The development of mathematical reasoning skills has increasingly been of focus for the teaching and learning of mathematics. This research utilizes a teaching simulation using the methodology of scriptwriting, in which prospective teachers are asked to complete a script of a dialogue from a classroom simulation involving fraction multiplication…

Practice-based pedagogies, such as representations of practice and approximations of practice, are increasingly common in mathematics teacher education. More needs to be known about how teacher candidates' (TCs') productions through such activities make visible the resources they bring to the work of teaching. In this paper, we highlight our use…

To leverage pedagogies of approximation to improve teacher education, educational researchers must first tackle the methodological question, "How can we determine the potential of pedagogies of approximation for supporting the growth of prospective teachers' knowledge and practices for teaching?" In this paper, we offer a model called…

With this article, we aim to spur a conversation on research implementation in the context of collaborations of mathematics teachers and educational researchers, with a special interest in projects situated in university mathematics education. Implementation has been often discussed in relation to the education of school teachers, and we suggest…

This study focuses on instances of creativity in the design of Lesson Play tasks and in prospective teachers' responses to the tasks. A Lesson Play task assumes a theatrical interpretation of the word "play" and requires teachers to write a script for an imaginary interaction between a teacher-character and student-characters, attending…

A significant body of research literature in mathematics education attends to mathematical proofs. However, scant research attends to proof comprehension, which is the focus of this study. We examine perspective secondary teachers' conceptions of what constitutes comprehension of a given proof and their ideas of how students' comprehension can be…

Collaboration scripts and heuristic worked examples are effective means to scaffold university freshmen's mathematical argumentation skills. Yet, which collaborative learning processes are responsible for these effects has remained unclear. Learners presumably will gain the most out of collaboration if the collaborators refer to each other's…

We discuss an innovative task used in teacher education--Lesson Play--that involves presenting a lesson in the form of an interaction between a teacher and students. We describe the motivation for the development of this task and, through specific examples, describe the iterative design process in which the task was refined and improved. We…

Dynamic geometry software (DGS) is often used for development of interactive teaching materials in many subjects, not only mathematics. These interactive materials can contain hundreds of elements in order to represent complex objects, and script programs to control their behavior. We propose an approach for creating, importing and using…