AI Puts Additional Pressure on Math Curriculum Overhaul

'Moon launch' math no longer cuts it

Photo by Greg Rosenke on Unsplash

In 1980 I was briefly a mathlete. My trigonometry class in high school had the option of participating in a couple of math competitions. Those excursions didn’t just confer extra credit. They transformed the way I thought about math.

Math was a subject I enjoyed, relatively speaking, but especially during high school I didn’t find it interesting or relevant. I’m inherently inclined toward solving problems, and math is practically the only part of the curriculum that addresses that skill. (Science is usually more focused on knowledge and discovery.) Through proofs I applied puzzle solving skill, but that was the minority of time and pretty hard to connect to practical benefit.

From the moment I cracked the cover on the first mathlete test, it was clear that it was a completely different beast from any math I’d previously experienced.  I remember there being seven challenges, each of which posed an abstract puzzle. Puzzles I had never seen before. For some questions, it wasn’t clear that they were asking about math at all.

“What the #*%@ is this?” was my initial reaction. I hopped through the questions, hoping to find one that I could do, or even one that made sense. No luck.

I knew my friends would be as snowed by the test as I was, but I learned that day that I’m pretty good under that kind of pressure. By the end I thought I had a solution to three of the seven problems. The others weren’t attempted. My friends solved no better than one. I gained confidence in weathering freak out test situations and got to experience “aha” moments that school rarely offered. More importantly, I learned that math isn’t as boring as I thought. (Frustratingly, my curiosity was not kindled. Nobody ever told me how well I did or what the solutions were.)

We’ve been told throughout our lives that math is so important to adult success and citizenship that it requires a big educational emphasis. Except over the past few decades people have ceded calculating to machines. Algebra, geometry, pre-calc, and calculus aren’t even coded by most who need the math. Rather, they borrow software that’s already written.

 The math we need most has little resemblance to what’s taught. And now AI can help us with math concepts and processes. A curriculum overhaul is long overdue.

Photo by NASA on Unsplash

Moon Launch Math

The early 80s was the dawn of personal computing, pivoting many workers from manual to automated calculations, and allowing increasingly sophisticated operations on data, much of them statistical. There was great consternation in math education circles that people would stop being good at doing arithmetic, and that would greatly affect their lives.

The curriculum in schools was still largely pre-calculator, though calculators had widespread ownership by the mid-70s. I call it “moon launch math” owing to its emphasis on manual problem solving, polynomials, and exact analytical solutions that characterize analysis of physical space, not information space.

I still call the math curriculum “moon launch”. When I asked AI (Claude 3.5 Sonnet, 8/7/2024) what fraction of the U.S. high school Common Core standards regard various skills, I got:

• Deterministic content and procedures: ~65-75% of standards

• Statistical thinking: ~15-20%

• Recognizing when and how to apply math: ~5-10%

• Algorithmic thinking and coding: 0%

• Critically evaluating tech-generated solutions: 0%

I did not verify these numbers, and some States and districts have included more than is in the Common Core, but I think you get the point. It’s pretty hard to argue that the math curriculum is on the cutting edge. Those who argue for the status quo have increasingly worse arguments.

I knew little about the big wide world in 1980, but I did know that the future of math was on the computer, not by hand. The consolation was that the job of working with a computer was to give it instructions for the process, so manually exercising the process had some value. I had some tentacle of belief that the math might be useful.

Students today should have a much harder time finding value in the largely unchanged curriculum. Those who disliked English class don’t grow up to hate the language, but those who dislike math do so with passion. As Tom Vander Ark, CEO of Getting Smart, has said, “The memorization of procedural computation that monopolizes math time in U.S. classrooms trips up most young people and discourages many from attending and completing a degree, and gaining meaningful employment.”   

It's a different world than the moon launch era. Not only have processes long required more judgment than repetition (e.g. in data science), but AI takes our interaction with math to an even higher abstraction level.

AI Collaboration

We used to solve math. Then we programmed computers to solve math. Now AI is automating coding, changing again our relationship with math.

I had a career in technology that touched many forms of math and many disciplines, and it’s interesting to think about the math skills that I used. It was almost all conceptual, not arithmetic. It is perhaps funny to consider that some math elites consider themselves bad at arithmetic.

Let me use the concepts of mean (the average) and median (the middle number) as an example. Moon launch math would give you a bunch of numbers and ask you to calculate both mean and median. Computer programming math would articulate a reusable process for calculating each quantity. Now the relevant knowledge is when mean or median is a more appropriate statistic, both for purposes of telling AI what to do, and in critically assessing how others (including AI) have used math. If my town gives me statistics on the mean sales price of a home in my town, then I’m going to be wary, because I know that a single, high-price home could skew the mean considerably. The median is a more appropriate measure for that circumstance.

AI’s emergence moves most of adult’s math needs to higher abstraction levels. When we get a new challenge, the first skill of math is always the same. Do we recognize aspects of the challenge for which math might be applicable? Secondly, what math might be appropriate given the assumptions and constraints of the challenge? What are the caveats in interpreting the math results?

“Wait”, you may say, “doesn’t AI stink at math?” Large-Language Models (LLMs) aren’t inherently good at math, but AI as a whole addresses many math challenges, and LLM math weaknesses are quickly being closed. A new paper from Deepmind uses two LLMs, and together and they were able to score very well on International Mathematical Olympiad problems.

On the contrary, I see the execution of math as entirely a machine function in the future. AI can even decide which math to use and how to use it, but we will need to critique and steer the approaches, including by deciding what aspects should stay human and what aspects are best for machines.

The Mathlete test I took decades ago is far more indicative of AI-era skill needs. Today’s math skills need are more about recognizing a situation as math relevant, and in framing the characteristics of the problem so that the right math can be applied and vetted. Those skills have little relationship with current math curricula.

Perhaps most importantly, math could be extended to be a center for interdisciplinary problem solving and systems thinking that are critical to modern life, but which fall through the cracks of conventional subject areas.

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The hardest part of any curriculum reform is to avoid it being an add-on that makes all learning increasingly shallow. Right now, many are trying to figure out how to how to squeeze in AI literacy. Middle school and high school math are great overhaul prospects.

There is of course always something lost in the process. The calculator is not an apt analogy to AI in terms of scope and impact, but the concern then was like the concern now. The concern was if a machine does calculations for people, then people will be worse at doing math in their heads. I am willing to stipulate that they were probably correct, though there is a lack of direct evidence for the pre- and post- calculator comparison.

Similarly, paring down moon launch math could make adults worse at those skills. It’s OK. That’s what the world demands. The opportunity cost of not teaching applied, challenge-oriented math that emphasizes statistical thinking and use of technology is far bigger.