## Abstract

The purpose of this article is to contribute to the discussion of mathematics teacher knowledge, and the question of what makes it specialized. In the first part of the article, central orientations in conceptualizing mathematics teacher knowledge are identified and the more serious limitations of the grounds on which they stand are explicated. In the second part of the article, alternative views are offered to each of these orientations that direct attention to underexplored issues about what makes mathematics teacher knowledge specialized. Collectively, these alternative views suggest that specialization in mathematics teacher knowledge cannot be comprehensively accounted for by ‘what’ teachers know, but rather by ‘how’ teachers’ knowing comes into being. We conclude that it is not a kind of knowledge but a style of knowing that signifies specialization in mathematics teacher knowledge.

This is a preview of subscription content, access via your institution.

## Notes

- 1.
We prefer using the term ‘specialized’ instead of ‘special’ with respect to mathematics teacher knowledge. The latter implies the assertion of a quality of teacher knowledge that is distinguishable from something. We use the term ‘specialized’ to indicate a quality of mathematics teacher knowledge that comes into being when enacted.

- 2.
This is not to be understood as dichotomizing teachers’ capacity for unpacking mathematics and their capacity for unpacking students’ understandings, but to re-emphasize that teaching is not (merely) a top-down approach of transposing subject matter to the students but a bottom-up approach of students constructing mathematical ideas that are used as points of departure in the teaching-leaning complex.

- 3.
Notice that we do not construe the relationship between knowing and knowledge as contradictory but rather as dialectical. In terms of the onto-semiotic approach, there is no mathematical practice without objects, or objects without practice, which is equivalent to the issues of knowing and knowledge discussed here.

## References

Adler, J. (1998). Lights and limits: Recontextualising Lave and Wenger to theorise knowledge of teaching and learning school mathematics. In A. Watson (Ed.),

*Situated cognition and the learning of mathematics*(pp. 161–177). Oxford, UK: CMER.Adler, J., & Davis, Z. (2006). Opening another black box: Research mathematics for teaching in mathematics teacher education.

*Journal for Research in Mathematics Education, 37*(4), 270–296.Askew, M. (2008). Mathematical discipline knowledge requirements for prospective primary teachers, and the structure and teaching approaches of programs designed to develop that knowledge. In P. Sullivan & T. Wood (Eds.),

*The international handbook of mathematics teacher education. Volume 1: Knowledge and beliefs in mathematics teaching and teaching development*(pp. 13–35). Rotterdam, The Netherlands: Sense.Ball, D. L. (1988).

*Knowledge and reasoning in mathematical pedagogy: Examining what prospective teachers bring to teacher education*(Unpublished doctoral dissertation). Michigan State University, East Lansing.Ball, D. L., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.),

*Multiple perspectives on the teaching and learning of mathematics*(pp. 83–104). Greenwich, CT: JAI/Albex.Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special?

*Journal of Teacher Education, 59*(5), 389–407.Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., . . . Tsai, Y.-M. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress.

*American Educational Research Journal, 47*(1), 133–180.Berry, A., Loughran, J., & van Driel, J. H. (2008). Revisiting the roots of pedagogical content knowledge.

*International Journal of Science Education, 30*(10), 1271–1279.Beswick, K., Callingham, R., & Watson, J. (2012). The nature and development of middle school mathematics teachers’ knowledge.

*Journal of Mathematics Teacher Education, 15*(2), 131–157.Blömeke, S., Hsieh, F.-J., Kaiser, G., & Schmidt, W. H. (Eds.). (2014).

*International perspectives on teacher knowledge, beliefs and opportunities to learn. TEDS-M results*. Dordrecht, The Netherlands: Springer.Blömeke, S., & Kaiser, G. (2017). Understanding the development of teachers’ professional competencies as personally, situationally, and socially determined. In D. J. Clandinin & J. Husu (Eds.),

*International handbook of research on teacher education*(pp. 783-802). Thousand Oakes, CA: Sage.Bromme, R. (1994). Beyond subject matter: A psychological topology of teachers’ professional knowledge. In R. Biehler, R. W. Scholz, R. Strässer, & B. Winkelmann (Eds.),

*Mathematics didactics as a scientific discipline: The state of the art*(pp. 73–88). Dordrecht, The Netherlands: Kluwer.Buchholtz, N., Leung, F. K., Ding, L., Kaiser, G., Park, K., & Schwarz, B. (2013). Future mathematics teachers’ professional knowledge of elementary mathematics from an advanced standpoint.

