Transition from secondary to tertiary mathematics: McMaster University experience

Abstract

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 stages: students’ voluntary preparation for university mathematics courses facilitated by the Mathematics Review Manual; administration of Mathematics Background Survey; and redesign of the first-year Calculus (and, subsequently, other mathematics courses).

Notes

‘Mathematical skills in the workplace are changing, with increasing numbers of people invovled in mathematics-related work, and with such involving increasingly sophisticated mathematical activities.’ (from the UK report: Hoyles, C. et al. Mathematical Skills in the Workplace. Final Report to the Science, Technology and Mathematics Council, June 2002).

A copy of the survey used in 2003 is in the appendix to this paper.

A more comprehensive analysis is the subject of a forthcoming paper by the authors.

The fact that both percentages are so low is of significant concern.

The question about the Pythagorean Theorem appears in earlier versions of the survey; it was not included in the 2003 version.

As a matter of fact, a whole 50-minute lecture was devoted to the Intermediate Value Theorem, with a discussion of ways in which the theorem is used; moreover, cases in which the theorem cannot be used (i.e. some/all assumptions are not satisfied) were also discussed.

The online version is at http://www.math.mcmaster.ca/lovric/rm.html

Due to a large class size (about 400), lecturing is the major (quite often the only) mode of classroom instruction.

Anecdotal evidence, obtained from talking to students after their final examination.

Inverse trigonometric functions are not covered in high schools in Ontario.