On One Unusual Method of Computation of Limits of Rational Functions in the Program Mathematica[R

ERIC Educational Resources Information Center

Hora, Jaroslav; Pech, Pavel

2005-01-01

Computing limits of functions is a traditional part of mathematical analysis which is very difficult for students. Now an algorithm for the elimination of quantifiers in the field of real numbers is implemented in the program Mathematica. This offers a non-traditional view on this classical theme. (Contains 1 table.)

`I'm a natural and I do it for love!': exploring students' accounts of studying mathematics

NASA Astrophysics Data System (ADS)

Bartholomew, Hannah; Darragh, Lisa; Ell, Fiona; Saunders, Jeanette

2011-10-01

Drawing on in-depth interviews with the third year students at a New Zealand university, we explore the ways in which students speak about studying mathematics, their relationship with the subject and how this has developed over time. These interviews were conducted as part of a project looking at undergraduate mathematics from the perspective of lecturers, students, and interactions in lectures, and funded by the Teaching and Learning Research Initiative in New Zealand. We use the work of Gee [Identity as an analytic lens for research in education, Rev. Res. Educ. 25 (2000), pp. 99-125] to tease out some discourses of mathematics that frame students' participation in the subject, and show that notions of 'natural ability', and of being passionate about the study of mathematics for its own sake, dominate the narratives of mathematics students. In developing this position, we turn to psycho-social theorists such as Hollway and Jefferson [Doing Qualitative Research Differently: Free Association, Narrative and the Interview Method, Sage, London, 1997] so as to question the 'face-value' meanings of these narratives and to argue that students' choices have less to do with rational decision making than with constructing identities that protect vulnerable aspects of themselves. Finally, we develop the metaphor of a 'maths club', which we feel captures something of the culture of mathematics and students' orientations towards the subject. This metaphor also allows us to raise questions about widening participation in mathematics.

Assessing Mathematics 4. Problem Solving: The APU Approach.

ERIC Educational Resources Information Center

Foxman, Derek; And Others

1984-01-01

Presented are examples of problem-solving items from practical and written mathematics tests. These tests are part of an English survey designed to assess the mathematics achievement of students aged 11 and 15. (JN)

Advances and Computational Tools towards Predictable Design in Biological Engineering

PubMed Central

2014-01-01

The design process of complex systems in all the fields of engineering requires a set of quantitatively characterized components and a method to predict the output of systems composed by such elements. This strategy relies on the modularity of the used components or the prediction of their context-dependent behaviour, when parts functioning depends on the specific context. Mathematical models usually support the whole process by guiding the selection of parts and by predicting the output of interconnected systems. Such bottom-up design process cannot be trivially adopted for biological systems engineering, since parts function is hard to predict when components are reused in different contexts. This issue and the intrinsic complexity of living systems limit the capability of synthetic biologists to predict the quantitative behaviour of biological systems. The high potential of synthetic biology strongly depends on the capability of mastering this issue. This review discusses the predictability issues of basic biological parts (promoters, ribosome binding sites, coding sequences, transcriptional terminators, and plasmids) when used to engineer simple and complex gene expression systems in Escherichia coli. A comparison between bottom-up and trial-and-error approaches is performed for all the discussed elements and mathematical models supporting the prediction of parts behaviour are illustrated. PMID:25161694

A short history of the Science and Mathematics Education Centre at Curtin University

NASA Astrophysics Data System (ADS)

Treagust, David F.

2011-09-01

This article is presented in four parts. In the first part, I describe the foundation of the Science and Mathematics Education Centre (SMEC) at Curtin University. In the second part, I explain the development of SMEC's teaching and research capacity under its three directors. In the third section, I describe how federal government support of SMEC as a national Key Centre for Teaching and Research in School Science and Mathematics provided enhanced postgraduate study opportunities for science and mathematics teachers throughout Australia by offering degree programs through distance education and face-to-face contact, short courses, and seminars. At the same time, research and teaching capacity of the academic staff was enhanced through the internationalisation of the programs being offered. In the final section, I describe current and future developments at SMEC.

On inferentialism

NASA Astrophysics Data System (ADS)

Radford, Luis

2017-12-01

This article is a critical commentary on inferentialism in mathematics education. In the first part, I comment on some of the major shortcomings that inferentialists see in the theoretical underpinnings of representationalist, empiricist, and socioconstructivist mathematics education theories. I discuss in particular the criticism that inferentialism makes of the social dimension as conceptualized by socioconstructivism and the question related to the objectivity of knowledge. In the second part, I discuss some of the theoretical foundations of inferentialism in mathematics education and try to answer the question of whether or not inferentialism overcomes the individual-social divide. In the third part, I speculate on what I think inferentialism accomplishes and what I think it does not.

Research on NC laser combined cutting optimization model of sheet metal parts

NASA Astrophysics Data System (ADS)

Wu, Z. Y.; Zhang, Y. L.; Li, L.; Wu, L. H.; Liu, N. B.

2017-09-01

The optimization problem for NC laser combined cutting of sheet metal parts was taken as the research object in this paper. The problem included two contents: combined packing optimization and combined cutting path optimization. In the problem of combined packing optimization, the method of “genetic algorithm + gravity center NFP + geometric transformation” was used to optimize the packing of sheet metal parts. In the problem of combined cutting path optimization, the mathematical model of cutting path optimization was established based on the parts cutting constraint rules of internal contour priority and cross cutting. The model played an important role in the optimization calculation of NC laser combined cutting.

Matematicas Para La Escuela Primaria, Grado 4 (Parte 1), Comentario. Traduccion Preliminar de la Edicion en Ingles Revisada. (Mathematics for the Elementary School, Grade 4, Part 1, Teacher's Commentary. Preliminary Translation of the Revised English Edition).

ERIC Educational Resources Information Center

Beatty, Leslie; And Others

This is Part 1 of the teacher's commentary for the grade 4 mathematics program. Part 1 includes the commentary for chapters 1 through 5. Topics covered include congruence, numbers and number bases, subtraction of numbers, division of numbers, and elementary geometry. References to the student text are cited. (RH)

Matematicas Para El Primer Ciclo Secundario, Volumen II (Parte 2). Traduccion Preliminar de la Edicion en Ingles Revisada. (Mathematics for Junior High School, Volume II, Part 2. Preliminary Translation of the Revised English Edition).

ERIC Educational Resources Information Center

Anderson, R. D.; And Others

This is part two of a two-part SMSG mathematics text for junior high school students. Key ideas emphasized are structure of arithmetic from an algebraic viewpoint, the real number system as a progressing development, and metric and non-metric relations in geometry. Chapter topics include real numbers, similar triangles, variation, polyhedrons,…

Matematicas Para El Primer Ciclo Secundario, Volumen I (Parte 2). Traduccion Preliminar de la Edicion Inglesa Revisada. (Mathematics for Junior High School, Volume I, Part 2. Preliminary Translation of the Revised English Edition).

ERIC Educational Resources Information Center

Anderson, R. D.; And Others

This is part two of a two-part SMSG mathematics text for junior high school students. Key ideas emphasized are structure of arithmetic from an algebraic viewpoint, the real number system, and metric and non-metric relations in geometry. Included are chapters on the rational number system; parallels, parallelograms, triangles, and right prisms;…

Mathematics in Early Childhood: Research-Based Rationale and Practical Strategies

ERIC Educational Resources Information Center

Linder, Sandra M.; Powers-Costello, Beth; Stegelin, Dolores A.

2011-01-01

Mathematics education is a critical part of the curriculum for students worldwide. The foundation for understanding mathematical concepts related to number sense begins early in life, and early childhood classrooms can provide the seeds for mathematical skills that will be needed later in life. In this article, the authors make a case for…

A Comparison of Pedagogical Practices and Beliefs in International and Domestic Mathematics Teaching Assistants

ERIC Educational Resources Information Center

Kim, Minsu

2014-01-01

International and domestic mathematics teaching assistants (MTAs) are a critical part of mathematics education because they teach a substantial portion of low-level mathematics courses at research institutions. Even if there are several factors to build on MTAs' pedagogical practices, MTAs' beliefs significantly influence the MTAs' practices. The…

Mathematics and Numeracy--Is There a Difference?

ERIC Educational Resources Information Center

Australian Mathematics Teacher, 2012

2012-01-01

The term "numeracy" seems to be commonly used in discussions about school mathematics education these days. It is not altogether clear what various school systems intend "numeracy" to mean and whether or not it is meant to replace the term "mathematics", whether it is just one part of mathematics or whether it is…

Mathematics Teachers' Support and Retention: Using Maslow's Hierarchy to Understand Teachers' Needs

ERIC Educational Resources Information Center

Fisher, Molly H.; Royster, David

2016-01-01

As part of a larger study, four mathematics teachers from diverse backgrounds and teaching situations report their ideas on teacher stress, mathematics teacher retention, and their feelings about the needs of mathematics teachers, as well as other information crucial to retaining quality teachers. The responses from the participants were used to…

Questions To Ask and Issues To Consider While Supervising Elementary Mathematics Student Teachers.

ERIC Educational Resources Information Center

Philip, Randolph A.

2000-01-01

Presents four questions to consider when supervising elementary mathematics teachers, who come with many preconceptions about teaching and learning mathematics: What mathematical concepts, procedures, or algorithms are you teaching? Are the concepts and procedures part of a unit? What types of questions do you pose? and What understanding of…

Using Five-Frames in Preschool Mathematics Instruction

ERIC Educational Resources Information Center

Rizer, Jennifer

2017-01-01

Mathematics education is a critical part of instruction for students around the globe. The foundation for understanding basic mathematical concepts begins early in life. Preschool classrooms can provide the early skills in mathematical reasoning that will be needed later in life. In this study, the author sought to determine if the use of…

An Introduction to Equilibrium Thermodynamics: A Rational Approach to Its Teaching. Part 1: Notation and Mathematics.

ERIC Educational Resources Information Center

Williams, Donald F.; Glasser, David

1991-01-01

Introduces and develops mathematical notation to assist undergraduate students in overcoming conceptual difficulties involving the underlying mathematics of state functions, which tend to be different from functions encountered by students in previous mathematical courses, because of the need to manipulate special types of partial derivatives and…

The Experiences and Effect of Two Post-Secondary Mathematics Remediation Programs

ERIC Educational Resources Information Center

Izard, Angie D.

2010-01-01

The purpose of this study was to describe the experience and effect of two post-secondary mathematics remediation programs at a Midwest university. The two mathematics remediation programs were provided as part of a summer bridge program designed to assist entering freshmen students who demonstrated low mathematics proficiency levels based on…

Many Right Answers: Learning in Mathematics through Speaking and Listening

ERIC Educational Resources Information Center

De Geest, Els

2007-01-01

This project, "Many Right Answers: Learning in mathematics through speaking and listening", was initiated to address two issues in the teaching of secondary mathematics: (1) speaking and listening and its relevance to engaging the disengaged; and (2) the use of speaking and listening by teachers of mathematics as part of their Continuous…

An Investigation of Prospective Secondary Mathematics Teachers' Conceptual Knowledge of and Attitudes Towards Statistics

ERIC Educational Resources Information Center

Hannigan, Ailish; Gill, Olivia; Leavy, Aisling M.

2013-01-01

The development of statistical literacy is fast becoming the focus of a large part of mathematics instruction at primary, secondary and tertiary levels. This broadening of the mathematics curriculum to encompass a focus on statistics makes considerable demands on teachers. Most mathematics teachers acknowledge the practical importance of…

Expert system verification and validation study. Delivery 3A and 3B: Trip summaries

NASA Technical Reports Server (NTRS)

French, Scott

1991-01-01

Key results are documented from attending the 4th workshop on verification, validation, and testing. The most interesting part of the workshop was when representatives from the U.S., Japan, and Europe presented surveys of VV&T within their respective regions. Another interesting part focused on current efforts to define industry standards for artificial intelligence and how that might affect approaches to VV&T of expert systems. The next part of the workshop focused on VV&T methods of applying mathematical techniques to verification of rule bases and techniques for capturing information relating to the process of developing software. The final part focused on software tools. A summary is also presented of the EPRI conference on 'Methodologies, Tools, and Standards for Cost Effective Reliable Software Verification and Validation. The conference was divided into discussion sessions on the following issues: development process, automated tools, software reliability, methods, standards, and cost/benefit considerations.

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 doing physics. It contrasts with their more common experience with mathematics as the practice of specified procedures to improve efficiency. This paper describes new curricular materials based on invention instruction provide students with opportunities to generate mathematical relationships in physics, and the paper presents preliminary evidence of the effectiveness of this method with mathematically underprepared engineering students.

Mathematics Fitness.

ERIC Educational Resources Information Center

Trezise, Kathleen A.

1998-01-01

Students receiving mathematics instruction relevant to life will understand that mathematics is part of the real world and not just another school subject. Presents an activity that integrates rational numbers with health-related science content as students collect data and engage in decision making. (ASK)

A Mixed Methods Study of Teach for America Teachers' Mathematical Beliefs, Knowledge, and Classroom Teaching Practices during a Reform-Based University Mathematics Methods Course

ERIC Educational Resources Information Center

Swars, Susan Lee

2015-01-01

This mixed methods study examined the mathematical preparation of elementary teachers in a Teach for America (TFA) program, focal participants for whom there is scant extant research. Data collection occurred before and after a university mathematics methods course, with a particular focus on the participants' (n = 22) mathematical beliefs,…

Moving toward Positive Mathematics Beliefs and Developing Socio-Mathematical Authority: Urban Preservice Teachers in Mathematics Methods Courses

ERIC Educational Resources Information Center

Saran, Rupam; Gujarati, Joan

2013-01-01

This article explores how preservice elementary teachers change their negative beliefs toward mathematics into positive ones after taking a mathematics methods course that follows the Concrete-Pictorial-Abstract (CPA) instructional method. Also explored is the relationship between those beliefs and sociomathematical authority. By administering…

Visual Learning in Application of Integration

NASA Astrophysics Data System (ADS)

Bt Shafie, Afza; Barnachea Janier, Josefina; Bt Wan Ahmad, Wan Fatimah

Innovative use of technology can improve the way how Mathematics should be taught. It can enhance student's learning the concepts through visualization. Visualization in Mathematics refers to us of texts, pictures, graphs and animations to hold the attention of the learners in order to learn the concepts. This paper describes the use of a developed multimedia courseware as an effective tool for visual learning mathematics. The focus is on the application of integration which is a topic in Engineering Mathematics 2. The course is offered to the foundation students in the Universiti Teknologi of PETRONAS. Questionnaire has been distributed to get a feedback on the visual representation and students' attitudes towards using visual representation as a learning tool. The questionnaire consists of 3 sections: Courseware Design (Part A), courseware usability (Part B) and attitudes towards using the courseware (Part C). The results showed that students demonstrated the use of visual representation has benefited them in learning the topic.

Matematica Para La Escuela Secundaria: Geometria (Parte 2). Traduccion Preliminar de la Edicion Inglesa Revisada. (Mathematics for High School: Geometry, Part 2. Preliminary Translation of the Revised English Edition).

ERIC Educational Resources Information Center

Allen, Frank B.; And Others

This is part two of a two-part SMSG mathematics text for high school students. Chapter topics include: (1) perpendicular lines and planes in space; (2) parallel lines in a plane; (3) parallel lines in space; (4) areas of polygonal regions: (5) similarity; (6) circles and spheres; (7) constructions; (8) the area of a circle and related topics; and…

Matematicas Para El Primer Ciclo Secundario, Volumen I (Parte 1). Traduccion Preliminar de la Edicion Inglesa Revisada. (Mathematics for Junior High School, Volume I, Part 1, Preliminary Translation of the Revised English Edition).

ERIC Educational Resources Information Center

Anderson, R. D.; And Others

This is part one of a two-part SMSG mathematics text for junior high school students. Key ideas emphasized are structure of arithmetic from an algebraic viewpoint, the real number system, and metric and non-metric relations in geometry. Topics included are numbers; cardinal numbers; geometry of lines, points, and planes; geometry of angles,…

Matematicas Para El Primer Ciclo Secundario, Volumen II (Parte 1). Traduccion Preliminar de la Edicion en Ingles Revisada. (Mathematics for Junior High School, Volume II, Part 1. Preliminary Translation of the Revised English Edition).

ERIC Educational Resources Information Center

Anderson, R. D.; And Others

This is part one of a two-part SMSG mathematics text for junior high school students. Key ideas emphasized are structure of arithmetic from an algebraic viewpoint, the real number system as a progressing development, and metric and non-metric relations in geometry. Chapter topics include number line and coordinates, equations, scientific notation,…

Evaporation of liquefied natural gas in conditions of compact storage containers heating

NASA Astrophysics Data System (ADS)

Telgozhayeva, D. S.

2014-08-01

Identical by its power, but located in different parts of the external surface of the tank, the heating sources are different intensity heat transfer modes is heating up, respectively, times of vapour pressure rise to critical values. Developed mathematical model and method of calculation can be used in the analysis of conditions of storage tanks for liquefied gases.

Impact of Classroom Design on Teacher Pedagogy and Student Engagement and Performance in Mathematics

ERIC Educational Resources Information Center

Imms, Wesley; Byers, Terry

2017-01-01

A resurgence in interest in classroom and school design has highlighted how little we know about the impact of learning environments on student and teacher performance. This is partly because of a lack of research methods capable of controlling the complex variables inherent to space and education. In a unique study that overcame such difficulties…

Ross, macdonald, and a theory for the dynamics and control of mosquito-transmitted pathogens.

PubMed

Smith, David L; Battle, Katherine E; Hay, Simon I; Barker, Christopher M; Scott, Thomas W; McKenzie, F Ellis

2012-01-01

Ronald Ross and George Macdonald are credited with developing a mathematical model of mosquito-borne pathogen transmission. A systematic historical review suggests that several mathematicians and scientists contributed to development of the Ross-Macdonald model over a period of 70 years. Ross developed two different mathematical models, Macdonald a third, and various "Ross-Macdonald" mathematical models exist. Ross-Macdonald models are best defined by a consensus set of assumptions. The mathematical model is just one part of a theory for the dynamics and control of mosquito-transmitted pathogens that also includes epidemiological and entomological concepts and metrics for measuring transmission. All the basic elements of the theory had fallen into place by the end of the Global Malaria Eradication Programme (GMEP, 1955-1969) with the concept of vectorial capacity, methods for measuring key components of transmission by mosquitoes, and a quantitative theory of vector control. The Ross-Macdonald theory has since played a central role in development of research on mosquito-borne pathogen transmission and the development of strategies for mosquito-borne disease prevention.

Ross, Macdonald, and a Theory for the Dynamics and Control of Mosquito-Transmitted Pathogens

PubMed Central

Smith, David L.; Battle, Katherine E.; Hay, Simon I.; Barker, Christopher M.; Scott, Thomas W.; McKenzie, F. Ellis

2012-01-01

Ronald Ross and George Macdonald are credited with developing a mathematical model of mosquito-borne pathogen transmission. A systematic historical review suggests that several mathematicians and scientists contributed to development of the Ross-Macdonald model over a period of 70 years. Ross developed two different mathematical models, Macdonald a third, and various “Ross-Macdonald” mathematical models exist. Ross-Macdonald models are best defined by a consensus set of assumptions. The mathematical model is just one part of a theory for the dynamics and control of mosquito-transmitted pathogens that also includes epidemiological and entomological concepts and metrics for measuring transmission. All the basic elements of the theory had fallen into place by the end of the Global Malaria Eradication Programme (GMEP, 1955–1969) with the concept of vectorial capacity, methods for measuring key components of transmission by mosquitoes, and a quantitative theory of vector control. The Ross-Macdonald theory has since played a central role in development of research on mosquito-borne pathogen transmission and the development of strategies for mosquito-borne disease prevention. PMID:22496640

Preventing Early Mathematics Difficulties: The Feasibility of a Rigorous Kindergarten Mathematics Curriculum

ERIC Educational Resources Information Center

Chard, David J.; Baker, Scott K.; Clarke, Ben; Jungjohann, Kathleen; Davis, Karen; Smolkowski, Keith

2008-01-01

Concern about poor mathematics achievement in U.S. schools has increased in recent years. In part, poor achievement may be attributed to a lack of attention to early instruction and missed opportunities to build on young children's early understanding of mathematics. This study examined the development and feasibility testing of a kindergarten…

A New View of Mathematics Will Help Mathematics Teachers

ERIC Educational Resources Information Center

Maasz, Juergen

2005-01-01

For many people mathematics is something like a very huge and impressive building. It has a given structure with lots of levels and rooms. For many people this structure and therefore mathematics itself is independent from society, culture and history. It exists and mathematicians try to recover (not: to construct!) new parts of it. From this…

Problem Solving in the Borderland between Mathematics and Physics

ERIC Educational Resources Information Center

Jensen, Jens Højgaard; Niss, Martin; Jankvist, Uffe Thomas

2017-01-01

The article addresses the problématique of where mathematization is taught in the educational system, and who teaches it. Mathematization is usually not a part of mathematics programs at the upper secondary level, but we argue that physics teaching has something to offer in this respect, if it focuses on solving so-called unformalized problems,…

Reality-Theoretical Models-Mathematics: A Ternary Perspective on Physics Lessons in Upper-Secondary School

ERIC Educational Resources Information Center

Hansson, Lena; Hansson, Örjan; Juter, Kristina; Redfors, Andreas

2015-01-01

This article discusses the role of mathematics during physics lessons in upper-secondary school. Mathematics is an inherent part of theoretical models in physics and makes powerful predictions of natural phenomena possible. Ability to use both theoretical models and mathematics is central in physics. This paper takes as a starting point that the…

The Social Outcomes of Learning Mathematics: Standard, Unintended or Visionary?

ERIC Educational Resources Information Center

Ernest, Paul

2015-01-01

Mathematics is a fundamental part of human knowledge and one of the central planks of the modern technological revolution. But in our enthusiasm to promote its benefits too rarely do we stop to question our intended aims of teaching mathematics and the outcomes of learning mathematics in school. In this paper the standard aims of school…

Method and Effectiveness of an Individualized Exercise of Fundamental Mathematics.

ERIC Educational Resources Information Center

Yoshioka, Takayoshi; Nishizawa, Hitoshi; Tsukamoto Takehiko

2001-01-01

Describes a method used to provide mathematics students in Japanese colleges of engineering with supplementary exercises to aid their learning. Outlines the online operation of individualized exercises that help the students to understand mathematical methods used to solve problems and also mathematical ideas or concepts upon which methods are…

Mathematical model of bone drilling for virtual surgery system

NASA Astrophysics Data System (ADS)

Alaytsev, Innokentiy K.; Danilova, Tatyana V.; Manturov, Alexey O.; Mareev, Gleb O.; Mareev, Oleg V.

2018-04-01

The bone drilling is an essential part of surgeries in ENT and Dentistry. A proper training of drilling machine handling skills is impossible without proper modelling of the drilling process. Utilization of high precision methods like FEM is limited due to the requirement of 1000 Hz update rate for haptic feedback. The study presents a mathematical model of the drilling process that accounts the properties of materials, the geometry and the rotation rate of a burr to compute the removed material volume. The simplicity of the model allows for integrating it in the high-frequency haptic thread. The precision of the model is enough for a virtual surgery system targeted on the training of the basic surgery skills.

CSMP Mathematics for the Intermediate Grades. Part V. Teacher's Guide. The Languages of Strings and Arrows. Geometry and Measurement. Probability and Statistics. Experimental Version.

ERIC Educational Resources Information Center

CEMREL, Inc., St. Louis, MO.

This Comprehensive School Mathematics Program (CSMP) guide is divided into three major parts. The first, the Languages of Strings and Arrows, opens with a suggested lesson order. Major sections cover instructional approaches for: (1) Games with Strings, (2) Necklaces, and (3) The Table Game. A Series of appendices is included. Part 2, Geometry and…

To What Extent Might Role Play Be a Useful Tool for Learning Mathematics?

ERIC Educational Resources Information Center

Williams, Helen

2012-01-01

To most children in primary school role-play is just something you do, and something you enjoy. It is part-and-parcel of being at school, part of the normal classroom activity. So, why can it not just be a normal part of learning mathematics? Can we study learners "in role", and make judgments about what they learn, and how they learn? This is the…

An examination of student attitudes and understanding of exponential functions using interactive instructional multimedia

NASA Astrophysics Data System (ADS)

Singleton, Cynthia M.

The purpose of this study was to examine students' attitudes and understanding of exponential functions using InterAct Math, a mathematics tutorial software. The researcher used a convenience sampling of a total of 78 students from two intact pre-calculus classes; the students in the experimental group totaled 41 and the control group totaled 37. The two groups were exposed to the same curriculum content taught by the same instructor, the researcher. The experimental group used the mathematics tutorial software as an integral part of the instructional delivery. The control group used traditional instruction without integration of the educational technology. Data were collected during a two week span using a mixed-methodology to address the major research questions: (1) Is there a statistically significant difference in the mean achievement test scores between the experimental and the control groups? (2) Is there a statistically significant difference in students' attitudes toward learning mathematics between the experimental group and the control group? The researcher utilized paired t-tests and independent t-tests as statistical methods to evaluate the effectiveness of the intervention and to establish whether there was a significant difference between the experimental and control groups. Based on the analyses of the quantitative data, it was established that the students who received the InterAct Math tutorial (experimental group) did not perform better than the control group on exponential functions, graphs and applications. However, the quantitative part of the study (Aiken-Dreger Mathematics Attitude Scale) revealed that, while students in the experimental and control groups started with similar attitudes about mathematics and the integration of technology, their attitudes were significantly different at the conclusion of the study. The fear of mathematics was reduced for the experimental group at the end of the study, and their enjoyment of the subject matter was increased as a result of the intervention. No significant difference was reported concerning attitudes toward fear and enjoyment of learning mathematics for the control group. The researcher concluded that the use of InterAct Math tutorial software as part of the instructional delivery was beneficial and contributed to a positive attitude change. Other qualitative data obtained from the unstructured interviews of the treatment group supported these findings and reported that the change in attitudes was attributable to the use of the InterAct software in the instructional delivery of the course. The researcher concluded that the results of the study did not provide evidence that InterAct Math software could be credited with producing better learning outcomes. However, it appears that the InterAct Math tutorial software is an effective tutorial tool in promoting positive change in students' attitudes toward learning mathematics; thus, it is an effective tool for mathematics instruction. Based on the above results, it was concluded that the InterAct Math tutorial is an effective tutorial tool in promoting positive attitude change in students toward learning mathematics.

Prospective Mathematics Teachers' Opinions about Mathematical Modeling Method and Applicability of This Method

ERIC Educational Resources Information Center

Akgün, Levent

2015-01-01

The aim of this study is to identify prospective secondary mathematics teachers' opinions about the mathematical modeling method and the applicability of this method in high schools. The case study design, which is among the qualitative research methods, was used in the study. The study was conducted with six prospective secondary mathematics…

[Mathematics, natural sciences and technology--parts of the encyclopedia Die Kultur der Gegenwart (The culture of today)].

PubMed

Tobies, Renate

2008-03-01

The paper explores the trend of the early 20th century to consolidate mathematics, natural sciences, medicine and technology under the umbrella of one integrative culture--a tendency which contrasts with the increasing mainstream trend of separating the humanities from the natural sciences. The unifying umbrella was framed by the great encyclopedia Die Kultur der Gegenwart which was published by B. G. Teubner from 1905 to 1925 and was planned to run up to 62 volumes. We analyze the quantitative rate of the parts devoted to the humanities, the natural sciences and technology, respectively, the degree to which these parts were completed in this encyclopedia. In particular, we investigate the role of mathematicians and their reasons to find a classification for the mathematical, natural scientific and engineering parts of culture as well as their reasons, to win Nobel prize winners and other famous scientists to become co-editors and authors. We examine the published volumes in the fields of mathematics, chemistry, physics, astronomy and technology in order to show what type of publication--professional or popular--was intended. Furthermore, we illuminate how the educational reform of mathematics, natural sciences and technology of this period--which included a reform of girls' and women's education--was reflected in the encyclopedia Die Kultur der Gegenwart.

Approximate Solutions for a Self-Folding Problem of Carbon Nanotubes

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

Y Mikata

2006-08-22

This paper treats approximate solutions for a self-folding problem of carbon nanotubes. It has been observed in the molecular dynamics calculations [1] that a carbon nanotube with a large aspect ratio can self-fold due to van der Waals force between the parts of the same carbon nanotube. The main issue in the self-folding problem is to determine the minimum threshold length of the carbon nanotube at which it becomes possible for the carbon nanotube to self-fold due to the van der Waals force. An approximate mathematical model based on the force method is constructed for the self-folding problem of carbonmore » nanotubes, and it is solved exactly as an elastica problem using elliptic functions. Additionally, three other mathematical models are constructed based on the energy method. As a particular example, the lower and upper estimates for the critical threshold (minimum) length are determined based on both methods for the (5,5) armchair carbon nanotube.« less

The experience of mathematical beauty and its neural correlates

PubMed Central

Zeki, Semir; Romaya, John Paul; Benincasa, Dionigi M. T.; Atiyah, Michael F.

