Why Teaching is Harder When the Math is Easier
I got humbled in class today.
Hey—great to see you again. You’re looking well. I’m Dan Meyer, and I’m back in your inbox after an eight-month hiatus. I took a break to draft a manuscript and create some new technology for teaching math. I plan to share more about both projects soon.
In the past, I emailed you every Wednesday about whatever interested me most that week. My new plan is to email you only on Wednesday, and only when something has interested me about both a) math education, and b) edtech. You will never ever receive this newsletter on any day other than Wednesday and those Wednesdays might be months apart. That’s the Dan Meyer promise.
First, some plugs.
Here are a couple of time-sensitive announcements.
A debate about AI in education in Washington, D.C. Next Monday, December 8 at 6:30PM Eastern, I will be debating the motion “Maximizing School Improvement by 2035 Means Integrating AI into Classrooms Today.” I will be arguing against the motion (surprised??) with Jake Tawney, a leader in a classical school network. Jake and I will debate Alex Kotran, founder of the AI in Education Project, and Shanika Hope, who works on education initiatives at Google. The American Enterprise Institute is hosting the debate and I hope all of us will walk away a little smarter. You can attend in person or watch online.
A prediction contest about AI in education. The EdTechnical duo of Libby Hill and Owen Henkel are inviting you to put down some concrete predictions about AI and its future impact on education. There are five tracks with a top prize of $2,500 in each track. I am happily serving as a judge in the “Teaching Profession” track. We’re inviting predictions for the question: “By the end of 2028, what percentage of non-interpersonal teacher activities (lesson planning, grading, and parent communication) will teachers routinely delegate to AI systems?”
Yesterday’s humiliation.
Richard Rohr prays for one good humiliation daily to help him see the difference between how he thinks things are and how things really are. I beg people to let me take over their classes for roughly the same reason.
It’s dishonest work—building tools for teachers. Figma designers do their design work in Figma. Cursor devs develop software with Cursor. Google employees use the Google Suite. They all use their own tools regularly. They all regularly feel the same pain as their customers. For a few good reasons and a lot of bad ones, it’s hard to find edtech developers “dogfooding” their own tools1. This is why our team here at Amplify ritualizes classroom visits. This is why I beg.
I was teaching kids to calculate slope from two coordinates yesterday here in Oakland, CA. Operationally, this is very easy. Subtract, subtract, and divide. Conceptually, this is a topic that’ll bloom for at least the next five years. What does the slope mean? Why do we divide the vertical change by the horizontal? Where do the graph and the algebra connect? What happens when the horizontal change becomes very, very small? What is the slope of the slope?
The core challenge.
How do you “press” 30 kids to develop important conceptual knowledge when the easy operational knowledge is right there? I found myself doing a lot of desk work, trying to figure out what ideas students were bringing to the table, offering them questions to help them develop their intuition about slope.
Okay which quadrant is this point in? Is this other point to the left or right? How do you know?
Here are some points. Pick a couple of them you think would make a downward sloping line.
How high did I have to climb from this point to this other one?
Let me offer a wrong answer. How can we know it’s for sure wrong?
Etc.
It would have hastened the whole interaction to direct them towards the easy operational knowledge. Subtract, subtract, and divide. I don’t know how to shortcut the conceptual work here. It’s possible to do some of it from the front of the class, but most of it requires serious, individual engagement with kids and their ideas. I don’t know how to do that across 30 kids. And when you turn that work over to a computer, it will happily encourage the kids to subtract, subtract, and divide.
I need new ideas for doing conceptual work at classroom scale. Let me know what you have on hand.
Odds & Ends
I have eight months of great links to catch you up on. Let’s start with five.
¶ I appreciate the skeptical posture Michael Pershan adopts towards just about everything. Recently, he directed it towards the overly tidy explanations our pundit class has offered for America’s declining test scores.
Here’s the situation: Americans are getting dumber...well, mostly not. But our lowest performing students seem to be losing ground. And, simultaneously, our adults. Some international tests show a similar decline happening in other countries. On other exams, America is on its own. What gives?
