My work on the AMS Teaching & Learning Blog

I don’t know why I didn’t think to tell you this earlier, but: in 2019 I joined the editorial board of the American Mathematical Society’s Teaching & Learning Blog, and I’ve written several pieces for it. I’m extremely proud of each of these, and would like to share them with you.

  • Some thoughts about epsilon and delta (August 19, 2019) is a deep dive on student difficulties with a notoriously challenging definition from calculus. I got pretty scholarly and read a bunch of research for it, but the core of the post is a discussion of challenges faced by specific learners I’ve known, one of whom is my own self. I also include a brief history of this definition.
  • The things in proofs are weird: a note on student difficulties (May 20, 2020) is a meditation on the nature of the objects we use in proofs, and the difficulties students have in getting used to working with objects with this strange nature. I again got pretty scholarly and read a bunch of research. Nonetheless, it includes an extended riff on Abbott and Costello’s Who’s on First?
  • A K-pop dance routine and the false dilemma of concept vs. procedure (August 18, 2020) is a… ok let me back up. People used to fight about whether conceptual or procedural knowledge was more important. I think we’ve more or less reached a place in the public conversation about math teaching where there’s an official public consensus that conceptual and procedural knowledge are both important and are mutually supportive. But just because we all can say these words doesn’t mean we’ve necessarily fully reconciled the impulses behind that older fight. For example, in spite of firm intellectual conviction that this view is correct, I have a bias toward the conceptual in my teaching, in the sense that I have a strong tendency to assume any student difficulty is rooted in a conceptual difficulty. This bias is really useful a lot of the time, but sometimes it can lead me to misdiagnose what a student needs to move forward. Anyway, so one day I was learning a BLACKPINK dance and the learning experience just really eloquently illustrated both the advantages and disadvantages of that exact bias. Hopefully you’re intrigued!
  • The rapid expansion of online instruction, occasioned by the pandemic, has forced academia to contend with the limits of the control that its usual physical setup allows it to exercise over students’ movements and choices. One place this manifests very clearly is in the setting of timed tests, which are historically proctored in person. Remote proctoring: a failed experiment in control (January 19, 2021) is my heartfelt contribution to the pushback against the Orwellian trend of turning to “remote proctoring” (where the student is surveilled in their home during tests) to try to claw back the lost control, rather than accepting that the game has changed and rethinking assessment from the ground up, as the situation demands.
  • Three foundational theorems of elementary school math (November 22, 2021) could have been titled, “The logical structure of elementary school math is actually extremely beautiful and intricate, and I want everyone to pay more attention to this.” It’s a love letter to three closely related facts from elementary school math that I think often don’t get their due, making the case that they deserve to be thought of as theorems. I discuss proofs (including some relevant student work) and connections. (If any long-time readers of this blog are still here in 2021, this post is a distant but direct descendant of this post I wrote nearly 12 years ago, when I was a baby blogger.)

I also solicited a piece from Michael Pershan, which I am also extremely proud of:

  • What math professors and k-12 teachers think of each other (November 18, 2019) is Michael’s synthesis of and meditation on an informal survey he ran, canvassing math educators teaching in schools and universities about what they think about the differences in the shape of math education at these different levels. Michael’s characteristic thoughtfulness is on full display here, and it’s all with an eye toward how we can collaborate effectively. I love it.

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