The Knowledge Quartet: The Genesis and Application of a Framework for Analysing Mathematics Teaching and Deepening Teachers’ Mathematics Knowledge

This paper describes a framework for mathematics lesson observation, the ‘Knowledge Quartet’, and the research and policy contexts in which it was developed. The framework has application in research and in mathematics teaching development. The research which led to the development of the framework drew on videotapes of mathematics lessons prepared and conducted by elementary pre-service teachers towards the end of their initial training. A grounded theory approach to data analysis led to the emergence of the framework, with four broad dimensions, through which the mathematics-related knowledge of these teachers could be observed in practice. This paper describes how each of these dimensions is characterised, and analyses two lessons, showing how each dimension of the Quartet can be identified in the lesson. The paper concludes by outlining recent developments in the use of the Knowledge Quartet