¶ Similar from Freddie deBoer: Was the United States Once a Global Leader in Educational Metrics? Have We Fallen From Those Lofty Heights? No and No
So here’s the nut of the whole thing: commentators often point to the recent decline in test scores (post-2020) as proof of a unique American failure. This ignores the global context: almost all developed nations have seen declining scores, especially in the context of the Covid-19 pandemic, and in fact in many countries these declines have been more pronounced than in the United States.
¶ Justin Reich’s podcast The Homework Machine concluded its run during my hiatus. It was extremely well-reported. Great interviews. Great perspectives on teaching, learning, and technology. In its final episode, a San Francisco English teacher named Sara Falls is asked why AI isn’t really helping her and she proceeds to describe the core challenge of teaching in a way that still haunts me months later. You should listen to her tone in that moment, but if you must, you can read what she says:
… this kid who just brought me this candy cane … this sweet kid … I’ve struggled … the fact that she brought me a candy cane is a big deal because at the beginning of the year she hated me. You know … and I’ve stuck with it … I’ve stuck with her and she just brought me a candy cane. This is the work.
¶ While I was out, OpenAI, Anthropic, and Google, all released “study mode” versions of their chatbots. These new versions won’t just throw you the answers when you ask. They’ll make you work for those answers. (The marshmallow test goes to college!) I enjoyed reading Mashable’s Chase DiBenedetto’s reports from test-driving each one, especially how the directive to not give the answer ever can drive a student to madness:
But here’s the unsettling part of using Claude: As conversations continued, it increasingly felt like I was trapped, in the sense that lessons seemed to go on forever. Because Claude wants to really make sure it knows where your head is at, the bot doesn’t provide you a clear stopping point for the lesson, sometimes making conversations hard to follow, and the learning experience frustrating. During our math session, Claude fervently lauded me when I got the answer right, but sent me approximately 100 follow-up questions. Even when I asked if we were done with the problem — AKA can I go home now? — it gave me more work to do.
¶ Related: I loved reading RAND’s survey of students and their use of AI and I don’t think I saw anyone report on it. One interesting question asked students “so what tools are your teachers recommending?” and then “what are you actually using?” I went ahead and plotted both sets of data simultaneously and you can get a preview of the popularity of these study modes. The max teacher recommendation was for Khanmigo—a Socratic tool. Kids went ahead and used vanilla ChatGPT anyway.
Maria Anderson, CEO of Socrait, still teaches daily, I think. Anyone else?





Really interesting to see how this prediction contest frames parent communication as a "non-interpersonal" activity! Of course some parent communication teachers do is pretty mechanical. But I think it also almost always involves some social, emotional, or relationship-building aspect, which they go on to say would be excluded. Caregivers are humans, too!
Loving Rohr's quotes here. Thanks to you and Fawn continually reminding those of us who are math leaders far removed from classrooms of the power of spending regular time teaching in classrooms, I am now doing it quite regularly. I need dust off my blog to write publically about it so help hold me accountable to that.
This question right here is the chef's kiss (as my 11 year old would say): "How do you “press” 30 kids to develop important conceptual knowledge when the easy operational knowledge is right there?"
I'm also left wondering if that building of conceptual knowledge must always intersect with students better understanding the algorithm. For example, proving the quadratic formula. I'm not sure if in a pinch I could rederive that proof right here as I type, but I have plenty of conceptual knowledge developed and stored away in long-term memory that I can solve any quadratic-related problem you throw at me without quite remembering the proof or why each coefficient and operation in the formula is what it is. Heck. Even if I have forgotten the quadratic formula, I have a whole toolbox of conceptual knowledge that would help me solve anything related to the topic.
I've found that conceptual knowledge always has a far more long-term lasting effect than procedural knowledge and that having a deep conceptual understanding often helps you do math when the formula or procedure may be long-forgotten. This happens to me often where kids (often my own high school kid) ask me for help and I have completely forgot the procedures on how to do the problem, but can figure it out because I retain the conceptual knowledge. It doesn't always mean I can re-derive the formula, but that the conceptual understanding I have retained endures so I can still solve the problem. Annnnnnnd....in the moment, with 30 students (more like 35+ in many public high schools) are awaiting your instruction, I know why pressing on with subtract, subtract, divide is where many turn. Thanks for that chef's kiss of a question to continue to ponder.