Provoking contingent moments: Knowledge for ‘powerful teaching’ at the horizon

What is it about?

This article is about the types of knowledge that teachers need for effectively teaching mathematics, particularly in junior and middle school contexts. It focuses on the knowledge and mindset needed by teachers in order to challenge their students and to make them think deeply about the mathematics with which they are working. It is also about teachers knowing the mathematics deeply and in a connected way, so that they can make explicit to their students the many connections within and between the 'big ideas' of mathematics.

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Why is it important?

Various models of teacher knowledge have been proposed since the 1980's and this article is an attempt to synthesize the contributions made by Shulman, Ball, Bass, Thames, Phelps, and Rowland (and others) to develop a new model based on the notion of contingency (Rowland). Rather than be reactive to contingent moments (opportunities that arise in teaching), the new model suggests that teachers should be actively seeking and provoking such moments in order to provide genuine challenges for their students. The thinking underpinning the model is that students learn better and are more effective problem solvers when they are taken 'out of their comfort zones'. The new model described in this article is important because the ability to meet challenges and solve problems is critically important.

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