Geoff Krall spoke at NCTM’s ShadowCon last week about “The Art of Mathematical Anthropology”. You can watch his talk here starting at about 52:30.

Geoff made a compelling argument for the value of reflections to help students see their own growth. His call to action was to:

- Assign complex tasks
- Invite written reflection
- Have a conversation

By giving students complex tasks and producing complex work, we can ask them where the work was difficult, where they struggled, and how they got better at it. I can learn a great deal about my students from these reflections and conversations. More importantly, students can authentically see their own growth, rather than focusing on shallow external indicators like grades.

I’m interested. I’m hoping to learn more from Geoff’s online course this fall. But in the meantime, I’ve been thinking about how to apply the lens of mathematical anthropology to other areas of my teaching. I have two ideas.

**Mathematics is…**

I wrote a while back about Nat Banting’s idea of asking students what they think mathematics is, and how much I learned from reading my students’ reflections. This year, I set up a progression of thinking about the purpose of mathematics from the beginning of the year. I began in the first week of class by asking students whether math is worth learning and making my elevator speech for the value of learning mathematics. I then returned to these ideas with content we are working with as the year goes on, and we talk about why these topics may or may not be worth learning and how students may or may not use that type of thinking again. At the end of this sequence, I ask students to finish the sentence or paragraph “Mathematics is…” however they’d like. I find it gives me useful feedback about the extent to which I have changed students’ beliefs about mathematics, as well as entertaining me with students’ reflections.

**Collaboration **

Sam Shah wrote recently about group work. In short, Sam argues for having the class generate a list of what they value in group work. Then, several weeks later, each student answers questions about how they are doing relative to these student-generated values. Then, students have a facilitated conversation in groups, discussing what they see going well and what they want to improve on. I’m excited to try this out, and I think individual student reflections on their own collaboration after these conversations could be both useful for students and illuminating for me.

**Mathematical Anthropology **

I’m excited about the idea of having conversations with students about rich artifacts that can help to illuminate their growth. Geoff convinced me that it is worth having these conversations about student work on complex tasks. In addition to students’ knowledge and mathematical skill, I also want them to think about the way they work together and their relationship with mathematics. As I think about collecting student work on complex tasks, I’d like to add to that portfolio student thinking about their collaboration and what they see as the role of mathematics in their lives. These ideas aren’t fully formed, but I’d like to keep thinking about what a portfolio looks like that effectively captures the range of goals I have for students. At the same time, I want to keep that portfolio small enough that it is manageable to look through the artifacts and have a conversation about what they mean. Definitely some figuring out left to do.