# Mathematics for teaching and deep subject knowledge: voices of Mathematics Enhancement Course students in England

## Abstract

This article reports an investigation into how students of a mathematics course for prospective secondary mathematics teachers in England talk about the notion of ‘understanding mathematics in depth’, which was an explicit goal of the course. We interviewed eighteen students of the course. Through our social practice frame and in the light of a review of the literature on mathematical knowledge for teaching, we describe three themes that weave through the students’ talk: reasoning, connectedness and being mathematical. We argue that these themes illuminate privileged messages in the course, as well as the boundary and relationship between mathematical and pedagogic content knowledge in secondary mathematics teacher education practice.

## Keywords

Mathematics for teaching Teacher education Deep subject knowledge Secondary Subject matter knowledge Pedagogic content knowledge## Notes

### Acknowledgments

This paper forms part of the QUANTUM-UK research project on Mathematics for Teaching, directed by Jill Adler, at King’s College London and the University of the Witwatersrand. This material is based upon work supported by King’s College London and the National Research Foundation South Africa under Grant number FA2006031800003, and undertaken by the collaborators authoring the paper. Any opinion, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Research Foundation.

## References

- Adler, J. (2000). Conceptualising resources as a theme for mathematics teacher education.
*The Journal of Mathematics Teacher Education,**3*(3), 205–224.Google Scholar - Adler, J., & Davis, Z. (2006). Opening another black box: Researching mathematics for teaching in mathematics teacher education.
*Journal for Research in Mathematics Education,**37*(4), 270–296.Google Scholar - Adler, J., & Davis, Z. (2011). Modelling teaching in mathematics teacher education and the constitution of mathematics for teaching. In T. Rowland & K. Ruthven (Eds.),
*Mathematical knowledge in teaching*(pp. 139–160). New York: Springer.Google Scholar - Adler, J., & Huillet, D. (2008). The social production of mathematics for teaching. In P. Sullivan & T. Wood (Eds.),
*International handbook of mathematics teacher education: Vol.1. Knowledge and beliefs in mathematics teaching and teaching development. Rotterdam, the Netherlands: Sense Publishers*. (Vol. 1, pp. 195–222). Rotterdam: Sense.Google Scholar - Artzt, A., Sultan, A., Curcio, F. and Gurl, T. (2011). A capstone mathematics course for prospective secondary mathematics teachers.
*Journal of Mathematics Teacher Education.*Retrieved from http://www.qc.cuny.edu/Academics/Degrees/Education/Documents/SEYS%20Publish.pdf. doi: 10.1007/s10857-011-9189-5. - Askew, M., Brown, M., Rhodes, V., Wiliam, D., & Johnson, D. (1997).
*Effective teachers of numeracy: Report of a study carried out for the teacher training agency*. London: King’s College, University of London.Google Scholar - Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special?
*Journal of Teacher Education,**59*, 389–407. doi: 10.1177/0022487108324554.CrossRefGoogle Scholar - Barton, B. (2009). Being mathematical, holding mathematics: Further steps in mathematical knowledge for teaching. In R. Hunter, B. Bicknell, & T. Burgess (Eds.),
*Crossing divides: Proceedings of the mathematics education research Group of Australasia*(Vol. 1). Palmerston North, NZ: MERGA.Google Scholar - Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., et al. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress.
*American Educational Research Journal,**47*(1), 133–180. doi: 10.3102/0002831209345157.CrossRefGoogle Scholar - Bernstein, B. (2000).
*Pedagogy, symbolic control and identity: Theory, research, critique*(2nd ed.). Oxford: Rowman & LIttlefield.Google Scholar - Crisan, C., Rodd, M. (2011).
*Teachers of mathematics to mathematics teachers: a report on a TDA Mathematics Development Programme for Teachers.*Paper presented at the British Society for Research in the Learning of Mathematics (BSRLM).Google Scholar - Davis, B., & Simmt, E. (2006). Mathematics-for-teaching: An ongoing investigation of the mathematics that teachers (need to) know.
*Educational Studies in Mathematics,**61*(3), 293–319.CrossRefGoogle Scholar - Davis, Z., Adler, J., & Parker, D. (2007). Identification with images of the teacher and teaching in formalized in-service mathematics teacher education and the constitution of mathematics for teaching.
*Journal of Education,**42*, 33–60.Google Scholar - Dowling, P., & Brown, A. (2010).
*Doing research/reading research: Re-interrogating education*(2nd ed.). London: Routledge.Google Scholar - Hatch, J. A. (2002).
*Doing qualitative research in education settings*. Albany, NY: State University of New York Press.Google Scholar - Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement.
*American Educational Research Journal,**42*(2), 371–406.CrossRefGoogle Scholar - Hodgen, J. (2011). Knowing and identity: A situated theory of mathematics knowledge in teaching. In T. Rowland & K. Ruthven (Eds.),
*Mathematical knowledge in teaching*(pp. 27–42). Dordrecht: Springer.CrossRefGoogle Scholar - Kilpatrick, J., Swafford, J., & Findell, B. (2001).
*Adding it up: Helping children learn mathematics*. Washington: National Academy Press.Google Scholar - Krauss, S., Baumert, J., & Blum, W. (2008). Secondary mathematics teachers’ pedagogical content knowledge and content knowledge: validation of the COACTIV constructs.
*ZDM,**40*(5), 873–892. doi: 10.1007/s11858-008-0141-9.CrossRefGoogle Scholar - Lave, J., & Wenger, E. (1991).
*Situated learning: Legitimate peripheral participation*. Cambridge: Cambridge University Press.CrossRefGoogle Scholar - Ma, L. (1999).
*Knowing and teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States*. New Jersey: Lawrence Erlbaum.Google Scholar - Ruthven, K. (2011). Conceptualising mathematical knowledge in teaching. In T. Rowland & K. Ruthven (Eds.),
*mathematical knowledge in teaching*(pp. 83–96). Dordrecht: Springer.CrossRefGoogle Scholar - Shulman, L. S. (1986). Those who understand knowledge growth in teaching.
*Educational Researcher,**15*(2), 4–14.CrossRefGoogle Scholar - Skemp, R. R. (1976).
*Relational understanding and instrumental understanding Mathematics Teaching in the Middle School,**77*, 20–26.Google Scholar - Stevenson, M. (forthcoming). Understanding mathematics in depth: An investigation into the conceptions of secondary mathematics teachers on two UK subject knowledge enhancement courses. PhD, Liverpool Hope.Google Scholar
- TTA. (2003). Specification for mathematics enhancement course.Google Scholar
- Watson, A. (2008). School mathematics as a special kind of mathematics.
*For the Learning of Mathematics,**28*(3), 3–7.Google Scholar - Watson, A., & Barton, B. (2011). Teaching mathematics as the contextual application of mathematical modes of enquiry. In T. Rowland & K. Ruthven (Eds.),
*Mathematical knowledge in teaching*(pp. 65–82). Dordrecht: Springer.CrossRefGoogle Scholar - Wenger, E. (1998).
*Communities of practice: Learning, Mmaning, and identity*. Cambridge: Cambridge University Press.CrossRefGoogle Scholar - Zazkis, R. (2011).
*Relearning mathematics: A challenge for prospective elementary school teachers*. Charlotte, NC: Information Age Publishing.Google Scholar - Zazkis, R., & Leikin, R. (2010). Advanced mathematical knowledge in teaching practice: Perceptions of secondary mathematics teachers.
*Mathematical Thinking & Learning*,*12*(4), 263–281. doi: 10.1080/10986061003786349.