2014-01-01

Many have written of the experience of mathematical beauty as being comparable to that derived from the greatest art. This makes it interesting to learn whether the experience of beauty derived from such a highly intellectual and abstract source as mathematics correlates with activity in the same part of the emotional brain as that derived from more sensory, perceptually based, sources. To determine this, we used functional magnetic resonance imaging (fMRI) to image the activity in the brains of 15 mathematicians when they viewed mathematical formulae which they had individually rated as beautiful, indifferent or ugly. Results showed that the experience of mathematical beauty correlates parametrically with activity in the same part of the emotional brain, namely field A1 of the medial orbito-frontal cortex (mOFC), as the experience of beauty derived from other sources. PMID:24592230

Spoken Language and Mathematics.

ERIC Educational Resources Information Center

Raiker, Andrea

2002-01-01

States teachers/learners use spoken language in a three part mathematics lesson advocated by the British National Numeracy Strategy. Recognizes language's importance by emphasizing correct use of mathematical vocabulary in raising standards. Finds pupils and teachers appear to ascribe different meanings to scientific words because of their…

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…

Constructivist Viewpoints for School Teaching and Learning in Mathematics and Science. Research Report 131.

ERIC Educational Resources Information Center

Ahtee, Maija, Ed.; Pehkonen, Erkki, Ed.

This research report contains a fairly concise overview of the role of constructivism in the teaching of mathematics and science in Finland. Included papers have been grouped into three parts. The first part, "General Considerations," consists of the seven articles on theoretical considerations, social constructivism, teachers' and pupils'…

A procedure of multiple period searching in unequally spaced time-series with the Lomb-Scargle method

NASA Technical Reports Server (NTRS)

Van Dongen, H. P.; Olofsen, E.; VanHartevelt, J. H.; Kruyt, E. W.; Dinges, D. F. (Principal Investigator)

1999-01-01

Periodogram analysis of unequally spaced time-series, as part of many biological rhythm investigations, is complicated. The mathematical framework is scattered over the literature, and the interpretation of results is often debatable. In this paper, we show that the Lomb-Scargle method is the appropriate tool for periodogram analysis of unequally spaced data. A unique procedure of multiple period searching is derived, facilitating the assessment of the various rhythms that may be present in a time-series. All relevant mathematical and statistical aspects are considered in detail, and much attention is given to the correct interpretation of results. The use of the procedure is illustrated by examples, and problems that may be encountered are discussed. It is argued that, when following the procedure of multiple period searching, we can even benefit from the unequal spacing of a time-series in biological rhythm research.

Study of multilayer thermal insulation by inverse problems method

NASA Astrophysics Data System (ADS)

Alifanov, O. M.; Nenarokomov, A. V.; Gonzalez, V. M.

2009-11-01

The purpose of this paper is to introduce a new method in the research of radiative and thermal properties of materials with further applications in the design of thermal control systems (TCS) of spacecrafts. In this paper the radiative and thermal properties (emissivity and thermal conductance) of a multilayered thermal-insulating blanket (MLI), which is a screen-vacuum thermal insulation as a part of the TCS for perspective spacecrafts, are estimated. Properties of the materials under study are determined in the result of temperature and heat flux measurement data processing based on the solution of the inverse heat transfer problem (IHTP) technique. Given are physical and mathematical models of heat transfer processes in a specimen of the multilayered thermal-insulating blanket located in the experimental facility. A mathematical formulation of the inverse heat conduction problem is presented as well. The practical approves were made for specimen of the real MLI.

A Contemporary Analysis of the Content of Mathematics for Liberal Education at the College Level

ERIC Educational Resources Information Center

Sporn, Howard Bruce

2010-01-01

The purpose of this study is to determine whether educators believe mathematics should be taught to liberal arts students, what topics are taught in liberal arts mathematics courses, and what the motivation is for teaching such topics. The study consists of two parts, a review of the opinions of educators regarding liberal arts mathematics, and a…

When Traditional Won't Do: Experiences from a "Lower-Level" Mathematics Classroom

ERIC Educational Resources Information Center

Hill, Crystal

2010-01-01

As the last bell rings, students scurry to their respective classrooms, doors begin to close, and the class period begins. Imagine that you are in the hallway of the school and you look into an advanced mathematics class, into an Algebra I, Part I, mathematics class (a course designed for students who have not found success in mathematics). What…

Vita Mathematica: Historical Research and Integration with Teaching. Mathematical Association of America Notes Series, No. 40.

ERIC Educational Resources Information Center

Calinger, Ronald, Ed.

This book brings together papers by scholars from around the globe on the historiography and history of mathematics and their integration with mathematical pedagogy. Of the three articles in Part 1, "Historiography and Sources", one identifies research trends in the history of mathematics, the second discusses the centrality of problems, and the…

Problem Fields in Mathematics Teaching. Part 3: Views of Finnish Seventh-Grades about Mathematics Teaching. Research Report 108.

ERIC Educational Resources Information Center

Pehkonen, Erkki

This study was conducted to examine the views of seventh-grade students in Finland with regard to the teaching and learning of mathematics. Data were gathered by a questionnaire survey, with follow-up interviews to validate response reliability. Fifty junior high school mathematics teachers in southern Finland were asked to present the…

Comparing Primary and Secondary Mathematics Teachers' Preferences Regarding Values about Mathematics Teaching in Turkey and Germany

ERIC Educational Resources Information Center

Dede, Yüksel

2015-01-01

This study presents a small part of a larger study investigating Turkish and German mathematics teachers' and their students' values (Values in Mathematics Teaching in Turkey and Germany). The main focus of the study was school levels of the teachers working at primary and secondary schools. The interactions related to nationality were also of…

Post-Primary Students' Images of Mathematics: Findings from a Survey of Irish Ordinary Level Mathematics Students

ERIC Educational Resources Information Center

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

2016-01-01

A questionnaire survey was carried out as part of a PhD research study to investigate the image of mathematics held by post-primary students in Ireland. The study focused on students in fifth year of post-primary education studying ordinary level mathematics for the Irish Leaving Certificate examination--the final examination for students in…

The "Verbification" of Mathematics: Using the Grammatical Structures of Mi'kmaq to Support Student Learning

ERIC Educational Resources Information Center

Borden, Lisa Lunney

2011-01-01

As part of a larger project focused on transforming mathematics education for Aboriginal students in Atlantic Canada, this paper reports on the role of the Mi'kmaw language in mathematics teaching. Examining how mathematical concepts are described in Mi'kmaq gives insight into ways of thinking. Shifting classroom discussions to reflect Mi'kmaw…

The State of Proof in Finnish and Swedish Mathematics Textbooks--Capturing Differences in Approaches to Upper-Secondary Integral Calculus

ERIC Educational Resources Information Center

Bergwall, Andreas; Hemmi, Kirsti

2017-01-01

Students' difficulties with proof, scholars' calls for proof to be a consistent part of K-12 mathematics, and the extensive use of textbooks in mathematics classrooms motivate investigations on how proof-related items are addressed in mathematics textbooks. We contribute to textbook research by focusing on opportunities to learn proof-related…

Rural Junior Secondary School Students' Perceptions of Classroom Learning Environments and Their Attitude and Achievement in Mathematics in West China

ERIC Educational Resources Information Center

Yang, Xinrong

2015-01-01

This paper reports findings from a survey of how rural junior secondary school students in the western part of China perceive their mathematics classroom learning environments and associations of learning environment with their attitudes toward mathematics and mathematics achievement. Using adaptations of the widely-used What Is Happening In this…

Findings and Implications from the Mathematics Support Center at Cornell University.

ERIC Educational Resources Information Center

Rosamond, Frances

The nature and use of the Cornell Mathematics Support Center (MSC) is discussed. It is viewed as significantly different from other existing support programs in that it is part of the Department of Mathematics and offers encouragement and support to any interested student, no matter what that pupil's mathematics level is. The MSC is based on the…

Quantum Social Science

NASA Astrophysics Data System (ADS)

Haven, Emmanuel; Khrennikov, Andrei

2013-01-01

Preface; Part I. Physics Concepts in Social Science? A Discussion: 1. Classical, statistical and quantum mechanics: all in one; 2. Econophysics: statistical physics and social science; 3. Quantum social science: a non-mathematical motivation; Part II. Mathematics and Physics Preliminaries: 4. Vector calculus and other mathematical preliminaries; 5. Basic elements of quantum mechanics; 6. Basic elements of Bohmian mechanics; Part III. Quantum Probabilistic Effects in Psychology: Basic Questions and Answers: 7. A brief overview; 8. Interference effects in psychology - an introduction; 9. A quantum-like model of decision making; Part IV. Other Quantum Probabilistic Effects in Economics, Finance and Brain Sciences: 10. Financial/economic theory in crisis; 11. Bohmian mechanics in finance and economics; 12. The Bohm-Vigier Model and path simulation; 13. Other applications to economic/financial theory; 14. The neurophysiological sources of quantum-like processing in the brain; Conclusion; Glossary; Index.

Advanced quantitative measurement methodology in physics education research

NASA Astrophysics Data System (ADS)

Wang, Jing

The ultimate goal of physics education research (PER) is to develop a theoretical framework to understand and improve the learning process. In this journey of discovery, assessment serves as our headlamp and alpenstock. It sometimes detects signals in student mental structures, and sometimes presents the difference between expert understanding and novice understanding. Quantitative assessment is an important area in PER. Developing research-based effective assessment instruments and making meaningful inferences based on these instruments have always been important goals of the PER community. Quantitative studies are often conducted to provide bases for test development and result interpretation. Statistics are frequently used in quantitative studies. The selection of statistical methods and interpretation of the results obtained by these methods shall be connected to the education background. In this connecting process, the issues of educational models are often raised. Many widely used statistical methods do not make assumptions on the mental structure of subjects, nor do they provide explanations tailored to the educational audience. There are also other methods that consider the mental structure and are tailored to provide strong connections between statistics and education. These methods often involve model assumption and parameter estimation, and are complicated mathematically. The dissertation provides a practical view of some advanced quantitative assessment methods. The common feature of these methods is that they all make educational/psychological model assumptions beyond the minimum mathematical model. The purpose of the study is to provide a comparison between these advanced methods and the pure mathematical methods. The comparison is based on the performance of the two types of methods under physics education settings. In particular, the comparison uses both physics content assessments and scientific ability assessments. The dissertation includes three parts. The first part involves the comparison between item response theory (IRT) and classical test theory (CTT). The two theories both provide test item statistics for educational inferences and decisions. The two theories are both applied to Force Concept Inventory data obtained from students enrolled in The Ohio State University. Effort was made to examine the similarity and difference between the two theories, and the possible explanation to the difference. The study suggests that item response theory is more sensitive to the context and conceptual features of the test items than classical test theory. The IRT parameters provide a better measure than CTT parameters for the educational audience to investigate item features. The second part of the dissertation is on the measure of association for binary data. In quantitative assessment, binary data is often encountered because of its simplicity. The current popular measures of association fail under some extremely unbalanced conditions. However, the occurrence of these conditions is not rare in educational data. Two popular association measures, the Pearson's correlation and the tetrachoric correlation are examined. A new method, model based association is introduced, and an educational testing constraint is discussed. The existing popular methods are compared with the model based association measure with and without the constraint. Connections between the value of association and the context and conceptual features of questions are discussed in detail. Results show that all the methods have their advantages and disadvantages. Special attention to the test and data conditions is necessary. The last part of the dissertation is focused on exploratory factor analysis (EFA). The theoretical advantages of EFA are discussed. Typical misunderstanding and misusage of EFA are explored. The EFA is performed on Lawson's Classroom Test of Scientific Reasoning (LCTSR), a widely used assessment on scientific reasoning skills. The reasoning ability structures for U.S. and Chinese students at different educational levels are given by the analysis. A final discussion on the advanced quantitative assessment methodology and the pure mathematical methodology is presented at the end.

Perception of mathematics teachers on cooperative learning method in the 21st century

NASA Astrophysics Data System (ADS)

Taufik, Nurshahira Alwani Mohd; Maat, Siti Mistima

2017-05-01

Mathematics education is one of the branches to be mastered by students to help them compete with the upcoming challenges that are very challenging. As such, all parties should work together to help increase student achievement in Mathematics education in line with the Malaysian Education Blueprint (MEB) 2010-2025. Teaching methods play a very important role in attracting and fostering student understanding and interested in learning Mathematics. Therefore, this study was conducted to identify the perceptions of teachers in carrying out cooperative methods in the teaching and learning of mathematics. Participants of this study involving 4 teachers who teach Mathematics in primary schools around the state of Negeri Sembilan. Interviews are used as a method for gathering data. The findings indicate that cooperative methods help increasing interest and understanding in the teaching and learning of mathematics. In conclusion, the teaching methods affect the interest and understanding of students in the learning of Mathematics in the classroom.

The effect of studying A-level mathematics on performance in A-level physics

NASA Astrophysics Data System (ADS)

Rutter, Pam

1994-01-01

Mathematics plays an important part in physics at all levels. At A-level, physics candidates who do not study A-level mathematics would seem to be at a disadvantage. This article presents statistical evidence to support this widely held belief.

Mathematical Modeling of Electrodynamics Near the Surface of Earth and Planetary Water Worlds

NASA Technical Reports Server (NTRS)

Tyler, Robert H.

2017-01-01

An interesting feature of planetary bodies with hydrospheres is the presence of an electrically conducting shell near the global surface. This conducting shell may typically lie between relatively insulating rock, ice, or atmosphere, creating a strong constraint on the flow of large-scale electric currents. All or parts of the shell may be in fluid motion relative to main components of the rotating planetary magnetic field (as well as the magnetic fields due to external bodies), creating motionally-induced electric currents that would not otherwise be present. As such, one may expect distinguishing features in the types of electrodynamic processes that occur, as well as an opportunity for imposing specialized mathematical methods that efficiently address this class of application. The purpose of this paper is to present and discuss such specialized methods. Specifically, thin-shell approximations for both the electrodynamics and fluid dynamics are combined to derive simplified mathematical formulations describing the behavior of these electric currents as well as their associated electric and magnetic fields. These simplified formulae allow analytical solutions featuring distinct aspects of the thin-shell electrodynamics in idealized cases. A highly efficient numerical method is also presented that is useful for calculations under inhomogeneous parameter distributions. Finally, the advantages as well as limitations in using this mathematical approach are evaluated. This evaluation is presented primarily for the generic case of bodies with water worlds or other thin spherical conducting shells. More specific discussion is given for the case of Earth, but also Europa and other satellites with suspected oceans.

Vibration of rotating-shaft design spindles with flexible bases

NASA Astrophysics Data System (ADS)

Tseng, Chaw-Wu

The purpose of this study is to demonstrate an accurate mathematical model predicting forced vibration of rotating-shaft HDD spindle motors with flexible stationary parts. The mathematical model consists of three parts: a rotating part, a stationary part, and bearings. The rotating part includes a flexible hub, a flexible shaft press-fit into the hub, and N elastic disks mounted on the hub. The stationary part can include motor bracket (stator), base casting, and top cover. The bearings under consideration can be ball bearings or hydrodynamic bearings (HDB). The rotating disks are modelled through the classical plate theory. The rotating part (except the disks) and the stationary part are modelled through finite element analyses (FEA). With mode shapes and natural frequencies obtained from FEA, the kinetic and potential energies of the rotating and stationary parts are formulated and discretized to compensate for the gyroscopic effects from rotation. Finally, use of Lagrange equation results in the equations of motion. To verify the mathematical model, frequency response functions are measured experimentally for an HDB spindle carrying two identical disks at motor and drive levels. Experimental measurements agree very well with theoretical predictions not only in resonance frequency but also in resonance amplitude.

Breast cancer evaluation by fluorescent dot detection using combined mathematical morphology and multifractal techniques

PubMed Central

2011-01-01

Background Fluorescence in situ hybridization (FISH) is very accurate method for measuring HER2 gene copies, as a sign of potential breast cancer. This method requires small tissue samples, and has a high sensitivity to detect abnormalities from a histological section. By using multiple colors, this method allows the detection of multiple targets simultaneously. The target parts in the cells become visible as colored dots. The HER-2 probes are visible as orange stained spots under a fluorescent microscope while probes for centromere 17 (CEP-17), the chromosome on which the gene HER-2/neu is located, are visible as green spots. Methods The conventional analysis involves the scoring of the ratio of HER-2/neu over CEP 17 dots within each cell nucleus and then averaging the scores for a number of 60 cells. A ratio of 2.0 of HER-2/neu to CEP 17 copy number denotes amplification. Several methods have been proposed for the detection and automated evaluation (dot counting) of FISH signals. In this paper the combined method based on the mathematical morphology (MM) and inverse multifractal (IMF) analysis is suggested. Similar method was applied recently in detection of microcalcifications in digital mammograms, and was very successful. Results The combined MM using top-hat and bottom-hat filters, and the IMF method was applied to FISH images from Molecular Biology Lab, Department of Pathology, Wielkoposka Cancer Center, Poznan. Initial results indicate that this method can be applied to FISH images for the evaluation of HER2/neu status. Conclusions Mathematical morphology and multifractal approach are used for colored dot detection and counting in FISH images. Initial results derived on clinical cases are promising. Note that the overlapping of colored dots, particularly red/orange dots, needs additional improvements in post-processing. PMID:21489192

Laser marking as a result of applying reverse engineering

NASA Astrophysics Data System (ADS)

Mihalache, Andrei; Nagîţ, Gheorghe; Rîpanu, Marius Ionuţ; Slǎtineanu, Laurenţiu; Dodun, Oana; Coteaţǎ, Margareta

2018-05-01

The elaboration of a modern manufacturing technology needs a certain quantum of information concerning the part to be obtained. When it is necessary to elaborate the technology for an existing object, such an information could be ensured by using the principles specific to the reverse engineering. Essentially, in the case of this method, the analysis of the surfaces and of other characteristics of the part must offer enough information for the elaboration of the part manufacturing technology. On the other hand, it is known that the laser marking is a processing method able to ensure the transfer of various inscriptions or drawings on a part. Sometimes, the laser marking could be based on the analysis of an existing object, whose image could be used to generate the same object or an improved object. There are many groups of factors able to affect the results of applying the laser marking process. A theoretical analysis was proposed to show that the heights of triangles obtained by means of a CNC marking equipment depend on the width of the line generated by the laser spot on the workpiece surface. An experimental research was thought and materialized to highlight the influence exerted by the line with and the angle of lines intersections on the accuracy of the marking process. By mathematical processing of the experimental results, empirical mathematical models were determined. The power type model and the graphical representation elaborated on the base of this model offered an image concerning the influences exerted by the considered input factors on the marking process accuracy.

An Analytical Design Method for a Regenerative Braking Control System for DC-electrified Railway Systems under Light Load Conditions

NASA Astrophysics Data System (ADS)

Saito, Tatsuhito; Kondo, Keiichiro; Koseki, Takafumi

A DC-electrified railway system that is fed by diode rectifiers at a substation is unable to return the electric power to an AC grid. Accordingly, the braking cars have to restrict regenerative braking power when the power consumption of the powering cars is not sufficient. However, the characteristics of a DC-electrified railway system, including the powering cars, is not known, and a mathematical model for designing a controller has not been established yet. Hence, the object of this study is to obtain the mathematical model for an analytical design method of the regenerative braking control system. In the first part of this paper, the static characteristics of this system are presented to show the position of the equilibrium point. The linearization of this system at the equilibrium point is then performed to describe the dynamic characteristics of the system. An analytical design method is then proposed on the basis of these characteristics. The proposed design method is verified by experimental tests with a 1kW class miniature model, and numerical simulations.

The Teaching Gap: Best Ideas from the World's Teachers for Improving Education in the Classroom.

ERIC Educational Resources Information Center

Stigler, James W.; Hiebert, James

This book is an action plan for improving education in the U.S, focusing on the key role of teachers in this improvement. It offers a detailed comparison of the educational methods of Germany, Japan, and the United States. The analysis begins with an international study of mathematics teaching in the three countries that was conducted as part of…

Intellectual Discussion in Mathematics.

ERIC Educational Resources Information Center

Cavaluzzi, Christina

In an attempt to unearth the characteristic communication practices of mathematical seminars, the perceptions and beliefs about them held by regular attendees, and the normative ideals about communication in the mathematics community, this paper considers how communication in math is an integral part of how mathematicians do their work. Responding…

Folding Corners of the Habits of Mind

ERIC Educational Resources Information Center

Wiles, Peter

2013-01-01

Reasoning is central to what Cuoco, Goldenberg, and Mark refer to as mathematical "habits of mind" (1996). "Reasoning is an integral part of doing mathematics. Students should enter the middle grades with the view that mathematics involves examining patterns and noting regularities, making conjectures about possible generalizations,…

How Are Questions That Students Ask in High Level Mathematics Classes Linked to General Giftedness?

ERIC Educational Resources Information Center

Leikin, Roza; Koichu, Boris; Berman, Avi; Dinur, Sariga

2017-01-01

This paper presents a part of a larger study, in which we asked "How are learning and teaching of mathematics at high level linked to students' general giftedness?" We consider asking questions, especially student-generated questions, as indicators of quality of instructional interactions. In the part of the study presented in this…

Comprehensive Instructional Management System (CIMS). A Cyclical Mathematics Curriculum. Workbook Part 2. Experimental. Level K.

ERIC Educational Resources Information Center

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

This document is part 2 of the workbook for kindergarten pupils in the Comprehensive Instructional Management System, a unified mathematics curriculum for kindergarten through grade 7. Each objective is developed by a variety of strategies, with mastery of objectives diagnosed through a testing component. The activities in the student workbook are…

Reorganizing Freshman Business Mathematics I: Background and Philosophy

ERIC Educational Resources Information Center

Green, Kris; Emerson, Allen

2008-01-01

This article is the first of the two-part discussion of the development of a new Freshman Business Mathematics (FBM) course at our college. Part I of the article describes the background and history behind the course, and provides a theoretical framework for the design of the course. This design involves students in learning and applying…

Infusing Mathematics Content into a Methods Course: Impacting Content Knowledge for Teaching

ERIC Educational Resources Information Center

Burton, Megan; Daane, C. J.; Giesen, Judy

2008-01-01

This study compared content knowledge for teaching mathematics differences between elementary pre-service teachers in a traditional versus an experimental mathematics methods course. The experimental course replaced 20 minutes of traditional methods, each class, with an intervention of elementary mathematics content. The difference between groups…

The Development of Proofs in Analytical Mathematics for Undergraduate Students

NASA Astrophysics Data System (ADS)

Ali, Maselan; Sufahani, Suliadi; Hasim, Nurnazifa; Saifullah Rusiman, Mohd; Roslan, Rozaini; Mohamad, Mahathir; Khalid, Kamil

2018-04-01

Proofs in analytical mathematics are essential parts of mathematics, difficult to learn because its underlying concepts are not visible. This research consists of problems involving logic and proofs. In this study, a short overview was provided on how proofs in analytical mathematics were used by university students. From the results obtained, excellent students obtained better scores compared to average and poor students. The research instruments used in this study consisted of two parts: test and interview. In this way, analysis of students’ actual performances can be obtained. The result of this study showed that the less able students have fragile conceptual and cognitive linkages but the more able students use their strong conceptual linkages to produce effective solutions

Proceeding of the International Scientific Colloquium: MATHEMATICS AND CHILDREN (How to Teach and Learn Mathematics) (Osijek, Croatia, April 13, 2007)

ERIC Educational Resources Information Center

Pavlekovic, Margita, Ed.

2007-01-01

The main aim of the Organisational Committee of the international scientific colloquium Mathematics and Children is to encourage additional scientific research in the field of mathematics teaching in Croatia. The development of science and education is a part of a long-term Education Sector Development Plan 2005-2010. Following the example of…

Learning Mathematics or Losing Money--Betting as a Topic for Mathematical Education

ERIC Educational Resources Information Center

Siller, Hans-Stefan; MaaB, Jurgen

2012-01-01

No risk, no fun--betting on sports events costs the gamblers a lot of money and brings excellent profits to those who offer the bets. Among the people who bet on a regular basis, the proportion of young adults is frighteningly high. We now suggest a concept (as part of a basic mathematics course) for acquiring the necessary mathematical knowledge…

Mathematical Sense, Mathematical Sensibility: The Role of the Secondary Geometry Course in Teaching Students to Be Like Mathematicians

ERIC Educational Resources Information Center

Weiss, Michael Kevin

2009-01-01

How can the secondary Geometry course serve as an opportunity for students to learn to "be like" a mathematician--that is, to acquire a mathematical sensibility? In the first part of this dissertation, I investigate what might be meant by "mathematical sensibility". By analyzing narratives of mathematicians and their work, I identify a collection…

Structural Exclusion through School Mathematics: Using Bourdieu to Understand Mathematics as a Social Practice

ERIC Educational Resources Information Center

Jorgensen, Robyn; Gates, Peter; Roper, Vanessa

2014-01-01

In this paper, we explore a sociological approach to mathematics education and offer a theoretical lens through which we can come to understand mathematics education as part of a wider set of social practices. Many studies of children's experiences in school show that a child's academic success is a product of many factors, some of which…

BOOK REVIEW: Advanced Topics in Computational Partial Differential Equations: Numerical Methods and Diffpack Programming

NASA Astrophysics Data System (ADS)

Katsaounis, T. D.

2005-02-01

The scope of this book is to present well known simple and advanced numerical methods for solving partial differential equations (PDEs) and how to implement these methods using the programming environment of the software package Diffpack. A basic background in PDEs and numerical methods is required by the potential reader. Further, a basic knowledge of the finite element method and its implementation in one and two space dimensions is required. The authors claim that no prior knowledge of the package Diffpack is required, which is true, but the reader should be at least familiar with an object oriented programming language like C++ in order to better comprehend the programming environment of Diffpack. Certainly, a prior knowledge or usage of Diffpack would be a great advantage to the reader. The book consists of 15 chapters, each one written by one or more authors. Each chapter is basically divided into two parts: the first part is about mathematical models described by PDEs and numerical methods to solve these models and the second part describes how to implement the numerical methods using the programming environment of Diffpack. Each chapter closes with a list of references on its subject. The first nine chapters cover well known numerical methods for solving the basic types of PDEs. Further, programming techniques on the serial as well as on the parallel implementation of numerical methods are also included in these chapters. The last five chapters are dedicated to applications, modelled by PDEs, in a variety of fields. The first chapter is an introduction to parallel processing. It covers fundamentals of parallel processing in a simple and concrete way and no prior knowledge of the subject is required. Examples of parallel implementation of basic linear algebra operations are presented using the Message Passing Interface (MPI) programming environment. Here, some knowledge of MPI routines is required by the reader. Examples solving in parallel simple PDEs using Diffpack and MPI are also presented. Chapter 2 presents the overlapping domain decomposition method for solving PDEs. It is well known that these methods are suitable for parallel processing. The first part of the chapter covers the mathematical formulation of the method as well as algorithmic and implementational issues. The second part presents a serial and a parallel implementational framework within the programming environment of Diffpack. The chapter closes by showing how to solve two application examples with the overlapping domain decomposition method using Diffpack. Chapter 3 is a tutorial about how to incorporate the multigrid solver in Diffpack. The method is illustrated by examples such as a Poisson solver, a general elliptic problem with various types of boundary conditions and a nonlinear Poisson type problem. In chapter 4 the mixed finite element is introduced. Technical issues concerning the practical implementation of the method are also presented. The main difficulties of the efficient implementation of the method, especially in two and three space dimensions on unstructured grids, are presented and addressed in the framework of Diffpack. The implementational process is illustrated by two examples, namely the system formulation of the Poisson problem and the Stokes problem. Chapter 5 is closely related to chapter 4 and addresses the problem of how to solve efficiently the linear systems arising by the application of the mixed finite element method. The proposed method is block preconditioning. Efficient techniques for implementing the method within Diffpack are presented. Optimal block preconditioners are used to solve the system formulation of the Poisson problem, the Stokes problem and the bidomain model for the electrical activity in the heart. The subject of chapter 6 is systems of PDEs. Linear and nonlinear systems are discussed. Fully implicit and operator splitting methods are presented. Special attention is paid to how existing solvers for scalar equations in Diffpack can be used to derive fully implicit solvers for systems. The proposed techniques are illustrated in terms of two applications, namely a system of PDEs modelling pipeflow and a two-phase porous media flow. Stochastic PDEs is the topic of chapter 7. The first part of the chapter is a simple introduction to stochastic PDEs; basic analytical properties are presented for simple models like transport phenomena and viscous drag forces. The second part considers the numerical solution of stochastic PDEs. Two basic techniques are presented, namely Monte Carlo and perturbation methods. The last part explains how to implement and incorporate these solvers into Diffpack. Chapter 8 describes how to operate Diffpack from Python scripts. The main goal here is to provide all the programming and technical details in order to glue the programming environment of Diffpack with visualization packages through Python and in general take advantage of the Python interfaces. Chapter 9 attempts to show how to use numerical experiments to measure the performance of various PDE solvers. The authors gathered a rather impressive list, a total of 14 PDE solvers. Solvers for problems like Poisson, Navier--Stokes, elasticity, two-phase flows and methods such as finite difference, finite element, multigrid, and gradient type methods are presented. The authors provide a series of numerical results combining various solvers with various methods in order to gain insight into their computational performance and efficiency. In Chapter 10 the authors consider a computationally challenging problem, namely the computation of the electrical activity of the human heart. After a brief introduction on the biology of the problem the authors present the mathematical models involved and a numerical method for solving them within the framework of Diffpack. Chapter 11 and 12 are closely related; actually they could have been combined in a single chapter. Chapter 11 introduces several mathematical models used in finance, based on the Black--Scholes equation. Chapter 12 considers several numerical methods like Monte Carlo, lattice methods, finite difference and finite element methods. Implementation of these methods within Diffpack is presented in the last part of the chapter. Chapter 13 presents how the finite element method is used for the modelling and analysis of elastic structures. The authors describe the structural elements of Diffpack which include popular elements such as beams and plates and examples are presented on how to use them to simulate elastic structures. Chapter 14 describes an application problem, namely the extrusion of aluminum. This is a rather\\endcolumn complicated process which involves non-Newtonian flow, heat transfer and elasticity. The authors describe the systems of PDEs modelling the underlying process and use a finite element method to obtain a numerical solution. The implementation of the numerical method in Diffpack is presented along with some applications. The last chapter, chapter 15, focuses on mathematical and numerical models of systems of PDEs governing geological processes in sedimentary basins. The underlying mathematical model is solved using the finite element method within a fully implicit scheme. The authors discuss the implementational issues involved within Diffpack and they present results from several examples. In summary, the book focuses on the computational and implementational issues involved in solving partial differential equations. The potential reader should have a basic knowledge of PDEs and the finite difference and finite element methods. The examples presented are solved within the programming framework of Diffpack and the reader should have prior experience with the particular software in order to take full advantage of the book. Overall the book is well written, the subject of each chapter is well presented and can serve as a reference for graduate students, researchers and engineers who are interested in the numerical solution of partial differential equations modelling various applications.

