# Frameworks for Conceptualizing Mathematics Teacher Knowledge

**DOI:**https://doi.org/10.1007/978-94-007-4978-8_63

- 1.1k Downloads

## Introduction

Discussion of the relationship between knowledge and the profession of teaching is particularly convoluted because knowledge is itself the commodity at the heart of education and the very goal of teaching. For a starting point in theorizing knowledge and teaching, one can turn to Aristotle’s (384–322 BC) aphorism “it is a sign of the man who knows, that he can teach” (Metaphysics, Book 1). This can be interpreted that “really” knowing something is best evidenced in the performance of teaching. The Oxford philosopher John Wilson (1975) endorsed and extended Aristotle’s position on teacher knowledge with the argument that comprehension of the logic of concepts offered guidance on how to teach them. In other words, not only do we need to know what we teach in the sense of understanding it, but such a profound quality of knowing actually acts as a guide to the pedagogy, i.e., the “how to teach,” of subjects such as mathematics. This position has recently been developed by...

## Keywords

Mathematics teacher knowledge Subject matter knowledge Pedagogical content knowledge Mathematical knowledge for teaching Knowledge Quartet## References

- Ball DL, Bass H (2003) Toward a practice-based theory of mathematical knowledge for teaching. In: Davis B, Simmt E (eds) Proceedings of the 2002 annual meeting of the Canadian Mathematics Education Study Group. CMESG, Edmonton, pp 3–14Google Scholar
- Ball DL, Thames MH, Phelps G (2008) Content knowledge for teaching: what makes it special? J Teach Educ 59(5):389–407CrossRefGoogle Scholar
- Dewey J (1903) The psychological and the logical in teaching geometry. Educ Rev 25:387–399Google Scholar
- Grossman P, Wilson S, Shulman L (1989) Teachers of substance: subject matter knowledge for teaching. In: Reynolds M (ed) Knowledge base for the beginning teacher. Pergamon, Oxford, pp 23–36Google Scholar
- Ma L (1999) Knowing and teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States. Lawrence Erlbaum Associates, MahwahGoogle Scholar
- Rowland T, Ruthven K (eds) (2011) Mathematical knowledge in teaching. Springer, London/New YorkGoogle Scholar
- Rowland T, Martyn S, Barber P, Heal C (2000) Primary teacher trainees’ mathematics subject knowledge and classroom performance. Res Math Educ 2:3–18CrossRefGoogle Scholar
- Rowland T, Huckstep P, Thwaites A (2005) Elementary teachers’ mathematics subject knowledge: the knowledge quartet and the case of Naomi. J Math Teach Educ 8(3):255–281CrossRefGoogle Scholar
- Rowland T, Turner F, Thwaites A, Huckstep P (2009) Developing primary mathematics teaching: reflecting on practice with the Knowledge Quartet. Sage, LondonGoogle Scholar
- Shulman LS (1986) Those who understand: knowledge growth in teaching. Educ Res 15(2):4–14CrossRefGoogle Scholar
- Watson A, Barton B (2011) Teaching mathematics as the contextual application of modes of mathematical enquiry. In: Rowland T, Ruthven K (eds) Mathematical knowledge in teaching. Springer, London/New York, pp 65–82CrossRefGoogle Scholar
- Wilson J (1975) Education theory and the preparation of teachers. NFER, WindsorGoogle Scholar