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# Break it Down for Me

I'm really proud of a lot of teaching ideas I've had (See: Beyoncé exponential growth worksheet), and less proud of some things that haven't worked out super well. I'm pretty sure I've figured out my crowning achievement of pandemic teaching: The Break it Down for Me assignment. Initially, I planned this as assigning a student a concept from class after we'd spoken about it. They could then focus on it, talk to me about it in office hours. Then, in class, the student would re-explan the concept to the class and their classmates would pretend to be freshmen students and ask lots of questions, making the students at the front of the room break the concept down for them. I changed it for a number of reasons:

1. Teaching a hybrid class during covid: I just couldn't figure out how to make it work

2. I didn't have enough brain space to figure out how I would asses students

3. Students who did not feel comfortable in the class would find this exercise to be nothing less than torture.

I feel like being able to communicate something you've learned from math class is important! It helps to synthesize ideas and think about what's really going on in a way that writing down proofs won't always. To be clear, I can't explain all the details of my research to a college freshman, but I can give them ideas of what manifolds and homotopy classes are on surfaces. That's what I was chasing with this assignment - can my students tell someone else the broad strokes of what we've been doing and leave that person feeling like they've learned some math?

And so, I revamped the assignment! Here's the first Break it Down for Me that I gave my Topology students last fall:

This is the link to the pdf version in drive with clickable links. If you don't want to go through the pdf but are interested in the things I linked to, here those are:

Look. I had a great time with this, and so did most of my students. I talked with a few of them in office hours about their plans and we worked out some of the kinks and the weirdness of explaining math you've just learned to someone else! For this first assignment, I received:

• A comprehensive 2 page document on what a metric is that gives reasonable ways to explain examples at every step!

• A literal video of my student explaining what a topology is to a person who has taken math up through calculus!

• A poem!

• A one page document putting a topology on the game of baseball!

• A two page document explaining how to put a topology on shopping carts!

• Another solid two page document breaking down the definitions without making them scary!

What I also received was a batman parody comic called Mathman Begins from one of my students! Hi, Emily Thompson! She has graciously agreed to let me share her work with all of you. (She will probably also be applying to grad school in the fall! Let me know if you're very excited at the thought of her attending your graduate program.)

I thought it was fun, creative, and did the job excellently!

I gave a second Break it Down for Me assignment at the end of the semester with more freedom to choose topics; and also to give them a chance to incorporate more feedback! Emily continued the adventures of Mathman explaining homeomorphisms:

The pdfs and tex for both versions of the assignment I handed out are here.

Reflections on this assignment:

• 10/10 will do some version of this again. If I can figure out a way to embed it into my intro math classes, I'll be assigning it there also. (Hi, future math students!)

• The variation in types of document they handed back to me was sort of amazing, but also harder than anticipated to assess. I might make a slightly more detailed rubric next time for myself and them. Also, now I have examples of what previous students have done that I can share with them

• Generally the feedback on how students felt about this assignment was very positive from the women in the class and less positive from the men in the class? When I repeat this, I will see if this is still the case. (Less positive: "What does this have to do with math? We are not doing real math in this assignment." On the contrary! You are learning the math super well by explaining it!)

• I had a great time talking to students as they were planning what to do; but I think that thinking of a format was stressful for some of them. See second bullet about giving more examples.

If you try this out, let me know how it goes!!

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