A programme of research at the University of Cambridge (SKIMA: subject knowledge in
mathematics) from 2002 to the present has investigated the mathematics content knowledge of primary trainee teachers, and the ways that this knowledge becomes visible both in their planning and in their teaching in the classroom. From this research, a framework for the observation, analysis and development of mathematics teaching was developed, with a focus on the contribution of the teacher’s mathematical content knowledge. Rather than considering the generic features of the lesson (behaviour management, classroom organisation and so forth), the framework, the Knowledge Quartet, categorises events in mathematics lessons with particular reference to the subject matter being taught, and the mathematics-related knowledge that teachers call upon. While Shulman’s distinction between subject matter knowledge and pedagogical knowledge underpins this consideration of mathematics teaching (Shulman 1986), the Knowledge Quartet (KQ) identifies situations in which such knowledge can be seen in the act of teaching. The origins of the KQ were in observations of primary mathematics teaching, and grounded theory methodology (Glaser and Strauss 1967; Strauss and Corbin 1990), in the context of one-year graduate primary teacher preparation.

From the perspective of the KQ, the knowledge and beliefs evidenced in mathematics
teaching can be seen in four dimensions (see image below), named foundation, transformation, connection and contingency. Each dimension is composed of a small number of subcategories that we judged, after extended discussion, to be of the same or a similar nature (itemized in the list of links on the menu on the right of this page).

Since 2002, there has been a process of refinement of the conceptualisation of the KQ, and enhancement of the constituent codes, both in response to additional classroom data and in the process of application.  This has included extending the framework into secondary grades as well as internationally.

For an introduction to the Knowledge Quartet see the following:

Rowland, T., Huckstep, P. and Thwaites, A. (2005) 'Elementary teachers' mathematics subject knowledge: the knowledge quartet and the case of Naomi'. Journal of Mathematics Teacher Education 8(3) pp. 255-281.

Rowland, T. (2014) The Knowledge Quartet: the genesis and application of a framework for analysing mathematics teaching and deepening teachers’ mathematics knowledge. SISYPHUS Journal of Education, 1(3), pp. 15-43 [downloadable from]

Rowland, T., Turner, F., Thwaites, A. and Huckstep, P. (2009) Developing Primary Mathematics Teaching: reflecting on practice with the Knowledge Quartet. London: Sage.