I’m nearing the end of my first semester as a PhD student in Math education. Of the many lessons and content I learned over the past few months, I’d like to share two (for now).

Lesson 1) There is a much richer scholarship and history of social justice in math education research than you’d think (or that I’d have thought).

I should certainly restrict this to myself, but my guess is it applies broadly. It wasn’t until, say 2014 or 2015 that social justice issues in math education began to appear in mainstream professional development and conferences. Or at least, that’s my perception based on my limited and biased math content that I consume. I certainly didn’t see “equity committees” or “director of equity” job positions until around the mid 2010’s (not that that’s the best indicator, as I’m skeptical that these positions help organizations actually promote equity in the world).

There is a robust library of scholarship around Critical Race Theory and social justice that we’re only now seeing in practitioner-based commentary, conferences, and professional development. And much of said commentary only appears in a mealy-mouthed or perfunctory manner. Imagine how much further along we’d be if we’d (again: I’d) done our homework, drawing on the expertise of some of the giants in the field such as the Maisie Gholson, Danny Martin, Rochelle Gutierrez, and other Black and Latino/a scholars. While I was cursorily familiar with some of these and other scholars’ work from recent articles, it behooves me to look back at research on social justice that predates 2010.

Lesson 2) I need to be doing more math in professional development.

Again, I’m writing this but pointing the finger at myself. 

In one of my classes we started off every session with fraction problems, most of which were taken from Lamon (2012). While ostensibly these are problems for students anywhere from Grade 3 to 5, they provided rich discussion and avenues for learning. We were able to question things like, “why can’t we have a fraction within a fraction?”

But you don’t have to take my word for it! There is also research to support this. In a lengthy study, Campbell et al. (2004) found that student growth occurred when teachers had both the belief that students could succeed and the requisite pedagogical and content knowledge. 

Going forward I’d like to incorporate more doing math in my professional development. A lot of times I facilitate a little bit of a problem, typically the launch to a problem-based activity. However, there’s also much to learn about the actual doing of the math itself and the discussion it produces.

Unfortunately, this does take time. Our fifth grade fraction problems would take 5-10 minutes to solve and up to 40 minutes to discuss. And as rich as those discussions are, it’s challenging to yield that much time in a conference or PD session. But if we want to be “research based” then I need to figure it out. 

And it’s also quite fun.

I have more lessons learned and insights based on my coursework that I’ll continue to share in future posts. I also learned quite a bit from producing papers on assessment that will surely appear on this blog and other places. 

If you’re interested (for some strange reason) on other reflections over the course of the semester, you can check out the tab at the top of this website that says “Geoff’s PhD Musings.” We were required to keep a journal of our weekly progression. Some of it is math research related, much of it is not. It’s certainly not required reading.


Campbell, P. F., Nishio, M., Smith, T. M., Clark, L. M., Conant, D. L., Rust, A. H., Neumayer DePiper, J., Frank, T. J., Griffin, M. J., & Choi, Y. (2014). The relationship between teachers’ mathematical content and pedagogical knowledge, teachers’ perceptions, and student achievement. Journal for Research in Mathematics Education, 45(4), 419-459.

Lamon, S. J. (2012). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers (3rd Edition). New York: Routledge. 

3 thoughts on “A couple of lessons from a semester of Math Education PhD coursework

  1. Are you familiar with Marilyn Frankenstein’s work or Nel Nodding’s work or Ole Skovsmose? Their work on critical mathematics education guided me in the late 1990’s.

    1. I was exposed to Frankenstein this semester, but haven’t seen as Nodding or Skovsmose. I’ll be sure to do so during the holiday break.

  2. Thank you sharing your thoughts and lessons with us. I stated a lot of scholarships for Mathematics education PhD.Please that is the very program I want to pursue.l need help.Thank you.

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