This line of research concerns the roles of university level mathematics in teacher education. In many countries, prospective mathematics teachers are required to complete extensive coursework in university level mathematics, or in some cases attain a bachelor’s degree in mathematics. This reality reflects a widespread disposition that engaging school teachers with mathematics that extends well beyond the school mathematics curriculum contributes to the quality of classroom instruction. However, specifying ways by which teachers' learning experiences in university mathematics courses may manifest in the work of teaching is a very challenging task, and consequently, this important aspect of teacher education is informed mostly by personal reflections and common sense, not by research.

M-Cubed (Mathematicians, Mathematics teachers, Mathematics) seeks to improve this situation by creating a rich corpus of examples of implementation of university mathematics in and for secondary mathematics teaching, in order to identify and delineate the processes underlying such implementations. In M-Cubed, mathematicians and practicing secondary teachers gather to watch lesson-episodes and inquire together into the pedagogical dilemmas that arise therein. These dilemmas are carefully selected to trigger cross-community interactions, in which diverse expertise, knowledge, perspectives and values are made explicit and explored in the context of concrete instructional situations. Data collected in these forums enable a systematic analysis of the various ways by which mathematicians and teachers’ mathematical and pedagogical knowledge can intertwine and generate new insights that extend teachers’ repertoire of options and considerations in their teaching. This study is entering its second year and is funded by a grant of the Israel Science Foundation.

These are some of the questions that we study:

- How can mathematicians and secondary teachers learn from and with one another while watching videotaped lessons and jointly inquiring into authentic teaching dilemmas therein?
- How can teachers adapt and utilize mathematicians’ ways of doing and thinking about mathematics to inform pedagogical decisions, example in contingent situations?
- How can practicing mathematics teachers draw on their teaching experiences and expertise to support their learning in university mathematics courses? How can professors in these courses draw on the teachers' teaching experiences and expertise?

**Project leader **

Alon Pinto

**Students**

Myriam Goor

Tsofant Hagin-Metzer

**Advisors**

Esther Sternfield-Gruenhut

Michael Gorodin

**Team**

Yael Adamovsky

Shlomit Bergman

Irit Elior

Ohad Noy Feldheim

Michael Gorodin

Raz Kupferman

Riva Machluf

Rachel Mann

Noa Nitzan

Irena Nuzhdin

Ori Parzanchevski

Esther Sternfield-Gruenhut

**Relevant papers**

Pinto, A., & Cooper, J. (2016). In the Pursuit of Relevance – Mathematicians Designing Tasks for Elementary School Teachers. *International Journal of Research in Undergraduate Mathematics Education, 3*(2), 311-337. DOI: https://doi.org/10.1007/s40753-016-0040-3

Cooper, J., & Pinto, A. (2017). Mathematical and pedagogical perspectives on warranting: approximating the root of 18. *For the Learning of Mathematics, 37*(2), 8-13.

Cooper, J., & Pinto, A. (2018). Jourdain and Dienes effects revisited – playing tic tac toe or learning non-Euclidean geometry? In E. Bergqvist, M. Österholm, C. Granberg, & L. Sumpter (Eds.) *Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education* (Vol. 2, pp. 307-314). Umeå, Sweden.

Pinto, A., & Cooper, J. (submitted). The road not taken - A methodology for investigating affordances of infinitesimal calculus for teaching secondary mathematics.