Chris Hurst

Teacher knowledge continues to be a topic of debate in Australasia and in other parts of the world. There have been many attempts by mathematics educators and researchers to define knowledge needed by teachers to effectively teach mathematics, and a plethora of terms such 681 as mathematical content knowledge, pedagogical content knowledge, horizon content knowledge and specialised content knowledge have been used to describe aspects of such knowledge. Here, I put forward a new model for teacher knowledge that embraces aspects of earlier models and which focuses on the notions of contingent knowledge and the connectedness of “big ideas” of mathematics to enact what is described as “powerful teaching”. Its power lies in the teacher’s ability to set up and provoke contingent moments to extend children’s mathematical horizons. The new model proposed here considers the various cognitive and affective components and domains that teachers require to enact “powerful teaching”. Contingency is described in Rowland’s Knowledge Quartet as the ability to respond to children’s questions, misconceptions and actions and to be able to deviate from a teaching plan as needed. It follows that a deeper level of knowledge might enable a teacher to respond better and indeed to plan and anticipate contingent moments. Taking this further and considering teacher knowledge as “dynamic”, I suggest that instead of responding to contingent events, powerful teaching is about provoking contingent events. In order to place genuine problem solving at the heart of learning, the idea is to actually plan for contingent events, to provoke them, and “set them up”. The proposed model attempts to represent that process.