This has been a unique semester in that I took two courses and taught a course. The course I taught is a one-hour seminar course, “Math for Elementary Teachers,” not to be confused with their “actual” math course, nor their math teaching methods course. This course is a small part of pre-service teachers’ (PSTs) teacher preparatory experience. So my time is limited and I have a bit of leeway with the content. It ties in with their math content course, but I have some freedom of movement in terms of activities.

My final assignment for the course was for students to write a reflection paper on math and/or a mathematical autobiography. Positioning this paper at the end of the course allowed for students to really open up about their past experiences in math and their hopes for the future. As you might expect, many of my students’ reflections included baggage stemming back to the time when they were in elementary school.

One student described an experience from third grade that she still remembered (which I obtained permission to reproduce here with). She had just completed a test.

I tried my best but clearly my best was only a 10/30. After [my teacher] had all of the test grades she talked to my math group. She was trying to explain to us that not everyone is good at everything. I knew she was talking about me. Soon after she was done talking, she held up my test with the ten out of thirty circled in bright red pen and said, “For example, Math is not for [student name]”.

The specificity with which my student described reminds me of something I wrote in *Necessary Conditions*: “sometimes [math] trauma is so deep that they can describe individual moments of ultimate anxiety and humiliation” (p. 15).

Reading through some of these papers made me realize that for some of these 19- and 20-year olds, this was a therapeutic experience. I am honored that they were willing to open up to me and I hope that signals that they felt safe doing so. After reading through my course evaluations as well, I’d like to think I succeeded in crafting a safe space in my math classroom.

This meandering preamble leads me to one broader takeaway. Some sort of therapy or reconciliation with mathematics should be a part of every pre-service teacher’s experience. Last year I wrote about a paper that described a restorative justice approach in which math was one of the parties. I sort of stumbled into this approach of a final paper which I’ll carry over into the Spring semester. However, the paper is only the final product after a semester of building a foundation of trust, respect, empathy, and academic safety.

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I also wanted to share some of the “greatest hits” of the semester. Because I had a decent amount of freedom with my lessons I had the opportunity to showcase a bunch of different tasks and task types. Based on students’ final papers, course evaluations, my own reflection and my experiences in the moment, here were students’ favorite tasks.

**Number Talks**. Students were surprised that you could solve 18 x 5 using a myriad of different strategies. Also, this tied in nicely with the area model for multiplication. Tragically many of my students had never seen the area model demonstrated in school.

**3-Act Math**. I showcased Graham’s “Rope Jumper” task. I had students co-develop the question, make estimations (“what’s the highest low / lowest high you’d reasonable predict”) and come to final tally for the number of times the individual jumps rope. The excitement for the conclusion in Act 3 was palpable. Cheers and everything.

**Games from Building Fact Fluency**. They particularly liked the Multiplying 7’s game. It introduced them to a means of developing fact fluency that isn’t just a list of dozens of multiplication problems.

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Next semester I’ll have the honor of teaching this course again. One thing I’m going to try differently is making their weekly assignments on Desmos, now that they have an upload feature for students. Each week I’d assign a single math problem and ask them to reflect on it. For the Spring I’m just recreating these problems in Desmos. Desmos makes it easy to share and discuss students’ solution. I also want students to get experience with Mathigon’s Polypad as I’ve found it an invaluable tool to craft math visuals. It should be in every teacher’s toolbox.

Take it away, Colonel.