Over the past two decades, mathematics education reformers have increasingly called for new approaches to assessment. This call urges mathematics teachers to merge their assessment with pedagogy, to employ assessments that engage students in the process of "doing mathematics," and to exploit assessment to support learning. This paper…

This paper is based on data gathered during visits to Uganda and Malawi, conducted by the International Math-teacher Professionalization Using Lesson Study (IMPULS) project and the Japanese International Cooperation Agency (JICA). The author's observations and experiences highlighted misconceptions about lesson study. The paper concludes that…

This case study explored how students disaffected with their school experience were scaffolded during their participation in a middle-school mathematics classroom. Of particular interest were the level of student engagement in discussion about the mathematics being presented by the teacher and the approach to doing mathematics being displayed by…

We investigate interpersonal difficulties that student teachers and cooperating teachers may experience during the teaching internship by exploring the tension between one high school mathematics student teacher and his cooperating teacher. We identified seven causes of this tension, which included different ideas about what mathematics should be…

As a secondary mathematics teacher, I used practitioner action research to determine effective ways to intervene with students working in groups, with the goal of improving their communication. Utilising transcripts of group interactions and teacher interventions, field notes, and student feedback, I discovered ten different issues that prevent…

The aim of this collaborative study was to understand what factors beginning secondary mathematics teachers attribute their success to in the classroom, regardless of their preparation program. Further description of how and when beginning teachers reported acquiring important teaching attributes provides a perspective on how they make the…

Current debates about successful mathematics pedagogy suggest that mathematical learning and problem solving can be enhanced by using metaphors as they provide students with a tool for thinking. But assisting pre-service teachers to understand the importance of careful and accurate explanations for mathematical concepts remains an issue. This…

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…

There remains a lack of empirical evidence about the relationship between the level of mathematics studied at high school and within tertiary degrees and primary school pre-service teachers' success in curriculum subjects. Further, there is little evidence to inform the structure and delivery of mathematics teacher preparation. In this study, the…

Definitions play an essential role in mathematics. As such, mathematics teachers and students need to flexibly and productively interact with mathematical definitions in the classroom. However, there has been little research about mathematics teachers' understanding of definitions. At an even more basic level, there is little clarity about what…

The importance of using real-life contexts in teaching mathematics is emphasised in many policy and curriculum statements. The literature indicates using contexts to teach mathematics can be difficult and few detailed exemplars exist. This article describes the use of real-life contexts in one New Zealand Year 11 algebra lesson. Data included a…

With increased accountability attached to students' results on national testing in Australia, teachers feel under pressure to prepare students for the tests. However, this can lead to shallow teaching of a narrowed curriculum. An alternative approach involves using data to identify common errors and misconceptions, discussing strategies aimed at…

The importance of teachers' content knowledge for effective teaching of mathematics has long been recognised. Recent national testing regimes in Australia (National Assessment Program-Literacy and Numeracy [NAPLAN]) have raised questions of the adequacy of teachers' content knowledge. This, in turn has focused attention upon the quality of teacher…

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…

In New South Wales the focus on assessment "for" learning requires teachers to consider carefully the alignment between assessment, curriculum, and pedagogy. This emerging agenda in teacher education seeks to ensure that assessment practices provide advice to teachers about what students know and where teaching might be directed to enhance…