The mathematical vitality of secondary mathematics graduates and prospective teachers: A comparative study

This article links two areas of contemporary interest in mathematics education. These are respectively; mathematical characteristics of prospective teachers, and the notion of levels of understanding.The study reported here considered questions relating to the mathematical appreciation of successful students at both senior secondary (university entrance) and tertiary level. The tertiary students were graduates embarking upon a post-graduate course of teacher-training.It was found that response patterns were stable across a variety of institutions, geographical regions (Australian States), and education systems. Mathematical malfunctions present among secondary graduates were found to exist in substantially the same proportions among the graduate teacher trainees. It was found that the type of understanding sought in this study was not enhanced merely by taking more mathematics courses. The problem of recycling of attitudes and mathematical misconceptions within the secondary teaching structure is addressed, and the question of the approach to the study of mathematics at both secondary and tertiary level is raised as a matter of continuing concern.