Reform-based approaches to teaching mathematics are proven to be most effective for students' learning, yet many novice secondary mathematics teachers still use traditional approaches. One reason for this is that novice teachers tend to teach the way that they experienced mathematics as students themselves. There is thus an onus on teacher…

In a multi-institutional study, the authors examine elementary preservice teachers' (PSTs') noticing skills before and after their engagement in a mathematics methods course. In particular, the authors examine their use of "Cognitively Guided Instruction" (CGI) as a means of supporting the development of PSTs' "professional noticing…

A transition from "doer" to "teacher" for prospective teachers requires them to reorient from thinking about how they do mathematics to engaging with students and their work, understanding student representations, and planning instruction accordingly. To scaffold a transition, we developed a five-step mathematics as teacher…

Researchers have generated a powerful framework that identifies three aspects of noticing students' mathematical thinking: attending to, interpreting, and deciding how to respond to student thinking. Previous research has tended to focus on evaluating how "well" teachers engaged in noticing, and how "well" they connected the…

Opportunities for teacher candidates to investigate and enact the work of teaching in settings of reduced complexity--what are called "approximations of practice"--offer a promising path toward preparing more ambitious and equitable mathematics teachers. However, these approaches face the risk of not preparing individuals to continue…

Supporting prospective teachers to enact high quality instruction requires transforming their methods preparation. This study follows three teachers through a practice-based elementary methods course. Weekly class sessions took place in an elementary school. The setting afforded opportunities for prospective teachers to engage in cycles of…

This study documents and describes efforts to develop robust forms of pre-service teachers' pedagogical content knowledge through a culturally responsive mathematics teaching approach. Embedded in a university K-8 mathematics methods course emphasising the connections among mathematics, children's mathematical thinking, and children's…

This article presents data from a group of secondary pre-service teachers who used vee diagrams to illustrate their conceptual and methodological analyses of a problem, as part of a required mathematics methods course assignment. The individually constructed vee diagrams were analysed in terms of the extent to which they displayed principles and…

This paper reports on a study focused upon 83 pre-service primary teachers in their first mathematics pedagogy subject at the University of Western Sydney. They completed three surveys: an achievement test of the mathematics they would be expected to teach; a survey of their beliefs about mathematics, mathematics teaching and mathematics learning;…