Some of the proposals I’ve seen for AI applications that are supposed to help students learn mathematics are deeply flawed, because they fail to take into account a fundamental principle of learning, a principle that applies to all education and training activities that are intended to develop proficiency and judgment.
I’ll illustrate with a personal example. A couple of years ago my grandson was pursuing a rigorous college program in food sciences, which involved a considerable amount of mathematics, chemistry, and other science and engineering courses. Every so often I’d help him on his homework. Most of the time it was material that I hadn’t seen myself in decades, so we worked our way through it together. But physics was a different story, since that was my major field of study. As a result, I was able to give him a lot more help with that homework.
Fast-forward to final exams: I believe this was the only course that my grandson took in that rigorous program for which he did not get an A.
I should have known better. One of the things I had learned very well in my “on-the-job” training as an educator at The Delphian School almost half a century ago is that giving a student too much help is as damaging to their education as giving them too little—and probably even more so. Students can often find their way through to a solution with too little help, but there is no such cure for too much.
I’ve written in other posts about the value of productive struggle to the learner. I imagine we have all experienced its benefits, not only in terms of learning but also in terms of the self-confidence generated by success in the face of adversity. That experience is so common that there’s probably no real need to explain why it works, but for what it’s worth in my own opinion it comes down to a basic truth of learning theory: the learner themself must create the mental connections between a new idea (or datum or principle) and their existing ideas, the connections that are the essence of understanding. No one else has the power to create those connections in the learner’s mind. And those connections are forged in the course of a student’s often challenging journey from confusion to understanding.
Whatever the explanation, productive struggle is very valuable. If we agree on this, then we have enough common ground to consider the proper constraints on the role of AI in mathematics learning. There are four things that AI can and should do for the math learner:
1) Aid them in developing conceptual understanding of concepts and principles, when that understanding is being properly measured (which precludes multiple choice assessment).
2) Diagnose failures and direct the learner to resources that address the concept, principle, or skill that they need to give more attention to in order to be successful.
3) Walk the student through model problems.
4) Pose appropriate exercises and problems which the student must learn to do independently.
And there is one thing AI should never do for a math learner who is in the process of doing those exercises or solving those problems: tell them exactly what they did wrong and guide them to do that step correctly. That is simply too much help, because rather than making the struggle productive, it's eliminated entirely.
Bottom line: If a student cannot successfully and independently do homework exercises or solve math problems, AI should help with 1, 2, or 3. And that’s all.
There are already too many obstacles to success in learning mathematics for many of our students. Let’s not also undermine their ability to overcome those obstacles.