Studies of mathematics teacher preparation frequently lament the divide between the more theoretically based university methods course and the practically grounded classroom field experience. In many instances, attempts to mediate this gap involve creating hybrid or third spaces, which seek to dissipate the differences in knowledge status as…

Based on findings from a semester-long study, this article examines the development of Samoan prospective teachers' mathematical understandings and mathematics attitudes when investigating authentic contexts and applying working mathematically processes, mental computations and problem-solving strategies to find solutions of problems. The…

Many learners hold traditional beliefs about mathematics that can hamper their learning in the discipline. To address this issue, a "history-based" intervention program entailing problem-solving and writing activities that instigate cognitive conflict was implemented. Data sources were pretest and posttest scores of a 12-theme…

The primary school mathematics curriculum in Ireland is based upon a constructivist philosophy of learning. As constructivism is a theory of learning and not teaching, implementing a constructivist approach in the classroom requires teachers to identify the implications and applications of constructivist philosophy for teaching. In this research,…

The study considers mathematical problem solving to be at the heart of mathematics teaching and learning, while mathematical challenge is a core element of any educational process. The study design addresses the complexity of teachers' knowledge. It is aimed at exploring the development of teachers' mathematical and pedagogical conceptions…

In this paper, we describe a one-day professional development activity for mathematics teachers that promoted the use of comparison as an instructional tool to develop students' flexibility in algebra. Effective use of comparison in mathematics instruction involves using side-by-side presentation of problems and solution methods and subsequent…

One danger of integrating inquiry-based problem-solving activities into mathematics lessons is that different strategies could be accepted without in-depth discussions on the cogency and efficiency of the strategies. To overcome this issue, Japanese teachers typically go through a series of lesson-study-based teacher learning sessions and learn…

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 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…

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…

The aim of this study is to characterize the discourse of two problem-solving courses for prospective teachers. The data, consisting of audio recordings and field notes, were examined from a dialogical approach combined with the theory of contextualization. I show not only the substantial differences between the two classroom discourses but also…

This paper describes an approach for pre-service or in-service mathematics education that teaches sophisticated mathematics using only the tools of high school mathematics. The idea is to start with a standard problem from high school mathematics and let the solution to this problem serve as a platform for asking good mathematical questions and…

This paper describes the implementation of extended analysis tasks (EATs) in a required mathematics course for prospective high school mathematics teachers, and investigates the mathematical discovery promoted through engagement with these tasks. Extended analysis tasks are designed to move students beyond the problem context to the underlying…

Teachers are expected today to assess student understanding as an integral part of instruction, using a combination of various assessment methods and tools, among which are observing students solve problems in class and listening to their mathematical discussions. The aim of our study is to explore what it might mean for a teacher to hear students…

In the past decade, there has been an increased emphasis on the preparation of teachers who can effectively engage students in meaningful mathematics with technology tools. This study presents a closer look at how three prospective teachers interpreted and developed in their role of facilitating students' mathematical problem solving with a…