Welcome to this month’s conversation hosted by members of AMATYC’s Research Community. Each week, we will introduce the community to one current research project focused on teaching mathematics at two-year colleges with research findings hot off the presses.

The underlying theme for each blog post on IMPACT Plus is using research findings as a way to take ** ownership** of our teaching. For example, in the second week of May, our colleague Claire Wladis will share some of her research on two-year college students’ algebraic symbol sense and essential algebraic understandings, such as the concept of equivalence. As an instructor, I am able to use what Claire finds in her research to inform my algebra teaching through understanding and acknowledging what is challenging for learners. I take ownership of my teaching as a consumer of research findings that help me become better at what I do.

Our colleagues will also share research findings on algebra instruction at two-year colleges, which can help us reflect on our *own* teaching, as well as findings from research projects involving two different forms of sustained professional learning -- lesson study and the scholarship of teaching and learning, and how these experiences changed participants’ perspectives of their classroom and student learning.

Each of these reports of current research will be framed in terms of a theoretical perspective on teaching that is informally called the “instructional triangle.’ This construct is illustrated in the figure below (Cohen, Raudenbush & Ball, 2003, p. 124).

The vertices of the triangle represent the instructor, the students who interact with one another, and the mathematics content of a lesson, a part of a lesson or even a sequence of lessons. The edges represent the interactions between instructor and students, students and mathematical content, and the instructor and mathematical content. All of these interactions occur in context. The context may be our department, a change in leadership at our college, the impact of legislation on mathematics education in our state, or teaching during a pandemic in a time of social unrest.

The ‘instructional triangle’ provides a way to focus on a particular part of instruction. For example, I am observing the interactions between students working on a mathematical task. If I am focused on whose voice dominates and whose voice is silenced, then as an instructor I am focused on the vertex that represents the student-to-student interactions, and perhaps also the interaction with a context that may position some students as more capable in mathematics. If I am focusing on the students’ collaborative mathematical work, then my focus is on the edge between the students and mathematical content. The instructional triangle is a lens for me to take ownership of my teaching, because it provides precise language to talk about my teaching with colleagues. If I want to get feedback on my work facilitating students’ collaborative work, I have language to point my colleague to exactly what part of my facilitation I want them to observe. Unpacking my instruction in this way allows me to take ownership of the work I am doing in the classroom, while at the same time acknowledging its complexity.

Participate in our first discussion this month on IMPACT in Action:

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