Mathematics as Ambiguity

https://twitter.com/math8_teacher/status/994628321110523909

Here's something I've changed in my teaching:

I came into teaching in part to help students become curious about mathematics and see learning math as a process of exploring and discovering beautiful ideas in the world of abstraction.

I still want to create opportunities for students to feel that curiosity and wonder. But as I get better at seeing what is actually happening in my classroom (not only what I wish was happening), I see students who feel like learning math is a process of following rules and jumping through hoops that were created to make them feel stupid and unsuccessful. To help these students feel a sense of agency and ownership over their learning, I have tried to slow down and unpack some of the ways that mathematics has been socially constructed -- the choices of content to include or not include in the curriculum, the emphasis on certain types of skills and practices, the notation that is common in textbooks, the conventions of mathematical communication, and much more, are full of arbitrary rules and ambiguities.

I've learned that seeking out those ambiguities as learning opportunities can actually help students to better understand content, and also create a space where students feel like mathematics is a human enterprise that is, like humans, imperfect and always changing.