Benchmarking the performance of fixed-image receptor digital radiographic systems part 1: a novel method for image quality analysis.

PubMed

Lee, Kam L; Ireland, Timothy A; Bernardo, Michael

2016-06-01

This is the first part of a two-part study in benchmarking the performance of fixed digital radiographic general X-ray systems. This paper concentrates on reporting findings related to quantitative analysis techniques used to establish comparative image quality metrics. A systematic technical comparison of the evaluated systems is presented in part two of this study. A novel quantitative image quality analysis method is presented with technical considerations addressed for peer review. The novel method was applied to seven general radiographic systems with four different makes of radiographic image receptor (12 image receptors in total). For the System Modulation Transfer Function (sMTF), the use of grid was found to reduce veiling glare and decrease roll-off. The major contributor in sMTF degradation was found to be focal spot blurring. For the System Normalised Noise Power Spectrum (sNNPS), it was found that all systems examined had similar sNNPS responses. A mathematical model is presented to explain how the use of stationary grid may cause a difference between horizontal and vertical sNNPS responses.

Comparing the Major Definitions of Mathematics Pedagogical Content Knowledge

ERIC Educational Resources Information Center

Johnson, Jeffrey

2017-01-01

The purpose of this research was to compare two definitions and assessments of Mathematics Pedagogical Content Knowledge (PCK). As part of a larger study, nine current and future teachers took an online version of the Measures of Knowledge for Teaching (MKT)--Mathematics assessment and the Cognitively Activating Instruction in Mathematics…

School Mathematics Qualifications and Work

ERIC Educational Resources Information Center

Drake, Pat; Noyes, Andrew; Wake, Geoff

2012-01-01

This article explores the relationship between school mathematics qualifications and the transition into employment. As part of a large-scale, three-year independent evaluation of pilot qualifications in 14-19 school mathematics, all 39 Sector Skills Councils and Employment Skills Boards in the UK were invited to provide evidence regarding their…

Teaching and Learning Mathematics in the 1990s: 1990 Yearbook.

ERIC Educational Resources Information Center

Cooney, Thomas J., Ed.; Hirsch, Christian R., Ed.

This yearbook includes 28 articles related to teachers and students of mathematics education and their changing roles. Part 1, "New Perspectives on Teaching and Learning," focuses on the relationship between research and practice and suggests a perspective based on the belief that mathematical learning consists of students constructing…

Towards a Constructivist Pedagogy for Year 12 Mathematics

ERIC Educational Resources Information Center

Sheppard, Ian

2008-01-01

Constructivist pedagogies are generally not considered to support the teaching of mathematics for externally assessed examination-based courses. In large part, teachers have believed that such approaches are inefficient in covering a set syllabus. This article summarises the author's learning journey in Year 12 mathematics in 2004 where attempts…

Making Connections

ERIC Educational Resources Information Center

Turner, Paul

2015-01-01

This article aims to illustrate a process of making connections, not between mathematics and other activities, but within mathematics itself--between diverse parts of the subject. Novel connections are still possible in previously explored mathematics when the material happens to be unfamiliar, as may be the case for a learner at any career stage.…

Technology Priorities and Preferences of Developmental Mathematics Instructors

ERIC Educational Resources Information Center

Zientek, Linda; Skidmore, Susan T.; Saxon, D. Patrick; Edmonson, Stacey

2015-01-01

With the omnipresence of technology in society came the inevitable integration into education. This manuscript provides results of a statewide survey of developmental mathematics instructors' technology preferences and priorities across all levels of developmental mathematics courses. The study was part of a larger project designed to explore the…

Self and Peer Assessment of Mathematical Processes

ERIC Educational Resources Information Center

Onion, Alice; Javaheri, Elnaz

2011-01-01

This article explores using Bowland assessment tasks and Nuffield Applying Mathematical Processes (AMP) activities as part of a scheme of work. The Bowland tasks and Nuffield AMP activities are designed to develop students' mathematical thinking; they are focused on key processes. Unfamiliar demands are made on the students and they are challenged…

The Relation between Patterning, Executive Function, and Mathematics

ERIC Educational Resources Information Center

Schmerold, Katrina Lea

2015-01-01

Patterning, or the ability to understand patterns, is a skill commonly taught to young children as part of school mathematics curricula. While a number of studies have demonstrated that patterning is beneficial for young children acquiring mathematical skills, little research exists that examines the cognitive components of the skill. It seems…

Video Based Developmental Mathematics Learning System For Community College Students.

ERIC Educational Resources Information Center

Gormley, Tyrone D.

The University of Maine at Augusta uses an individualized video-taped mathematics instructional system to eliminate students' math weaknesses before they attempt college math. The course, "1 Mth Developmental Mathematics," is part of the Educational Assistance Program and teaches basic skills and concepts of arithmetic and algebra. The…

Focus in High School Mathematics: Statistics and Probability

ERIC Educational Resources Information Center

National Council of Teachers of Mathematics, 2009

2009-01-01

Reasoning about and making sense of statistics and probability are essential to students' future success. This volume belongs to a series that supports National Council of Teachers of Mathematics' (NCTM's) "Focus in High School Mathematics: Reasoning and Sense Making" by providing additional guidance for making reasoning and sense making part of…

Technology in K-12 Mathematics Classrooms

ERIC Educational Resources Information Center

Ozel, Serkan; Yetkiner, Zeynep Ebrar; Capraro, Robert M.

2008-01-01

Technology integration in mathematics classrooms is important to the field of education, not only because today's society is becoming more and more advanced and reliant upon technology but also because schools are beginning to embrace technology as an essential part of their curricula. The Principles and Standards for School Mathematics (National…

How to begin a new topic in mathematics: does it matter to students' performance in mathematics?

PubMed

Ma, Xin; Papanastasiou, Constantinos

2006-08-01

The authors use Canadian data from the Third International Mathematics and Science Study to examine six instructional methods that mathematics teachers use to introduce new topics in mathematics on performance of eighth-grade students in six mathematical areas (mathematics as a whole, algebra, data analysis, fraction, geometry, and measurement). Results of multilevel analysis with students nested within schools show that the instructional methods of having the teacher explain the rules and definitions and looking at the textbook while the teacher talks about it had little instructional effects on student performance in any mathematical area. In contrast, the instructional method in which teachers try to solve an example related to the new topic was effective in promoting student performance across all mathematical areas.

The method of expected number of deaths, 1786-1886-1986.

PubMed

Keiding, N

1987-04-01

"The method of expected number of deaths is an integral part of standardization of vital rates, which is one of the oldest statistical techniques. The expected number of deaths was calculated in 18th century actuarial mathematics...but the method seems to have been forgotten, and was reinvented in connection with 19th century studies of geographical and occupational variations of mortality.... It is noted that standardization of rates is intimately connected to the study of relative mortality, and a short description of very recent developments in the methodology of that area is included." (SUMMARY IN FRE) excerpt

Analysis of entry of additional energy to gunpowder in electrothermal chemical shot

NASA Astrophysics Data System (ADS)

Burkin, Viktor; Ishchenko, Alexandr; Kasimov, Vladimir; Samorokova, Nina; Sidorov, Aleksey

2017-11-01

In the article two series of ballistic experiments conducted according to the scheme of electrothermal chemical control of ballistic parameters of the shot at the Research Institute of Applied Mathematics and Mechanics of Tomsk State University (RIAMM TSU, Russia) are considered. The experimental part of the work is described. The analysis of the electro physical data of ballistic experiments is carried out. A methodical approach that allows to take into account the entry of an electric discharge plasma in a gunpowder in the mathematical model of internal ballistic processes in barrel systems is proposed and tested. Under the conditions of these experiments, the effects of various characteristics of the plasmatron on the nature of the energy entry are estimated.

Promoting Students' Self-Directed Learning Ability through Teaching Mathematics for Social Justice

ERIC Educational Resources Information Center

Voss, Richard; Rickards, Tony

2016-01-01

Mathematics is a subject which is often taught using abstract methods and processes. These methods by their very nature may for students alienate the relationship between Mathematics and real life situations. Further, these abstract methods and processes may disenfranchise students from becoming self-directed learners of Mathematics. A solution to…

The Implementation of APIQ Creative Mathematics Game Method in the Subject Matter of Greatest Common Factor and Least Common Multiple in Elementary School

NASA Astrophysics Data System (ADS)

Rahman, Abdul; Saleh Ahmar, Ansari; Arifin, A. Nurani M.; Upu, Hamzah; Mulbar, Usman; Alimuddin; Arsyad, Nurdin; Ruslan; Rusli; Djadir; Sutamrin; Hamda; Minggi, Ilham; Awi; Zaki, Ahmad; Ahmad, Asdar; Ihsan, Hisyam

2018-01-01

One of causal factors for uninterested feeling of the students in learning mathematics is a monotonous learning method, like in traditional learning method. One of the ways for motivating students to learn mathematics is by implementing APIQ (Aritmetika Plus Intelegensi Quantum) creative mathematics game method. The purposes of this research are (1) to describe students’ responses toward the implementation of APIQ creative mathematics game method on the subject matter of Greatest Common Factor (GCF) and Least Common Multiple (LCM) and (2) to find out whether by implementing this method, the student’s learning completeness will improve or not. Based on the results of this research, it is shown that the responses of the students toward the implementation of APIQ creative mathematics game method in the subject matters of GCF and LCM were good. It is seen in the percentage of the responses were between 76-100%. (2) The implementation of APIQ creative mathematics game method on the subject matters of GCF and LCM improved the students’ learning.

Decision-Making under Criteria Uncertainty

NASA Astrophysics Data System (ADS)

Kureychik, V. M.; Safronenkova, I. B.

2018-05-01

Uncertainty is an essential part of a decision-making procedure. The paper deals with the problem of decision-making under criteria uncertainty. In this context, decision-making under uncertainty, types and conditions of uncertainty were examined. The decision-making problem under uncertainty was formalized. A modification of the mathematical decision support method under uncertainty via ontologies was proposed. A critical distinction of the developed method is ontology usage as its base elements. The goal of this work is a development of a decision-making method under criteria uncertainty with the use of ontologies in the area of multilayer board designing. This method is oriented to improvement of technical-economic values of the examined domain.

What's the Word for... ? Is There a Word for... ? How Understanding Mi'kmaw Language Can Help Support Mi'kmaw Learners in Mathematics

ERIC Educational Resources Information Center

Borden, Lisa Lunney

2013-01-01

As part of a larger project focused on decolonising mathematics education for Aboriginal students in Atlantic Canada, this article reports on the role of the Mi'kmaw language in mathematics teaching. By exploring how mathematical concepts are talked about (or not talked about) in the Mi'kmaw language, teachers and researchers can gain insight into…

Goals for Mathematical Education of Elementary School Teachers: A Report of the Cambridge Conference on Teacher Training.

ERIC Educational Resources Information Center

Education Development Center, Inc., Newton, MA.

This report is intended to provide attention to issues that the Cambridge Conference feels are related to the mathematical training of elementary school teachers. The document is divided into three parts. Part I, titled "The Problems and Proposals Towards the Solution," contains the following chapters: (1) Introduction to the Report; (2)…

Mathematics for the Workplace. Applications from Radiological Technology. A Teacher's Guide.

ERIC Educational Resources Information Center

Wallace, Johnny M.; Nichols, Gay

This module presents a real-world context in which mathematics skills are used as part of a daily routine. The context is the radiological technology field, and the module aims to help students use ratios and exponents as part of real-life problem solving. Materials in the module, most of which are designed for the teacher to duplicate and…

Research Reports from the Fourth and Fifth National Conferences on Diagnostic and Prescriptive Mathematics. 1980 Research Monograph. Revised Third Edition.

ERIC Educational Resources Information Center

Romberg, Thomas A., Ed.

This document contains 15 research papers presented at the Fourth and Fifth Annual Conferences of the Research Council for Diagnostic and Prescriptive Mathematics. The papers are organized into four sections. In part I, four position papers by Romberg, Engelhardt, Ashlock, and Heddens reflect research ideas which underlie the Council. Part II…

76 FR 21715 - Notice of Submission for OMB Review

Federal Register 2010, 2011, 2012, 2013, 2014

2011-04-18

...: Revision. Title of Collection: Hispanic-Serving Institutions Science Technology Engineering, Mathematics... Technology Engineering, Mathematics and Articulation Program, authorized under section 371 of Part F of the...

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

PubMed

Gilbert, Scott F

2018-01-31

Mathematical modeling has recently become a much-lauded enterprise, and many funding agencies seek to prioritize this endeavor. However, there are certain dangers associated with mathematical modeling, and knowledge of these pitfalls should also be part of a biologist's training in this set of techniques. (1) Mathematical models are limited by known science; (2) Mathematical models can tell what can happen, but not what did happen; (3) A model does not have to conform to reality, even if it is logically consistent; (4) Models abstract from reality, and sometimes what they eliminate is critically important; (5) Mathematics can present a Platonic ideal to which biologically organized matter strives, rather than a trial-and-error bumbling through evolutionary processes. This "Unity of Science" approach, which sees biology as the lowest physical science and mathematics as the highest science, is part of a Western belief system, often called the Great Chain of Being (or Scala Natura), that sees knowledge emerge as one passes from biology to chemistry to physics to mathematics, in an ascending progression of reason being purification from matter. This is also an informal model for the emergence of new life. There are now other informal models for integrating development and evolution, but each has its limitations. Copyright © 2018 Elsevier Ltd. All rights reserved.

Cumulative advantages and the emergence of social and ethnic inequality: Matthew effects in reading and mathematics development within elementary schools?

PubMed

Baumert, Jürgen; Nagy, Gabriel; Lehmann, Rainer

2012-01-01

This article examines the development of social and ethnic disparities in academic achievement in elementary schooling. It investigated whether reading and mathematics development in 136 mixed-ability classes shows path-dependent processes of cumulative advantage (Matthew effects) from Grades 4 to 6 (Grade 4 mean age = 10.62, SD = 0.57) resulting in growing inequality. Status-dependent processes of cumulative advantage, their interaction with path-dependent processes, and consequences for the degree of social and ethnic inequality are examined. Two complementary methods for analyzing multilevel data are used: growth curve and quasi-simplex models. No evidence for a Matthew effect was found in either domain. A compensation effect emerged for reading, to the benefit of ethnic minorities. A fan-spread effect was found for mathematics, partly attributable to status-dependent processes of cumulative advantage. © 2012 The Authors. Child Development © 2012 Society for Research in Child Development, Inc.

Interrelation Between Safety Factors and Reliability

NASA Technical Reports Server (NTRS)

Elishakoff, Isaac; Chamis, Christos C. (Technical Monitor)

2001-01-01

An evaluation was performed to establish relationships between safety factors and reliability relationships. Results obtained show that the use of the safety factor is not contradictory to the employment of the probabilistic methods. In many cases the safety factors can be directly expressed by the required reliability levels. However, there is a major difference that must be emphasized: whereas the safety factors are allocated in an ad hoc manner, the probabilistic approach offers a unified mathematical framework. The establishment of the interrelation between the concepts opens an avenue to specify safety factors based on reliability. In cases where there are several forms of failure, then the allocation of safety factors should he based on having the same reliability associated with each failure mode. This immediately suggests that by the probabilistic methods the existing over-design or under-design can be eliminated. The report includes three parts: Part 1-Random Actual Stress and Deterministic Yield Stress; Part 2-Deterministic Actual Stress and Random Yield Stress; Part 3-Both Actual Stress and Yield Stress Are Random.

What Math Matters? Types of Mathematics Knowledge and Relationships to Methods Course Performance

ERIC Educational Resources Information Center

Kajander, Ann; Holm, Jennifer

2016-01-01

This study investigated the effect of a departmental focus on enhanced mathematics knowledge for teaching on overall performance in upper elementary mathematics methods courses. The study examined the effect of performance on a new course in mathematics for teaching on performance at the methods course level. In addition, the effect of performance…

Some problems in mechanics of growing solids with applications to AM technologies

NASA Astrophysics Data System (ADS)

Manzhirov, A. V.

2018-04-01

Additive Manufacturing (AM) technologies are an exciting area of the modern industrial revolution and have applications in engineering, medicine, electronics, aerospace industry, etc. AM enables cost-effective production of customized geometry and parts by direct fabrication from 3D data and mathematical models. Despite much progress in AM technologies, problems of mechanical analysis for AM fabricated parts yet remain to be solved. This paper deals with three main mechanical problems: the onset of residual stresses, which occur in the AM process and can lead to failure of the parts, the distortion of the final shape of AM fabricated parts, and the development of technological solutions aimed at improving existing AM technologies and creating new ones. An approach proposed deals with the construction of adequate analytical model and effective methods for the simulation of AM processes for fabricated solid parts.

Mathematical simulation of power conditioning systems. Volume 1: Simulation of elementary units. Report on simulation methodology

NASA Technical Reports Server (NTRS)

Prajous, R.; Mazankine, J.; Ippolito, J. C.

1978-01-01

Methods and algorithms used for the simulation of elementary power conditioning units buck, boost, and buck-boost, as well as shunt PWM are described. Definitions are given of similar converters and reduced parameters. The various parts of the simulation to be carried out are dealt with; local stability, corrective network, measurements of input-output impedance and global stability. A simulation example is given.

To What Extent Does Participation in Extracurricular Music Affect the Future Aspirations of 11-12-Year-Olds? A Small-Scale Investigation

ERIC Educational Resources Information Center

Denny, Eleanor

2007-01-01

I undertook this project as a 12-year-old student while studying research methods at the Children's Research Centre at the Open University. It has already been shown that doing music improves children's Mathematics and English scores. The aim of this study was to find out if it also raises the aspirations of the children taking part. A…

Curso: Auxiliar de Farmacia. Guia. Farmacia Teorica: Manual del Estudiante. Matematica General: Manual del Estudiante. Documento de Trabajo (Pharmacy Assistant Course Guide. Theoretical Pharmacy Student Manual. General Mathematics Student Manual. Working Document).

ERIC Educational Resources Information Center

Puerto Rico State Dept. of Education, Hato Rey. Area for Vocational and Technical Education.

The three parts of this document are intended for a 3-semester course for pharmacy assistants. The course guide contains the following sections: occupational description; educational philosophy; general objectives; tasks/competencies for each unit; course organization; brief description of the topics; student standards; and evaluation methods.…

Evaluation of a Tethered Kite Anemometer.

DTIC Science & Technology

1981-02-01

Solar Eclipse , Part I - Atmospheric Sciences Laboratory Field Program Summary," ASL-TR-0059, May 1980 131. Miller, Walter B., "User’s Guide for Passive...the smaller kite and 500 m with the larger version. Therefore, the kite has been evaluated with reference to methods of obtaining winds to equivalent...advantage over remote sensors where noise can be mistakenly identified as signal , and complex mathematical algorithms are often required to obtain

Lithium Niobate Arithmetic Logic Unit

DTIC Science & Technology

1991-03-01

Boot51] A.D. Booth, "A Signed Binary Multiplication Technique," Quarterly Journal of Mechanics and Applied Mathematics , Vol. IV Part 2, 1951. [ChWi79...Trans. Computers, Vol. C-26, No. 7, July 1977, pp. 681-687. [Wake8 I] John F. Wakerly , "Miocrocomputer Architecture and Programming," John Wiley and...different division methods and discusses their applicability to simple bit serial implementation. Several different designs are then presented and

Some new mathematical methods for variational objective analysis

NASA Technical Reports Server (NTRS)

Wahba, Grace; Johnson, Donald R.

1994-01-01

Numerous results were obtained relevant to remote sensing, variational objective analysis, and data assimilation. A list of publications relevant in whole or in part is attached. The principal investigator gave many invited lectures, disseminating the results to the meteorological community as well as the statistical community. A list of invited lectures at meetings is attached, as well as a list of departmental colloquia at various universities and institutes.

Students' Attitudes towards Mathematics in Single-Sex and Coeducational Schools.

ERIC Educational Resources Information Center

Norton, Stephen J.; Rennie, Leonie J.

1998-01-01

Discusses part of study stimulated by the continuing debate over differences between boys and girls in their attitudes towards mathematics and their participation and performance in this subject at school. Concludes that there were clear differences between boys and girls on the Mathematics as a Male Domain scale with girls being less stereotyped…

A Preliminary Discourse Analysis of Constructivist-Oriented Mathematics Instruction for a Student with Learning Disabilities

ERIC Educational Resources Information Center

Xin, Yan Ping; Liu, Jia; Jones, Sarah R.; Tzur, Ron; Si, Luo

2016-01-01

Reform efforts in mathematics education arose, in part, in response to constructivist works on conceptual learning. However, little research has examined how students with learning disabilities (LD) respond to constructivist-oriented instruction in mathematics, particularly in moment-to-moment interactions. To understand the nature of…

Learning Mathematics by Designing, Programming, and Investigating with Interactive, Dynamic Computer-Based Objects

ERIC Educational Resources Information Center

Marshall, Neil; Buteau, Chantal

2014-01-01

As part of their undergraduate mathematics curriculum, students at Brock University learn to create and use computer-based tools with dynamic, visual interfaces, called Exploratory Objects, developed for the purpose of conducting pure or applied mathematical investigations. A student's Development Process Model of creating and using an Exploratory…

Use of Open-Ended Problems in Mathematics Classroom. Research Report 176.

ERIC Educational Resources Information Center

Pehkonen, Erkki, Ed.

During the years 1993-96, there has existed an active discussion group entitled "Using Open-Ended Problems in Mathematics" as a part of the scientific program of the Psychology of Mathematics Education (PME) conference. This report contains revised versions of presentations given in the discussion group. Since the PME is an international…

Students' Quality of Mathematical Discussion and Their Self-Determination in Mathematics

ERIC Educational Resources Information Center

Kosko, Karl W.; Wilkins, Jesse L. M.

2012-01-01

Mathematical discussion allows for students to reflect upon math concepts and understand such concepts at a deeper level. This process of reflection requires a certain amount of internalization on the part of the student. This internalization is facilitated by meeting the needs of autonomy, competence, and relatedness as advocated by…

Mathematics in the K-8 Classroom and Library

ERIC Educational Resources Information Center

McKinney, Sueanne; Hinton, KaaVonia

2010-01-01

Two experts on education offer a rich and diverse selection of children's literature and teaching strategies for the K-8 mathematics classroom. To date, a vast majority of classrooms continue to fall short in the implementation and direction of NCTM Principles and Standards for School Mathematics (PSSM), in part because most of these classrooms…

Let's Talk Math: Encouraging Children To Explore Ideas.

ERIC Educational Resources Information Center

Lilburn, Pat; Rawson, Pam

This book presents mathematics activities to help children talk and write mathematically. Children are encouraged to talk about and share their ideas, to use everyday language to describe mathematical situations, and to restate problems in their own words. There are two sections in this book. Part 1 discusses the following issues and implications…

Integrating History of Mathematics into the Classroom: Was Aristotle Wrong?

ERIC Educational Resources Information Center

Panasuk, Regina M.; Horton, Leslie Bolinger

2013-01-01

This article describes a part of a large scale study which helped to gain understanding of the high school mathematics teachers' perceptions related to the integration of history of mathematics into instruction. There is obvious lack of correspondence between general perception about possible benefits of students learning the history of…

CAS-Induced Difficulties in Learning Mathematics?

ERIC Educational Resources Information Center

Jankvist, Uffe Thomas; Misfeldt, Morten

2015-01-01

In recent years computer algebra systems (CAS) have become an integrated part of the upper secondary school mathematics program. Despite the many positive possibilities of CAS, there also seems to be a flip side of the coin in relation to actual difficulties in learning mathematics, not least because a strong dependence on CAS for mathematical…

Robotic Toys as a Catalyst for Mathematical Problem Solving

ERIC Educational Resources Information Center

Highfield, Kate

2010-01-01

Robotic toys present unique opportunities for teachers of young children to integrate mathematics learning with engaging problem-solving tasks. This article describes a series of tasks using Bee-bots and Pro-bots, developed as part a larger project examining young children's use of robotic toys as tools in developing mathematical and metacognitive…

Provoking Contingent Moments: Knowledge for "Powerful Teaching" at the Horizon

ERIC Educational Resources Information Center

Hurst, Chris

2017-01-01

Background: Teacher knowledge continues to be a topic of debate in Australasia and in other parts of the world. There have been many attempts by mathematics educators and researchers to define the knowledge needed by teachers to teach mathematics effectively. A plethora of terms, such as mathematical content knowledge, pedagogical content…

Gestures as Semiotic Resources in the Mathematics Classroom

ERIC Educational Resources Information Center

Arzarello, Ferdinando; Paola, Domingo; Robutti, Ornella; Sabena, Cristina

2009-01-01

In this paper, we consider gestures as part of the resources activated in the mathematics classroom: speech, inscriptions, artifacts, etc. As such, gestures are seen as one of the semiotic tools used by students and teacher in mathematics teaching-learning. To analyze them, we introduce a suitable model, the "semiotic bundle." It allows focusing…

Programmable Calculators: Implications for the Mathematics Curriculum.

ERIC Educational Resources Information Center

Spikell, Mark A., Ed.

This document is a collection of reports presented at a programable calculator symposium held in Seattle, Washington, in April, 1980, as part of the annual meeting of the National Council of Teachers of Mathematics (NCTM). The session was designed to review whether the programable calculator has a place in the school mathematics program, in light…

Let's Keep the College in Our Community Colleges: Mathematics for College Transfer.

ERIC Educational Resources Information Center

Curnutt, Larry

Preparing students for transfer to four-year colleges remains a significant part of the mission of most community college mathematicians. For some 30 years, calculus has been synonymous with entry-level college mathematics. Recent educational and technological changes, however, demand that the definition of college-level work in mathematics be…

Technology: The Key to the Reformation of Developmental Mathematics Pedagogy

ERIC Educational Resources Information Center

Ben-Jacob, Marion G.

2016-01-01

There is a movement nationwide to enhance the learning experience of college students who need to take courses in developmental mathematics. Technology is instrumental in eliminating the non-credit bearing courses from their programs of study. The restructuring of the mathematics programs allows for greater confidence on the parts of the students…

Professional Development of Mathematics Teachers Implementing Probabilistic Simulations in Elementary School Classrooms

ERIC Educational Resources Information Center

de Oliveira Souza, Leandro; Lopes, Celi Espasandin; de Oliveira Mendonça, Luzinete

2014-01-01

The inclusion of statistics and probability in the mathematics curriculum has always generated challenges to mathematics teachers of elementary schools. This article discusses activities that promote the professional development of such teachers. We present part of a doctoral research study of 16 teachers in which we discuss two case studies of…

Team-Based Introductory Research Experiences in Mathematics

ERIC Educational Resources Information Center

Baum, Brittany Smith; Rowell, Ginger Holmes; Green, Lisa; Yantz, Jennifer; Beck, Jesse; Cheatham, Thomas; Stephens, D. Christopher; Nelson, Donald

2017-01-01

As part of Middle Tennessee State University's (MTSU's) initiative to improve retention of at-risk STEM majors, they recruit first-time, full-time freshman STEM majors with mathematics ACT scores of 19 to 23 to participate in MTSU's "Mathematics as a FirstSTEP to Success in STEM" project (FirstSTEP). This article overviews MTSU's…

Making Mathematics Relevant for Students in Bali

ERIC Educational Resources Information Center

Sema, Pryde Nubea

2008-01-01

The reactions of students towards mathematics in Bali (in the NW Province of Cameroon) are appalling. This is due to a misconception regarding its uses. The author thinks that these problems derive partly from the influence that the Western curriculum has had in Bali--mathematical contexts are based around train times in Liverpool instead of from…

High Achieving Girls in Mathematics: What's Wrong with Working Hard?

