Research often reports an overt discrepancy between theoretically/out-of context expressed teacher beliefs about mathematics and pedagogy and actual practice. In order to explore teacher knowledge in situation-specific contexts we have engaged mathematics teachers with classroom scenarios (Tasks) which: are hypothetical but grounded on learning…

This article discusses certain aspects of mathematics teacher education in Russia. To be able successfully to teach through problems, a teacher must know how to select the necessary assignments, to construct mathematical tasks according to methodological principles, and to organize work on these assignments in the classroom; in short, as they say…

We discuss mathematical tasks used in a first mathematics content course for elementary teachers at our university to foster a deep conceptual understanding of early arithmetic, including basic concepts of number, number relationships and strategies, and coordinating units of different rank. Our approach is to immerse our students in a base 8…

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…

"Lesson explaining" has been developed in China from an evaluative resource to an effective form of teacher professional development with the value of emphasizing teacher reflective practice. This paper begins with a general description of lesson explaining. Then an example of "explaining" a mathematics lesson for teaching probability is…

In this study we created, implemented, and evaluated the impact of proportional reasoning authentic investigative tasks on the mathematical content and pedagogical knowledge and attitudes of pre-service elementary and middle school mathematics teachers. For this purpose, a special teaching model was developed, implemented, and tested as part of…

Using the work of teaching as a central resource, practice-based approaches to teacher professional development attempt to coordinate and link different facets of teacher knowledge to each other and to the settings in which the knowledge is used. Advocates for practice-based professional development argue that learning experiences that are highly…

The paper describes a design research study with experienced mathematics teachers of post-16 low-attaining students. The study explored the use of generic collaborative mathematics tasks in promoting professional development. I describe the theoretical basis for the design of the tasks, the tasks themselves and a professional development programme…

In this paper we illustrate the use of a tool from a teaching programme with one year graduate students. This tool is designed to help them to develop tasks for the classroom. It is described in its three stages, for analysing mathematics, for connecting the curriculum, and for informing in-the-moment shifts. We finally discuss the role of tools…

In this paper we describe a strand of activities for teachers of mathematics that we used with two cohorts of participants in a professional development program called Revitalizing Algebra (REAL). We first discuss our goals and describe the participants, and then we describe the construction and selection of the tasks followed by teacher…

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…

This article discusses the design of tasks for teacher education. It focuses on tasks that are used in a university course for pre-service secondary school mathematics teachers. Special attention is given to tasks that use analogical thinking in their construction or implementation. These tasks are categorized by type of teacher education goal and…

Reforms in education have repeatedly been confronted with the challenge of policy implementation. Recent initiatives in mathematics are no exception. Pressing for fundamental and complex changes to pedagogy, the initiatives demand much from teachers. In this article, we propose a conceptual frame for understanding how teachers and schools work to…

The new Queensland "Mathematics Years 1-10 Syllabus" differs from previous syllabuses in that it has an outcomes structure that describes how students think, reason, and work mathematically. The main challenge for secondary teachers implementing the new syllabus lies in taking a more investigative approach to "working mathematically". This paper…

Gaps between teaching practices and research recommendations have been well documented. One challenge for research is in understanding the processes and systems that promote a bridging of these gaps. A year-long study with four primary teachers documented ten support mechanisms, or connection levers, that the teachers raised as important for…