A PRACTICE-BASED THEORY OF MATHEMATICAL KNOWLEDGE FOR TEACHING

A central challenge of professional education is to prepare novices for skilful beginning practice. Doing this depends on robust theory about the relationship between teaching practice and teacher education. Theories of instruction can help provide a foundation for a professional curriculum centred on learning the practice of teaching. Teachers need to know and be able to use mathematics in the work of teaching pupils and they need to be able to carry off specific instructional practices that enable pupils to learn. This paper reports from a set of coordinated studies that have developed a practice-based theory of mathematical knowledge for teaching and theories about ways to teach it, designed assessments keyed to this practice-based theory of teachers' usable knowledge of mathematics, and developed a coding scheme for appraising the mathematical quality of instruction.