Teaching Math in the Age of AI

Will AI finally drive us into teaching math hands-on, instead of with worksheets?

Recently I tried out the AI program Bard's latest update. Bard now allows the user to input math problems, including photos of equations. It then returns step-by-step solutions and a background discussion as well as the answer. In other words, it shows its work and gives you the answer. In my limited test it performed quite well.

This means that from here on out, it's pretty questionable to grade students based on their rendition of the odd-numbered problems from the textbook. But was that a good way to assess math in the first place?

For the last several years. Rich Cameron and I have been working to develop hand-on math materials for our colleagues at Make: . Many of you are probably already familiar with our Make:Geometry, Make:Trigonometry and Make:Calculus books. One of thing we hear all the time is, "People love to learn this way, but it's just too hard to come up with a way to assess math learning by making something."

Now is the time to figure out how to teach and assess math with hands-on models and projects.

For a student, using a protractor and tape measure to figure out the height of a tree is a powerful lesson in trigonometry. Calculus problems particularly lend themselves to hands-on demonstration, whether it be figuring out the volume of a weirdly-shaped container several different ways, or calculating the flight path of a ball.

We made 3D printed models to illustrate our books, but once a way of thinking about a problem this way is apparent, craft materials and cheap classroom stuff can often suffice. Our models are open source, too, so the 3D printers that are collecting dust in many schools can be put to good use.

To be clear, I am not suggesting students never learn algebra and calculation of actual values. I am, however, suggesting they not learn that first. A mix of free simulation tools and hands-on maker tech mean that it is much cheaper and easier to teach conceptually first, and ask students to demonstrate they understand a concept by creating something. Then, move into calculation. At that point they should have enough intuition to tell whether their answer is right. Today, so much math is aimed at "preparing" students for solving problems that they hardly ever solve realistic problems.

If an AI helps them figure it out, so what? As long as they can explain what they did and why to a teacher, they learned it. And often they will pick up the calculation stuff they need along the way.

There are many advantages to teaching concept-first and hands-on:

• Fun stuff with clear applications (like trajectories) can be taught in third or fourth grade. We have taught from our Make:Calculus book in enrichment classes for third to fifth graders. They might not be able to compute an integral beyond simple polynomials, but they understand what an integral and derivative is by the end. And they are motivated to learn the algebra and other techniques going forward, instead of endlessly drilling "because you'll need it later."
• Teaching this way is inherently more accessible, for instance to visually-impaired learners, than paper worksheets.
• Learning this way works well in groups, teaching collaboration and other social skills. It also creates discussions about assumptions, how good a model is and so on that does not come from doing problems 1 through 10 that address every possible oddball edge case.

In short: it's time we started thinking about teaching math in ways that use our human style best, instead of teaching kids as if they were machines.

We know there are issues with this approach in classroom management, entrenched structures and more. But change will come, and this is an opportunity to consider what types of learning might best fit this new landscape. This isn't new, of course - Constructivist learning and problem-based learning have been around for a long time. You might also enjoy the book, "A Mathematician's Lament" by Paul Lockhart, who has made a similar argument eloquently for many years.

To learn more about our approach, check out our Make: math books (at makershed.com and other retailers). I'd love to see your thoughts in the comments about the best ways to make this happen, and the obstacles to be overcome.