ERIC Educational Resources Information Center

Howe, Ann C.; Berenson, Sarah B.

2003-01-01

The participation of women in graduate studies and mathematics-related careers remains a social and economic problem in the United States. Part of a larger study to understand this lack of participation, here we present preliminary findings of girls who are high achievers in middle grades mathematics. This interpretive study documents girls'…

A Framework for Mathematical Thinking: The Case of Linear Algebra

ERIC Educational Resources Information Center

Stewart, Sepideh; Thomas, Michael O. J.

2009-01-01

Linear algebra is one of the unavoidable advanced courses that many mathematics students encounter at university level. The research reported here was part of the first author's recent PhD study, where she created and applied a theoretical framework combining the strengths of two major mathematics education theories in order to investigate the…

Fractal geometry of music.

PubMed Central

Hsü, K J; Hsü, A J

1990-01-01

Music critics have compared Bach's music to the precision of mathematics. What "mathematics" and what "precision" are the questions for a curious scientist. The purpose of this short note is to suggest that the mathematics is, at least in part, Mandelbrot's fractal geometry and the precision is the deviation from a log-log linear plot. PMID:11607061

Using Internet Aesthetic Mathematical Texts to Develop Secondary School Learners' Thinking Skills

ERIC Educational Resources Information Center

Nyaumwe, Lovemore J.

2011-01-01

This paper presents some internet aesthetic texts collected over a period of two years through chain message communications with colleagues located in different parts of the world. The aesthetic texts are grouped into four themes of mathematical magic, values, beauty, and prediction. Mathematical magic aesthetics show fascinating things that can…

Computer Programming in the UK Undergraduate Mathematics Curriculum

ERIC Educational Resources Information Center

Sangwin, Christopher J.; O'Toole, Claire

2017-01-01

This paper reports a study which investigated the extent to which undergraduate mathematics students in the United Kingdom are currently taught to programme a computer as a core part of their mathematics degree programme. We undertook an online survey, with significant follow-up correspondence, to gather data on current curricula and received…

Measuring Mathematics Teachers' Professional Competence by Using Video Clips (COACTIV Video)

ERIC Educational Resources Information Center

Bruckmaier, G.; Krauss, S.; Blum, W.; Leiss, D.

2016-01-01

The COACTIV video study is part of the COACTIV research program in which secondary mathematics teachers whose students participated in PISA 03/04 were examined, with respect to their professional knowledge, motivational orientations, beliefs, and self-regulation. In the video study, 284 German secondary mathematics teachers were asked to specify…

Best Known Problem Solving Strategies in "High-Stakes" Assessments

ERIC Educational Resources Information Center

Hong, Dae S.

2011-01-01

In its mathematics standards, National Council of Teachers of Mathematics (NCTM) states that problem solving is an integral part of all mathematics learning and exposure to problem solving strategies should be embedded across the curriculum. Furthermore, by high school, students should be able to use, decide and invent a wide range of strategies.…

The Instructor Experience of Fully Online Tertiary Mathematics: A Challenge and an Opportunity

ERIC Educational Resources Information Center

Trenholm, Sven; Alcock, Lara; Robinson, Carol

2016-01-01

As part of a dramatic recent shift in tertiary education, many undergraduate students now learn mathematics via fully online courses. At present, the mathematics education research community knows very little about this shift. The authors consider implications of an investigation into the instructor experience of fully online undergraduate…

Generalized fourier analyses of the advection-diffusion equation - Part II: two-dimensional domains

NASA Astrophysics Data System (ADS)

Voth, Thomas E.; Martinez, Mario J.; Christon, Mark A.

2004-07-01

Part I of this work presents a detailed multi-methods comparison of the spatial errors associated with the one-dimensional finite difference, finite element and finite volume semi-discretizations of the scalar advection-diffusion equation. In Part II we extend the analysis to two-dimensional domains and also consider the effects of wave propagation direction and grid aspect ratio on the phase speed, and the discrete and artificial diffusivities. The observed dependence of dispersive and diffusive behaviour on propagation direction makes comparison of methods more difficult relative to the one-dimensional results. For this reason, integrated (over propagation direction and wave number) error and anisotropy metrics are introduced to facilitate comparison among the various methods. With respect to these metrics, the consistent mass Galerkin and consistent mass control-volume finite element methods, and their streamline upwind derivatives, exhibit comparable accuracy, and generally out-perform their lumped mass counterparts and finite-difference based schemes. While this work can only be considered a first step in a comprehensive multi-methods analysis and comparison, it serves to identify some of the relative strengths and weaknesses of multiple numerical methods in a common mathematical framework. Published in 2004 by John Wiley & Sons, Ltd.

Mathematics and the surgeon.

PubMed Central

Crank, J.

1976-01-01

The surgeon uses elementary mathematics just as much as any other educated layman. In his professional life, however, much of the knowledge and skill on which he relies has had a mathematical strand in its development, possibly woven into the supporting disciplines such as physics, chemistry, biology, and bioengineering. The valves and limitations of mathematical models are examined briefly in the general medical field and particularly in relation to the surgeon. Arithmetic and statistics are usually regarded as the most immediately useful parts of mathematics. Examples are cited, however, of medical postgraduate work which uses other highly advanced mathematical techniques. The place of mathematics in postgraduate and postexperience teaching courses is touched on. The role of a mathematical consultant in the medical team is discussed. PMID:942167

A Comparison of Pre- and Post- Levels of Mathematics Anxiety among Preservice Teacher Candidates Enrolled in a Mathematics Methods Course.

ERIC Educational Resources Information Center

Sloan, Tina Rye; Vinson, Beth; Haynes, Jonita; Gresham, Regina

This study examined the effectiveness of a methods course in the reduction of mathematics anxiety levels among three groups of preservice teachers majoring in elementary education. The sample included 61 novices enrolled in a course entitled Mathematics for the Young Child. This methods course utilized concrete manipulatives and active learning…

CFD Analysis of the SBXC Glider Airframe

DTIC Science & Technology

2016-06-01

mathematically on finite element methods. To validate and verify the methodology developed, a mathematical comparison was made with the previous research data...greater than 15 m/s. 14. SUBJECT TERMS finite element method, computational fluid dynamics, Y Plus, mesh element quality, aerodynamic data, fluid...based mathematically on finite element methods. To validate and verify the methodology developed, a mathematical comparison was made with the

The Training of Teachers of Mathematics for the Secondary Schools of the Countries Represented in the International Commission on the Teaching of Mathematics. Bulletin, 1917, No. 27

ERIC Educational Resources Information Center

Archibald, Raymond Clare

1918-01-01

This bulletin is based upon reports to the International Commission on the Teaching of Mathematics concerning the development of the teacher of mathematics in the better secondary schools of different countries. For the most part, only those schools which are under the immediate direction of the Government have been considered. And even here…

A Conceptual Framework for Digital Libraries for K-12 Mathematics Education: Part 1, Information Organization, Information Literacy, and Integrated Learning

ERIC Educational Resources Information Center

Chen, Hsin-liang; Doty, Philip

2005-01-01

This article is the first of two that present a six-part conceptual framework for the design and evaluation of digital libraries meant to support mathematics education in K-12 settings (see also pt. 2). This first article concentrates on (1) information organization, (2) information literacy, and (3) integrated learning with multimedia materials.…

Financial Analysis and Mathematics of Business: Part IV in a Series--Preparation for Certified Professional Secretary Examination. An Instructor's Guide for an Adult Course.

ERIC Educational Resources Information Center

Gonyea, Adrian C.

The instructor's guide provides a review for those preparing to take Part IV of the Certified Professional Secretary (CPS) examination. Course content can also help secretaries update their skills in accounting and business mathematics. Organized into lessons with objectives, content outline, and teaching suggestions and references, the units…

(Re)Envisioning Mathematics Education: Examining Equity and Social Justice in an Elementary Mathematics Methods Course

ERIC Educational Resources Information Center

Koestler, Courtney

2010-01-01

In this dissertation, I present my attempts at designing an elementary mathematics methods course to support prospective teachers in developing an understanding of how to teach all students in learning powerful mathematics. To do this, I introduced them to teaching mathematics for equity and social justice by discussing ways to support students'…

Thermal Imaging Applied to Cryocrystallography: Cryocooling and Beam Heating (Part I)

NASA Technical Reports Server (NTRS)

Snell, Edward; Bellamy, Henry; Rosenbaum, Gerd; vanderWoerd, Mark; Kazmierczak, Michael

2006-01-01

Thermal imaging provides a non-invasive method to study both the cryocooling process and the heating due to the X-ray beam interaction with a sample. The method has been used successfully to image cryocooling in a number of experimental situations, i.e. cooling as a function of sample volume and as a function of cryostream orientation. Although there are experimental limitations to the method, it has proved a powerful technique to aid cryocrystallography development. Due to the rapid spatial temperature information provided about the sample it is also a powerful tool in the testing of mathematical models. Recently thermal imaging has been used to measure the temperature distribution on both a model and typical crystal samples illuminated with an X-ray beam produced by an undulator. A brief overview of thermal imaging and previous results will be presented. In addition, a detailed description of the calibration and experimental aspects of the beam heating measurements will be described. This will complement the following talk on the mathematical modeling and analysis of the results.

The Physics of Vibration

NASA Astrophysics Data System (ADS)

Pippard, A. B.

1989-11-01

The study of vibration in physical systems is an important part of almost all fields in physics and engineering. This work, originally published in two volumes, examines the classical aspects in Part I and the quantum oscillator in Part II. The classical linear vibrator is treated first and the underlying unity of all linear oscillations in electrical, mechanical and acoustic systems is emphasized. Following this the book turns to the treatment of nonlinear vibrations, a field with which engineers and physicists are generally less familiar. In Part II the emphasis turns to quantum systems, that is those systems which can only be adequately described by quantum mechanics. The treatment concentrates on vibrations in atoms and molecules and their interaction with electromagnetic radiation. The similarities of classical and quantum methods are stressed and the limits of the classical treatment are examined. Throughout the book, each phenomenon discussed is illustrated with many examples and theory and experiment are compared. Although the reader may find that the physics discussed is demanding and the concepts are subtle in places, all mathematics used is familiar to both engineers and experimental scientists. Although not a textbook this is a useful introduction to the more advanced mathematical treatment of vibrations as it bridges the gap between the basic principles and more specialized concepts. It will be of great interest to advanced undergraduates and postgraduates as well as applied mathematicians, physicists and engineers in university and industry.

Developing Teachers' Models for Assessing Students' Competence in Mathematical Modelling through Lesson Study

ERIC Educational Resources Information Center

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

2017-01-01

Applications and modelling have gained a prominent role in mathematics education reform documents and curricula. Thus, there is a growing need for studies focusing on the effective use of mathematical modelling in classrooms. Assessment is an integral part of using modelling activities in classrooms, since it allows teachers to identify and manage…

Using Cooperative Teams-Game-Tournament in 11 Religious School to Improve Mathematics Understanding and Communication

ERIC Educational Resources Information Center

Veloo, Arsaythamby; Md-Ali, Ruzlan; Chairany, Sitie

2016-01-01

Purpose: This paper was part of a larger study which looked into the effect of implementing Cooperative Teams-Games-Tournament (TGT) on understanding of and communication in mathematics. The study had identified the main and interaction effect of using Cooperative TGT for learning mathematics in religious secondary school classrooms. A…

Implementing Reform Curriculum: Voicing the Experiences of an ESL/Mathematics Teacher

ERIC Educational Resources Information Center

Celedon-Pattichis, Sylvia

2010-01-01

The purpose of this 18-month case study is to highlight the successes and challenges that an ESL/mathematics teacher encountered as she made a shift from traditional mathematics curriculum to a standards-based curriculum as part of a statewide systemic initiative. The study was conducted in an urban, public middle school in Central Texas that…

Administering and Implementing the Singapore Mathematics Curriculum at a Learning Center

ERIC Educational Resources Information Center

Reaume, Hannah Colette

2013-01-01

A learning center in the southeastern part of the United States used the Singapore mathematics curriculum (SMC) to support student learning of a wide range of mathematics skills. However, a study had yet to be conducted to gain an understanding about the administration and implementation of the program. This case study was conceptually based on…

[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…

Tablet-Based Math Assessment: What Can We Learn from Math Apps?

ERIC Educational Resources Information Center

Cayton-Hodges, Gabrielle A.; Feng, Gary; Pan, Xingyu

2015-01-01

In this report, we describe a survey of mathematics education apps in the Apple App Store, conducted as part of a research project to develop a tablet-based assessment prototype for elementary mathematics. This survey was performed with the goal of understanding the design principles and techniques used in mathematics apps designed for tablets. We…

Building Connections between Sociomathematical Norms and Cognitive Demand to Improve the Quality of Whole Class Mathematics Conversations

ERIC Educational Resources Information Center

Williams, Lori

2010-01-01

Mathematical discussions support and promote student learning as an integral part of the contexts in which students learn mathematics. Yet, American school practices often focus on teachers disseminating knowledge to students and students acquiring that knowledge through rote rehearsal rather than higher order thinking. One barrier to change in…

Mathematics for the Workplace. Applications from Medical Laboratory Technology. A Teacher's Guide.

ERIC Educational Resources Information Center

Wallace, Johnny M.; Jones, Dallas

This module presents a real-world context in which mathematics skills are used as part of a daily routine. The context is the medical laboratory technology field, and the module aims to help students develop the ability to use mathematics computations while performing tasks similar to those performed by a medical technologist. Materials in the…

Penguins and Pandas: A Note on Teaching Cantor's Diagonal Argument

ERIC Educational Resources Information Center

Rauff, James V.

2008-01-01

Cantor's diagonal proof that the set of real numbers is uncountable is one of the most famous arguments in modern mathematics. Mathematics students usually see this proof somewhere in their undergraduate experience, but it is rarely a part of the mathematical curriculum of students of the fine arts or humanities. This note describes contexts that…

Students' Experiences of Mathematics during the Transition from Primary to Secondary School

ERIC Educational Resources Information Center

Attard, Catherine

2010-01-01

As part of a longitudinal case study on engagement in middle years mathematics, 20 students attending their first year of secondary school in Western Sydney were asked to provide views on their experiences of the transition to secondary school in relation to mathematics teaching and learning. Differences in teacher-student relationships caused the…

The Autonomy to Choose--The Case of Ninth-Grade Mathematics Students

ERIC Educational Resources Information Center

Lavy, Ilana; Zarfin, Orly

2013-01-01

In this study we explored the effects of providing ninth-grade students with the chance to take part in decision making concerning the mathematics level they would be assigned to in high school. Decisions concerned their self-competence regarding their mathematical abilities, their learning goals and the class atmosphere. The students were taught…

Student Enrichment in Mathematics: A Case Study with First Year University Students

ERIC Educational Resources Information Center

Wiggins, Harry; Harding, Ansie; Engelbrecht, Johann

2017-01-01

This paper presents an enrichment case study to showcase a possible avenue for attending to the needs of academically strong mathematics students. We report on a group of university students who were presented with the opportunity of exploring a specific first year mathematics topic deeper, using an inquiry-based learning approach as part of an…

Matrices. New Topics for Secondary School Mathematics: Materials and Software.

ERIC Educational Resources Information Center

North Carolina School of Science and Mathematics. Dept. of Mathematics and Computer Science.

This material on matrices is part of "Introduction to College Mathematics" (ICM), designed to prepare high school students who have students who have completed algebra II for the variety of mathematics they will encounter in college and beyond. The concept goals of this unit are to use matrices to model real-world phenomena, to use matrices as…

Mathematics: Report of the Project 2061 Phase I Mathematics Panel.

ERIC Educational Resources Information Center

Blackwell, David; Henkin, Leon

This is one of five panel reports that have been prepared as part of the first phase of Project 2061, a long-term multipurpose undertaking of the American Association for the Advancement of Science designed to help reform science, mathematics, and technology education in the United States. Major sections included are: (1) "Introduction";…

Improving Geometric and Trigonometric Knowledge and Skill for High School Mathematics Teachers: A Professional Development Partnership

ERIC Educational Resources Information Center

Merrill, Chris; Devine, Kevin L.; Brown, Joshua W.; Brown, Ryan A.

2010-01-01

In the summer of 2009, a professional development partnership was established between the Peoria Public School District (PPSD), a local education agency (LEA), and Illinois State University (ISU) to improve geometric and trigonometric knowledge and skill for high school mathematics teachers as part of the Illinois Mathematics and Science…

Using Task Like PISA's Problem to Support Students' Creativity in Mathematics

ERIC Educational Resources Information Center

Novita, Rita; Putra, Mulia

2016-01-01

Creativity is one of keys to success in the evolving global economy and also be a fundamental skill that is absolutely necessary in the 21st century. Also in mathematics, creativity or thinking creatively is important to be developed because creativity is an integral part of mathematics. However, limiting the use of creativity in the classroom…

Playing with Mathematics: Play in Early Childhood as a Context for Mathematical Learning

ERIC Educational Resources Information Center

Mathematics Education Research Group of Australasia, 2010

2010-01-01

Play is an essential part of young children's lives. This symposium highlights the integral role of play in young children's mathematics learning and examines the teacher's role in facilitating and extending this. Papers examine key tenets of play, contributing to theoretical understandings and presenting data on teacher's perceptions of play and…

Teachers' Attitudes towards Mathematics in Early Childhood Education

ERIC Educational Resources Information Center

Thiel, Oliver

2010-01-01

In Germany during the past few years the nursery school (for ages three-six) is increasingly regarded as an educational institution rather than a childcare centre. This is reflected in the increasing number of curricula for young children, which include mathematics as a domain of learning skills. In the past mathematics has not been part of the…

Mathematics as Liberal Education: Whitehead and the Rhythm of Life

ERIC Educational Resources Information Center

Woodhouse, Howard

2012-01-01

In several of his works, Alfred North Whitehead (1861-1947) presents mathematics as a way of learning about general ideas that increase our understanding of the universe. The danger is that students get bogged down in its technical operations. He argues that mathematics should be an integral part of a new kind of liberal education, incorporating…

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

ERIC Educational Resources Information Center

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

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

Attracting Primary School Children to Mathematics: The Case of a City Mathematical Marathon

ERIC Educational Resources Information Center

Applebaum, Mark; Freiman, Viktor

2013-01-01

In this paper we report on the first year of an online competition in which 480 students took part. After a brief presentation of the organizational structure of the marathon and general data about students' participation, we discuss findings from questionnaires about participants' attitudes towards mathematics, technology, and their perception of…

Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 4

ERIC Educational Resources Information Center

Boaler, Jo; Munson, Jen; Williams, Cathy

2017-01-01

The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the fourth-grade level through visualization, play, and…

Understanding and Supporting Teacher Horizon Knowledge around Limits: A Framework for Evaluating Textbooks for Teachers

ERIC Educational Resources Information Center

Kajander, Ann; Lovric, Miroslav

2017-01-01

As part of recent scrutiny of teacher capacity, the question of teachers' content knowledge of higher level mathematics emerges as important to the field of mathematics education. Elementary teachers in North America and some other countries tend to be subject generalists, yet it appears that some higher level mathematics background may be…

Gaining Modelling and Mathematical Experience by Constructing Virtual Sensory Systems in Maze-Videogames

ERIC Educational Resources Information Center

Sacristán, Ana Isabel; Pretelín-Ricárdez, Angel

2017-01-01

This work is part of a research project that aims to enhance engineering students' learning of how to apply mathematics in modelling activities of real-world situations, through the construction (design and programming) of videogames. We want also for students to relate their mathematical knowledge with other disciplines (e.g., physics, computer…

The Design of a Mathematics Problem Using Real-Life Context for Young Children

ERIC Educational Resources Information Center

Cheng, Lu Pien

2013-01-01

In this paper the teachers' learning journey on designing a mathematics problem that involves a real-life context is reported. This is part of a larger project undertaken in a primary school in Singapore where the teachers were engaged in planning, observing and critiquing mathematics lessons to investigate teaching and learning. These unique…

The Sixth U.S.A. Mathematical Olympiad

ERIC Educational Resources Information Center

Greitzer, Samuel L.

1978-01-01

One hundred and seven students of 365,000 students given the annual High School Mathematics Examination took part in the sixth U.S.A. Mathematical Olympiad. The top eight scores are listed along with comparative Exam and Olympiad scores for the group and individual problem scores. The problems proposed on the U.S.A. Olympiad on an International…

Student Performance in Mathematics: Should We Be Concerned? Evidence from a Retail Course

ERIC Educational Resources Information Center

Enderson, Mary C.; Mann, Manveer

2018-01-01

This article describes how for many college students the transition to college-level mathematics courses presents new challenges beyond those that were part of the high school experience. In this interdisciplinary study forty-four non-mathematics and non-science majors, enrolled in a retail-buying course, were studied to examine student confidence…

Synchronous Online Collaborative Professional Development for Elementary Mathematics Teachers

ERIC Educational Resources Information Center

Francis, Krista; Jacobsen, Michele

2013-01-01

Math is often taught poorly emphasizing rote, procedural methods rather than creativity and problem solving. Alberta Education developed a new mathematics curriculum to transform mathematics teaching to inquiry driven methods. This revised curriculum provides a new vision for mathematics and creates opportunities and requirements for professional…

Some problems of control of dynamical conditions of technological vibrating machines

NASA Astrophysics Data System (ADS)

Kuznetsov, N. K.; Lapshin, V. L.; Eliseev, A. V.

2017-10-01

The possibility of control of dynamical condition of the shakers that are designed for vibration treatment of parts interacting with granular media is discussed. The aim of this article is to develop the methodological basis of technology of creation of mathematical models of shake tables and the development of principles of formation of vibrational fields, estimation of their parameters and control of the structure vibration fields. Approaches to build mathematical models that take into account unilateral constraints, the relationships between elements, with the vibrating surface are developed. Methods intended to construct mathematical model of linear mechanical oscillation systems are used. Small oscillations about the position of static equilibrium are performed. The original method of correction of vibration fields by introduction of the oscillating system additional ties to the structure are proposed. Additional ties are implemented in the form of a mass-inertial device for changing the inertial parameters of the working body of the vibration table by moving the mass-inertial elements. The concept of monitoring the dynamic state of the vibration table based on the original measuring devices is proposed. Estimation for possible changes in dynamic properties is produced. The article is of interest for specialists in the field of creation of vibration technology machines and equipment.

From analytic inversion to contemporary IMRT optimization: Radiation therapy planning revisited from a mathematical perspective

PubMed Central

Censor, Yair; Unkelbach, Jan

2011-01-01

In this paper we look at the development of radiation therapy treatment planning from a mathematical point of view. Historically, planning for Intensity-Modulated Radiation Therapy (IMRT) has been considered as an inverse problem. We discuss first the two fundamental approaches that have been investigated to solve this inverse problem: Continuous analytic inversion techniques on one hand, and fully-discretized algebraic methods on the other hand. In the second part of the paper, we review another fundamental question which has been subject to debate from the beginning of IMRT until the present day: The rotation therapy approach versus fixed angle IMRT. This builds a bridge from historic work on IMRT planning to contemporary research in the context of Intensity-Modulated Arc Therapy (IMAT). PMID:21616694

Mathematical modelling of the human cardiovascular system in the presence of stenosis

NASA Technical Reports Server (NTRS)

Sud, V. K.; Srinivasan, R. S.; Charles, J. B.; Bungo, M. W.

1993-01-01

This paper reports a theoretical study on the distribution of blood flow in the human cardiovascular system when one or more blood vessels are affected by stenosis. The analysis employs a mathematical model of the entire system based on the finite element method. The arterial-venous network is represented by a large number of interconnected segments in the model. Values for the model parameters are based upon the published data on the physiological and rheological properties of blood. Computational results show how blood flow through various parts of the cardiovascular system is affected by stenosis in different blood vessels. No significant changes in the flow parameters of the cardiovascular system were found to occur when the reduction in the lumen diameter of the stenosed vessels was less than 65%.

Problem solving in the borderland between mathematics and physics

NASA Astrophysics Data System (ADS)

Jensen, Jens Højgaard; Niss, Martin; Jankvist, Uffe Thomas

2017-01-01

The article addresses the problématique of where mathematization is taught in the educational system, and who teaches it. Mathematization is usually not a part of mathematics programs at the upper secondary level, but we argue that physics teaching has something to offer in this respect, if it focuses on solving so-called unformalized problems, where a major challenge is to formalize the problems in mathematics and physics terms. We analyse four concrete examples of unformalized problems for which the formalization involves different order of mathematization and applying physics to the problem, but all require mathematization. The analysis leads to the formulation of a model by which we attempt to capture the important steps of the process of solving unformalized problems by means of mathematization and physicalization.

Programming an interim report on the SETL project. Part I: generalities. Part II: the SETL language and examples of its use

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

Schwartz, J T

1975-06-01

A summary of work during the past several years on SETL, a new programming language drawing its dictions and basic concepts from the mathematical theory of sets, is presented. The work was started with the idea that a programming language modeled after an appropriate version of the formal language of mathematics might allow a programming style with some of the succinctness of mathematics, and that this might ultimately enable one to express and experiment with more complex algorithms than are now within reach. Part I discusses the general approach followed in the work. Part II focuses directly on the detailsmore » of the SETL language as it is now defined. It describes the facilities of SETL, includes short libraries of miscellaneous and of code optimization algorithms illustrating the use of SETL, and gives a detailed description of the manner in which the set-theoretic primitives provided by SETL are currently implemented. (RWR)« less

Mathematics and academic diversity in Japan.

PubMed

Woodward, John; Ono, Yumiko

2004-01-01

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

Formalizing structured file services for the data storage and retrieval subsystem of the data management system for Spacestation Freedom

NASA Technical Reports Server (NTRS)

Jamsek, Damir A.

1993-01-01

A brief example of the use of formal methods techniques in the specification of a software system is presented. The report is part of a larger effort targeted at defining a formal methods pilot project for NASA. One possible application domain that may be used to demonstrate the effective use of formal methods techniques within the NASA environment is presented. It is not intended to provide a tutorial on either formal methods techniques or the application being addressed. It should, however, provide an indication that the application being considered is suitable for a formal methods by showing how such a task may be started. The particular system being addressed is the Structured File Services (SFS), which is a part of the Data Storage and Retrieval Subsystem (DSAR), which in turn is part of the Data Management System (DMS) onboard Spacestation Freedom. This is a software system that is currently under development for NASA. An informal mathematical development is presented. Section 3 contains the same development using Penelope (23), an Ada specification and verification system. The complete text of the English version Software Requirements Specification (SRS) is reproduced in Appendix A.

A Quantitative and Qualitative Study of Math Anxiety among Preservice Teachers

ERIC Educational Resources Information Center

Sloan, Tina Rye

2010-01-01

This project investigated the effects of a standards-based mathematics methods course on the mathematics anxiety levels of preservice teachers. The qualitative portion of the study examined aspects of a math methods course that affected mathematics anxiety levels and the antecedents of mathematics anxiety. Findings revealed a significant…

Mathematical Difficulty: Does Early Intervention Enhance Mathematical Performance?

ERIC Educational Resources Information Center

Graham, Jennifer

2008-01-01

The need to ask educators about their opinions on the subject to what extent early intervention methods enhance mathematical performance is long overdue. The purpose of this quantitative research is to examine the extent to which teachers agree that early intervention methods enhance the mathematical performance of students with mathematical…

Hobbes on natural philosophy as "True Physics" and mixed mathematics.

PubMed

Adams, Marcus P

2016-04-01

In this paper, I offer an alternative account of the relationship of Hobbesian geometry to natural philosophy by arguing that mixed mathematics provided Hobbes with a model for thinking about it. In mixed mathematics, one may borrow causal principles from one science and use them in another science without there being a deductive relationship between those two sciences. Natural philosophy for Hobbes is mixed because an explanation may combine observations from experience (the 'that') with causal principles from geometry (the 'why'). My argument shows that Hobbesian natural philosophy relies upon suppositions that bodies plausibly behave according to these borrowed causal principles from geometry, acknowledging that bodies in the world may not actually behave this way. First, I consider Hobbes's relation to Aristotelian mixed mathematics and to Isaac Barrow's broadening of mixed mathematics in Mathematical Lectures (1683). I show that for Hobbes maker's knowledge from geometry provides the 'why' in mixed-mathematical explanations. Next, I examine two explanations from De corpore Part IV: (1) the explanation of sense in De corpore 25.1-2; and (2) the explanation of the swelling of parts of the body when they become warm in De corpore 27.3. In both explanations, I show Hobbes borrowing and citing geometrical principles and mixing these principles with appeals to experience. Copyright © 2015 Elsevier Ltd. All rights reserved.

