When my first book Math with Bad Drawings came out, I kept having a strange experience.
“Yes!” a stranger would say, pointing at the stick figure on the cover. “We need more of this.”
My enthusiastic supporter had, until 30 seconds prior, never heard of the book. They still hadn’t cracked the spine. I was honored by the support, but it was obvious that I hadn’t yet earned it. For all they knew, I had written 376 pages of vulgar limericks. What convinced them that I was on the right path?
I’ve come to see this as a basic dynamic in math education reform: an illusory spirit of consensus. Clearly math education needs more something. But more what?
One popular answer: “more data science.” Let’s renounce all of those fusty, old-fashioned trigonometric formulas. Instead, fill math class with 21st-century virtues: data visualization, probabilistic thinking, and statistical literacy. This isn’t necessarily about new pedagogy; it’s about new content. It’s about re-centering math class on techniques that will cash out, on skills that students might actually apply.
Another popular answer: “more student-centered.” Let’s banish all tasks mechanical and rote. Instead, fill math class with open-ended puzzles, inquiry-based learning, and creative projects. This isn’t necessarily about new content; it’s about new pedagogy. It’s about re-centering math class on the voices, the ideas, and the ingenuity of the students themselves.
I see value in both of these approaches (and many others besides). My first book, Math with Bad Drawings, with its long sections on statistics and probability, was largely about data literacy. My second book, Change is the Only Constant, was a human-centered take on calculus.
But when it comes to systemic change, the two are orthogonal at best, and opposites at worst.
Should we dismantle our regime of standardized tests? Or are they a vital tool for measuring the success of a new curriculum?
Should math education impart deep experiences of beauty? Or practical, wage-raising skills?
Should students pursue open-ended, creative thinking? Or develop concrete knowledge with immediate applications?
Is math a liberal art, akin to art or music? Or is it a practical craft, like computer programming or home economics?
Should economic productivity be the guiding principle for secondary education? And if not, then what should be?
I wouldn’t endorse either vision in its purest form. Math education pursues a hodgepodge of goals: quantitative literacy, humanistic growth, preparation for STEM careers. The educators I admire most don’t subscribe to easy dichotomies. They value student voices and factual knowledge, algebraic fluency and open-ended exploration. Myself, I am comfortable with only two universal claims about math education: there are always tensions, and there are always tradeoffs.
That’s why I worry about the illusory consensus around reform. How can we make wise tradeoffs if we don’t acknowledge the tensions?
The solution, I think, is simple: show your work.
Show us what a good lesson (or unit, or year) looks like, and explain why.
I’m trying to do this in my own teaching now: to resolve all these contradictory possibilities in a way that works for my students. It’s not easy! There are days when I do an adequate job, and days when I do quite the opposite.
Anyway, take this as a pledge: in 2025, I’d like to show more of my work. I’m teaching two classes this term: Intro to Statistics, and Liberal Arts Mathematics (a kind of escape hatch for students who don’t want to take college algebra as their final required math class). I approach them both with a muddle of overlapping values, and a desire to do whatever works best for my students’ learning. More forthcoming.
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