- 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.