The Effectiveness of the Mathematics, Engineering, Science Achievement (MESA) Program's Administrative and Policy-Making Processes. A Report to the Legislature in Response to Assembly Bill 610 (1985). Commission Report 89-4.

ERIC Educational Resources Information Center

California State Postsecondary Education Commission, Sacramento.

The Mathematics, Engineering, Science Achievement (MESA) Program was established in 1970 to increase the number of minority students in college programs. This paper reports the MESA administrative operations and policy-making processes. Part 1 summarizes the background of this study. Part 2 describes MESA's administrative operations and provides…

Methods for cost estimation in software project management

NASA Astrophysics Data System (ADS)

Briciu, C. V.; Filip, I.; Indries, I. I.

2016-02-01

The speed in which the processes used in software development field have changed makes it very difficult the task of forecasting the overall costs for a software project. By many researchers, this task has been considered unachievable, but there is a group of scientist for which this task can be solved using the already known mathematical methods (e.g. multiple linear regressions) and the new techniques as genetic programming and neural networks. The paper presents a solution for building a model for the cost estimation models in the software project management using genetic algorithms starting from the PROMISE datasets related COCOMO 81 model. In the first part of the paper, a summary of the major achievements in the research area of finding a model for estimating the overall project costs is presented together with the description of the existing software development process models. In the last part, a basic proposal of a mathematical model of a genetic programming is proposed including here the description of the chosen fitness function and chromosome representation. The perspective of model described it linked with the current reality of the software development considering as basis the software product life cycle and the current challenges and innovations in the software development area. Based on the author's experiences and the analysis of the existing models and product lifecycle it was concluded that estimation models should be adapted with the new technologies and emerging systems and they depend largely by the chosen software development method.

Mathematical model of rolling an elastic wheel over deformable support base

NASA Astrophysics Data System (ADS)

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

2018-02-01

One of the main direction of economic growth in Russia remains to be a speedy development of north and northeast regions that are the constituents of the 60 percent of the country territory. The further development of these territories requires new methods and technologies for solving transport and technological problems when off-road transportation of cargoes and people is conducting. One of the fundamental methods of patency prediction is imitation modeling of wheeled vehicles movement in different operating conditions. Both deformable properties of tires and physical and mechanical properties of the ground: normal tire deflection and gauge depth; variation of contact patch area depending on the load and pressure of air in the tire; existence of hysteresis losses in the tire material which are influencing on the rolling resistance due to friction processes between tire and ground in the contact patch; existence of the tangential reaction from the ground by entire contact area influence on the tractive patency. Nowadays there are two main trends in theoretical research of interaction wheeled propulsion device with ground: analytical method involving mathematical description of explored process and finite element method based on computational modeling. Mathematical models of interaction tire with the ground are used both in processes of interaction individual wheeled propulsion device with ground and researches of mobile vehicle dynamical models operated in specific road and climate conditions. One of the most significant imperfection of these models is the description of interaction wheel with flat deformable support base whereas profile of real support base surface has essential height of unevenness which is commensurate with radius of the wheel. The description of processes taking place in the ground under influence of the wheeled propulsion device using the finite element method is relatively new but most applicable lately. The application of this method allows to provide the most accurate description of the interaction process of a wheeled propulsion devices and the ground, also this method allows to define tension in the ground, deformation of the ground and the tire and ground’s compression. However, the high laboriousness of computations is essential shortcoming of that method therefore it’s hard to use these models as part of the general motion model of multi-axis wheeled vehicles. The purpose of this research is the elaboration of mathematical model of elastic wheel rolling over deformable rough support base taking into account the contact patch deformation. The mathematical model of rectilinear rolling an elastic wheel over rough deformable support base, taking into account variation of contact patch area and variation in the direction of the radial and tangential reactions also load bearing capacity of the ground, is developed. The efficiency of developed mathematical model of rectilinear rolling an elastic wheel over rough deformable support base is proved by the simulation methods.

Jigsaw: Because Reading Your Math Book Shouldn't Be a Puzzle.

ERIC Educational Resources Information Center

Draper, Roni Jo

1997-01-01

Describes a jigsaw puzzle activity, a two-part cooperative learning activity useful at any level of mathematics instruction, intended to teach students to become "strategic readers" of their mathematics textbooks. (SR)

Part height control of laser metal additive manufacturing process

NASA Astrophysics Data System (ADS)

Pan, Yu-Herng

Laser Metal Deposition (LMD) has been used to not only make but also repair damaged parts in a layer-by-layer fashion. Parts made in this manner may produce less waste than those made through conventional machining processes. However, a common issue of LMD involves controlling the deposition's layer thickness. Accuracy is important, and as it increases, both the time required to produce the part and the material wasted during the material removal process (e.g., milling, lathe) decrease. The deposition rate is affected by multiple parameters, such as the powder feed rate, laser input power, axis feed rate, material type, and part design, the values of each of which may change during the LMD process. Using a mathematical model to build a generic equation that predicts the deposition's layer thickness is difficult due to these complex parameters. In this thesis, we propose a simple method that utilizes a single device. This device uses a pyrometer to monitor the current build height, thereby allowing the layer thickness to be controlled during the LMD process. This method also helps the LMD system to build parts even with complex parameters and to increase material efficiency.

Solution of task related to control of swiss-type automatic lathe to get planes parallel to part axis

NASA Astrophysics Data System (ADS)

Tabekina, N. A.; Chepchurov, M. S.; Evtushenko, E. I.; Dmitrievsky, B. S.

2018-05-01

The work solves the problem of automation of machining process namely turning to produce parts having the planes parallel to an axis of rotation of part without using special tools. According to the results, the availability of the equipment of a high speed electromechanical drive to control the operative movements of lathe machine will enable one to get the planes parallel to the part axis. The method of getting planes parallel to the part axis is based on the mathematical model, which is presented as functional dependency between the conveying velocity of the driven element and the time. It describes the operative movements of lathe machine all over the tool path. Using the model of movement of the tool, it has been found that the conveying velocity varies from the maximum to zero value. It will allow one to carry out the reverse of the drive. The scheme of tool placement regarding the workpiece has been proposed for unidirectional movement of the driven element at high conveying velocity. The control method of CNC machines can be used for getting geometrically complex parts on the lathe without using special milling tools.

Examining Teachers' Struggles as They Attempt to Implement Dialogical Interaction as Part of Promoting Mathematical Reasoning within Their Classrooms

ERIC Educational Resources Information Center

Akkus, Recai; Hand, Brian

2011-01-01

This study examines the changes in teaching practices during the implementation of a pedagogical model called the mathematics reasoning approach (MRA), which was founded on 2 critical areas in mathematics, problem solving, and writing to learn. Three algebra teachers implemented the approach with their classes, which were divided into control…

Study on Latvian Mathematics Teachers' Espoused Beliefs about Teaching and Learning and Reported Practices

ERIC Educational Resources Information Center

Sapkova, Alesja

2013-01-01

The aim of the research was to compare espoused beliefs about teaching and learning and reported practices for the teachers of mathematics in Latvia. The sample consisted of 390 teachers of mathematics from different regions of Latvia. The present research is a part of an international comparative research within the NorBa project (Nordic-Baltic…

Engaging in Problem Posing Activities in a Dynamic Geometry Setting and the Development of Prospective Teachers' Mathematical Knowledge

ERIC Educational Resources Information Center

Lavy, Ilana; Shriki, Atara

2010-01-01

In the present study we explore changes in perceptions of our class of prospective mathematics teachers (PTs) regarding their mathematical knowledge. The PTs engaged in problem posing activities in geometry, using the "What If Not?" (WIN) strategy, as part of their work on computerized inquiry-based activities. Data received from the PTs'…

An Experimental Text in Transformational Geometry, Student Text; Cambridge Conference on School Mathematics Feasibility Study No. 43a.

ERIC Educational Resources Information Center

Cambridge Conference on School Mathematics, Newton, MA.

This is part of a student text which was written with the aim of reflecting the thinking of The Cambridge Conference on School Mathematics (CCSM) regarding the goals and objectives for mathematics. The instructional materials were developed for teaching geometry in the secondary schools. This document is chapter six and titled Motions and…

Careers in Applied Mathematics and Computational Sciences.

ERIC Educational Resources Information Center

Society for Industrial and Applied Mathematics, Philadelphia, PA.

This booklet provides some answers to questions on how mathematics is used in the world of work, what kinds of problems it solves, and why it is the key to so many careers, particularly to the jobs of the 21st century. Part of that preparation is mathematical knowledge, tools such as derivatives, probability, and matrices as well as central themes…

Self-Efficacy for Learning Mathematics Asynchronously: Instrument Refinement and the Relationship to Mathematics Achievement

ERIC Educational Resources Information Center

Hodges, Charles; Jones, R. Caroline; Prater, Alyssa

2014-01-01

The purpose of this paper is to report the results of a two-part study. Study 1 was conducted to refine and validate a survey instrument, SELMA (Hodges, 2008), used to measure learners' self-efficacy toward learning mathematics in online or technology-intensive, asynchronous learning environments. Study 2 was conducted to investigate the…

Mathematics for the Workplace. Applications from Machine Tool Technology (Michelin Tire Corporation). A Teacher's Guide.

ERIC Educational Resources Information Center

Wallace, Johnny M.; Stewart, Grover

This module presents a real-world context in which mathematics skills (geometry and trigonometry) are used as part of a daily routine. The context is the machine tool technology field, and the module aims to help students develop the ability to analyze diagrams in order to make mathematical computations. The modules, which features applications…

The Relevance of Mathematics: Leaders and Teachers as Gatekeeper for Queensland Senior Calculus Mathematics

ERIC Educational Resources Information Center

Easey, Michael; Gleeson, Jim

2016-01-01

The aim of the larger study, of which this paper is a part, is to investigate the decline in Year 10 male students' participation in senior calculus mathematics courses at an independent boys' school located in metropolitan Queensland. This paper draws on Sealey and Noyes's (2010) relevance framework to conduct document analysis and interviews…

Partnership in Being a Specialist Mathematics and Computing College--Who Gains What, How and Why?

ERIC Educational Resources Information Center

Sinkinson, Anne J.

2007-01-01

The research took place in a mathematics and computing specialist school. The article reports on part of a case study of the mathematics department's experience of being a major contributor to the requirements of being a specialist school. This article aims to explore and describe one model of partnership within the "community" remit of…

Interdisciplinary Student/Teacher Materials in Energy, the Environment, and the Economy: Mathematics in Energy, Grades 8-9.

ERIC Educational Resources Information Center

Brown, Evelyn; And Others

This publication is part of a series of instructional units produced by NSTA's Project for an Energy-Enriched Curriculum. The teacher's manual and the student guide for a mathematics unit in this series are presented here. This unit attempts to teach students some necessary mathematical skills needed to understand quantitative facts about energy.…

A Comparison of Teacher and Lecturer Perspectives on the Transition from Secondary to Tertiary Mathematics Education

ERIC Educational Resources Information Center

Hong, Ye Yoon; Kerr, Suzanne; Klymchuk, Sergiy; McHardy, Johanna; Murphy, Priscilla; Spencer, Sue; Thomas, Michael O. J.; Watson, Peter

2009-01-01

The transition from school to tertiary study of mathematics comes under increasing scrutiny in research. This article reports on some findings from a project analysing the transition from secondary to tertiary education in mathematics. One key variable in this transition is the teacher or lecturer. This article deals with a small part of the data…

"I'm a Natural and I Do It for Love!": Exploring Students' Accounts of Studying Mathematics

ERIC Educational Resources Information Center

Bartholomew, Hannah; Darragh, Lisa; Ell, Fiona; Saunders, Jeanette

2011-01-01

Drawing on in-depth interviews with the third year students at a New Zealand university, we explore the ways in which students speak about studying mathematics, their relationship with the subject and how this has developed over time. These interviews were conducted as part of a project looking at undergraduate mathematics from the perspective of…

Adults Learning Mathematics: What We Should Know about Betting and Bookkeeping?

ERIC Educational Resources Information Center

Maasz, Juergen; Siller, Hans-Stefan

2010-01-01

A lot of people risk money with bets on sport events or other events. Bookkeepers that offer such bets earn a lot of money. We are making a proposal (more exactly: a concept for a part of a basic mathematics course) for learning mathematics behind the screen (internet bets are very popular). Learners should organize a "sports event"…

Putting Research into Practice in the Elementary Grades: Readings from Journals of the National Council of Teachers of Mathematics.

ERIC Educational Resources Information Center

Chambers, Donald L., Ed.

This book describes children's mathematical thinking to guide and support teachers in their reflection upon student thinking and teaching and learning. It is organized into five parts: (1) reasoning, student thinking, and invented strategies independent of the mathematics content domain which addresses the role of discourse in helping students…

The Interrelationship of Sex, Visual Spatial Abilities, and Mathematical Problem Solving Ability in Grade Seven. Parts 1, 2, and 3.

ERIC Educational Resources Information Center

Schonberger, Ann Koch

This three-volume report deals with the hypothesis that males are more successful at solving mathematical and spatial problems than females. The general relationship between visual spatial abilities and mathematical problem-solving ability is also investigated. The research sample consisted of seventh graders. Each pupil took five spatial tests…

Relationships between Student and Instructional Factors and Algebra Achievement of Students in the United States and Japan: An Analysis of TIMSS 2003 Data

ERIC Educational Resources Information Center

House, J. Daniel; Telese, James A.

2008-01-01

Algebra knowledge is a critical part of middle-school mathematics achievement, and success in algebra is necessary for taking higher level mathematics courses and leads to higher scores on standardized tests. The purpose of this study was to simultaneously examine relationships between mathematics beliefs, classroom instructional strategies, and…

Biological evolution and statistical physics

NASA Astrophysics Data System (ADS)

Drossel, Barbara

2001-03-01

This review is an introduction to theoretical models and mathematical calculations for biological evolution, aimed at physicists. The methods in the field are naturally very similar to those used in statistical physics, although the majority of publications have appeared in biology journals. The review has three parts, which can be read independently. The first part deals with evolution in fitness landscapes and includes Fisher's theorem, adaptive walks, quasispecies models, effects of finite population sizes, and neutral evolution. The second part studies models of coevolution, including evolutionary game theory, kin selection, group selection, sexual selection, speciation, and coevolution of hosts and parasites. The third part discusses models for networks of interacting species and their extinction avalanches. Throughout the review, attention is paid to giving the necessary biological information, and to pointing out the assumptions underlying the models, and their limits of validity.

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…

Reframing Research on Methods Courses to Inform Mathematics Teacher Educators' Practice

ERIC Educational Resources Information Center

Kastberg, Signe E.; Tyminski, Andrew M.; Sanchez, Wendy B.

2017-01-01

Calls have been made for the creation of a shared knowledge base in mathematics teacher education with the power to inform the design of scholarly inquiry and mathematics teacher educators' (MTEs) scholarly practices. Focusing on mathematics methods courses, we summarize and contribute to literature documenting activities MTEs use in mathematics…

Mathematical models used in segmentation and fractal methods of 2-D ultrasound images

NASA Astrophysics Data System (ADS)

Moldovanu, Simona; Moraru, Luminita; Bibicu, Dorin

2012-11-01

Mathematical models are widely used in biomedical computing. The extracted data from images using the mathematical techniques are the "pillar" achieving scientific progress in experimental, clinical, biomedical, and behavioural researches. This article deals with the representation of 2-D images and highlights the mathematical support for the segmentation operation and fractal analysis in ultrasound images. A large number of mathematical techniques are suitable to be applied during the image processing stage. The addressed topics cover the edge-based segmentation, more precisely the gradient-based edge detection and active contour model, and the region-based segmentation namely Otsu method. Another interesting mathematical approach consists of analyzing the images using the Box Counting Method (BCM) to compute the fractal dimension. The results of the paper provide explicit samples performed by various combination of methods.

Diagnosis of the Computer-Controlled Milling Machine, Definition of the Working Errors and Input Corrections on the Basis of Mathematical Model

NASA Astrophysics Data System (ADS)

Starikov, A. I.; Nekrasov, R. Yu; Teploukhov, O. J.; Soloviev, I. V.; Narikov, K. A.

2016-10-01

Manufactures, machinery and equipment improve of constructively as science advances and technology, and requirements are improving of quality and longevity. That is, the requirements for surface quality and precision manufacturing, oil and gas equipment parts are constantly increasing. Production of oil and gas engineering products on modern machine tools with computer numerical control - is a complex synthesis of technical and electrical equipment parts, as well as the processing procedure. Technical machine part wears during operation and in the electrical part are accumulated mathematical errors. Thus, the above-mentioned disadvantages of any of the following parts of metalworking equipment affect the manufacturing process of products in general, and as a result lead to the flaw.

Quantitative PET Imaging in Drug Development: Estimation of Target Occupancy.

PubMed

Naganawa, Mika; Gallezot, Jean-Dominique; Rossano, Samantha; Carson, Richard E

2017-12-11

Positron emission tomography, an imaging tool using radiolabeled tracers in humans and preclinical species, has been widely used in recent years in drug development, particularly in the central nervous system. One important goal of PET in drug development is assessing the occupancy of various molecular targets (e.g., receptors, transporters, enzymes) by exogenous drugs. The current linear mathematical approaches used to determine occupancy using PET imaging experiments are presented. These algorithms use results from multiple regions with different target content in two scans, a baseline (pre-drug) scan and a post-drug scan. New mathematical estimation approaches to determine target occupancy, using maximum likelihood, are presented. A major challenge in these methods is the proper definition of the covariance matrix of the regional binding measures, accounting for different variance of the individual regional measures and their nonzero covariance, factors that have been ignored by conventional methods. The novel methods are compared to standard methods using simulation and real human occupancy data. The simulation data showed the expected reduction in variance and bias using the proper maximum likelihood methods, when the assumptions of the estimation method matched those in simulation. Between-method differences for data from human occupancy studies were less obvious, in part due to small dataset sizes. These maximum likelihood methods form the basis for development of improved PET covariance models, in order to minimize bias and variance in PET occupancy studies.

Assessing Students' Mathematical Problem Posing

ERIC Educational Resources Information Center

Silver, Edward A.; Cai, Jinfa

2005-01-01

Specific examples are used to discuss assessment, an integral part of mathematics instruction, with problem posing and assessment of problem posing. General assessment criteria are suggested to evaluate student-generated problems in terms of their quantity, originality, and complexity.

Isaac Newton: Man, Myth, and Mathematics.

ERIC Educational Resources Information Center

Rickey, V. Frederick

1987-01-01

This article was written in part to celebrate the anniversaries of landmark mathematical works by Newton and Descartes. It's other purpose is to dispel some myths about Sir Isaac Newton and to encourage readers to read Newton's works. (PK)

Pre-service teachers’ challenges in presenting mathematical problems

NASA Astrophysics Data System (ADS)

Desfitri, R.

2018-01-01

The purpose of this study was to analyzed how pre-service teachers prepare and assigned tasks or assignments in teaching practice situations. This study was also intended to discuss about kind of tasks or assignments they gave to students. Participants of this study were 15 selected pre-service mathematics teachers from mathematics education department who took part on microteaching class as part of teaching preparation program. Based on data obtained, it was occasionally found that there were hidden errors on questions or tasks assigned by pre-service teachers which might lead their students not to be able to reach a logical or correct answer. Although some answers might seem to be true, they were illogical or unfavourable. It is strongly recommended that pre-service teachers be more careful when posing mathematical problems so that students do not misunderstand the problems or the concepts, since both teachers and students were sometimes unaware of errors in problems being worked on.

Analysis of mathematical literacy ability based on goal orientation in model eliciting activities learning with murder strategy

NASA Astrophysics Data System (ADS)

Wijayanti, R.; Waluya, S. B.; Masrukan

2018-03-01

The purpose of this research are (1) to analyze the learning quality of MEAs with MURDER strategy, (2) to analyze students’ mathematical literacy ability based on goal orientation in MEAs learning with MURDER strategy. This research is a mixed method research of concurrent embedded type where qualitative method as the primary method. The data were obtained using the methods of scale, observation, test and interviews. The results showed that (1) MEAs Learning with MURDER strategy on students' mathematical literacy ability is qualified, (2) Students who have mastery goal characteristics are able to master the seven components of mathematical literacy process although there are still two components that the solution is less than the maximum. Students who have performance goal characteristics have not mastered the components of mathematical literacy process with the maximum, they are only able to master the ability of using mathematics tool and the other components of mathematical literacy process is quite good.

Authentic Teaching Experiences in Secondary Mathematics Methods

ERIC Educational Resources Information Center

Stickles, Paula R.

2015-01-01

Often secondary mathematics methods courses include classroom peer teaching, but many pre-service teachers find it challenging to teach their classmate peers as there are no discipline issues and little mathematical discourse as the "students" know the content. We will share a recent change in our methods course where pre-service…

Mathematical and information maintenance of biometric systems

NASA Astrophysics Data System (ADS)

Boriev, Z.; Sokolov, S.; Nyrkov, A.; Nekrasova, A.

2016-04-01

This article describes the different mathematical methods for processing biometric data. A brief overview of methods for personality recognition by means of a signature is conducted. Mathematical solutions of a dynamic authentication method are considered. Recommendations on use of certain mathematical methods, depending on specific tasks, are provided. Based on the conducted analysis of software and the choice made in favor of the wavelet analysis, a brief basis for its use in the course of software development for biometric personal identification is given for the purpose of its practical application.

The variational method in quantum mechanics: an elementary introduction

NASA Astrophysics Data System (ADS)

Borghi, Riccardo

2018-05-01

Variational methods in quantum mechanics are customarily presented as invaluable techniques to find approximate estimates of ground state energies. In the present paper a short catalogue of different celebrated potential distributions (both 1D and 3D), for which an exact and complete (energy and wavefunction) ground state determination can be achieved in an elementary way, is illustrated. No previous knowledge of calculus of variations is required. Rather, in all presented cases the exact energy functional minimization is achieved by using only a couple of simple mathematical tricks: ‘completion of square’ and integration by parts. This makes our approach particularly suitable for undergraduates. Moreover, the key role played by particle localization is emphasized through the entire analysis. This gentle introduction to the variational method could also be potentially attractive for more expert students as a possible elementary route toward a rather advanced topic on quantum mechanics: the factorization method. Such an unexpected connection is outlined in the final part of the paper.

Mathematical modeling of the in-mold coating process for injection-molded thermoplastic parts

NASA Astrophysics Data System (ADS)

Chen, Xu

In-Mold Coating (IMC) has been successfully used for many years for exterior body panels made from compression molded Sheet Molding Compound (SMC). The coating material is a single component reactive fluid, designed to improve the surface quality of SMC moldings in terms of functional and cosmetic properties. When injected onto a cured SMC part, IMC cures and bonds to provide a pain-like surface. Because of its distinct advantages, IMC is being considered for application to injection molded thermoplastic parts. For a successful in mold coating operation, there are two key issues related to the flow of the coating. First, the injection nozzle should be located such that the thermoplastic substrate is totally covered and the potential for air trapping is minimized. The selected location should be cosmetically acceptable since it most likely will leave a mark on the coated surface. The nozzle location also needs to be accessible for easy of maintenance. Secondly, the hydraulic force generated by the coating injection pressure should not exceed the available clamping tonnage. If the clamping force is exceeded, coating leakage will occur. In this study, mathematical models for IMC flow on the compressible thermoplastic substrate have been developed. Finite Difference Method (FDM) is first used to solve the 1 dimensional (1D) IMC flow problem. In order to investigate the application of Control Volume based Finite Element Method (CV/FEM) to more complicated two dimensional IMC flow, that method is first evaluated by solving the 1D IMC flow problem. An analytical solution, which can be obtained when a linear relationship between the coating thickness and coating injection pressure is assumed, is used to verify the numerical results. The mathematical models for the 2 dimensional (2D) IMC flow are based on the generalized Hele-Shaw approximation. It has been found experimentally that the power law viscosity model adequately predicts the rheological behavior of the coating. The compressibility of the substrate is modeled by the 2-domain Tait PVT equation. CV/FEM is used to solve the discretized governing equations. A computer code has been developed to predict the fill pattern of the coating and the injection pressure. A number of experiments have been conducted to verify the numerical predictions of the computer code. It has been found both numerically and experimentally that the substrate thickness plays a significant role on the IMC fill pattern.

Modeling in the quality by design environment: Regulatory requirements and recommendations for design space and control strategy appointment.

PubMed

Djuris, Jelena; Djuric, Zorica

2017-11-30

Mathematical models can be used as an integral part of the quality by design (QbD) concept throughout the product lifecycle for variety of purposes, including appointment of the design space and control strategy, continual improvement and risk assessment. Examples of different mathematical modeling techniques (mechanistic, empirical and hybrid) in the pharmaceutical development and process monitoring or control are provided in the presented review. In the QbD context, mathematical models are predominantly used to support design space and/or control strategies. Considering their impact to the final product quality, models can be divided into the following categories: high, medium and low impact models. Although there are regulatory guidelines on the topic of modeling applications, review of QbD-based submission containing modeling elements revealed concerns regarding the scale-dependency of design spaces and verification of models predictions at commercial scale of manufacturing, especially regarding real-time release (RTR) models. Authors provide critical overview on the good modeling practices and introduce concepts of multiple-unit, adaptive and dynamic design space, multivariate specifications and methods for process uncertainty analysis. RTR specification with mathematical model and different approaches to multivariate statistical process control supporting process analytical technologies are also presented. Copyright © 2017 Elsevier B.V. All rights reserved.

Proofs and Refutations in the Undergraduate Mathematics Classroom

ERIC Educational Resources Information Center

Larsen, Sean; Zandieh, Michelle

2008-01-01

In his 1976 book, "Proofs and Refutations," Lakatos presents a collection of case studies to illustrate methods of mathematical discovery in the history of mathematics. In this paper, we reframe these methods in ways that we have found make them more amenable for use as a framework for research on learning and teaching mathematics. We present an…

Effects of Mathematics Integration in a Teaching Methods Course on Mathematics Ability of Preservice Agricultural Education Teachers

ERIC Educational Resources Information Center

Stripling, Christopher T.; Roberts, T. Grady

2014-01-01

The purpose of this study was to determine the effects of incorporating mathematics teaching and integration strategies (MTIS) in a teaching methods course on preservice agricultural teachers' mathematics ability. The research design was quasi-experimental and utilized a nonequivalent control group. The MTIS treatment had a positive effect on the…

Does CAS Use Disadvantage Girls in VCE Mathematics?

ERIC Educational Resources Information Center

Forgasz, Helen; Tan, Hazel

2010-01-01

In 2009, four mathematics subjects were offered at the year 12 level in the Victorian Certificate of Education (VCE). The two subjects at the intermediate level--Mathematical Methods and Mathematical Methods CAS--run in parallel, that is, a student can be enrolled in only one or the other, the choice being made at the school level. The curricular…

Developing Mathematical Thinking in the Primary Classroom: Liberating Students and Teachers as Learners of Mathematics

ERIC Educational Resources Information Center

Hudson, Brian; Henderson, Sheila; Hudson, Alison

2015-01-01

This paper reports on a research study conducted with a group of practising primary school teachers (n = 24) in North East Scotland during 2011-2012. The teachers were all participants in a newly developed Masters course that had been designed with the aim of promoting the development of mathematical thinking in the primary classroom as part of…

Las Matematicas: Lenguaje Universal. Grados Intermedios, Niveles 1-3. Teacher's Guide I (Mathematics: A Universal Language. Intermediate Grades, Level 1-3. Teacher's Guide I).

ERIC Educational Resources Information Center

Dissemination and Assessment Center for Bilingual Education, Austin, TX.

This guide covers the first part of a bilingual, sequential mathematics course. The course integrates culturally relevant situations and illustrations with mathematics to reinforce the student's self-concept and encourage cultural pride. This program may be used as a self-contained continuum, as a supplement to another course of study, for…

Las Matematicas: Lenguaje Universal. Grados Intermedios, Niveles 4-6. Teacher's Guide II (Mathematics: A Universal Language. Intermediate Grades, Levels 4-6. Teacher's Guide II).

ERIC Educational Resources Information Center

Dissemination and Assessment Center for Bilingual Education, Austin, TX.

