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Farmaki, V.; Paschos, T. – International Journal of Mathematical Education in Science and Technology, 2007

This paper reports studies of the interaction between the intuitive, the formal and the procedural aspects in the processes of mathematical understanding of Peter, a first-year undergraduate of Mathematics. Using an activity and an interview, an attempt is made to analyse his mental operations. The way in which he handles visual-graphic…

Descriptors: Mathematics, Thinking Skills, College Freshmen, Case Studies

Roberts, A. L.; Sharma, M. D.; Britton, S.; New, P. B. – International Journal of Mathematical Education in Science and Technology, 2007

This project aimed to quantitatively measure the ability of first year science students to transfer their mathematical skills and knowledge to a physical context. An instrument used in earlier studies to measure transfer of mathematical knowledge was modified for this project, and tested with 49 student volunteers. This paper presents the Transfer…

Descriptors: Student Volunteers, Predictive Validity, Mathematics Skills, Mathematics

Groetsch, C. W. – International Journal of Mathematical Education in Science and Technology, 2004

The origin of the function concept is usually traced to Galileo's work on motion. We argue that specific proto-function concepts appeared in the work of Tartaglia a century before the publication of Galileo's Two New Sciences. The study of Tartaglia's ideas can be used in the classroom as a historical introduction to various function concepts,…

Descriptors: Mathematics Instruction, Mathematical Concepts, Mathematics, History

Ching, Wai-Ki; Fung, Eric S.; Ng, Michael K. – International Journal of Mathematical Education in Science and Technology, 2004

Categorical data sequences occur in many applications such as forecasting, data mining and bioinformatics. In this note, we present higher-order Markov chain models for modelling categorical data sequences with an efficient algorithm for solving the model parameters. The algorithm can be implemented easily in a Microsoft EXCEL worksheet. We give a…

Descriptors: Mathematics, Markov Processes

Tong, Jingcheng – International Journal of Mathematical Education in Science and Technology, 2004

This article discusses the mean value theorem and its importance to calculus. It focuses on Flett's mean value theorem. It includes five theorems with proofs and two examples.

Descriptors: Least Squares Statistics, Calculus, Mathematics

Nunokawa, Kazuhiko – International Journal of Mathematical Education in Science and Technology, 2004

The purpose of this paper was to investigate how it becomes possible for solvers to make drawings to advance their problem solving processes, in order to understand the use of drawings in mathematical problem solving more deeply. For this purpose, three examples in which drawings made by the solver played a critical role in the solutions have been…

Descriptors: Cognitive Processes, Problem Solving, Mathematics, Mathematics Instruction

Periago, Francisco – International Journal of Mathematical Education in Science and Technology, 2003

In this paper, a didactical proposal is presented to introduce the variational methods for solving boundary value problems to engineering students. Starting from a couple of simple models arising in linear elasticity and heat diffusion, the concept of weak solution for these models is motivated and the existence, uniqueness and continuous…

Descriptors: Engineering, Engineering Education, Models, Simulation

Gutierrez, Rosa Maria Afonso; Diaz, Jose Angel Dorta – International Journal of Mathematical Education in Science and Technology, 2002

The continuous technological progress of the past few decades affords a different orientation to the teaching-learning process, which is useful and advantageous when mathematical concepts are transmitted. This article pursues two different aims. The first one is to examine the present state of the traditional process in relation to the concepts of…

Descriptors: Computer Software, Mathematical Concepts, Mathematics Education, Higher Education

Abramovich, Sergei; Strock, Tracy – International Journal of Mathematical Education in Science and Technology, 2002

The paper describes the use of a spreadsheet in a mathematics teacher education course. It shows how the tool can serve as a link between seemingly disconnected mathematical concepts. The didactical triad of using a spreadsheet as an agent, consumer, and amplifier of mathematical activities allows for an extended investigation of simple yet…

Descriptors: Preservice Teacher Education, Education Courses, Mathematical Concepts, Mathematics Instruction

Fay, Temple H. – International Journal of Mathematical Education in Science and Technology, 2002

This paper compliments two recent articles by the author in this journal concerning solving the forced harmonic oscillator equation when the forcing is periodic. The idea is to replace the forcing function by its Fourier series and solve the differential equation term-by-term. Herein the convergence of such series solutions is investigated when…

Descriptors: Calculus, Mathematical Concepts, Mathematics Education, Equations (Mathematics)

Guyker, James – International Journal of Mathematical Education in Science and Technology, 2002

A lively example to use in a first course in linear algebra to clarify vector space notions is the space of square matrices of fixed order with its subspaces of affine, coaffine, doubly affine, and magic squares. In this note, the projection theorem is illustrated by explicitly constructing the orthogonal projections (in closed forms) of any…

Descriptors: Geometric Concepts, Matrices, Algebra, Computation

Asiru, Muniru Aderemi – International Journal of Mathematical Education in Science and Technology, 2002

The method for geometric transforms (probability generating functions) is used to study the expected number of observations until the pattern 123123 . . . 123 is obtained. These results provide a first generalization of similar problems considered by other authors. (Contains 1 figure.)

Descriptors: Probability, Geometric Concepts, Computation, Item Response Theory

Chen, Hongwei – International Journal of Mathematical Education in Science and Technology, 2002

In this note, using the method of undetermined coefficients, we obtain the power series for exp ( f ( x )) and ln ( f ( x )) by means of a simple recursion. As applications, we show how those power series can be used to reproduce and improve some well-known results in analysis. These results may be used as enrichment material in an advanced…

Descriptors: Calculus, Mathematical Formulas, Mathematics, Multiplication

Martinez, F.; Vinuesa, C. – International Journal of Mathematical Education in Science and Technology, 2002

This note presents some simple examples illustrating the differences between the concepts of continuity, existence of partial derivatives and differentiability. (Contains 2 tables and 10 figures.)

Descriptors: Mathematics, Calculus, Mathematical Logic, Validity

McCartney, Mark – International Journal of Mathematical Education in Science and Technology, 2002

In this paper, the author introduces a simple problem relating to a pair of ladders. A mathematical model of the problem produces an equation which can be solved in a number of ways using mathematics appropriate to "A" level students or first year undergraduates. The author concludes that the ladder problem can be used in class to develop and…

Descriptors: Mathematical Models, Mathematics, Undergraduate Students