Bramlett and Drake (2013) suggest that the ability of teachers to teach proof is crucial for students to learn and develop formal and informal proofs. Teachers need to be involved in the process of proving and have a firm understanding of the critical role of proofs in order to effectively engage their students in proving activities. It is…

Many students do not have a deep understanding of the integral concept. This article defines what a deep understanding of the integral is in respect to integration involving one independent variable; briefly discusses factors which may inhibit such an understanding; and then describes the design of a mathematical resource for introducing students…

This article deals with a short historical introduction to determinants with applications to the theory of equations, geometry, multiple integrals, differential equations and linear algebra. Included are some properties of determinants with proofs, eigenvalues, eigenvectors and characteristic equations with examples of applications to simple…

The study of the number of intersection points of y = a[superscript x] and y = log[subscript a]x can be an interesting topic to present in a single-variable calculus class. In this article, the authors present a classroom presentation outline involving the basic algebra and the elementary calculus of the exponential and logarithmic functions. The…

This article describes a hands-on approach to learning proofs by induction. Students create patterns of dominos so that when the first domino is pushed, the entire design collapses, one domino at a time. Students then build designs that do not work. By constructing a list of conditions that ensure a given pattern will collapse, students discover…

Senior secondary students cover numerical integration techniques in their mathematics courses. In particular, students would be familiar with the "midpoint rule," the elementary "trapezoidal rule" and "Simpson's rule." This article derives these techniques by methods which secondary students may not be familiar with…

Developing students' ability to reason has long been a fundamental goal of mathematics education. A primary way in which mathematics students develop reasoning skills is by constructing mathematical proofs. This article presents a number of nontypical results, along with their proofs, that can be explored with students in any calculus classroom.…

This article presents an instructional approach to constructing discovery-oriented activities. The cornerstone of the approach is a systematically asked question "If a mathematical statement under consideration is plausible, but wrong anyway, how can one fix it?" or, in brief, "If not, what yes?" The approach is illustrated with examples from…

This submission contains the Proceedings of the 2010 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at Simon Fraser University in Burnaby, British Columbia. 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…

This submission contains the Proceedings of the 2002 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at Queen's University in Kingston, Ontario. 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 Study…

The first volume of the 29th annual conference of the International Group for the Psychology of Mathematics Education contains plenary lecture and research forum papers as listed below. Short oral communications papers, poster presentations, brief summaries of discussion groups, and working sessions are also included in the volume. The plenary…