Teaching Cognitive Science

I wrote in November about my “meta-curriculum“, an attempt to be more deliberate in the ways I ask students to think about why math is worth learning and how that learning actually happens. One element that I’ve been revisiting is teaching students some background in cognitive science, much of it adapted from Make It Stick, to illuminate why I structure my class the way I do.

When I first started thinking about explicitly teaching elements of cognitive science to my students, my plans were pretty vague. I developed this document, which amounts to a pretty clumsy summary of nearly every idea presented in Make It Stick. One of my values at the time was to honor the content in the way I presented it — to space and interleave it over time, so that this wasn’t a one-off cognitive science lesson that students would forget by next week. I am still working to incorporate those principles, but I think I was too ambitious in my initial attempts to teach this content — it was disorganized, unfocused, and seemed generally unconvincing for many students.

New Approach

My new approach is to trim what I’m trying to communicate so that students have fewer, more concrete takeaways. I decided on three big ideas that I want to focus on:

• Mixing up practice leads to more durable learning
• Difficulties during learning lead to larger gains — if you persevere through them
• Probing for deeper structure leads to more transferable learning

I put together a one-page handout for each point: practice, difficulties, and structure. Now, I hand out each of these a week or two apart, giving students a chance to read and discuss with a group before I jump in to clarify how these principles have affected the way I structure class time and make decisions.

My goals are for students to:

• buy into homework, and some classwork, that consists mostly of spaced and interleaved practice and connect that practice to their long-term learning
• recognize that math class is supposed to be hard, and that those challenges are opportunites for learning
• engage with questions that ask students to make connections between different problems or strategies and probe for deeper structure

This isn’t going to happen overnight; returning to Make It Stick, the authors outline learning as a three-step process. From the book:

Learning is at least a three-step process: initial encoding of information is held in short-term working memory before being consolidated into a cohesive representation of knowledge in long-term memory. Consolidation reorganizes and stabilizes memory traces, gives them meaning, and makes connections to past experiences and to other knowledge already stored in long-term memory. Retrieval updates learning and enables you to apply it when you need it (100).

So first, students encode when they first read about each topic, briefly discuss it, and I have the chance to drive home key points and clarify misconceptions that come up in the discussion. I don’t dedicate a ton of time to this, but enough to be confident that each student has engaged with the key ideas.

Then, I use language on a regular basis in class that consolidates these ideas, and frames assignments or questions I ask in terms of the cognitive principles we talked about. This is tricky — I don’t want to distract from the mathematical content, while still emphasizing all of the different ways that each of these principles manifests themselves in my class to broaden their understanding.

Over time, ideally, this becomes less and less necessary, as students need to retrieve less often to retain their knowledge, and have assimilated it to the point that they bring it up themselves.

This is still in the experimental stage, but I’m excited with the extent to which students have engaged with these ideas — and acknowledged that they make sense — when I present them in class. Next step is to design some type of year-end post-assessment to see if students have actually retained these principles and learned something about their own cognition. If I get some positive feedback on that front, I’ll give it a shot starting from the beginning in the fall, ideally maximizing the impact for students.