*ZDM—The International Journal of Mathematics Education, 45*(1), 107–120.Carrillo, J., Climent, N., Contreras L. C., & Muñoz-Catalán, M. C. (2013). Determining specialised knowledge for mathematics teaching. In B. Ubuz, Ç. Haser & M. Mariotti (Eds.),

*Proceedings of the Eighth Congress of the European Society for Research in Mathematics Education*(pp. 2985–2994). Antalya, Turkey: ERME.Cochran, K. F., DeRuiter, J. A., & King, R. A. (1993). Pedagogical content knowing: An integrative model for teacher preparation.

*Journal of Teacher Education, 44*, 263–272.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.Ernest, P. (1989). The knowledge, beliefs and attitudes of the mathematics teacher: A model.

*Journal of Education for Teaching, 15*(1), 13–33.Even, R., & Ball, D. L. (Eds.). (2010).

*The professional education and development of teachers of mathematics: The 15th ICMI study*. New York, NY: Springer.Fauconnier, G., & Turner, M. (2002).

*The way we think: Conceptual blending and the mind’s hidden complexities*. New York, NY: Basic Books.Fennema, E., & Franke, M. (1992). Teachers’ knowledge and its impact. In D. Grouws (Ed.),

*Handbook of research on mathematics teaching and learning*(pp. 147–163). New York, NY: Macmillan.Flores, E., Escudero, D., & Carrillo, J., (2013). A theoretical review of specialised content knowledge. In B. Ubuz, Ç. Haser & M. Mariotti (Eds.),

*Proceedings of the Eighth Congress of the European Society for Research in Mathematics Education*(pp. 3055–3064). Antalya, Turkey: ERME.Font, V., Godino, J. D., & Gallardo, J. (2013). The emergence of objects from mathematical practices.

*Educational Studies in Mathematics*,*82*, 97–124.Godino, J. D., Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education.

*ZDM – The International Journal on Mathematics Education*,*39*(1-2), 127–135.Godino, J. D., Font, V., Wilhelmi, M. R., & Lurduy, O. (2011). Why is the learning of elementary arithmetic concepts difficult? Semiotic tools for understanding the nature of mathematical objects.

*Educational Studies in Mathematics*,*77*(2/3), 247–265.Grossman, P. L., Wilson, S. M., & Shulman, L. S. (1989). Teachers of substance: Subject matter knowledge for teaching. In M. C. Reynolds (Ed.),

*Knowledge base for the beginning teacher*(pp. 23–36). Elmsford, NY: Pergamon Press.Hashweh, M. Z. (2005). Teacher pedagogical constructions: A reconfiguration of pedagogical content knowledge.

*Teachers and Teaching, 11*(3), 273–292.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, The Netherlands: Springer.Kaiser, G., Blömeke, S., König, J., Busse, A., Döhrmann, M., & Hoth, J. (2017). Professional competencies of (prospective) mathematics teachers—cognitive versus situated approaches.

*Educational Studies in Mathematics, 94*, 161–182.Kunter, M., Baumert, J., Blum, W., Klusmann, U., Krauss, S., & Neubrand, M. (Eds.). (2013).

*Cognitive activation in the mathematics classroom and professional competence of teachers: Results from the COACTIV project*. New York, NY: Springer.Lerman, S. (2013). Theories in practice: Mathematics teaching and mathematics teacher education.

*ZDM—The International Journal on Mathematics Education, 43*(3), 623–631.Ma, L. (1999).

*Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States*. Mahwah, NJ: Lawrence Erlbaum.Marks, R. (1990). Pedagogical content knowledge: From a mathematical case to a modified conception.

*Journal of Teacher Education, 41*(3), 3–11.McEwan, H., & Bull, B. (1991). The pedagogic nature of subject matter knowledge.

*American Educational Research Journal, 28*(2), 316–334.Monk, D. H. (1994). Subject area preparation of secondary mathematics and science teachers and student achievement.

*Economics of Education Review, 13*(2), 125–145.Petrou, M., & Goulding, M. (2011). Conceptualising teachers’ mathematical knowledge in teaching. In T. Rowland & K. Ruthven (Eds.),

*Mathematical knowledge in teaching*(pp. 9–25). Dordrecht, The Netherlands: Springer.Pino-Fan, L., Assis, A., & Castro, W. F. (2015). Towards a methodology for the characterization of teachers’ didactic-mathematical knowledge.

