Anne Thwaites

Developing primary mathematics teaching : reflecting on practice with the Knowledge Quartet

This book helps readers to become better, more confident teachers of mathematics by enabling them to focus critically on what they know and what they do in the classroom. Building on their close observation of primary mathematics classrooms, the authors provide those starting out in the teaching profession with a four-stage framework which acts as a tool of support for developing their teaching: -Making sense of foundation knowledge – focusing on what teachers know about mathematics -Transforming knowledge – representing mathematics to learners through examples, analogies, illustrations, and demonstrations -Connection – helping learners to make sense of mathematics through understanding how ideas and concepts are linked to each other -Contingency – what to do when the unexpected happens Each chapter includes practical activities, lesson descriptions, and extracts of classroom transcripts to help teachers reflect on effective practice. Video versions of these lessons are also available on a companion website.

Analysing secondary mathematics teaching with the Knowledge Quartet

This paper describes how the Knowledge Quartet (KQ), which was developed with mathematics teachers in primary schools, has been tested in a secondary mathematics context. Aspects of this research are illustrated with reference to a lesson on completing the square. First we exemplify the mapping of episodes in the lesson to the KQ, then we report how one of these episodes, concerning the choice of examples, was subsequently used in a secondary mathematics PGCE teaching session.