This paper describes part of an international project considering graphical construction of antiderivative functions in the secondary mathematics classroom. We use Schoenfeld's resources, orientations, and goals (ROGs) framework to analyse the decisions made by a teacher, Adam, during a lesson on graphical antiderivatives. We present details…

Mathematics teachers play a unique role as experts who provide opportunities for students to engage in the practices of the mathematics community. Proof is a tool essential to the practice of mathematics, and therefore, if teachers are to provide adequate opportunities for students to engage with this tool, they must be able to validate student…

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…

This retrospective phenomenological study investigates activities and actions identified by secondary statistics teachers who exhibit robust understandings of variation as deepening their understandings of statistical variation. Using phenomenological methods and a frame of Mezirow's transformation theory, analysis revealed learning factors…

This study compared conversations among groups of teachers of high school geometry that had been elicited by a representation of instruction (either a video or an animation) and facilitated with an open-ended agenda. All artifacts used represented instruction scenarios that departed from what, according to prior work, had been hypothesized as…

Recent research efforts (Schmidt et al. in "The preparation gap: teacher education for middle school mathematics in six countries," MSU Center for Research in Mathematics and Science Education, 2007) demonstrate that teacher development programs in high-performing countries offer experiences that are designed to develop both mathematical…

Although skilled mathematics teachers and teacher educators often "know" when interruptions in the flow of a lesson provide an opportunity to modify instruction to improve students' mathematical understanding, others, particularly novice teachers, often fail to recognize or act on such moments. These pivotal teaching moments (PTMs), however, are…

In this article, we report on the use of a teacher profiling instrument with 62 middle school teachers at the start of a 3-year professional learning programme. The instrument was designed to assess the aspects of teachers' knowledge identified by Shulman ("1987") refined by Ball et al. ("2008") and extended to include teachers' confidence to use…

Although potentially powerful for educators, the construct of teacher reflection has become diluted, rendering teacher engagement with meaningful reflection problematic. This article presents a theoretical framework that divides teacher reflection into two broad categories. The first and most common "incident reflection" occurs as specific…

A professional learning program for teachers of junior secondary mathematics regarding the content and pedagogy of senior secondary mathematics is the context for this study of teachers' mathematical and pedagogical knowledge. The analysis of teachers' reflections on their learning explored teachers' understanding of mathematical connections and…

Current reform efforts call for an emphasis on the use of representation in the mathematics classroom across levels and topics. The aim of the study was to examine teachers' conceptions of representation as a process in doing mathematics, and their perspectives on the role of representations in the teaching and learning of mathematics at the…

This article analyzes the experiences of prospective secondary mathematics teachers during a teaching methods course, offered prior to their student teaching, but involving actual teaching and reflexive analysis of this teaching. The study focuses on the pedagogical difficulties that arose during their teaching, in which prospective teachers…

This article reports on the results of a survey of 45 secondary mathematics cooperating teachers' perceptions of the primary purposes of student teaching and their roles in accomplishing those purposes. The most common purposes were interacting with an experienced, practising teacher, having a real classroom experience, and experiencing and…

Although growing numbers of secondary school mathematics teachers and students use calculators to study graphs, they mainly rely on paper-and-pencil when manipulating algebraic symbols. However, the Computer Algebra Systems (CAS) on computers or handheld calculators create new possibilities for teaching and learning algebraic manipulation. This…

This article describes the collaborative inquiry activity of a group of high school mathematics teachers interested in increasing student engagement and problem solving in the classroom. Specific findings related to the nature of the teacher interactions and subsequent impacts on practice are discussed. The findings focus on (a) the nature of the…