## 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.

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## Notes

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.

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.

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.

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## 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.

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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

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DOI: https://doi.org/10.1007/s10763-017-9859-6

### Keywords

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