What is the connection between advanced mathematics and teaching secondary mathematics? I address this question, drawing on insights from the Special Issue on "Personal Mathematical Knowledge in the Work of Teaching" ("CJSMTE" 13(2), 2013) and reflecting on my personal teaching experience.

We examine different definitions presented in textbooks and other mathematical sources for "continuity of a function at a point" and "continuous function" in the context of introductory level Calculus. We then identify problematic issues related to definitions of continuity and discontinuity: inconsistency and absence of…

Role-playing is an unscripted dramatic technique that encourages participants to improvise behaviors that illustrate expected actions of persons involved in defined situations. However, among various uses in developing professionals, the use of role-playing in teacher education is rather rare. To give all students the opportunity to participate in…

Our study investigates perspectives of mathematics teacher educators related to the usage of their mathematical knowledge in teaching "Methods of Teaching Elementary Mathematics" courses. Five mathematics teacher educators, all with experience in teaching methods courses for prospective elementary school teachers, participated in this study. In a…

This study focuses on instances of creativity in the design of Lesson Play tasks and in prospective teachers' responses to the tasks. A Lesson Play task assumes a theatrical interpretation of the word "play" and requires teachers to write a script for an imaginary interaction between a teacher-character and student-characters, attending…

This article extends the notion of "knowledge at the mathematical horizon" or "horizon knowledge" introduced by Ball and colleagues as a part of teachers' subject matter knowledge. Our focus is on teachers' mathematical knowledge beyond the school curriculum, that is, on mathematics learnt during undergraduate college or university studies. We…

We discuss an innovative task used in teacher education--Lesson Play--that involves presenting a lesson in the form of an interaction between a teacher and students. We describe the motivation for the development of this task and, through specific examples, describe the iterative design process in which the task was refined and improved. We…

This study is concerned with the first experiences of in-service mathematics teachers in consuming scholarly mathematics education literature. Growing from the meta-didactical transposition model, we were interested in the praxeologies that may develop from teachers' engagement with research articles. The data were collected from a cohort of 13…

This paper elaborates the notion of a personal example space as the set of mathematical objects and construction techniques that a learner has access to as examples of a concept while working on a given task. This is different from the conventional space of examples that is represented by the worked examples and exercises in textbooks. We refer to…

This study examines future secondary physics teachers' knowledge related to the teaching of sound waves, and specifically the topics of sound level and sound intensity. The data is comprised of future teachers' responses to a task in which they had to compose a script for an imaginary dialogue between a teacher and a group of students and to…

In this study we consider a classic paradox of infinity and its variations and suggest how the sources of misleading intuition can be analysed using the concept of uniform convergence of functions. We then examine how six mathematics honour students engage with a variation of the paradox. Despite their advanced mathematical training, the…

In this paper, we highlight a further use of scripting tasks in the work of researchers-teacher-educators, which we present in two parts. In Part 1, we study prospective secondary school mathematics teachers' responses to a scripting task on the topic of functions. The generated examples for a function that satisfies certain constraints provide a…

Mathematical terminology is sometimes created according to conventions that are not obvious to students who will use the term. When this is the case, investigating the choice of a name can reveal interesting and unforeseen connections among mathematical topics. In this study, we tasked prospective and practicing teachers to consider: What is…

In this study we introduce "lesson play experience" (LPE) for implementation as professional development for in-service teachers. LPE is an extension of the "lesson play" notion, which refers to a script for an imagined lesson, written by a teacher, presented as dialogue of teacher-student(s) interaction. In mathematics teacher…

A Mathematics course for elementary school teachers (MFET) is required in North America in most teacher education programs. Our study investigates the perceptions of prospective elementary school teachers with respect to the contributions of such a course to their teaching. The results show that acquiring an understanding of concepts from the…