# ‘Mathematician’ is a real job?

This semester I’ve been a Graduate Teaching Assistant (GTA) for EDUTL 5005: Equity & Diversity in Education. I’ve immensely enjoyed meeting with my section of 16 students each week to discuss, wrestle with, and pose questions about issues of equity in education. These early and middle childhood pre-service teachers have shown up each week ready to engage with the material, each other, and me. Before the semester began I was really anxious about how my experience teaching mathematics in higher education would be different from and not applicable to their preparation to teach younger children. However, I’ve found that sometimes this difference can lead to interesting conversations for all of us.

A conversation from two weeks ago has really stuck with me. One theme that I’ve noticed the students grappling with all semester is the tension between implementing what they believe and being taught are “best practices” and every day realities and outside pressures that affect teaching decisions and the classroom. I shared with them how I had seen this manifest in my own pre-calculus classroom at the two-year college where I also teach. I had a student in class that very day that was much more interested in exploring a problem he had posed for himself than the pre-calculus content the Ohio Transfer Module requires my class to cover. I explained to my pre-service teachers that I was amazed by the deep thinking my pre-calculus student was showing when he was working on his own problem and how the work he was doing at that moment was much more like the work of mathematicians than I had seen him engage in the rest of the semester, yet I still needed to make sure he learned the content included in the course learning objectives so that he would be ready for Calculus. Ultimately, I explained to my pre-service teachers, I made a deal with the student. He showed me what he was working on for a few minutes and then I asked him to work with his classmates on the pre-calculus content. I promised that I would talk more with him about his own explorations after class (and we did).

I thought this was an interesting anecdote from my experience that would help bring the theories that we were talking about directly back to the classroom. As is likely to happen in a classroom, though, it opened up an entirely new conversation. One of my students raised her hand and said “Wait, you said he was working like a mathematician, is that like actually a real job?”

Her question took me by surprise and has been what has stuck with me these last two weeks. I had forgotten that even entering my undergraduate program with the intention of being a math major, I didn’t really understand that there were real live people still “creating” or “discovering” new mathematics (we’ll leave that debate for another day). I’ve since learned from and worked with mathematicians in my undergraduate and graduate education and this has been a valuable experience that has given me an entirely different view of what it means to do mathematics. By asking her question, my student brought me back to the time before I knew that “mathematician was a real job”.

So of-course I answered her question. I explained not only were there mathematicians who posed and proved new theorems, but that there were even such people at Ohio State! I went on to explain that while some mathematics was very abstract and may not have a specific use yet, other mathematicians focused on very real problems that help us and our society. Another hand shot up.

“Can you show us some newer math?”

I was now starting to worry that this recitation session was getting pretty far from “differences versus deficit” topic that was listed on the syllabus for that week—but I also felt like something important was happening here.

I had to think pretty quickly on my feet—since this was not how I had expected the recitation to go at all—but luckily I had just the example.

This past summer I led a session for the Columbus Math Teachers’ Circle about Stable Matchings, a problem that mathematicians David Gale and Lloyd Shapley posed in their article *College Admissions and the Stability of Marriage*in 1962. Not only was this a research level problem that can easily be explained without any complicated formulas or specialized knowledge of higher level mathematics, it is work that has had lasting impact on society. This work changed the algorithm that matches new doctors to their residency program, it’s been used by large school districts to assign students to schools, and in 2004 it helped develop a way to help match transplant patients find donors (you can read more about all of this here: *How a matchmaking algorithm saved lives) *

The room was quiet when I finished talking about the Stable Matching problem and the impact it’s had—but I noticed something: none of the students were looking at their computers or their phones. They were on the edge of their seats hearing about mathematicians and research. While I would love to believe that this was because of my very impassioned way of talking about it, I think it was because this was a completely new idea (that mathematics is still a topic of research and discovery)—one that was surprising and exciting to these pre-service teachers.

So why has this class session stuck with me? Sure, maybe part of it is because I got to share with my students something that I *really*enjoy talking about. But I also think it’s stuck with me because the questions posed by my students surprised me that day. I had forgotten that it’s not common knowledge that there are *still *mathematicians. And now I wonder: what does knowing or not knowing this mean for any teachers of mathematics? What does it mean for learners of mathematics? How can we as mathematics educators share the work of mathematicians with pre-service teachers in meaningful ways?