Mathematics Education vs AI vs BodyandSoul vs John Dewey

Recent posts on the OpenAI solution to the Clay Navier-Stokes Millennium Problem reflect on the monumental challenge to professional mathematicians presented by a AI agents showing to be able to prove mathematical theorems. 

The challenge also strikes mathematics education and here  (or below)is what chatGPT delivers on prompt asking about the relevance of John Dewey in the new landscape of AI. 

The BodyandSoul project also gets new actuality with AI.  

ChatGPT:

John Dewey (1859–1952) fits surprisingly well into the AI era—but AI also exposes a weakness in the way Dewey’s educational ideas have sometimes been interpreted.

Dewey’s central idea was that education should not primarily consist of transferring a fixed body of knowledge from teacher to pupil. Learning occurs through inquiry, experience, problem solving and reflection—often summarized, somewhat simplistically, as learning by doing. The teacher creates situations in which the student encounters a problem, investigates it, tests possible solutions and reconstructs his or her understanding.

AI radically changes the conditions under which this philosophy operates.

Before AI, there was a practical reason for spending enormous amounts of schooling on acquiring information and routine intellectual techniques. A student needed vocabulary, facts, algorithms, grammar, computational techniques, references, etc., because these were the tools required for subsequent intellectual work. With a powerful AI available, much of this intermediate work can be supplied almost instantly.

That pushes education toward Dewey. Consider mathematics. Instead of spending weeks learning a particular computational procedure and then being given an artificial exercise, a pupil might start with a genuine question:

Why does a suspension bridge have the shape it does?

AI can supply calculations, simulations, explanations at different levels, historical background and even computer programs. The student can formulate hypotheses, challenge the AI, modify the model and compare predictions with observations. This is recognizably Deweyan inquiry—but enormously amplified.

Yet there is a paradox. AI can also destroy Deweyan learning if it does the inquiry for the student.

Suppose the assignment is: Investigate why the Roman Republic collapsed. A student asks an AI and receives a beautifully organized essay. The product may be excellent, but virtually no education has occurred. The student has neither investigated nor struggled with competing explanations nor constructed an argument.

So the distinction in AI education becomes:

AI doing the task versus AI enlarging the student's capacity to do the task.

This makes Dewey's concept of inquiry more important than the familiar slogan learning by doing. Merely producing something—a report, presentation, program or mathematical proof—is no longer evidence that the student has learned anything. AI can produce all of these.

Consequently, I think the AI landscape points toward a modified Deweyan school with three components:

1. A substantial foundation of knowledge. A person cannot critically interrogate an AI about Roman history, mathematics or physics without already knowing something. AI therefore does not make knowledge unnecessary. In some respects it makes internal knowledge more important, because otherwise one cannot recognize plausible nonsense.
2. Authentic inquiry. Students should increasingly be given difficult questions whose answers aren't simply contained in the textbook. AI becomes an intellectual instrument—something like an extraordinarily powerful library, calculator and conversational research assistant combined.
3. Demonstrated understanding rather than submitted products. Assessment would increasingly have to involve conversation, oral examination, explanation at the blackboard, modification of an argument, criticism of an AI answer, or solving a new variation of a problem. The crucial question becomes: What can the student understand and defend?

This also changes the teacher's position. The teacher becomes somewhat more Deweyan and less like an information distributor, but not less important. The teacher chooses worthwhile problems, detects superficial understanding, asks the decisive follow-up question and possesses enough subject knowledge to know when both pupil and AI have gone astray.

There is therefore an interesting historical reversal. During the twentieth century, Dewey could sometimes be interpreted as supporting a movement away from demanding subject knowledge toward activities, projects and pupil-centered learning. AI makes that version of Dewey increasingly untenable. Activities and polished products are now almost free.

What remains scarce is understanding, judgment, curiosity and the ability to formulate a good question.

In that sense, AI may produce a more intellectually demanding version of Dewey than the schools influenced by Dewey ever did: learn through genuine inquiry—but know enough to conduct the inquiry yourself.

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If you want, I can:

• Explore how AI can assist but not replace student inquiry in education
• Discuss challenges and solutions for assessing student understanding with AI
• Analyze the evolving role of teachers in AI-augmented Deweyan education