This guide covers the second part of a bilingual, sequential mathematics course. The course integrates culturally relevant situations and illustrations with mathematics to reinforce the student's self-concept and encourage cultural pride. This program may be used as a self-contained continuum, as a supplement to another course of study, for…

ILS Glide Slope Performance Prediction. Volume B

DTIC Science & Technology

1974-09-01

figures are identical in both volumes. 󈧔. Abottec A mathematical model for predicting the performance of ILS glide slope arrays in the presence of...irregularities on the performance of ILS Glide Slope antenna systems, a mathematical -electromagnetic scattering computer model has been developed. This work was...Antenna ........... 4-4 9. Test Case Results ..................................... r-3 ix PART I. IEO -j 1.INTRODUCTION IA mathematical model has been

Mathematical Research in Materials Science: Opportunities and Perspectives. Part 2

DTIC Science & Technology

1993-01-01

spheres and Lennard - Jones potentials , but have not been extended to a general framework that will allow input from more complicated interatomic...focuses on directions for potentially promising collaboration between materials scientists and mathematical scientists, and encourages both communities...interface between the mathematical sciences and other fields. The purpose of this report is not only to focus on directions for potentially promising

Using Video Analysis to Support Prospective K-8 Teachers' Noticing of Students' Multiple Mathematical Knowledge Bases

ERIC Educational Resources Information Center

Roth McDuffie, Amy; Foote, Mary Q.; Bolson, Catherine; Turner, Erin E.; Aguirre, Julia M.; Bartell, Tonya Gau; Drake, Corey; Land, Tonia

2014-01-01

As part of a larger research project aimed at transforming preK-8 mathematics teacher preparation, the purpose of this study was to examine the extent to which prospective teachers notice children's competencies related to children's mathematical thinking, and children's community, cultural, and linguistic funds of knowledge or what…

Building a Community of Scholars: One University's Story of Students Engaged in Learning Science, Mathematics, and Engineering through a NSF S-STEM Grant--Part II

ERIC Educational Resources Information Center

Kalevitch, Maria; Maurer, Cheryl; Badger, Paul; Holdan, Greg; Sirinterlikci, Arif

2015-01-01

The School of Engineering, Mathematics, and Science (SEMS) at Robert Morris University (RMU) was awarded a five-year grant from the National Science Foundation (NSF) to fund scholarships to 21 academically talented but financially challenged students majoring in the disciplines of science, technology, engineering, and mathematics (STEM). Each…

Part I--A Case Study in Post-Secondary Mathematics: The Importance of Mental Health Awareness

ERIC Educational Resources Information Center

Resch, Janelle

2015-01-01

Due to the shift of civilization from the Industrial Age to the Information Age, mathematical literacy has become a necessity in the twenty-first century. However, in order to learn and contribute to the mathematical community, one has to be in a state of good mental health. Where "good mental health," is defined as one who has developed…

Patterns of Interaction and Mathematical Thinking of High School Students in Classroom Environments That Include Use of Java-Based, Curriculum-Embedded Software

ERIC Educational Resources Information Center

Fonkert, Karen L.

2012-01-01

This study analyzes the nature of student interaction and discourse in an environment that includes the use of Java-based, curriculum-embedded mathematical software. The software "CPMP-Tools" was designed as part of the development of the second edition of the "Core-Plus Mathematics" curriculum. The use of the software on…

The Origins of Diverse Domains of Mathematics: Generalist Genes but Specialist Environments

ERIC Educational Resources Information Center

Kovas, Y.; Petrill, S. A.; Plomin, R.

2007-01-01

The authors assessed 2,502 ten-year-old children, members of 1,251 pairs of twins, on a Web-based battery of problems from 5 diverse aspects of mathematics assessed as part of the U.K. national curriculum. This 1st genetic study into the etiology of variation in different domains of mathematics showed that the heritability estimates were moderate…

The Mathematics Textbook at Tertiary Level as Curriculum Material--Exploring the Teacher's Decision-Making Process

ERIC Educational Resources Information Center

Randahl, Mira

2016-01-01

This paper reports on a study about how the mathematics textbook was perceived and used by the teacher in the context of a calculus part of a basic mathematics course for first-year engineering students. The focus was on the teacher's choices and the use of definitions, examples and exercises in a sequence of lectures introducing the derivative…

A Model of Professional Competences in Mathematics to Update Mathematical and Didactic Knowledge of Teachers

ERIC Educational Resources Information Center

Díaz, Verónica; Poblete, Alvaro

2017-01-01

This paper describes part of a research and development project carried out in public elementary schools. Its objective was to update the mathematical and didactic knowledge of teachers in two consecutive levels in urban and rural public schools of Region de Los Lagos and Region de Los Rios of southern Chile. To that effect, and by means of an…

Attitude determination of a high altitude balloon system. Part 1: Development of the mathematical model

NASA Technical Reports Server (NTRS)

Nigro, N. J.; Elkouh, A. F.; Shen, K. S.; Nimityongskul, P.; Jhaveri, V. N.; Sethi, A.

1975-01-01

A mathematical model for predicting the three dimensional motion of the balloon system is developed, which includes the effects of bounce, pendulation and spin of each subsystem. Boundary layer effects are also examined, along with the aerodynamic forces acting on the balloon. Various simplified forms of the system mathematical model were developed, based on an order of magnitude analysis.

Project LAUNCH: Bringing Space into Math and Science Classrooms

NASA Technical Reports Server (NTRS)

Fauerbach, M.; Henry, D. P.; Schmidt, D. L.

2005-01-01

Project LAUNCH is a K-12 teacher professional development program, which has been created in collaboration between the Whitaker Center for Science, Mathematics and Technology Education at Florida Gulf Coast University (FGCU), and the Florida Space Research Institute (FSRI). Utilizing Space as the overarching theme it is designed to improve mathematics and science teaching, using inquiry based, hands-on teaching practices, which are aligned with Florida s Sunshine State Standards. Many students are excited about space exploration and it provides a great venue to get them involved in science and mathematics. The scope of Project LAUNCH however goes beyond just providing competency in the subject area, as pedagogy is also an intricate part of the project. Participants were introduced to the Conceptual Change Model (CCM) [1] as a framework to model good teaching practices. As the CCM closely follows what scientists call the scientific process, this teaching method is also useful to actively engage institute participants ,as well as their students, in real science. Project LAUNCH specifically targets teachers in low performing, high socioeconomic schools, where the need for skilled teachers is most critical.

Sequential mathematical solution for authentication and authorization technique implementing encryption methodology creating secure transaction using various methods also at quantum level

NASA Astrophysics Data System (ADS)

Gharami, Snigdha; Dinakaran, M.

2017-11-01

We see challenges in authenticating each aspect of electronic usage, starting from transaction to social interaction the authenticity and availability of correct information is guided in various ways. Authentication and authorization follow one another; a process of authentication is calculated on multiple layers of steps. In this paper we discuss various possibilities of modifying and using ways to deal with authentication and authorization mechanism. Idea is to work through authentication with mathematical calculations. We will go through various scenarios and find out the system of information that fits best at the moment of need. We will take account of new approaches of authentication and authorization while working on mathematical paradigm of information. The paper also takes an eye on quantum cryptography and discusses on how it could help one in the present scenario. This paper is divided into sections discussing on various paradigm of authentication and how one can achieve it in secure way, this paper is part of research work where analysis of various constraints are to be followed in the extended research work.

On Inferentialism

ERIC Educational Resources Information Center

Radford, Luis

2017-01-01

This article is a critical commentary on inferentialism in mathematics education. In the first part, I comment on some of the major shortcomings that inferentialists see in the theoretical underpinnings of representationalist, empiricist, and socioconstructivist mathematics education theories. I discuss in particular the criticism that…

"MAPHICS", its development and influence on the future of Science.

NASA Astrophysics Data System (ADS)

Castellano, Doc

2001-11-01

On the fifth 'anniversary' of his conferences with Einstein, the Author reviewed the State of the Art of Mathematical Physics. During this review, 1960, the Author formulated an Omega Science. Namely, combining the Philosophy of Mathematics with the Philosophy of Physics into ONE Philosophy, "MAPHICS". "MA from MAthematics and PH--ICS" from Physics; "MAPHICS" (TM). The PhD co. views Science in general, and Mathematical Physics in particular, from a Historic-Philosophical viewpoint. Thus, it remained anonymous and 'in the background' as publicly known Mathematicians and Physicists, with their great reservoir of rhetoric expertise in said Fields; gradually presented and refined the essence of what the Author calls "Spirito Mathematics". A Philosophical concept that now appears to be publicly developing, with the utilization of some its speed and resolution power. The Author will give at least three examples of its speed and resolution power. One being the partial differential equation in the development of Wave Mechanics & Quantum Mechanics. Namely, [(-ih bar(squared)/2m)(2nd Part.Der. psi/ respect to x)] + V psi = ih bar -(Part.Der. psi/respect to t).

Silent method for mathematics instruction: An overview of teaching subsets

NASA Astrophysics Data System (ADS)

Sugiman, Apino, Ezi

2017-05-01

Generally, teachers use oral communication for teaching mathematics. Taking an opposite perspective, this paper describes how instructional practices for mathematics can be carried out namely a silent method. Silent method uses body language, written, and oral communication for classroom interaction. This research uses a design research approach consisting of four phases: preliminary, prototyping and developing the instruction, and assessment. There are four stages of silent method. The first stage is conditioning stage in which the teacher introduces the method and makes agreement about the `rule of the game'. It is followed by the second one, elaborating stage, where students guess and explore alternative answers. The third stage is developing mathematical thinking by structuring and symbolizing. Finally, the method is ended by reinforcing stage which aims at strengthening and reflecting student's understanding. In this paper, every stage is described on the basis of practical experiences in a real mathematics classroom setting.

The Postmodern Perfectionist, the Pragmatic Hedonist and the Materialist Maximalist: Understanding High School Students' Profile Choices towards or away from Mathematics, Science and Technology (MST) Fields in the Netherlands

ERIC Educational Resources Information Center

Yazilitas, D.; Saharso, S.; de Vries, G. C.; Svensson, J. S.

2017-01-01

This study focuses on high school students' profile choices and the choice for or against the Nature and Technology (NT) profile in the Netherlands. A mixed-methods approach is used to study cultural values that affect this choice. The quantitative part of the study shows that being female is negatively correlated with the choice for the…

Student perception of the impact of mathematics support in higher education

NASA Astrophysics Data System (ADS)

Fhloinn, E. Ní; Fitzmaurice, O.; Bhaird, C. Mac an; O'Sullivan, C.

2014-10-01

Mathematics support in higher education has become increasingly widespread over the past two decades, particularly in the UK, Ireland and Australia. Despite this, reliable evaluation of mathematics support continues to present challenges for those working in this area. One reason is because ideally, properly structured support should function as an integral part of the overall educational experience of the student, in tandem with lectures and tutorials. When this occurs, it makes it difficult to isolate the impact of mathematics support from these other entities. In this paper, the results of a large-scale nationwide survey conducted with first-year service mathematics students in nine higher education institutes in Ireland are considered, exploring students' perceptions of the impact of mathematics support upon their retention, mathematical confidence, examination performance and overall ability to cope with the mathematical demands they face. Students were extremely positive about the effectiveness of mathematics support in all of these areas, providing valuable insights into the value of learning support in mathematics.

An Investigation of Mathematics Anxiety among Sixth through Eighth Grade Students in Turkey

ERIC Educational Resources Information Center

Birgin, Osman; Baloglu, Mustafa; Catlioglu, Hakan; Gurbuz, Ramazan

2010-01-01

The purpose of the present study is to investigate mathematics anxiety among 220 sixth through eighth grade Turkish students in terms of mathematics achievement levels, perceived enjoyment of the mathematics teaching method, perceived enjoyment of mathematics, and perceived help with mathematics from parents. The Mathematics Anxiety Scale for…

Computational and mathematical methods in brain atlasing.

PubMed

Nowinski, Wieslaw L

2017-12-01

Brain atlases have a wide range of use from education to research to clinical applications. Mathematical methods as well as computational methods and tools play a major role in the process of brain atlas building and developing atlas-based applications. Computational methods and tools cover three areas: dedicated editors for brain model creation, brain navigators supporting multiple platforms, and atlas-assisted specific applications. Mathematical methods in atlas building and developing atlas-aided applications deal with problems in image segmentation, geometric body modelling, physical modelling, atlas-to-scan registration, visualisation, interaction and virtual reality. Here I overview computational and mathematical methods in atlas building and developing atlas-assisted applications, and share my contribution to and experience in this field.

Strategy for integration of coastal culture in learning process of mathematics in junior high school

NASA Astrophysics Data System (ADS)

Suyitno, H.; Zaenuri; Florentinus, T. S.; Zakaria, E.

2018-03-01

Traditional life in the fishing family is part of the local culture. Many School-age children in the fishing family drop-outs due to lack of parents motivation and the environment was less supportive. The problems were: (1) How the strategy of integration of local culture in learning process of mathematics in Junior High School (JHS)? (2) How to prepare the Mathematics Student’s Book for grade 7 of JHS that based on coastal culture, that has an ISBN, has international level, applicable, and in accordance with the current curriculum? The purposes of this research were: (1) to obtain the strategy of integration of local culture in learning process of mathematics in JHS, through FGD between UNNES and UKM; (2) to obtain the experts validation, through Focus Group Discussion (FGD) between UNNES and UKM toward the draft of the Mathematics Student’s Book for grade 7 of JHS that based on coastal culture; (3) produces Mathematics Student’s Book for grade 7 SMP which based on coastal culture and has an ISBN, international, applicable, and in accordance with the curriculum. The research activity was a qualitative research, so that the research methods include: (1) data reduction, (2) display data, (3) data interpretation, and (4) conclusion/verification. The main activities of this research: drafting the Mathematics Student’s Book of Grade 7 which based on coastal culture; get the validation from international partners;conducting FGD at Education Faculty of Universiti Kebangsaan Malaysia through the program of visiting lecturers for getting the Mathematics Student’s Book of grade 7 which based on coastal culture, registering for ISBN, and publishing the reasearch results in International seminar and International Journals. The results of this research were as follows. (1) Getting a good strategy for integration of local culture in learning process of mathematics in JHS. (2) Getting the Mathematics Student’s Book for grade 7 of JHS that based on coastal culture, that has an ISBN, international level, applicable, and in accordance with the current curriculum.

Analysis of measured data of human body based on error correcting frequency

NASA Astrophysics Data System (ADS)

Jin, Aiyan; Peipei, Gao; Shang, Xiaomei

2014-04-01

Anthropometry is to measure all parts of human body surface, and the measured data is the basis of analysis and study of the human body, establishment and modification of garment size and formulation and implementation of online clothing store. In this paper, several groups of the measured data are gained, and analysis of data error is gotten by analyzing the error frequency and using analysis of variance method in mathematical statistics method. Determination of the measured data accuracy and the difficulty of measured parts of human body, further studies of the causes of data errors, and summarization of the key points to minimize errors possibly are also mentioned in the paper. This paper analyses the measured data based on error frequency, and in a way , it provides certain reference elements to promote the garment industry development.

Momentum Advection on a Staggered Mesh

NASA Astrophysics Data System (ADS)

Benson, David J.

1992-05-01

Eulerian and ALE (arbitrary Lagrangian-Eulerian) hydrodynamics programs usually split a timestep into two parts. The first part is a Lagrangian step, which calculates the incremental motion of the material. The second part is referred to as the Eulerian step, the advection step, or the remap step, and it accounts for the transport of material between cells. In most finite difference and finite element formulations, all the solution variables except the velocities are cell-centered while the velocities are edge- or vertex-centered. As a result, the advection algorithm for the momentum is, by necessity, different than the algorithm used for the other variables. This paper reviews three momentum advection methods and proposes a new one. One method, pioneered in YAQUI, creates a new staggered mesh, while the other two, used in SALE and SHALE, are cell-centered. The new method is cell-centered and its relationship to the other methods is discussed. Both pure advection and strong shock calculations are presented to substantiate the mathematical analysis. From the standpoint of numerical accuracy, both the staggered mesh and the cell-centered algorithms can give good results, while the computational costs are highly dependent on the overall architecture of a code.

Closed-form summations of Dowker's and related trigonometric sums

NASA Astrophysics Data System (ADS)

Cvijović, Djurdje; Srivastava, H. M.

2012-09-01

Through a unified and relatively simple approach which uses complex contour integrals, particularly convenient integration contours and calculus of residues, closed-form summation formulas for 12 very general families of trigonometric sums are deduced. One of them is a family of cosecant sums which was first summed in closed form in a series of papers by Dowker (1987 Phys. Rev. D 36 3095-101 1989 J. Math. Phys. 30 770-3 1992 J. Phys. A: Math. Gen. 25 2641-8), whose method has inspired our work in this area. All of the formulas derived here involve the higher-order Bernoulli polynomials. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker's 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’.

Approach to Computer Implementation of Mathematical Model of 3-Phase Induction Motor

NASA Astrophysics Data System (ADS)

Pustovetov, M. Yu

2018-03-01

This article discusses the development of the computer model of an induction motor based on the mathematical model in a three-phase stator reference frame. It uses an approach that allows combining during preparation of the computer model dual methods: means of visual programming circuitry (in the form of electrical schematics) and logical one (in the form of block diagrams). The approach enables easy integration of the model of an induction motor as part of more complex models of electrical complexes and systems. The developed computer model gives the user access to the beginning and the end of a winding of each of the three phases of the stator and rotor. This property is particularly important when considering the asymmetric modes of operation or when powered by the special circuitry of semiconductor converters.

An Introduction to Kristof's Theorem for Solving Least-Square Optimization Problems Without Calculus.

PubMed

Waller, Niels

2018-01-01

Kristof's Theorem (Kristof, 1970 ) describes a matrix trace inequality that can be used to solve a wide-class of least-square optimization problems without calculus. Considering its generality, it is surprising that Kristof's Theorem is rarely used in statistics and psychometric applications. The underutilization of this method likely stems, in part, from the mathematical complexity of Kristof's ( 1964 , 1970 ) writings. In this article, I describe the underlying logic of Kristof's Theorem in simple terms by reviewing four key mathematical ideas that are used in the theorem's proof. I then show how Kristof's Theorem can be used to provide novel derivations to two cognate models from statistics and psychometrics. This tutorial includes a glossary of technical terms and an online supplement with R (R Core Team, 2017 ) code to perform the calculations described in the text.

Academic self-concept, learning motivation, and test anxiety of the underestimated student.

PubMed

Urhahne, Detlef; Chao, Sheng-Han; Florineth, Maria Luise; Luttenberger, Silke; Paechter, Manuela

2011-03-01

BACKGROUND. Teachers' judgments of student performance on a standardized achievement test often result in an overestimation of students' abilities. In the majority of cases, a larger group of overestimated students and a smaller group of underestimated students are formed by these judgments. AIMS. In this research study, the consequences of the underestimation of students' mathematical performance potential were examined. SAMPLE. Two hundred and thirty-five fourth grade students and their fourteen mathematics teachers took part in the investigation. METHOD. Students worked on a standardized mathematics achievement test and completed a self-description questionnaire about motivation and affect. Teachers estimated each individual student's potential with regard to mathematics test performance as well as students' expectancy for success, level of aspiration, academic self-concept, learning motivation, and test anxiety. The differences between teachers' judgments on students' test performance and students' actual performance were used to build groups of underestimated and overestimated students. RESULTS. Underestimated students displayed equal levels of test performance, learning motivation, and level of aspiration in comparison with overestimated students, but had lower expectancy for success, lower academic self-concept, and experienced more test anxiety. Teachers expected that underestimated students would receive lower grades on the next mathematics test, believed that students were satisfied with lower grades, and assumed that the students have weaker learning motivation than their overestimated classmates. CONCLUSION. Teachers' judgment error was not confined to test performance but generalized to motivational and affective traits of the students. © 2010 The British Psychological Society.

The Opinions of Middle School Mathematics Teachers on the Integration of Mathematics Course and Social Issues

ERIC Educational Resources Information Center

Turhan Turkkan, Buket; Karakus, Memet

2018-01-01

The purpose of this study is to examine the opinions of middle school mathematics teachers on the integration of mathematics course and social issues. For this purpose, qualitative research method was used in this study. As for determining the participants of the research, criterion sampling among purposeful sampling methods was used. Being a…

Investigating Mathematics Self-Efficacy Beliefs of Elementary Pre-Service Teachers in a Reform-Based Mathematics Methods Course

ERIC Educational Resources Information Center

Setra, Abdelghani

2017-01-01

For the last thirty years research has unfailingly shown that teacher efficacy has a positive impact on student outcomes, making teacher efficacy an critical element in quality mathematics instruction. The purpose of this study is to examine the impact of a math methods course on the mathematics teaching efficacy beliefs of elementary pre-service…

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

ERIC Educational Resources Information Center

Ciltas, Alper; Isik, Ahmet

2013-01-01

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

Teaching by Open-Approach Method in Japanese Mathematics Classroom.

ERIC Educational Resources Information Center

Nohda, Nobuhiko

Mathematics educators in Japan have traditionally emphasized mathematical perspectives in research and practice. This paper features an account of changes in mathematics education in Japan that focus on the possibilities of individual students as well as their mathematical ways of thinking. Students' mathematical thinking, mathematical…

Mathematics and statistics research progress report, period ending June 30, 1983

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

Beauchamp, J. J.; Denson, M. V.; Heath, M. T.

1983-08-01

This report is the twenty-sixth in the series of progress reports of Mathematics and Statistics Research of the Computer Sciences organization, Union Carbide Corporation Nuclear Division. Part A records research progress in analysis of large data sets, applied analysis, biometrics research, computational statistics, materials science applications, numerical linear algebra, and risk analysis. Collaboration and consulting with others throughout the Oak Ridge Department of Energy complex are recorded in Part B. Included are sections on biological sciences, energy, engineering, environmental sciences, health and safety, and safeguards. Part C summarizes the various educational activities in which the staff was engaged. Part Dmore » lists the presentations of research results, and Part E records the staff's other professional activities during the report period.« less

Pre-Service Secondary Mathematics Teachers' Reflections on Good and Bad Mathematics Teaching

ERIC Educational Resources Information Center

Dayal, Hem Chand

2013-01-01

Researchers suggest that teachers' beliefs about teaching are strongly influenced by their personal experiences with mathematics. This study aimed to explore Pacific Island pre-service secondary mathematics teachers' perceptions about good and bad mathematics teachers. Thirty pre-service teachers, enrolled in a mathematics teaching methods course…

The Mathematics Education Debates: Preparing Students to Become Professionally Active Mathematics Teachers

ERIC Educational Resources Information Center

Munakata, Mika

2010-01-01

The Mathematics Education Debate is an assignment designed for and implemented in an undergraduate mathematics methods course for prospective secondary school mathematics teachers. For the assignment, students read and analyze current research and policy reports related to mathematics education, prepare and present their positions, offer…

An Exploratory Study of Taiwanese Mathematics Teachers' Conceptions of School Mathematics, School Statistics, and Their Differences

ERIC Educational Resources Information Center

Yang, Kai-Lin

2014-01-01

This study used phenomenography, a qualitative method, to investigate Taiwanese mathematics teachers' conceptions of school mathematics, school statistics, and their differences. To collect data, we interviewed five mathematics teachers by open questions. They also responded to statements drawn on mathematical/statistical conceptions and…

Efficacy of the Cooperative Learning Method on Mathematics Achievement and Attitude: A Meta-Analysis Research

ERIC Educational Resources Information Center

Capar, Gulfer; Tarim, Kamuran

2015-01-01

This research compiles experimental studies from 1988 to 2010 that examined the influence of the cooperative learning method, as compared with that of traditional methods, on mathematics achievement and on attitudes towards mathematics. The related field was searched using the following key words in Turkish "matematik ve isbirlikli ögrenme,…

Examinations in the Final Year of Transition to Mathematical Methods Computer Algebra System (CAS)

ERIC Educational Resources Information Center

Leigh-Lancaster, David; Les, Magdalena; Evans, Michael

2010-01-01

2009 was the final year of parallel implementation for Mathematical Methods Units 3 and 4 and Mathematical Methods (CAS) Units 3 and 4. From 2006-2009 there was a common technology-free short answer examination that covered the same function, algebra, calculus and probability content for both studies with corresponding expectations for key…

Didactic Aspects of the Academic Discipline "History and Methodology of Mathematics"

ERIC Educational Resources Information Center

Sun, Hai; Varankina, Vera I.; Sadovaya, Victoriya V.

2017-01-01

The purpose of this article is to develop the content and methods, as well as the analysis of the approbation of the program of the academic discipline "History and methodology of mathematics" for graduate students of the Master's program of mathematical program tracks. The leading method in the study of this problem was the method of…

Using the Scientific Method to Engage Mathematical Modeling: An Investigation of pi

ERIC Educational Resources Information Center

Archer, Lester A. C.; Ng, Karen E.

2016-01-01

The purpose of this paper is to explain how to use the scientific method as the framework to introduce mathematical model. Two interdisciplinary activities, targeted for students in grade 6 or grade 7, are explained to show the application of the scientific method while building a mathematical model to investigate the relationship between the…

Reflections from the Application of Different Type of Activities: Special Training Methods Course

ERIC Educational Resources Information Center

Karadeniz, Mihriban Hacisalihoglu

2017-01-01

The aim of this study is to reveal the benefits gained from "Special Training Methods II" course and the problems prospective mathematics teachers encountered with it. The case study method was used in the study. The participants in the study were 34 prospective mathematics teachers studying at a Primary School Mathematics Education…

Integrating to Learn and Learning to Integrate: A Case Study of an Online Master's Program on Science-Mathematics Integration for Middle School Teachers

ERIC Educational Resources Information Center

Lee, Mimi Miyoung; Chauvot, Jennifer; Plankis, Brian; Vowell, Julie; Culpepper, Shea

2011-01-01

iSMART (Integration of Science, Mathematics, and Reflective Teaching) Program is an online science and mathematics integrated graduate program for middle school teachers across the state of Texas. As part of a large design-based research project, this paper describes the initial stages of the design process of the iSMART program for its first…

The effectiveness of resources created by students as partners in explaining the relevance of mathematics in engineering education

NASA Astrophysics Data System (ADS)

Dunn, Michelle; Loch, Birgit; Scott, Wendy

2018-01-01

First-year engineering students often struggle to see the relevance of theoretical mathematical concepts for their future studies and professional careers. This is an issue, as students who do not see relevance in fundamental parts of their studies may disengage from these parts and focus their efforts on other subjects they think will be more useful to them. In this study, we surveyed engineering students enrolled in a first-year mathematics subject on their perceptions of the relevance of the individual mathematical topics taught. Surveys were administered at the start of semester when some of these topics were unknown to them, and again at the end of semester when students had not only studied all these topics but also watched a set of animated videos. These videos had been produced by higher-year students to explain where they had seen applications of the mathematical concepts presented in the first year. We notice differences between the perceived relevance of topics for future study and for professional careers, with relevance to study rated higher than relevance to careers. We also find that the animations are seen as helpful in understanding the relevance of first-year mathematics. The majority of students indicated that lecturers with students as partners should work collaboratively to produce future videos.

TIMSS Advanced 2015 Assessment Frameworks

ERIC Educational Resources Information Center

Mullis, Ina V. S., Ed.; Martin, Michael O., Ed.

2014-01-01

The "TIMSS Advanced 2015 Assessment Frameworks" provides the foundation for the two international assessments to take place as part of the International Association for the Evaluation of Educational Achievement's TIMSS (Trends in International Mathematics and Science Study) Advanced 2015--Advanced Mathematics and Physics. Chapter 1 (Liv…

Integrating Mathematics throughout the Curriculum: Using the Poetry of Shel Silverstein.

ERIC Educational Resources Information Center

Caniglia, Joanne

1997-01-01

Suggests several activities integrating mathematics with literature, the poems of Shel Silverstein in particular. Activities can also be used as part of a classroom's Earth Day celebration to help make an impression about responsibility to care for the earth. (AIM)

The Positioning Accuracy of BAUV Using Fusion of Data from USBL System and Movement Parameters Measurements

PubMed Central

Krzysztof, Naus; Aleksander, Nowak

2016-01-01

The article presents a study of the accuracy of estimating the position coordinates of BAUV (Biomimetic Autonomous Underwater Vehicle) by the extended Kalman filter (EKF) method. The fusion of movement parameters measurements and position coordinates fixes was applied. The movement parameters measurements are carried out by on-board navigation devices, while the position coordinates fixes are done by the USBL (Ultra Short Base Line) system. The problem of underwater positioning and the conceptual design of the BAUV navigation system constructed at the Naval Academy (Polish Naval Academy—PNA) are presented in the first part of the paper. The second part consists of description of the evaluation results of positioning accuracy, the genesis of the problem of selecting method for underwater positioning, and the mathematical description of the method of estimating the position coordinates using the EKF method by the fusion of measurements with on-board navigation and measurements obtained with the USBL system. The main part contains a description of experimental research. It consists of a simulation program of navigational parameter measurements carried out during the BAUV passage along the test section. Next, the article covers the determination of position coordinates on the basis of simulated parameters, using EKF and DR methods and the USBL system, which are then subjected to a comparative analysis of accuracy. The final part contains systemic conclusions justifying the desirability of applying the proposed fusion method of navigation parameters for the BAUV positioning. PMID:27537884

The Positioning Accuracy of BAUV Using Fusion of Data from USBL System and Movement Parameters Measurements.

