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).

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This study examined the mathematical understandings and beliefs held by preservice elementary teachers in a mathematics methods course taken as part of a one year teacher certification program, and reexamined these characteristics at the end of the course. The notion of 'understanding mathematics for teaching' was examined in a way that might begin to support the work of mathematics educators working with such preservice teacher candidates. Preservice teacher beliefs about what is important in mathematics learning and therefore the teaching of it are examined along with mathematics understanding at both procedural and conceptual levels. The goal was to shed some light on how initial understanding and beliefs about mathematics teaching co-exist, and how these might develop during a preservice teacher education program.

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As part of a 5-year project that examined teachers' knowledge and beliefs about mathematics and teaching mathematics, interviews were conducted with preservice elementary teachers during their certification year. The transcripts of five of these sets of pretest/posttest interviews were chosen as illustrative of the significant challenges that preservice teachers continue to face as they strive to deepen their subject-specific teaching knowledge and begin to address their beliefs about teaching and learning mathematics.Résumé: Dans le cadre d'un projet de 5 ans visantà analyser les connaissances en mathématiques des enseignants, ainsi que leurs points de vue sur cette discipline et son enseignement, des entrevues ontété menées auprès de futurs enseignants au primaire pendant leur année de certification. La transcription de cinq des séries d'entrevues (pré-test et post-test) aété choisie pour illustrer l'importance des défis que doivent continuellement affronter les enseignants en formation alors qu'ils visentà approfondir leur niveau de connaissances spécifiquesà l'enseignement des mathématiques et commencentà réfléchir sur leurs propres points de vue concernant l'enseignement et l'apprentissage de leur discipline.