# Mathematical Knowledge for Teaching In Co-teachers at the Post-secondary Level: A Cognitive and Enacted Approach

#### Abstract

Mathematical Knowledge for Teaching (MKT), the knowledge used by a teacher to teach mathematics, has often been examined as a cognitive construct in K-6 teachers, but little research exists examining MKT in the post-secondary teaching context. Schoenfeld (2020) extended the definition of knowledge and thus MKT to include tacit and explicit perceptions. In doing so, Schoenfeld created the terms "big K" mKt and "little k" mkt, where mKt refers to the tacit and explicit perceptions used by a teacher to teach mathematics and mkt includes the teacher's understanding used in teaching mathematics (similar to cognitive MKT). Building from Schoenfeld’s conceptualization of knowledge (i.e., knowledge vs. Knowledge [2020]), this study investigated MKT by examining how the knowledge of a pair of mentor-mentee co-teachers (big K knowledge known by Schoenfeld as mKt) impacted the learning environment of a calculus course for pre-service teachers from a combined cognitive and enacted lens. The TRU Math framework was used to evaluate the impact of mKt on the learning environment. Three cycles of pre-lesson interviews, classroom observation, and post-lesson interviews were conducted and analyzed using Schoenfeld’s model of mKt and Schoenfeld et al.’s (2014) Teaching for Robust Understanding Math Framework. Investigating mKt using Schoenfeld’s (2020) model of MKT with an eye toward the learning environment provided a more complete picture of the dimensions involved in the decisions that produced the learning environment. As the co-teaching pair collaborated to teach, they made explicit their goals, resources, and orientations toward the students and content. The co-teachers’ sharing of their mKt allowed them to reflect on the classes they taught and informed the planning of future classes. Thus, by collaborating in the mentorship pair, the co-teachers developed their mathematical knowledge for teaching teachers as Masingila et al. (2018) described.

*This paper has been withdrawn.*