PubMed

Krzysztof, Naus; Aleksander, Nowak

2016-08-15

The article presents a study of the accuracy of estimating the position coordinates of BAUV (Biomimetic Autonomous Underwater Vehicle) by the extended Kalman filter (EKF) method. The fusion of movement parameters measurements and position coordinates fixes was applied. The movement parameters measurements are carried out by on-board navigation devices, while the position coordinates fixes are done by the USBL (Ultra Short Base Line) system. The problem of underwater positioning and the conceptual design of the BAUV navigation system constructed at the Naval Academy (Polish Naval Academy-PNA) are presented in the first part of the paper. The second part consists of description of the evaluation results of positioning accuracy, the genesis of the problem of selecting method for underwater positioning, and the mathematical description of the method of estimating the position coordinates using the EKF method by the fusion of measurements with on-board navigation and measurements obtained with the USBL system. The main part contains a description of experimental research. It consists of a simulation program of navigational parameter measurements carried out during the BAUV passage along the test section. Next, the article covers the determination of position coordinates on the basis of simulated parameters, using EKF and DR methods and the USBL system, which are then subjected to a comparative analysis of accuracy. The final part contains systemic conclusions justifying the desirability of applying the proposed fusion method of navigation parameters for the BAUV positioning.

Time Analysis of Building Dynamic Response Under Seismic Action. Part 1: Theoretical Propositions

NASA Astrophysics Data System (ADS)

Ufimtcev, E. M.

2017-11-01

The first part of the article presents the main provisions of the analytical approach - the time analysis method (TAM) developed for the calculation of the elastic dynamic response of rod structures as discrete dissipative systems (DDS) and based on the investigation of the characteristic matrix quadratic equation. The assumptions adopted in the construction of the mathematical model of structural oscillations as well as the features of seismic forces’ calculating and recording based on the data of earthquake accelerograms are given. A system to resolve equations is given to determine the nodal (kinematic and force) response parameters as well as the stress-strain state (SSS) parameters of the system’s rods.

Research on particulate filter simulation and regeneration control strategy

NASA Astrophysics Data System (ADS)

Dawei, Qu; Jun, Li; Yu, Liu

2017-03-01

This paper reports a DPF (Diesel Particulate Filter) collection mathematical model for a new regeneration control strategy. The new strategy is composed by main parts, such as regeneration time capturing, temperature rising strategy and regeneration control strategy. In the part of regeneration time capturing, a multi-level regeneration capturing method is put forward based on the combined effect of the PM (Particulate Matter) loading, pressure drop and fuel consumption. The temperature rising strategy proposes the global temperature for all operating conditions. The regeneration control process considers the particle loading density, temperature and oxygen respectively. Based on the analysis of the initial overheating, runaway temperature and local hot spot, the final control strategy is established.

New method for springback compensation for the stamping of sheet metal components

NASA Astrophysics Data System (ADS)

Birkert, A.; Hartmann, B.; Straub, M.

2017-09-01

The need for car body structures of higher strength and at the same time lower weight results in serious challenges for the stamping process. Especially the use of high strength steel and aluminium sheets is causing growing problems with regard to elastic springback. To produce accurate parts the stamping dies must be adjusted more or less by the amount of the springback in the opposite direction. For this purpose well-known software solutions use the Displacement Adjustment Method or algorithms which are closely based on that method. A crucial issue of this method is that the generated die surfaces deviate from those of the target geometry with regard to surface area. A new Physical Compensation Method has been developed and validated which takes geometrical nonlinearity into account and creates compensated die geometries with equal-in-area die surfaces. In contrast to the standard mathematical/geometrical approach, the adjusted geometry is generated by a physical approach, which makes use of the virtual part stiffness. Hereby the target geometry is being deformed mechanically in a virtual process based on the springback simulation results by applying virtual forces in an additional elastic simulation. By doing so better part dimensions can be obtained in less tool optimization loops.

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

NASA Astrophysics Data System (ADS)

Wardono; Mariani, S.

2018-03-01

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

Sensorimotor coordination and the structure of space.

PubMed

McCollum, Gin

2003-01-01

Embedded in neural and behavioral organization is a structure of sensorimotor space. Both this embedded spatial structure and the structure of physical space inform sensorimotor control. This paper reviews studies in which the gravitational vertical and horizontal are crucial. The mathematical expressions of spatial geometry in these studies indicate methods for investigating sensorimotor control in freefall. In freefall, the spatial structure introduced by gravitation - the distinction between vertical and horizontal - does not exist. However, an astronaut arriving in space carries the physiologically-embedded distinction between horizontal and vertical learned on earth. The physiological organization based on this distinction collapses when the strong otolith activity and other gravitational cues for sensorimotor behavior become unavailable. The mathematical methods in this review are applicable in understanding the changes in physiological organization as an astronaut adapts to sensorimotor control in freefall. Many mathematical languages are available for characterizing the logical structures in physiological organization. Here, group theory is used to characterize basic structure of physical and physiological spaces. Dynamics and topology allow the grouping of trajectory ranges according to the outcomes or attractors. The mathematics of ordered structures express complex orderings, such as in multiphase movements in which different parts of the body are moving in different phase sequences. Conditional dynamics, which combines dynamics with the mathematics of ordered structures, accommodates the parsing of movement sequences into trajectories and transitions. Studies reviewed include those of the sit-to-stand movement and early locomotion, because of the salience of gravitation in those behaviors. Sensorimotor transitions and the conditions leading to them are characterized in conditional dynamic control structures that do not require thinking of an organism as an input-output device. Conditions leading to sensorimotor transitions on earth assume the presence of a gravitational vertical which is lacking in space. Thus, conditions used on earth for sensorimotor transitions may become ambiguous in space. A platform study in which sensorimotor transition conditions are ambiguous and are related to motion sickness is reviewed.

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

Mathematics is always invisible, Professor Dowling

NASA Astrophysics Data System (ADS)

Cable, John

2015-09-01

This article provides a critical evaluation of a technique of analysis, the Social Activity Method, recently offered by Dowling (2013) as a `gift' to mathematics education. The method is found to be inadequate, firstly, because it employs a dichotomy (between `expression' and `content') instead of a finer analysis (into symbols, concepts and setting or phenomena), and, secondly, because the distinction between `public' and `esoteric' mathematics, although interesting, is allowed to obscure the structure of the mathematics itself. There is also criticism of what Dowling calls the `myth of participation', which denies the intimate links between mathematics and the rest of the universe that lie at the heart of mathematical pedagogy. Behind all this lies Dowling's `essentially linguistic' conception of mathematics, which is criticised on the dual ground that it ignores the chastening experience of formalism in mathematical philosophy and that linguistics itself has taken a wrong turn and ignores lessons that might be learnt from mathematics education.

A Multiple Intelligence Pedagogical Approach in Fifth Grade Mathematics: A Mixed Method Study

ERIC Educational Resources Information Center

Davis, Claudine Davillier

2012-01-01

The need for mathematics intervention has increased tremendously over the years, particularly after the No Child Left Behind Act of 2001.Students who lack basic mathematics skills and students who experience mathematics difficulties greatly benefit from mathematics interventions. This study examined mathematics intervention through the use of the…

Peirce's Philosophy of Mathematical Education: Fostering Reasoning Abilities for Mathematical Inquiry

ERIC Educational Resources Information Center

Campos, Daniel G.

2010-01-01

I articulate Charles S. Peirce's philosophy of mathematical education as related to his conception of mathematics, the nature of its method of inquiry, and especially, the reasoning abilities required for mathematical inquiry. The main thesis is that Peirce's philosophy of mathematical education primarily aims at fostering the development of the…

Endobiogeny: a global approach to systems biology (part 1 of 2).

PubMed

Lapraz, Jean-Claude; Hedayat, Kamyar M

2013-01-01

Endobiogeny is a global systems approach to human biology that may offer an advancement in clinical medicine based in scientific principles of rigor and experimentation and the humanistic principles of individualization of care and alleviation of suffering with minimization of harm. Endobiogeny is neither a movement away from modern science nor an uncritical embracing of pre-rational methods of inquiry but a synthesis of quantitative and qualitative relationships reflected in a systems-approach to life and based on new mathematical paradigms of pattern recognition.

Assessing metacognition of grade 2 and grade 4 students using an adaptation of multi-method interview approach during mathematics problem-solving

NASA Astrophysics Data System (ADS)

Kuzle, A.

2018-06-01

The important role that metacognition plays as a predictor for student mathematical learning and for mathematical problem-solving, has been extensively documented. But only recently has attention turned to primary grades, and more research is needed at this level. The goals of this paper are threefold: (1) to present metacognitive framework during mathematics problem-solving, (2) to describe their multi-method interview approach developed to study student mathematical metacognition, and (3) to empirically evaluate the utility of their model and the adaptation of their approach in the context of grade 2 and grade 4 mathematics problem-solving. The results are discussed not only with regard to further development of the adapted multi-method interview approach, but also with regard to their theoretical and practical implications.

Listening to Early Career Teachers: How Can Elementary Mathematics Methods Courses Better Prepare Them to Utilize Standards-Based Practices in Their Classrooms?

ERIC Educational Resources Information Center

Coester, Lee Anne

2010-01-01

This study was designed to gather input from early career elementary teachers with the goal of finding ways to improve elementary mathematics methods courses. Multiple areas were explored including the degree to which respondents' elementary mathematics methods course focused on the NCTM Process Standards, the teachers' current standards-based…

EQUALS Investigations: Remote Rulers.

ERIC Educational Resources Information Center

Mayfield, Karen; Whitlow, Robert

EQUALS is a teacher education program that helps elementary and secondary educators acquire methods and materials to attract minority and female students to mathematics. It supports a problem-solving approach to mathematics which has students working in groups, uses active assessment methods, and incorporates a broad mathematics curriculum…

Two Meanings of Algorithmic Mathematics.

ERIC Educational Resources Information Center

Maurer, Stephen B.

1984-01-01

Two mathematical topics are interpreted from the viewpoints of traditional (performing algorithms) and contemporary (creating algorithms and thinking in terms of them for solving problems and developing theory) algorithmic mathematics. The two topics are Horner's method for evaluating polynomials and Gauss's method for solving systems of linear…

Research in Mathematics Education: Multiple Methods for Multiple Uses

ERIC Educational Resources Information Center

Battista, Michael; Smith, Margaret S.; Boerst, Timothy; Sutton, John; Confrey, Jere; White, Dorothy; Knuth, Eric; Quander, Judith

2009-01-01

Recent federal education policies and reports have generated considerable debate about the meaning, methods, and goals of "scientific research" in mathematics education. Concentrating on the critical problem of determining which educational programs and practices reliably improve students' mathematics achievement, these policies and reports focus…

Laser-induced plasma spectroscopy (LIPS): use of a geological tool in assessing bone mineral content.

PubMed

Andrássy, László; Gomez, Izabella; Horváth, Ágnes; Gulyás, Katalin; Pethö, Zsófia; Juhász, Balázs; Bhattoa, Harjit Pal; Szekanecz, Zoltan

2018-02-17

Bone may be similar to geological formulations in many ways. Therefore, it may be logical to apply laser-based geological techniques in bone research. The mineral and element oxide composition of bioapatite can be estimated by mathematical models. Laser-induced plasma spectrometry (LIPS) has long been used in geology. This method may provide a possibility to determine the composition and concentration of element oxides forming the inorganic part of bones. In this study, we wished to standardize the LIPS technique and use mathematical calculations and models in order to determine CaO distribution and bone homogeneity using bovine shin bone samples. We used polished slices of five bovine shin bones. A portable LIPS instrument using high-power Nd++YAG laser pulses has been developed (OpLab, Budapest). Analysis of CaO distribution was carried out in a 10 × 10 sampling matrix applying 300-μm sampling intervals. We assessed both cortical and trabecular bone areas. Regions of interest (ROI) were determined under microscope. CaO peaks were identified in the 200-500 nm wavelength range. A mathematical formula was used to calculate the element oxide composition (wt%) of inorganic bone. We also applied two accepted mathematical approaches, the Bartlett's test and frequency distribution curve-based analysis, to determine the homogeneity of CaO distribution in bones. We were able to standardize the LIPS technique for bone research. CaO concentrations in the cortical and trabecular regions of B1-5 bones were 33.11 ± 3.99% (range 24.02-40.43%) and 27.60 ± 7.44% (range 3.58-39.51%), respectively. CaO concentrations highly corresponded to those routinely determined by ICP-OES. We were able to graphically demonstrate CaO distribution in both 2D and 3D. We also determined possible interrelations between laser-induced craters and bone structure units, which may reflect the bone structure and may influence the heterogeneity of CaO distributions. By using two different statistical methods, we could confirm if bone samples were homogeneous or not with respect to CaO concentration distribution. LIPS, a technique previously used in geology, may be included in bone research. Assessment of element oxide concentrations in the inorganic part of bone, as well as mathematical calculations may be useful to determine the content of CaO and other element oxides in bone, further analyze bone structure and homogeneity and possibly apply this research to normal, as well as diseased bones.

The Mathematical Education of Engineers.

ERIC Educational Resources Information Center

Gnedenko, B. V.; Khalil, Z.

1979-01-01

Several general aspects are discussed. These include the role of mathematics in scientific and technical progress, some deficiencies in training, the role of mathematics in engineering faculties, and methods of improving mathematical training. (MP)

Motor-Enriched Learning Activities Can Improve Mathematical Performance in Preadolescent Children.

PubMed

Beck, Mikkel M; Lind, Rune R; Geertsen, Svend S; Ritz, Christian; Lundbye-Jensen, Jesper; Wienecke, Jacob

2016-01-01

Objective: An emerging field of research indicates that physical activity can benefit cognitive functions and academic achievements in children. However, less is known about how academic achievements can benefit from specific types of motor activities (e.g., fine and gross) integrated into learning activities. Thus, the aim of this study was to investigate whether fine or gross motor activity integrated into math lessons (i.e., motor-enrichment) could improve children's mathematical performance. Methods: A 6-week within school cluster-randomized intervention study investigated the effects of motor-enriched mathematical teaching in Danish preadolescent children ( n = 165, age = 7.5 ± 0.02 years). Three groups were included: a control group (CON), which received non-motor enriched conventional mathematical teaching, a fine motor math group (FMM) and a gross motor math group (GMM), which received mathematical teaching enriched with fine and gross motor activity, respectively. The children were tested before (T0), immediately after (T1) and 8 weeks after the intervention (T2). A standardized mathematical test (50 tasks) was used to evaluate mathematical performance. Furthermore, it was investigated whether motor-enriched math was accompanied by different effects in low and normal math performers. Additionally, the study investigated the potential contribution of cognitive functions and motor skills on mathematical performance. Results: All groups improved their mathematical performance from T0 to T1. However, from T0 to T1, the improvement was significantly greater in GMM compared to FMM (1.87 ± 0.71 correct answers) ( p = 0.02). At T2 no significant differences in mathematical performance were observed. A subgroup analysis revealed that normal math-performers benefitted from GMM compared to both CON 1.78 ± 0.73 correct answers ( p = 0.04) and FMM 2.14 ± 0.72 correct answers ( p = 0.008). These effects were not observed in low math-performers. The effects were partly accounted for by visuo-spatial short-term memory and gross motor skills. Conclusion: The study demonstrates that motor enriched learning activities can improve mathematical performance. In normal math performers GMM led to larger improvements than FMM and CON. This was not the case for the low math performers. Future studies should further elucidate the neurophysiological mechanisms underlying the observed behavioral effects.

Motor-Enriched Learning Activities Can Improve Mathematical Performance in Preadolescent Children

PubMed Central

Beck, Mikkel M.; Lind, Rune R.; Geertsen, Svend S.; Ritz, Christian; Lundbye-Jensen, Jesper; Wienecke, Jacob

2016-01-01

Objective: An emerging field of research indicates that physical activity can benefit cognitive functions and academic achievements in children. However, less is known about how academic achievements can benefit from specific types of motor activities (e.g., fine and gross) integrated into learning activities. Thus, the aim of this study was to investigate whether fine or gross motor activity integrated into math lessons (i.e., motor-enrichment) could improve children's mathematical performance. Methods: A 6-week within school cluster-randomized intervention study investigated the effects of motor-enriched mathematical teaching in Danish preadolescent children (n = 165, age = 7.5 ± 0.02 years). Three groups were included: a control group (CON), which received non-motor enriched conventional mathematical teaching, a fine motor math group (FMM) and a gross motor math group (GMM), which received mathematical teaching enriched with fine and gross motor activity, respectively. The children were tested before (T0), immediately after (T1) and 8 weeks after the intervention (T2). A standardized mathematical test (50 tasks) was used to evaluate mathematical performance. Furthermore, it was investigated whether motor-enriched math was accompanied by different effects in low and normal math performers. Additionally, the study investigated the potential contribution of cognitive functions and motor skills on mathematical performance. Results: All groups improved their mathematical performance from T0 to T1. However, from T0 to T1, the improvement was significantly greater in GMM compared to FMM (1.87 ± 0.71 correct answers) (p = 0.02). At T2 no significant differences in mathematical performance were observed. A subgroup analysis revealed that normal math-performers benefitted from GMM compared to both CON 1.78 ± 0.73 correct answers (p = 0.04) and FMM 2.14 ± 0.72 correct answers (p = 0.008). These effects were not observed in low math-performers. The effects were partly accounted for by visuo-spatial short-term memory and gross motor skills. Conclusion: The study demonstrates that motor enriched learning activities can improve mathematical performance. In normal math performers GMM led to larger improvements than FMM and CON. This was not the case for the low math performers. Future studies should further elucidate the neurophysiological mechanisms underlying the observed behavioral effects. PMID:28066215

Guided discovery learning in geometry learning

NASA Astrophysics Data System (ADS)

Khasanah, V. N.; Usodo, B.; Subanti, S.

2018-03-01

Geometry is a part of the mathematics that must be learned in school. The purpose of this research was to determine the effect of Guided Discovery Learning (GDL) toward geometry learning achievement. This research had conducted at junior high school in Sukoharjo on academic years 2016/2017. Data collection was done based on student’s work test and documentation. Hypothesis testing used two ways analysis of variance (ANOVA) with unequal cells. The results of this research that GDL gave positive effect towards mathematics learning achievement. GDL gave better mathematics learning achievement than direct learning. There was no difference of mathematics learning achievement between male and female. There was no an interaction between sex differences and learning models toward student’s mathematics learning achievement. GDL can be used to improve students’ mathematics learning achievement in geometry.

10 CFR Appendix B to Part 73 - General Criteria for Security Personnel

Code of Federal Regulations, 2012 CFR

2012-01-01

... or pass an equivalent performance examination designed to measure basic job-related mathematical... equivalent performance examination designed to measure basic mathematical, language, and reasoning skills... administered by a licensed physician. The examination shall be designed to measure the individual's physical...

Teaching Secondary Mathematics. Second Edition.

ERIC Educational Resources Information Center

Brumbaugh, Douglas K.; Rock, David

This book for future mathematics teachers emphasizes technology as a teaching tool; development of teachers who are self-motivated, lifelong learners; and pedagogical features that engage and motivate students. It includes examples and activities to enhance learning. Part 1, "General Fundamentals," includes (1) "Introduction"; (2) "Learning,…

39 CFR 3050.1 - Definitions applicable to this part.

Code of Federal Regulations, 2010 CFR

2010-07-01

..., mathematical, or statistical theory, precept, or assumption applied by the Postal Service in producing a... manipulation technique whose validity does not require the acceptance of a particular economic, mathematical, or statistical theory, precept, or assumption. A change in quantification technique should not change...

A Literature Approach to Middle Grade Math.

ERIC Educational Resources Information Center

Greenlaw, M. Jean; Tipps, Steve

1997-01-01

Suggests ways that teachers can use picture books, chapter books, poems, newspapers, and reference materials to fulfill the National Council of Teachers of Mathematics 1989 curriculum standards which state that problem solving, reasoning, communications, and connections should be part of every mathematics learning experience. Discusses number…

Ikons for Mathematics, Part I. Problem Solving and Strategy Games.

ERIC Educational Resources Information Center

Melrose, Jean; Rowe, Susan

1989-01-01

Described are some designs in the playground of an infant school, and indicated are some mathematical activities that resulted from their use. Games included are Schlegel diagram of Dodecahedron, Pong Hau K'i, Ko No, Achi, Draughts, and Star with their diagrams. (YP)

The TIMSS Videotape Study.

ERIC Educational Resources Information Center

Stigler, James W.; Hiebert, James

1998-01-01

As part of the Third International Mathematics and Science Study (TIMSS), videotapes of classroom instruction were collected from 231 eighth-grade mathematics classrooms in Germany, the United States, and Japan. Findings suggest that written reports about teaching disseminated to teachers may have little effect on classroom practices. (SLD)

Optimizing lighting, thermal performance, and energy production of building facades by using automated blinds and PV cells

NASA Astrophysics Data System (ADS)

Alzoubi, Hussain Hendi

Energy consumption in buildings has recently become a major concern for environmental designers. Within this field, daylighting and solar energy design are attractive strategies for saving energy. This study seeks the integrity and the optimality of building envelopes' performance. It focuses on the transparent parts of building facades, specifically, the windows and their shading devices. It suggests a new automated method of utilizing solar energy while keeping optimal solutions for indoor daylighting. The method utilizes a statistical approach to produce mathematical equations based on physical experimentation. A full-scale mock-up representing an actual office was built. Heat gain and lighting levels were measured empirically and correlated with blind angles. Computational methods were used to estimate the power production from photovoltaic cells. Mathematical formulas were derived from the results of the experiments; these formulas were utilized to construct curves as well as mathematical equations for the purpose of optimization. The mathematical equations resulting from the optimization process were coded using Java programming language to enable future users to deal with generic locations of buildings with a broader context of various climatic conditions. For the purpose of optimization by automation under different climatic conditions, a blind control system was developed based on the findings of this study. This system calibrates the blind angles instantaneously based upon the sun position, the indoor daylight, and the power production from the photovoltaic cells. The functions of this system guarantee full control of the projected solar energy on buildings' facades for indoor lighting and heat gain. In winter, the system automatically blows heat into the space, whereas it expels heat from the space during the summer season. The study showed that the optimality of building facades' performance is achievable for integrated thermal, energy, and lighting models in buildings. There are blind angles that produce maximum energy from the photovoltaic cells while keeping indoor light within the acceptable limits that prevent undesired heat gain in summer.

Thermostatted kinetic equations as models for complex systems in physics and life sciences.

PubMed

Bianca, Carlo

2012-12-01

Statistical mechanics is a powerful method for understanding equilibrium thermodynamics. An equivalent theoretical framework for nonequilibrium systems has remained elusive. The thermodynamic forces driving the system away from equilibrium introduce energy that must be dissipated if nonequilibrium steady states are to be obtained. Historically, further terms were introduced, collectively called a thermostat, whose original application was to generate constant-temperature equilibrium ensembles. This review surveys kinetic models coupled with time-reversible deterministic thermostats for the modeling of large systems composed both by inert matter particles and living entities. The introduction of deterministic thermostats allows to model the onset of nonequilibrium stationary states that are typical of most real-world complex systems. The first part of the paper is focused on a general presentation of the main physical and mathematical definitions and tools: nonequilibrium phenomena, Gauss least constraint principle and Gaussian thermostats. The second part provides a review of a variety of thermostatted mathematical models in physics and life sciences, including Kac, Boltzmann, Jager-Segel and the thermostatted (continuous and discrete) kinetic for active particles models. Applications refer to semiconductor devices, nanosciences, biological phenomena, vehicular traffic, social and economics systems, crowds and swarms dynamics. Copyright © 2012 Elsevier B.V. All rights reserved.

Post-primary students' images of mathematics: findings from a survey of Irish ordinary level mathematics students

NASA Astrophysics Data System (ADS)

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

2016-10-01

A questionnaire survey was carried out as part of a PhD research study to investigate the image of mathematics held by post-primary students in Ireland. The study focused on students in fifth year of post-primary education studying ordinary level mathematics for the Irish Leaving Certificate examination - the final examination for students in second-level or post-primary education. At the time this study was conducted, ordinary level mathematics students constituted approximately 72% of Leaving Certificate students. Students were aged between 15 and 18 years. A definition for 'image of mathematics' was adapted from Lim and Wilson, with image of mathematics hypothesized as comprising attitudes, beliefs, self-concept, motivation, emotions and past experiences of mathematics. A questionnaire was composed incorporating 84 fixed-response items chosen from eight pre-established scales by Aiken, Fennema and Sherman, Gourgey and Schoenfeld. This paper focuses on the findings from the questionnaire survey. Students' images of mathematics are compared with regard to gender, type of post-primary school attended and prior mathematical achievement.

Evolution of Supernova Remnants

NASA Astrophysics Data System (ADS)

Arbutina, B.

2017-12-01

This book, both a monograph and a graduate textbook, is based on my original research and partly on the materials prepared earlier for the 2007 and 2008 IARS Astrophysics Summer School in Istanbul, AstroMundus course 'Supernovae and Their Remnants' that was held for the first time in 2011 at the Department of Astronomy, Faculty of Mathematics, University of Belgrade, and a graduate course 'Evolution of Supernova Remnants' that I teach at the aforementioned university. The first part Supernovae (introduction, thermonuclear supernovae, core-collapse supernovae) provides introductory information and explains the classification and physics of supernova explosions, while the second part Supernova remnants (introduction, shock waves, cosmic rays and particle acceleration, magnetic fields, synchrotron radiation, hydrodynamic and radio evolution of supernova remnants), which is the field I work in, is more detailed in scope i.e. technical/mathematical. Special attention is paid to details of mathematical derivations that often cannot be found in original works or available literature. Therefore, I believe it can be useful to both, graduate students and researchers interested in the field.

Cell population heterogeneity and evolution towards drug resistance in cancer: Biological and mathematical assessment, theoretical treatment optimisation.

PubMed

Chisholm, Rebecca H; Lorenzi, Tommaso; Clairambault, Jean

2016-11-01

Drug-induced drug resistance in cancer has been attributed to diverse biological mechanisms at the individual cell or cell population scale, relying on stochastically or epigenetically varying expression of phenotypes at the single cell level, and on the adaptability of tumours at the cell population level. We focus on intra-tumour heterogeneity, namely between-cell variability within cancer cell populations, to account for drug resistance. To shed light on such heterogeneity, we review evolutionary mechanisms that encompass the great evolution that has designed multicellular organisms, as well as smaller windows of evolution on the time scale of human disease. We also present mathematical models used to predict drug resistance in cancer and optimal control methods that can circumvent it in combined therapeutic strategies. Plasticity in cancer cells, i.e., partial reversal to a stem-like status in individual cells and resulting adaptability of cancer cell populations, may be viewed as backward evolution making cancer cell populations resistant to drug insult. This reversible plasticity is captured by mathematical models that incorporate between-cell heterogeneity through continuous phenotypic variables. Such models have the benefit of being compatible with optimal control methods for the design of optimised therapeutic protocols involving combinations of cytotoxic and cytostatic treatments with epigenetic drugs and immunotherapies. Gathering knowledge from cancer and evolutionary biology with physiologically based mathematical models of cell population dynamics should provide oncologists with a rationale to design optimised therapeutic strategies to circumvent drug resistance, that still remains a major pitfall of cancer therapeutics. This article is part of a Special Issue entitled "System Genetics" Guest Editor: Dr. Yudong Cai and Dr. Tao Huang. Copyright © 2016 Elsevier B.V. All rights reserved.

Mathematics and Statistics Research Department progress report, period ending June 30, 1982

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

Denson, M.V.; Funderlic, R.E.; Gosslee, D.G.

1982-08-01

This report is the twenty-fifth in the series of progress reports of the Mathematics and Statistics Research Department of the Computer Sciences Division, Union Carbide Corporation Nuclear Division (UCC-ND). Part A records research progress in analysis of large data sets, biometrics research, computational statistics, materials science applications, moving boundary problems, numerical linear algebra, and risk analysis. Collaboration and consulting with others throughout the UCC-ND complex are recorded in Part B. Included are sections on biology, chemistry, energy, engineering, environmental sciences, health and safety, materials science, safeguards, surveys, and the waste storage program. Part C summarizes the various educational activities inmore » which the staff was engaged. Part D lists the presentations of research results, and Part E records the staff's other professional activities during the report period.« less

Mathematics and statistics research department. Progress report, period ending June 30, 1981

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

Lever, W.E.; Kane, V.E.; Scott, D.S.

1981-09-01

This report is the twenty-fourth in the series of progress reports of the Mathematics and Statistics Research Department of the Computer Sciences Division, Union Carbide Corporation - Nuclear Division (UCC-ND). Part A records research progress in biometrics research, materials science applications, model evaluation, moving boundary problems, multivariate analysis, numerical linear algebra, risk analysis, and complementary areas. Collaboration and consulting with others throughout the UCC-ND complex are recorded in Part B. Included are sections on biology and health sciences, chemistry, energy, engineering, environmental sciences, health and safety research, materials sciences, safeguards, surveys, and uranium resource evaluation. Part C summarizes the variousmore » educational activities in which the staff was engaged. Part D lists the presentations of research results, and Part E records the staff's other professional activities during the report period.« less

EQUALS Investigations: Telling Someone Where To Go.

