Shulman (1986, 1987) coined the term "pedagogical content knowledge" (PCK) to address what at that time had become increasingly evident--that content knowledge itself was not sufficient for teachers to be successful. Throughout the past two decades, researchers within the field of mathematics teacher education have been expanding the notion of PCK…

This paper reports on the beliefs of a group of K-8 mathematics teachers about appropriate goals and methods of mathematics teaching for students with mathematics learning difficulties and for students generally. The teachers were involved in a brief professional learning program that aimed to provide them with effective strategies for mathematics…

This paper describes the experiences of two pre-service primary teachers in a teacher education subject focusing on mathematics and learning difficulties. It describes how bibliotherapy was a powerful reflective tool that provided them with the opportunity to respond cognitively and affectively to their own schooling. By analysing readings about…

I argue in this article that identity as a mathematical thinker develops through self-directed learning within a supportive community of practice. The dynamic nature of identity as a mathematical thinker is illustrated by considering the experiences of primary pre-service teachers who undertook a mathematics and technology subject in their…

This paper examines some of the complexities involved in the actual work of classroom instruction by examining interactions among the goals of teaching. The research is part of a case study of teaching a Year 7 Singapore class comprising students of average mathematical ability. Among the complexities of teaching analysed here are the problems…

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…

It is generally perceived that Chinese elementary teachers have a profound understanding of the school mathematics they teach. This perception has led to further interest in understanding teacher education practices in China. As some dramatic changes in elementary teacher preparation have taken place in China over the past decade, this article…

Detracking and heterogeneous groupwork are two educational practices that have been shown to have promise for affording all students needed learning opportunities to develop mathematical proficiency. However, teachers face significant pedagogical challenges in organizing productive groupwork in these settings. This study offers an analysis of one…

Although video cases are increasingly being used in teacher education as a means of situating learning and developing habits of reflection, there has been little evidence of the outcomes of such use. This study investigates the effects of using a coherent video-case curriculum in a university mathematics methods course by addressing two issues:…

School students of all ages, including those who subsequently become teachers, have limited experience posing their own mathematical problems. Yet problem posing, both as an act of mathematical inquiry and of mathematics teaching, is part of the mathematics education reform vision that seeks to promote mathematics as an worthy intellectual…

Prospective teachers' (PT) beliefs and views regarding teaching and learning affect the way they teach after they have graduated. Often, these views are a consequence of their past experience as pupils themselves. In recent years there has been a great effort toward changing the teaching and learning of mathematics, which raises the need to…

The challenge that we address concerns teachers' shifts toward student-centered instruction. We report on a yearlong professional development study in which two United States elementary school teachers engaged in a teaching experiment, as described by Steffe and Thompson (in: Lesh and Kelly (eds) Research on design in mathematics and science…

This article is situated in the research domain that investigates what mathematical knowledge is useful for, and usable in, mathematics teaching. Specifically, the article contributes to the issue of understanding and describing what knowledge about proof is likely to be important for teachers to have as they engage students in the activity of…

As mathematics educators think about teaching that promotes students' opportunities to learn, attention must be given to the conceptualization of the professional development of teachers and those who teach teachers. In this article, we generalize and expand the instructional triangle to consider different interactions in a variety of teacher…

Students learn more when they attempt to make sense of a mathematical situation they face. For example, a question like why square root of 25 is not + or - 5. Providing the intermediate steps and the reasoning of a technique with graphs can help make better sense of mathematics.