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4.2 · Learning with AI: Explanation, Counterexample and Independent Understanding
Goal: use AI as a tutor without confusing an elegant explanation with real learning.
A convincing lesson may conceal an error
Imagine studying compound interest. A model supplies a clear table and an intuitive definition but silently confuses an effective annual rate with a nominal rate compounded monthly. Memorizing the answer would teach an error. A better study cycle makes understanding visible.
Four stages of learning
- Initial grasp: request a definition with variables, assumptions and a modest example.
- Challenge: ask for a counterexample where superficial understanding fails; identify the condition that was missing.
- Reconstruction: revise the explanation to include the overlooked condition.
- Independent test: solve a new problem without looking at the model’s answer, then compare to a primary source or verified calculation.
Teach me [concept] using an accessible example, then give a case where the initial explanation becomes inadequate. Ask what I would change and wait for my answer before explaining it. Finally provide a new problem I can solve without assistance and a traceable reference to check.
A 2026 extension
If a spreadsheet or coding feature is available, make the model implement its formula. Change units, time periods or denominators and verify whether the result behaves correctly. For nonnumerical topics, verify that a purported quotation really appears in the cited work. A generated bibliography is not evidence that the sources were read.
Exercise: choose a concept you believe you understand. Explain it before using AI, then write what changed after a counterexample and a source check. A tutor that can answer almost everything still cannot certify your understanding merely because the conversation was long.
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