ERIC Educational Resources Information Center

Mayfield, Karen; Whitlow, Robert

EQUALS is a teacher education program that helps elementary and secondary educators acquire methods and materials to attract minority and female students to mathematics. It supports a problem-solving approach to mathematics which has students working in groups, uses active assessment methods, and incorporates a broad mathematics curriculum…

A transient laboratory method for determining the hydraulic properties of 'tight' rocks-I. Theory

USGS Publications Warehouse

Hsieh, P.A.; Tracy, J.V.; Neuzil, C.E.; Bredehoeft, J.D.; Silliman, Stephen E.

1981-01-01

Transient pulse testing has been employed increasingly in the laboratory to measure the hydraulic properties of rock samples with low permeability. Several investigators have proposed a mathematical model in terms of an initial-boundary value problem to describe fluid flow in a transient pulse test. However, the solution of this problem has not been available. In analyzing data from the transient pulse test, previous investigators have either employed analytical solutions that are derived with the use of additional, restrictive assumptions, or have resorted to numerical methods. In Part I of this paper, a general, analytical solution for the transient pulse test is presented. This solution is graphically illustrated by plots of dimensionless variables for several cases of interest. The solution is shown to contain, as limiting cases, the more restrictive analytical solutions that the previous investigators have derived. A method of computing both the permeability and specific storage of the test sample from experimental data will be presented in Part II. ?? 1981.

Vectorial method used to monitor an evolving system: Titanium oxide thin films under UV illumination

NASA Astrophysics Data System (ADS)

Béchu, Solène; Humbert, Bernard; Fernandez, Vincent; Fairley, Neal; Richard-Plouet, Mireille

2018-07-01

Under in situ UV illumination, some materials present evolution of their opto-electronic properties that can be monitored by spectroscopy. We present here a mathematical method which can be applied to spectroscopic measurements when an evolving set of data is recorded: the vectorial method. The investigations and quantifications are performed by Infrared spectroscopy and XPS on organic-inorganic thin films prepared by sol-gel. The inorganic part of these hybrid thin films contains Ti oxide-network based whereas the organic part is composed of N,N-dimethylformamide and its hydrolysis products. Under UV illumination, those films exhibit intermediate bandgap behavior due to the photoreduction of Ti(IV) in Ti(III). The role of the solvent in the thin film is underlined during the process of photoreduction together with an understanding of the condensation of the Ti oxide-based network, as these evolutions are critical for the opto-electronic properties of those thin films.

Pedagogical Reform and College WOMEN’S Persistence in Mathematics

NASA Astrophysics Data System (ADS)

Strand, Kerry J. Strand; Mayfield, M. Elizabeth

Significant gender differences persist in the election of mathematics courses and math-related majors in college. Recent research suggests that part of the blame lies with conventional pedagogical approaches and that alternative approaches emphasizing practical applications, collaborative problem solving, and group work make mathematics more understandable and appealing to all students, particularly women. Using questionnaires administered to 355 traditional-age female college students, the authors examined the relationship between alternative teaching strategies in high school mathematics classes and two categories of outcome variables: mathematics-related attitudes and mathematics persistence in college. Multivariate analysis showed that experience with this so-called female-friendly pedagogy is positively related to students’ math-related attitudes and that these attitudes predict math persistence in college. However, the authors’ data also indicate that alternative teaching strategies have no discernible direct effect on students’ choices of mathematics courses or mathrelated

Is There a Relationship between Pre-Service Teachers' Mathematical Values and Their Teaching Anxiety in Mathematics?

ERIC Educational Resources Information Center

Yazici, Ersen; Peker, Murat; Ertekin, Erhan; Dilmac, Bulent

2011-01-01

Introduction: The aim of this study is to investigate the relation between the pre-service teachers' mathematical values and teaching anxieties in mathematics. Method: The research was carried out on 359 teacher candidates attending the elementary school mathematics, secondary school mathematics and primary school teaching programs. To this end,…

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…

Effect of plasma spraying modes on material properties of internal combustion engine cylinder liners

NASA Astrophysics Data System (ADS)

Timokhova, O. M.; Burmistrova, O. N.; Sirina, E. A.; Timokhov, R. S.

2018-03-01

The paper analyses different methods of remanufacturing worn-out machine parts in order to get the best performance characteristics. One of the most promising of them is a plasma spraying method. The mathematical models presented in the paper are intended to anticipate the results of plasma spraying, its effect on the properties of the material of internal combustion engine cylinder liners under repair. The experimental data and research results have been computer processed with Statistica 10.0 software package. The pare correlation coefficient values (R) and F-statistic criterion are given to confirm the statistical properties and adequacy of obtained regression equations.

2D modeling of direct laser metal deposition process using a finite particle method

NASA Astrophysics Data System (ADS)

Anedaf, T.; Abbès, B.; Abbès, F.; Li, Y. M.

2018-05-01

Direct laser metal deposition is one of the material additive manufacturing processes used to produce complex metallic parts. A thorough understanding of the underlying physical phenomena is required to obtain a high-quality parts. In this work, a mathematical model is presented to simulate the coaxial laser direct deposition process tacking into account of mass addition, heat transfer, and fluid flow with free surface and melting. The fluid flow in the melt pool together with mass and energy balances are solved using the Computational Fluid Dynamics (CFD) software NOGRID-points, based on the meshless Finite Pointset Method (FPM). The basis of the computations is a point cloud, which represents the continuum fluid domain. Each finite point carries all fluid information (density, velocity, pressure and temperature). The dynamic shape of the molten zone is explicitly described by the point cloud. The proposed model is used to simulate a single layer cladding.

Inverse transport calculations in optical imaging with subspace optimization algorithms

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

Ding, Tian, E-mail: tding@math.utexas.edu; Ren, Kui, E-mail: ren@math.utexas.edu

2014-09-15

Inverse boundary value problems for the radiative transport equation play an important role in optics-based medical imaging techniques such as diffuse optical tomography (DOT) and fluorescence optical tomography (FOT). Despite the rapid progress in the mathematical theory and numerical computation of these inverse problems in recent years, developing robust and efficient reconstruction algorithms remains a challenging task and an active research topic. We propose here a robust reconstruction method that is based on subspace minimization techniques. The method splits the unknown transport solution (or a functional of it) into low-frequency and high-frequency components, and uses singular value decomposition to analyticallymore » recover part of low-frequency information. Minimization is then applied to recover part of the high-frequency components of the unknowns. We present some numerical simulations with synthetic data to demonstrate the performance of the proposed algorithm.« less

Selecting and Using Mathematics Methods Texts: Nontrivial Tasks

ERIC Educational Resources Information Center

Harkness, Shelly Sheats; Brass, Amy

2017-01-01

Mathematics methods textbooks/texts are important components of many courses for preservice teachers. Researchers should explore how these texts are selected and used. Within this paper we report the findings of a survey administered electronically to 132 members of the Association of Mathematics Teacher Educators (AMTE) in order to answer the…

The Effect of Explanations on Mathematical Reasoning Tasks

ERIC Educational Resources Information Center

Norqvist, Mathias

2018-01-01

Studies in mathematics education often point to the necessity for students to engage in more cognitively demanding activities than just solving tasks by applying given solution methods. Previous studies have shown that students that engage in creative mathematically founded reasoning to construct a solution method, perform significantly better in…

Keystone Method: A Learning Paradigm in Mathematics

ERIC Educational Resources Information Center

Siadat, M. Vali; Musial, Paul M.; Sagher, Yoram

2008-01-01

This study reports the effects of an integrated instructional program (the Keystone Method) on the students' performance in mathematics and reading, and tracks students' persistence and retention. The subject of the study was a large group of students in remedial mathematics classes at the college, willing to learn but lacking basic educational…

Educational Neuroscience: New Horizons for Research in Mathematics Education

ERIC Educational Resources Information Center

Campbell, Stephen R.

2006-01-01

This paper outlines an initiative in mathematics education research that aims to augment qualitative methods of research into mathematical cognition and learning with quantitative methods of psychometrics and psychophysiology. Background and motivation are provided for this initiative, which is coming to be referred to as educational neuroscience.…

Effects of Mastery Learning Strategies on Community College Mathematics Students' Achievement and Success Rate.

ERIC Educational Resources Information Center

Abadir, Laila; And Others

The effects of mastery learning strategies, interactive video mathematics (IVM), individualized instruction (IND), and the lecture method on mathematics achievement of community college students was studied. Interactions among instructional methods, gender, and age were examined; and the grade success rate was determined for each instructional…

Using Propensity Scores to Reduce Selection Bias in Mathematics Education Research

ERIC Educational Resources Information Center

Graham, Suzanne E.

2010-01-01

Selection bias is a problem for mathematics education researchers interested in using observational rather than experimental data to make causal inferences about the effects of different instructional methods in mathematics on student outcomes. Propensity score methods represent 1 approach to dealing with such selection bias. This article…

Structural and Conceptual Interweaving of Mathematics Methods Coursework and Field Practica

ERIC Educational Resources Information Center

Bahr, Damon L.; Monroe, Eula Ewing; Eggett, Dennis

2014-01-01

This paper describes a study of observed relationships between the design of a preservice elementary mathematics methods course with accompanying field practicum and changes in the extent to which participating prospective teachers identified themselves with the mathematics reform movement after becoming practicing teachers. The curriculum of the…

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

ERIC Educational Resources Information Center

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

2015-01-01

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

The RAMANITA © method for non-destructive and in situ semi-quantitative chemical analysis of mineral solid-solutions by multidimensional calibration of Raman wavenumber shifts

NASA Astrophysics Data System (ADS)

Smith, David C.

2005-08-01

The "RAMANITA ©" method, for semi-quantitative chemical analysis of mineral solid-solutions by multidimensional calibration of Raman wavenumber shifts and mathematical calculation by simultaneous equations, is published here in detail in English for the first time. It was conceived by the present writer 20 years ago for binary and ternary pyroxene and garnet systems. The mathematical description was set out in 1989, but in an abstract in an obscure French special publication. Detailed "step-by-step" calibration of two garnet ternaries, followed by their linking, by M. Pinet and D.C. Smith in the early 1990s provided a hexary garnet database. Much later, using this garnet database, which forms part of his personal database called RAMANITA ©, the present writer began to develop the method by improving the terminology, automating the calculations, discussing problems and experimenting with different real chemical problems in archaeometry. Although this RAMANITA © method has been very briefly mentioned in two recent books, the necessary full mathematical explanation is given only here. The method will find application in any study which requires obtaining a non-destructive semi-quantitative chemical analysis from mineral solid solutions that cannot be analysed by any destructive analytical method, in particular for archaeological, geological or extraterrestrial research projects, e.g. from gemstones or other crystalline artworks of the cultural heritage (especially by Mobile Raman Microscopy (MRM)) in situ in museums or at archaeological sites, including under water for subaquatic archaeometry; from scientifically precious mineral microinclusions (such as garnet or pyroxene within diamond); from minerals in rocks analysed in situ on planetary bodies by a rover (especially "at distance" by telescopy). Recently some other workers have begun deducing chemical compositions from Raman wavenumber shifts in multivariate chemical space, but the philosophical approach is quite different.

Mathematicians and the Selection Task

ERIC Educational Resources Information Center

Inglis, Matthew; Simpson, Adrian

2004-01-01

Learning to think logically and present ideas in a logical fashion has always been considered a central part of becoming a mathematician. In this paper we compare the performance of three groups: mathematics undergraduates, mathematics staff and history undergraduates (representative of a "general population"). These groups were asked to solve…

Matematiques: Niveau A (Mathematics: Level A).

ERIC Educational Resources Information Center

Duron, Dolores; And Others

A teacher's manual was developed for an elementary level mathematics course in French as part of an immersion program for English speaking children. The Level A manual is designed for kindergarten and grade 1 pupils. Teaching procedures, conceptual and language objectives, vocabulary, structures, and learning activities are included. Activities…

Insights into Fourier Synthesis and Analysis: Part 2--A Simplified Mathematics.

ERIC Educational Resources Information Center

Moore, Guy S. M.

1988-01-01

Introduced is an analysis of a waveform into its Fourier components. Topics included are simplified analysis of a square waveform, a triangular waveform, half-wave rectified alternating current (AC), and impulses. Provides the mathematical expression and simplified analysis diagram of each waveform. (YP)

SSMILes: School Science and Mathematics Integrated Lessons: Chocolate Chip Cookies: A Consumer Unit, Part III: Investigating Snacks.

ERIC Educational Resources Information Center

Pearlman, Susan; Pericak-Spector, Kathleen

1995-01-01

Gives lesson plans for activities integrating mathematics and science in which students collect data on the nutritional makeup of a number of snack foods and relate this information to the recommendations of the food guide pyramid. (MKR)

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…

Interactive computer aided technology, evolution in the design/manufacturing process

NASA Technical Reports Server (NTRS)

English, C. H.

1975-01-01

A powerful computer-operated three dimensional graphic system and associated auxiliary computer equipment used in advanced design, production design, and manufacturing was described. This system has made these activities more productive than when using older and more conventional methods to design and build aerospace vehicles. With the use of this graphic system, designers are now able to define parts using a wide variety of geometric entities, define parts as fully surface 3-dimensional models as well as "wire-frame" models. Once geometrically defined, the designer is able to take section cuts of the surfaced model and automatically determine all of the section properties of the planar cut, lightpen detect all of the surface patches and automatically determine the volume and weight of the part. Further, his designs are defined mathematically at a degree of accuracy never before achievable.

From analytic inversion to contemporary IMRT optimization: radiation therapy planning revisited from a mathematical perspective.

PubMed

Censor, Yair; Unkelbach, Jan

2012-04-01

In this paper we look at the development of radiation therapy treatment planning from a mathematical point of view. Historically, planning for Intensity-Modulated Radiation Therapy (IMRT) has been considered as an inverse problem. We discuss first the two fundamental approaches that have been investigated to solve this inverse problem: Continuous analytic inversion techniques on one hand, and fully-discretized algebraic methods on the other hand. In the second part of the paper, we review another fundamental question which has been subject to debate from the beginning of IMRT until the present day: The rotation therapy approach versus fixed angle IMRT. This builds a bridge from historic work on IMRT planning to contemporary research in the context of Intensity-Modulated Arc Therapy (IMAT). Copyright © 2011 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Determination of element affinities by density fractionation of bulk coal samples

USGS Publications Warehouse

Querol, X.; Klika, Z.; Weiss, Z.; Finkelman, R.B.; Alastuey, A.; Juan, R.; Lopez-Soler, A.; Plana, F.; Kolker, A.; Chenery, S.R.N.

2001-01-01

A review has been made of the various methods of determining major and trace element affinities for different phases, both mineral and organic in coals, citing their various strengths and weaknesses. These include mathematical deconvolution of chemical analyses, direct microanalysis, sequential extraction procedures and density fractionation. A new methodology combining density fractionation with mathematical deconvolution of chemical analyses of whole coals and their density fractions has been evaluated. These coals formed part of the IEA-Coal Research project on the Modes of Occurrence of Trace Elements in Coal. Results were compared to a previously reported sequential extraction methodology and showed good agreement for most elements. For particular elements (Be, Mo, Cu, Se and REEs) in specific coals where disagreement was found, it was concluded that the occurrence of rare trace element bearing phases may account for the discrepancy, and modifications to the general procedure must be made to account for these.

Radiative-conductive inverse problem for lumped parameter systems

NASA Astrophysics Data System (ADS)

Alifanov, O. M.; Nenarokomov, A. V.; Gonzalez, V. M.

2008-11-01

The purpose of this paper is to introduce a iterative regularization method in the research of radiative and thermal properties of materials with applications in the design of Thermal Control Systems (TCS) of spacecrafts. In this paper the radiative and thermal properties (emissivity and thermal conductance) of a multilayered thermal-insulating blanket (MLI), which is a screen-vacuum thermal insulation as a part of the (TCS) for perspective spacecrafts, are estimated. Properties of the materials under study are determined in the result of temperature and heat flux measurement data processing based on the solution of the Inverse Heat Transfer Problem (IHTP) technique. Given are physical and mathematical models of heat transfer processes in a specimen of the multilayered thermal-insulating blanket located in the experimental facility. A mathematical formulation of the inverse heat conduction problem is presented too. The practical testing were performed for specimen of the real MLI.

Examining Student Attitudes in Introductory Physics via the Math Attitude and Expectations Survey (MAX)

NASA Astrophysics Data System (ADS)

Hemingway, Deborah; Eichenlaub, Mark; Losert, Wolfgang; Redish, Edward F.

2017-01-01

Student often face difficulties with using math in science, and this exploratory project seeks to address the underlying mechanisms that lead to these difficulties. This mixed-methods project includes the creation of two novel assessment surveys, the Mathematical Epistemic Games Survey (MEGS) and the Math Attitude and Expectations Survey (MAX). The MAX, a 30-question Likert-scale survey, focuses on the attitudes towards using mathematics of the students in a reformed introductory physics course for the life sciences (IPLS) which is part of the National Experiment in Undergraduate Education (NEXUS/Physics) developed at the University of Maryland (UMD). Preliminary results from the MAX are discussed with specific attention given to students' attitudes towards math and physics, opinions about interdisciplinarity, and the usefulness of physics in academic settings as well as in professional biological research and modern medicine settings.

Fractional Parts. Elementary Module for Use in a Mathematics Laboratory Setting.

ERIC Educational Resources Information Center

Charbonneau, Manon P.

This module, concerned with fractional parts, contains 15 activity sheets, 12 of these involve students in making fractional parts and discovering the relationships of less than, equal to, and greater than, between different fractional parts. The last three sheets are for extending and enriching experiences with fractional parts. Teaching…

Technology Development, Implementation and Assessment: K-16 Pre-Service, In-Service and Distance Learning Initiatives

NASA Technical Reports Server (NTRS)

Williams, William B., Jr.

1999-01-01

The technologies associated with distance learning are evolving rapidly, giving to educators a potential tool for enhancing the educational experiences of large numbers of students simultaneously. This enhancement, in order to be effective, must take into account the various agendas of teachers, administrators, state systems, and of course students. It must also make use of the latest research on effective pedagogy. This combination, effective pedagogy and robust information technology, is a powerful vehicle for communicating, to a large audience of school children the excitement of mathematics and science--an excitement that for the most part is now well-hidden. This project,"Technology Development, Implementation and Assessment," proposed to bring to bear on the education of learners in grades 3 - 8 in science and mathematics both advances in information technology and in effective pedagogy. Specifically, the project developed components NASA CONNECT video series--problem-based learning modules that focus on the scientific method and that incorporate problem-based learning scenarios tied to national mathematics and science standards. These videos serve two purposes; they engage students in the excitement of hands-on learning and they model for the teachers of these students the problem-based learning practices that are proving to be excellent ways to teach science and mathematics to school students. Another component of NASA CONNECT is the accompanying web-site.

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

Park, C; Zhang, H; Chen, Y

Purpose: Recently, compressed sensing (CS) based iterative reconstruction (IR) method is receiving attentions to reconstruct high quality cone beam computed tomography (CBCT) images using sparsely sampled or noisy projections. The aim of this study is to develop a novel baseline algorithm called Mask Guided Image Reconstruction (MGIR), which can provide superior image quality for both low-dose 3DCBCT and 4DCBCT under single mathematical framework. Methods: In MGIR, the unknown CBCT volume was mathematically modeled as a combination of two regions where anatomical structures are 1) within the priori-defined mask and 2) outside the mask. Then we update each part of imagesmore » alternatively thorough solving minimization problems based on CS type IR. For low-dose 3DCBCT, the former region is defined as the anatomically complex region where it is focused to preserve edge information while latter region is defined as contrast uniform, and hence aggressively updated to remove noise/artifact. In 4DCBCT, the regions are separated as the common static part and moving part. Then, static volume and moving volumes were updated with global and phase sorted projection respectively, to optimize the image quality of both moving and static part simultaneously. Results: Examination of MGIR algorithm showed that high quality of both low-dose 3DCBCT and 4DCBCT images can be reconstructed without compromising the image resolution and imaging dose or scanning time respectively. For low-dose 3DCBCT, a clinical viable and high resolution head-and-neck image can be obtained while cutting the dose by 83%. In 4DCBCT, excellent quality 4DCBCT images could be reconstructed while requiring no more projection data and imaging dose than a typical clinical 3DCBCT scan. Conclusion: The results shown that the image quality of MGIR was superior compared to other published CS based IR algorithms for both 4DCBCT and low-dose 3DCBCT. This makes our MGIR algorithm potentially useful in various on-line clinical applications. Provisional Patent: UF#15476; WGS Ref. No. U1198.70067US00.« less

"Mathematics made no contribution to the public weal": why Jean Fernel (1497-1558) became a physician.

PubMed

Henry, John

2011-01-01

This paper offers a caution that emphasis upon the importance of mathematics in recent historiography is in danger of obscuring the historical fact that, for the most part, mathematics was not seen as important in the pre-modern period. The paper proceeds by following a single case study, and in so doing offers the first account of the mathematical writings of Jean Fernel (1497-1558), better known as a leading medical innovator of the 16th century. After establishing Fernel's early commitment to mathematics, and attempt to forge a career as a cosmographer, it goes on to explain his abandonment of mathematics for a career in medicine. The 'mathematization of the world picture' is usually explained in terms of the perceived usefulness of mathematics, but Fernel's case shows that for many pre-modern thinkers, mathematics was not regarded as a useful pursuit. The paper should serve as a reminder, therefore, that the take-up of mathematics by natural philosophers was by no means inevitable, but had to be carefully managed by early modern mathematical practitioners. The case of Fernel indicates that perhaps he was not the only would-be mathematical practitioner to abandon mathematics in favor of a calling that was more appreciated by contemporaries.

Mathematics is differentially related to reading comprehension and word decoding: Evidence from a genetically-sensitive design

PubMed Central

Harlaar, Nicole; Kovas, Yulia; Dale, Philip S.; Petrill, Stephen A.; Plomin, Robert

2013-01-01

Although evidence suggests that individual differences in reading and mathematics skills are correlated, this relationship has typically only been studied in relation to word decoding or global measures of reading. It is unclear whether mathematics is differentially related to word decoding and reading comprehension. The current study examined these relationships at both a phenotypic and etiological level in a population-based cohort of 5162 twin pairs at age 12. Multivariate genetic analyses of latent phenotypic factors of mathematics, word decoding and reading comprehension revealed substantial genetic and shared environmental correlations among all three domains. However, the phenotypic and genetic correlations between mathematics and reading comprehension were significantly greater than between mathematics and word decoding. Independent of mathematics, there was also evidence for genetic and nonshared environmental links between word decoding and reading comprehension. These findings indicate that word decoding and reading comprehension have partly distinct relationships with mathematics in the middle school years. PMID:24319294

Mathematics is differentially related to reading comprehension and word decoding: Evidence from a genetically-sensitive design.

PubMed

Harlaar, Nicole; Kovas, Yulia; Dale, Philip S; Petrill, Stephen A; Plomin, Robert

2012-08-01

Although evidence suggests that individual differences in reading and mathematics skills are correlated, this relationship has typically only been studied in relation to word decoding or global measures of reading. It is unclear whether mathematics is differentially related to word decoding and reading comprehension. The current study examined these relationships at both a phenotypic and etiological level in a population-based cohort of 5162 twin pairs at age 12. Multivariate genetic analyses of latent phenotypic factors of mathematics, word decoding and reading comprehension revealed substantial genetic and shared environmental correlations among all three domains. However, the phenotypic and genetic correlations between mathematics and reading comprehension were significantly greater than between mathematics and word decoding. Independent of mathematics, there was also evidence for genetic and nonshared environmental links between word decoding and reading comprehension. These findings indicate that word decoding and reading comprehension have partly distinct relationships with mathematics in the middle school years.

Competence with Fractions Predicts Gains in Mathematics Achievement

PubMed Central

Bailey, Drew H.; Hoard, Mary K.; Nugent, Lara; Geary, David C.

2012-01-01

Competence with fractions predicts later mathematics achievement, but the co-developmental pattern between fractions knowledge and mathematics achievement is not well understood. We assessed this co-development through examination of the cross-lagged relation between a measure of conceptual knowledge of fractions and mathematics achievement in sixth and seventh grade (n = 212). The cross-lagged effects indicated that performance on the sixth grade fractions concepts measure predicted one year gains in mathematics achievement (β = .14, p<.01), controlling for the central executive component of working memory and intelligence, but sixth grade mathematics achievement did not predict gains on the fractions concepts measure (β = .03, p>.50). In a follow-up assessment, we demonstrated that measures of fluency with computational fractions significantly predicted seventh grade mathematics achievement above and beyond the influence of fluency in computational whole number arithmetic, performance on number fluency and number line tasks, and central executive span and intelligence. Results provide empirical support for the hypothesis that competence with fractions underlies, in part, subsequent gains in mathematics achievement. PMID:22832199

Stochastic model of the NASA/MSFC ground facility for large space structures with uncertain parameters: The maximum entropy approach, part 2

NASA Technical Reports Server (NTRS)

Hsia, Wei Shen

1989-01-01

A validated technology data base is being developed in the areas of control/structures interaction, deployment dynamics, and system performance for Large Space Structures (LSS). A Ground Facility (GF), in which the dynamics and control systems being considered for LSS applications can be verified, was designed and built. One of the important aspects of the GF is to verify the analytical model for the control system design. The procedure is to describe the control system mathematically as well as possible, then to perform tests on the control system, and finally to factor those results into the mathematical model. The reduction of the order of a higher order control plant was addressed. The computer program was improved for the maximum entropy principle adopted in Hyland's MEOP method. The program was tested against the testing problem. It resulted in a very close match. Two methods of model reduction were examined: Wilson's model reduction method and Hyland's optimal projection (OP) method. Design of a computer program for Hyland's OP method was attempted. Due to the difficulty encountered at the stage where a special matrix factorization technique is needed in order to obtain the required projection matrix, the program was successful up to the finding of the Linear Quadratic Gaussian solution but not beyond. Numerical results along with computer programs which employed ORACLS are presented.

What is the Role of Mathematics Education in the Computer Age?

ERIC Educational Resources Information Center

Popp, Jerome A.

1986-01-01

Proposes that the role of mathematics education be re-examined in terms of an increased emphasis on mathematical knowledge rather than attainment of calculational speed. Offers perspectives on the reform movement in mathematics education and advocates the teaching of the history, logic, and method of mathematical thinking. (ML)

Why Singaporean 8th Grade Students Gain Highest Mathematics Ranking in TIMSS (1999-2011)

ERIC Educational Resources Information Center

Lessani, Abdolreza; Yunus, Aida Suraya Md; Tarmiz, Rohani Ahmad; Mahmud, Rosnaini

2014-01-01

The international comparison of students' mathematics knowledge and competencies is an effective method of evaluating students' mathematics performance and developing policies to improve their achievements in mathematics. Trends in International Mathematics and Science Study (TIMSS) are among the most well-recognized international comparisons that…

The Language of Mathematics: The Importance of Teaching and Learning Mathematical Vocabulary

ERIC Educational Resources Information Center

Riccomini, Paul J.; Smith, Gregory W.; Hughes, Elizabeth M.; Fries, Karen M.

2015-01-01

Vocabulary understanding is a major contributor to overall comprehension in many content areas, including mathematics. Effective methods for teaching vocabulary in all content areas are diverse and long standing. Teaching and learning the language of mathematics is vital for the development of mathematical proficiency. Students' mathematical…

Influence of Writing Ability and Computation Skill on Mathematics Writing

ERIC Educational Resources Information Center

Powell, Sarah R.; Hebert, Michael A.

2016-01-01

Mathematics standards expect students to communicate about mathematics using oral and written methods, and some high-stakes assessments ask students to answer mathematics questions by writing. Assumptions about mathematics communication via writing include (a) students possess writing skill, (b) students can transfer this writing skill to…

Developing Teaching Material Software Assisted for Numerical Methods

NASA Astrophysics Data System (ADS)

Handayani, A. D.; Herman, T.; Fatimah, S.

2017-09-01

The NCTM vision shows the importance of two things in school mathematics, which is knowing the mathematics of the 21st century and the need to continue to improve mathematics education to answer the challenges of a changing world. One of the competencies associated with the great challenges of the 21st century is the use of help and tools (including IT), such as: knowing the existence of various tools for mathematical activity. One of the significant challenges in mathematical learning is how to teach students about abstract concepts. In this case, technology in the form of mathematics learning software can be used more widely to embed the abstract concept in mathematics. In mathematics learning, the use of mathematical software can make high level math activity become easier accepted by student. Technology can strengthen student learning by delivering numerical, graphic, and symbolic content without spending the time to calculate complex computing problems manually. The purpose of this research is to design and develop teaching materials software assisted for numerical method. The process of developing the teaching material starts from the defining step, the process of designing the learning material developed based on information obtained from the step of early analysis, learners, materials, tasks that support then done the design step or design, then the last step is the development step. The development of teaching materials software assisted for numerical methods is valid in content. While validator assessment for teaching material in numerical methods is good and can be used with little revision.

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"…