The Problem-Solving Cycle: A Model to Support the Development of Teachers' Professional Knowledge

Abstract

This article focuses on the Problem-Solving Cycle (PSC), a model of professional development designed to assist teachers in supporting their students' mathematical reasoning. Each PSC is a series of three interrelated workshops in which teachers share a common mathematical and pedagogical experience, organized around a rich mathematical task. Throughout the workshops, teachers delve deeply into issues involving mathematical content, pedagogy, and student thinking as they pertain to the selected task. We analyze this professional development model in relation to the ways it supports the development of content and pedagogical content knowledge. We highlight the ways in which specific knowledge strands are foregrounded during each of the three PSC workshops, while also demonstrating their interconnectedness. The improvement of students' opportunities to learn mathematics depends fundamentally on teachers' skill and knowledge. No curriculum or framework is self-enacting, nostudents self-teaching. Moreover, teachers are often expected to teach mathematical topics and skills in ways substantially different from the ways in which they themselves learned that content.… Hence, if students' learning is to improve, teachers' professional learning opportunities are key. (Boaler & Humphreys, 2005 Boaler, J. and Humphreys, C. 2005. Connecting mathematical ideas: Middle school video cases to support teaching and learning., Portsmouth, NH: Heinemann. [Google Scholar])

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