Concept image and concept definition is an important construct in mathematics education. Its use, however, has been limited to cognitive studies. This article revisits concept image in the context of research on undergraduate students' understanding of the derivative which regards the context of learning as paramount. The literature, mainly on…

This article presents an anecdote of the author's experience of working "in the usual way" using animation with Year 7 and with National Academy of Gifted and Talented Youth students (Y7-11) at a recent summer school in Lancaster. When he tried the animation with Year 7 and NAGTY students, the author found that this could easily be used…

There is a large body of literature on the types of questions asked by teachers. Questions are a way that teachers use to bring students around to the correct mathematical concepts and procedures through "the negotiation of meaning for necessary condition of learning" (Voigt, 1992, p. 43). Teachers ask many questions, but we are not sure what…

We present an approach of defining certain transcendental functions as solutions to initial value problems or systems of such problems. This material is suitable for use in a second-semester one-variable calculus course.

How might one define a functional operator D[superscript I]f(x), say for f(x) = 1 + x[superscript 2] + sin x, such that D[superscript +1](1 + x[superscript 2] + sin x) = 2x + cos x and D[superscript -1](1 + x[superscript 2] + sin x) = x + x[superscript 3]/3 - cos x? Our task in this article is to describe such an operator using a single formula…

In this article, the author discusses Sudoku--a logic puzzle that has appeared in many newspapers in recent years. In its introductory form it consists of a 9x9 grid in which the digits 1 to 9 inclusive are each to be placed nine times in the 81 separate cells of the grid. Each row and each column may not have any digit repeated. If these were the…

This article presents a way of computing a surface integral when the vector field of the integrand is a curl field. Presented in some advanced calculus textbooks such as [1], the technique, as the author experienced, is simple and applicable. The computation is based on Stokes' theorem in 3-space calculus, and thus provides not only a means to…

We investigate the possibility of approximating the value of a definite integral by approximating the integrand rather than using numerical methods to approximate the value of the definite integral. Particular cases considered include examples where the integral is improper, such as an elliptic integral. (Contains 4 tables and 2 figures.)

In this article, we discuss an alternative method of teaching students about the Dirac [delta]-function. The method provides students with the mechanical tools they need in order to work with the [delta]-function in practice, while also fostering a sense of cohesion in the calculus curriculum by presenting the [delta]-function as an evolution of…

A remarkable property of a large class of functions is exploited to generate exact solutions to the one-dimensional Schrodinger equation. The method is simple and easy to implement. (Contains 1 table and 1 figure.)

Synthetic division is viewed as a change of basis for polynomials written under the Newton form. Then, the transition matrices obtained from a sequence of changes of basis are used to factorize the inverse of a bidiagonal matrix or a block bidiagonal matrix.

In this note, a simple proof of the Generalized Ceva Theorem in plane geometry is presented. The approach is based on the principle of equilibrium in mechanics. (Contains 2 figures.)

The authors explore how children's play can support the development of the foundations of mathematics learning and how adults can support children's representation of--and thus the "mathematization" of--their play. The authors review research about the amount and nature of mathematics found in the free play of children. They briefly…

The purpose of this study was to explore the ways instructors' subject matter beliefs regarding mathematics shape their courses in a community college environment. Data were collected and analysed from instructors' philosophical definitions of mathematics and observations of teaching episodes using a constructivist grounded theory research design.…

The purpose of this paper is to share the results of a fourteen-week study that focused on the effects of teaching mathematics instruction with the implementation of manipulatives in an elementary classroom. Students that fill our classrooms deserve the opportunity to use manipulatives to help them grasp all the different concepts that are taught…