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 here ]

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

To read about the project associated with this website see:

Weston, T.L., Kleve, B. and Rowland, T. (2013) Developing an online coding manual for the Knowledge Quartet: An international project. Proceedings of the British Society for Research into Learning Mathematics 32(3) pp. 179-84.

Selected Knowledge Quartet publications:

Gumiero, B. S., and Pazuch, V. (2021). Teachers' Knowledge Mobilized in Geometry Lessons and Contingency Situations. International Electronic Journal of Mathematics Education, 16(1), em0620.

Oates, G, Callingham, R and Hay, I (2019) A consideration of technology with Rowland's Knowledge Quartet framework.  In M. Graven, H. Venkat, A. Essien & P. Vale (Eds.). Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp 145-152). Pretoria, South Africa: PME.

Weston, T.L. (2018). Using the Knowledge Quartet to support prospective teacher development during methods coursework. In S.E. Kastberg, A.M. Tyminski, A.E. Lischka & W.B. Sanchez (Eds.), Building support for scholarly practices in mathematics methods. Charlotte, NC: Information Age Publishing.

Rowland, T., Thwaites, A. and Jared, L. (2015) Triggers of contingency in mathematics teaching. Research in Mathematics Education 17(2), pp. 74-91 DOI:10.1080/14794802.2015.1018931

Rowland, T., Turner, F. and Thwaites, A. (2014) Research into teacher knowledge: a stimulus for development in teacher education practice. ZDM: The International Journal on Mathematics Education, 46(2), pp. 317-328

Rowland, T. (2013) Mathematics teacher knowledge. In P. Andrews and T. Rowland (Eds.) MasterClass in Mathematics Education: International Perspectives on Teaching and Learning (pp. 87-98). London, Bloomsbury.

Rowland, T. and Zazkis, R. (2013) Contingency in the mathematics classroom: Opportunities taken and opportunities missed. Canadian Journal of Science, Mathematics and Technology Education 13(2), pp. 137–153.

Weston, T.L. (2013). Using the Knowledge Quartet to quantify mathematical knowledge in teaching: The development of a protocol for initial teacher education. Research in Mathematics Education, 15(3), pp. 286-302.

Rowland, T. (2012) Contrasting knowledge for elementary and secondary mathematics teaching. For the Learning of Mathematics 32(1), pp. 16-21

Rowland, T., Jared, L. and Thwaites, A. (2011) Secondary mathematics teachers’ content knowledge: the case of Heidi. In M. Pytlak, T. Rowland and E. Swoboda (Eds.) Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education, 2827-2837. Rzeszow, Poland: University of Rzeszow.

Turner, F. and Rowland, T. (2011) The Knowledge Quartet as an organising framework for developing and deepening teachers’ mathematics knowledge. In T. Rowland & K. Ruthven (Eds) Mathematical Knowledge in Teaching (pp.195-212). London and New York: Springer.

Rowland, T. (2008) ‘The purpose, design and use of examples in the teaching of elementary mathematics.’ Educational Studies in Mathematics 69(2) pp. 149-163