How teachers make sense of new academic standards significantly shapes the implementation of those standards. Professional development organized around the analysis of mathematical tasks has potential to prepare teachers for standards implementation by helping them develop common understandings of standards and how to help students meet ambitious…

This study explores in-service high school mathematics teachers' conception of various forms of complex numbers and ways in which they transition between different representations of these forms. One 90-min interview was conducted with three high school mathematics teachers after they completed three professional development sessions, each 4 h, on…

Collaborations between mathematicians and mathematics teacher educators are increasingly being expected, and realized, within the context of mathematics teacher education. Most research related to collaborative efforts between members of the mathematics and mathematics education communities has focused on the products, rather than the process of…

This article reports an investigation into how students of a mathematics course for prospective secondary mathematics teachers in England talk about the notion of "understanding mathematics in depth", which was an explicit goal of the course. We interviewed eighteen students of the course. Through our social practice frame and in the…

In this study, we explored the relationship between prospective teachers' algebraic thinking and the questions they posed during one-on-one diagnostic interviews that focused on investigating the algebraic thinking of middle school students. To do so, we evaluated prospective teachers' algebraic thinking proficiency across 125…

This study is about prospective secondary mathematics teachers' understanding and sense making of representational quantities generated by algebra tiles, the quantitative units (linear vs. areal) inherent in the nature of these quantities, and the quantitative addition and multiplication operations--referent preserving versus referent…

A major research concern for teacher education is the impact of university credentialing programs on K-12 teaching and the disjuncture between university-promoted practices and what teachers actually do in their classrooms. In particular, mathematics-credential programs typically promote reform-oriented methods, while mathematics teaching in the…

In this article, we report on a study of beliefs about mathematics, teaching, and proof conducted with six prospective secondary mathematics teachers as they completed a two-semester sequence of a content course and a methods course. The initial beliefs of the participants were identified using interview and survey data, and potential shifts in…

The mathematics-education community stresses the importance of real-world connections in teaching. The extant literature suggests that in actual classrooms this practice is infrequent and cursory, but few studies have specifically examined whether, how, and why teachers connect mathematics to the real world. In this study, I surveyed 62 secondary…

In the research reported in this article, we sought to understand the instructional practices of 26 secondary teachers from one district who use a problems-based mathematics textbook series (Core-Plus). Further, we wanted to examine beliefs that may be associated with their instructional practices. After analyzing data from classroom…

Eight teachers were interviewed concerning how students verify conjectures. The study is a sequel to a previous study, "How Students Verify Conjectures" [Bergqvist, T. (2000). "How students verify conjectures." "Research reports in Mathematics Education" 3]. Teachers' expectations of students' reasoning and performance are examined, and also how…

This paper examines two types of discourse in which teachers engage when discussing case studies based on classroom episodes, and the ways in which the availability of video data of these episodes may motivate a shift in the mode of discourse used. We interviewed two pairs of secondary school mathematics teachers after they had read a case study…

This case study of a preservice secondary mathematics teacher focuses on the teacher's beliefs about his role as mathematics teacher. Data were collected over the final 5 months of the teacher?s university teacher education program through interviews, written course assignments, and observations of student-teaching. Findings indicate that the…