Many academics like to isolate a piece of the world to study: an important social issue, a central philosophical problem, a key moment in history. They know they're oversimplifying but they do it anyway--it's the only way to make progress, and what's more, their little worlds are often more beautiful than the real one. This paper shares a story of…

Using case study analysis and a cognitive theoretical orientation, we examine elements of knowledge for teaching needed by a mathematician to orchestrate whole-class discussions in an undergraduate mathematics classroom. The instructor, an experienced teacher and mathematics researcher, used an inquiry-oriented curriculum to teach a differential…

This submission contains the Proceedings of the 2014 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at the University of Alberta in Edmonton, Alberta. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the…

This study sought to compare the performance of students in the College Board Advanced Placement Program® (AP®) compared to non-AP students on a number of college outcome measures. Ten individual AP Exams were examined in this study of students in four entering classes (1998-2001) at the University of Texas at Austin. The four main groups of…

Describes the production of pilot tape that used the strengths of video successfully. (BD)

Presents a method for writing epsilon-delta proofs for polynomial limit problems in calculus. (MKR)

Outlines ideas and exercises for two topics that accompany the standard treatment of integral calculus. Emphasizes intuition to help facilitate student comprehension of the definite integral as a limit of Riemann Sums. (Author/MM)

A simple mathematical model for how vehicles follow each other along a stretch of road is presented. The resulting linear second-order differential equation with constant coefficients is solved and interpreted. The model can be used as an application of solution techniques taught at first-year undergraduate level and as a motivator to encourage…

The transition ('gap') between secondary and tertiary education in mathematics is a complex phenomenon covering a vast array of problems and issues. The aim of this paper is to present the ways in which the issues of mathematics transition have been dealt with at McMaster University. Roughly, the process of transition has been broken into three…

A series defining the antiderivative of an n th order differentiable function is defined. This series provides an explicit expression for the second part of the Fundamental Theorem of Calculus and can facilitate the establishment of new antiderivative functions.

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.

An engineering problem concerned with relating the coordinates of the centre of a spherical cutting tool to the actual cutting surface leads to a potentially rich example of problem-solving techniques. Basic calculus, Lagrange multipliers and vector calculus techniques are employed to produce solutions that may be compared to better understand…

The aim of this note is to give some insight into the formal unity of a very applicable area of mathematics by showing an interesting analogy between the weak part of the Rouche-Frobenius theorem and the existence result for the initial value problem for the general first-order linear two-dimensional PDE.