2. Three ways of thinking about Teaching Teaching Relationships Teaching Models Reflection Teaching Skills

4. Achievement of students Number of students Reaching for the Double Sigma Effect Whole class Group Individual

6. General Teaching Knowledge Generalised pedagogical knowledge Effective subject teaching

7. Disconnected Knowledge Generalised pedagogical knowledge Knowledge of the discipline Effective subject teaching

8. Pedagogical Content Knowledge Generalised pedagogical knowledge Knowledge of the discipline Effective subject teaching Pedagogical content knowledge

9. Capacity to Learn Principles of learning Effort is a more important determinant of achievement than ability Given the right time and support, almost all can become proficient learners Principles of teaching High expectations and challenging targets should be set for all While the standards should remain constant, time and support should be varied according to individual student need Are there standards in place and targets for all students? Do we vary time and support?

11. So … We teach not to produce little living libraries on a subject, but rather to get students to think mathematically for themselves, to consider matters as an historian does, to take part in the process of knowledge-getting. Knowing is a process not a product. Adapted from: Jerome Bruner, Toward a Theory of Instruction (1966)