Developing and using the ‘Knowledge Quartet’: A framework for the observation of mathematics teaching

This paper describes a framework for mathematics lesson observation and illustrates the ways that this framework is being used in practice, for 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 students towards the end of their initial training. A grounded theory approach to data analysis led to the emergence of the framework - a ‘knowledge quartet’, with four broad dimensions, through which the mathematics-related knowledge of these teachers could be observed in practice. We term the four units: foundation, transformation, connection and contingency. This paper describes how each of these units is characterised, and analyses a fragment of one of the videotaped lessons, showing how each dimension of the quartet can be identified in the lesson.