Every few months, I meet with other beginning math and science teachers to discuss teaching and what it looks like for us (though the Knowles Science Teaching Fellowship). Recently, this has meant collecting data on our classrooms, presenting it to two other fellows, then discussing it.

The lesson I discussed was an exploration of the Pythagorean Theorem. Students read a reading guide and used Pythagorean Tangrams to see if the two smaller area squares added up to the bigger area square. (photos below)

Part of our assignment was to think about the Standards for Mathematical Practices, which, admittedly, I didn’t.

A couple of thoughts:

- Students sometimes got stuck when trying to put together the two smaller squares to make the big square and I’d have to show them a hint or first step.This felt useful in terms of keeping the kiddos moving and not letting them get stuck on anything that was probably not hugely important (though if it wasn’t hugely important…) In general, I think I need to try and push students to struggle with math without giving up before asking for help. It feels like such a fine line between getting them engaged and than letting them be independent.
- We also established that the students may not have understood the goal of the activity. Do they fully understand what it means when they make the two smaller squares equal the big square? Do they think that putting together the two smaller squares means that this will work for all squares?
- It’s interesting to see how students explain and justify. One student says “I don’t know how to explain” which is frustrating because they probably could explain, but at least shows that they know they need to explain. It’s also interesting to see how students explain something tricky like “why do we need to write the small 2.” (This maybe feels like a “guess what the teacher is thinking” question)
- In thinking about standards for mathematical practices, I go back and forth about which ones are “most important” (they’re all important, which makes it difficult for me to try and focus). So I might try and get our department (four people) to pick a math practice to focus on across courses next year. We’ll see.

**Photos 1 and 2: Student A**

**Photos 3 and 4: Student B****Photos 5 and 6: Student C**

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