In this study, we analyse 23 prospective teachers' lesson plans for short whole-class mathematics discussions held with students at a middle school. The plans are in the form of "lesson plays", where an imagined discussion between the teacher and students is written verbatim. We use the Knowledge Quartet as a framework to investigate…

In this study, we examined the ability of grades 1-8 pre-service teachers (PSTs) to engage in thinking about patterns, relationships, and functional rules. Using the algebraic habit of mind Building Rules to Represent Functions as a framework, we examined whether and how well our PSTs (n = 18) used seven features of this habit of mind: organize…

This paper reports on the reflections of twenty-one primary preservice teachers following a microteaching experience that focused on the use of talk and collaborative group work, as part of a primary mathematics specialist education programme. Based on the didactic strategies of exploratory talk, the experience intended to develop knowledge for…

Establishing the mathematical content knowledge of pre-service teachers is a requirement in New Zealand. However, this knowledge is not clearly defined and is a challenge for initial teacher education providers to assess. We develop the concept of foundation content knowledge and suggest how it can be assessed using two forms of diagnostic…

This paper reports on an investigation into pre-service teachers' mathematical content knowledge and their ability to interpret students' responses to a multi-digit multiplication task and make subsequent appropriate teaching decisions. Using a combination of quantitative and qualitative methods, the researchers tested aspects of the mathematical…

Successful teacher preparation programs provide learning experiences that help teacher candidates make the shift from "student" to "teacher." In this paper we present research on the implementation of a process for providing candidates such experiences. Utilizing the Mathematics as Teacher Heuristic (MATH) process, prospective…

This paper reports on the results of three different investigations into pre-service teachers' understanding of the mathematical concepts of area and perimeter. Different test instruments were used with three cohorts from two universities in order to identify pre-service teachers' understandings and common misconceptions. The results indicated…

This paper presents data on the mathematical content knowledge and attitudes of pre-service primary teacher education students. The assessment consisted of nine tasks, including 2-digit computations and proportional reasoning. Students rated their liking for mathematics at three time points: primary, secondary, .and when assessed. Fewer than half…

The limited mathematical knowledge of preservice primary teachers is an international concern. The areas of mathematical difficulties have been well documented, which has led to many universities instituting testing regimes to ensure that preservice teachers have appropriate knowledge of primary school mathematics. In our study, the preservice…

This paper reports on the knowledge for teaching mathematics of 294 pre-service primary teachers from seven Australian universities participating in a project aimed at establishing a culture of evidence-based improvement of teacher education. The project was funded by the Australian Learning and Teaching Council. Rasch measurement techniques were…

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 study investigated the changes in conceptions on mathematics teaching and learning of preservice BScEd teachers after 12 weeks of full time teaching practice. Written answers to open ended questions administered at the beginning and end of student teaching were triangulated with interviews. The preservice teachers exhibited more differences…

Recent developments about cognitions underlying mathematical learning are beginning to suggest that the activation and appropriate use of prior knowledge by students is, to a large measure, controlled by the quality of organisation of that knowledge. Thus, teaching needs to support the construction of well-connected mathematical knowledge. An…