Recent research into students' reasoning about variation refers specifically to notions of distribution that emerge. This paper reports on research where written responses, from tertiary introductory statistics students, were coded according to the level of consideration of variation. A hierarchy of reasoning about distribution is proposed, based…

The paper is based on research carried out on secondary school students and students commencing their university studies in mathematics. The basic purpose of the research was to investigate the understanding of the concept of a sequence and to determine the sources of the formation of revealed conceptions. To achieve the objectives an expanded set…

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…

The general question examined by this study was whether the tendency of subjects to ignore the known score in giving the best guess for a sample mean was due to a descriptive heuristic such as representativeness or to a mechanistic one such as active balancing. Two experiments were conducted. In Experiment 1, subjects estimated: (1) the mean of a…

The mathematics curriculum in the first 2 years of college is a tool created to assist in solving problems. The current mathematics curriculum has changed little; the same topics, tied to the engineering and science curriculum, are taught as they were being taught in 1945. The problems that students need to solve have changed however. Both the…

This document contains two units that examine integral transforms and series expansions. In the first module, the user is expected to learn how to use the unified method presented to obtain Laplace transforms, Fourier transforms, complex Fourier series, real Fourier series, and half-range sine series for given piecewise continuous functions. In…

One of 12 books developed for use with the core material (Book O) of the Elements of Mathematics Program, this text covers material well beyond the scope of the usual secondary mathematics sequences. These materials are designed for highly motivated students with strong verbal abilities; mathematical theories and ideas are developed through…

The effectiveness of an advanced organizer based on examples is compared with that of one based on counter examples. The counter examples strategy was found to be more effective for the unit on finite groups. (SD)

The author argues that undergraduates, and especially those not planning to pursue mathematics, are not ready for a definitional approach to mathematics. He interprets data on student attribution of five terms (theorem, law, fact about numbers, definition, axiom) to definitions in support of his argument. (SD)

A collection of brief articles on mathematics and teaching mathematics. (FL)

This study, based on individual interviews with 100 students (aged 16 to 22 years), was designed to investigate understanding of elementary calculus (particularly integration and differentiation). Results indicated that items related to understanding integration as the limit of a sum were difficult even for good students. (Author/MP)

The material presents an alternative method for arranging proofs, which arranges development in levels. The method is described as triggered by recent ideas from computer science and is intended to increase the comprehensibility of mathematical presentations while retaining their rigor. Several examples using this approach are presented.…

The harmonic mean is defined, and examples of problems viewed suitable for classroom exploration are presented. Such exercises provide many opportunities for students to engage in interesting nontrivial problem-solving activities and practice on many algebraic skills. Class discussion of the arithmetic, geometric, and harmonic means is suggested.…

A program written in PASCAL designed to find the number of binary trees possible for a given number of nodes is presented. The problem was found to be highly motivating and exciting for the group of introductory computer science students with whom it was used. (MP)