Mathematics experts often choose appropriate procedures to produce an efficient or elegant solution to a mathematical task. This "flexible procedural knowledge" distinguishes novice and expert procedural performances. This article reports on an intervention intended to aid the development of undergraduate calculus students' flexible use…

To ensure the competitiveness of the USA in the global economy, and its role as a leader in science and engineering, it is important to cultivate the next generation of home grown mathematicians. However, while universities across the USA offer calculus classes to thousands of undergraduate students each year, very few of them go on to major in…

Partial fraction decomposition is a useful technique often taught at senior secondary or undergraduate levels to handle integrations, inverse Laplace transforms or linear ordinary differential equations, etc. In recent years, an improved Heaviside's approach to partial fraction decomposition was introduced and developed by the author. An important…

A portion of all students in introductory or developmental undergraduate mathematics courses find themselves at an unfortunate tipping point: the border between passing and failing. These high-stakes courses often come with high enrollments, and a recurring problem: high failure rates. The measure of success used at the author's institution, the…

Multimodal feedback could promote college students' conceptual, procedural and heuristic knowledge learning. This study used an experimental design to investigate the interaction effects of instructor's narrated feedback (with procedural feedback delivered visually and heuristic feedback auditorily) and gender on their post-test performance of a…

The aim of this article is to present a scheme for coding and categorizing students' written explanations of mathematical problem-solving activities. The scheme was used successfully within a study project carried out to determine whether student problem-solving behaviour could be positively affected by writing explanatory strategies to…