The goal of ambitious teaching and mathematical reform is we want our students to be (and see themselves as) knowers and doers of math. So, with that frame, I have spent a lot of time considering what that phrase The role of students' math identities in this process of moving towards students knowing and doing math strikes me as paramount (II.b.v). Coming back from hybrid learning students identities and view of themselves as people who could overcome challenges and persevere to accomplish hard things was at a deficit. This manifested itself in many ways, but the most noticeable to me as an observer in math classrooms this year, was how students avoided engaging with challenging tasks more than any time I'd witnessed before. Teachers were left with the unenviable choice of guiding students through the lesson and doing most of the thinking for the class, or battling behaviors and apathy and minimal (if any engagement). Teachers I spoke with agreed. So, the goal of this work this spring was to create resources that can be used in the fall to "go slow" initially, spending time redefining the classroom as a place where students struggle through challenging concepts and have success in many forms, to "go fast" later as students are more willing to engage with high cognitive demand tasks (II.a.i). As I reflect on this work, I realize that prior to the fall, I need to find effective means of communicating these ideas to the teachers, as well as support them in building routines that continue these practices throughout the year (II.a.iv). This work also is deeply rooted in building equity-based practices in a math classroom. It allows students to go deep with math, draw on their multiple resources of knowledge (that they may not recognize in themselves), affirm and develop mathematics learners' identities and leverage their multiple mathematical competencies (III.v.c).
i. Utilize and build upon learners’ existing knowledge, skills, understandings, conceptions and misconceptions to advance learning;
iv. Create social learning contexts that engage learners in discussions and mathematical explorations among peers to motivate and extend learning opportunities.
II. Pedagogical Knowledge for Teaching Mathematics.
b. Teaching. MS professionals must know and be able to:
v. Develop learners' abilities to give clear and coherent public mathematical communications in a classroom setting;
vi. Model effective problem solving and mathematical practices—questioning, representing, communicating, conjecturing, making connections, reasoning and proving, self-monitoring and cultivate the development of such practices in learners.
v.c. develop appropriate classroom- or school-level learning environments
link to full list of Standards for Mathematics Specialists (MS) (AMTE, 2013) and descriptions.