6 years, 3 months ago Posted in: Dimensions 0

This is an image that we use to indicate our conceptualization of and the connections between the four dimensions in the Knowledge Quartet.

6 years, 3 months ago Posted in: Dimensions, Foundation 0

This category consists of knowledge, beliefs and understanding acquired in the academy, in preparation (intentionally or otherwise) for their role in the classroom. Such knowledge and beliefs inform pedagogical choices and strategies in a fundamental way. The key components of this theoretical background are: knowledge and understanding of mathematics per se and knowledge of significanttracts […]

6 years, 3 months ago Posted in: Dimensions, Transformation 0

This category concerns knowledge-in-action as demonstrated both in planning to teach and in the act of teaching itself. At the heart of this category, is Shulman’s observation that the knowledge base for teaching is distinguished by “ … the capacity of a teacher to transform the content knowledge he or she possesses into forms that […]

6 years, 3 months ago Posted in: Dimensions, Connection 0

This category binds together certain choices and decisions that are made for the more or less discrete parts of mathematical content. It concerns the coherence of the planning or teaching displayed across an episode, lesson or series of lessons. Our conception of coherence includes the sequencing of topics of instruction within and between lessons, including […]

6 years, 3 months ago Posted in: Dimensions, Contingency 0

This category concerns classroom events that are almost impossible to plan for. In commonplace language it is the ability to ‘think on one’s feet’. In particular, the readiness to respond to children’s ideas and a consequent preparedness, when appropriate, to deviate from an agenda set out when the lesson was prepared. A constructivist view of […]