*Eurasia Journal of Mathematics, Science, & Technology Education*,*11*(6), 1429–1456.Ponte, J. P. (1994). Mathematics teachers’ professional knowledge. In J. P. Ponte & J. F. Matos (Eds.),

*Proceedings of the 18th conference of the International Group for the Psychology of Mathematics Education*(Vol. 1, pp. 195–210). Lisbon, Portugal: PME.Ponte, J. P., & Chapman, O. (2016). Prospective mathematics teachers’ learning and knowledge for teaching. In L. D. English & D. Kirshner (Eds.),

*Handbook of international research in mathematics education*(3rd ed., pp. 275–296). New York, NY: Routledge.Putnam, T. T., & Borko, H. (2000). What do new views of knowledge and thinking have to say about research on teacher learning?

*Educational Researcher, 29*(2), 4–15.Rowland, T. (2009).

*Developing primary mathematics teaching: Reflecting on practice with the knowledge quartet*. London, UK: Sage.Rowland, T. (2014). Frameworks for conceptualizing mathematics teacher knowledge. In S. Lerman (Ed.),

*Encyclopedia of mathematics education*(pp. 235–238). Dordrecht, The Netherlands: Springer.Rowland, T., Huckstep, P., & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: The knowledge quartet and the case of Naomi.

*Journal of Mathematics Teacher Education, 8*(3), 255–281.Rowland, T., & Ruthven, K. (Eds.). (2011).

*Mathematical knowledge in teaching*. Dordrecht, The Netherlands: Springer.Scheiner, T. (2015). Shifting the emphasis toward a structural description of (mathematics) teachers’ knowledge. In K. Bewick, T. Muir, & J. Wells (Eds.).

*Proceedings of the 39th conference of the International Group for the Psychology of Mathematics Education*(Vol. 4, pp. 129–136). Hobart, Australia: PME.Schoenfeld, A. H., & Kilpatrick, J. (2008). Toward a theory of proficiency in teaching mathematics. In D. Tirosh & T. Wood (Eds.),

*International handbook of mathematics teacher education. Vol. 2: Tools and processes in mathematics teacher education*(pp. 321–354). Rotterdam, The Netherlands: Sense Publishers.Schwab, J. J. (1978). Education and the structure of the disciplines. In I. Westbury & N. J. Wilkof (Eds.),

*Science, curriculum, and liberal education*(pp. 229–272). Chicago, IL: University of Chicago Press. (Original work published 1961).Sherin, M. G. (2002). When teaching becomes learning.

*Cognition and Instruction, 20*(2), 119–150.Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching.

*Educational Researcher, 15*(2), 4–14.Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform.

*Harvard Educational Review, 57*, 1–22.Silverman, J., & Thompson, P. W. (2008). Toward a framework for the development of mathematical knowledge for teaching.

*Journal of Mathematics Teacher Education, 11*(6), 499–511.Sullivan, P., & Wood, T. (Eds.). (2008).

*The international handbook of mathematics teacher education. Volume 1: Knowledge and beliefs in mathematics teaching and teaching development*. Rotterdam, The Netherlands: Sense.Van Zoest, L., & Thames, M. (2013). Building coherence in research on mathematics teacher characteristics by developing practice-based approaches.

*ZDM—The International Journal on Mathematics Education, 45*(4), 583–594.

## Acknowledgments

Writing was done while the first author, Thorsten Scheiner, was a Klaus Murmann Fellow of the Foundation of German Business and completed while he was recipient of the Research Excellent Scholarship of Macquarie University. This work was supported, in part, by grant number EDU2013-44047-P (Spanish Ministry of Economy and Competitiveness) to José Carrillo and Miguel A. Montes, EDU2016-74848-P (FEDER, AEI) to Juan D. Godino, and FONDECYT Nº11150014 (CONICYT, Chile) to Luis R. Pino-Fan.

## Author information

### Affiliations

### Corresponding author

## Rights and permissions

## About this article

### Cite this article

Scheiner, T., Montes, M.A., Godino, J.D. *et al.* What Makes Mathematics Teacher Knowledge Specialized? Offering Alternative Views.
*Int J of Sci and Math Educ* **17, **153–172 (2019). https://doi.org/10.1007/s10763-017-9859-6

Received:

Accepted:

Published:

Issue Date:

### Keywords

- Mathematical knowledge for teaching
- Pedagogical content knowledge
- Specialized knowledge
- Teacher knowledge
- Teacher professionalism