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Most students open an AI chat with the whole problem and the words "solve this". The answer arrives, and someone else has chosen the method. A small change fixes this: write a three-line plan first, and ask the AI to judge only the plan. You still do the solving.
Why plan before you ask AI to solve?
Because choosing the method is the part you must do alone in an exam, and it is the part AI quietly takes away. In a field experiment with nearly a thousand high school maths students, published in PNAS in 2025, Hamsa Bastani and colleagues gave some students a plain ChatGPT-style GPT-4 tutor during practice. Their grades rose by 48% while they had access, but when access was taken away they scored 17% lower than students who never had it. A second version with prompts designed to safeguard learning largely avoided that harm. The authors write that without guardrails, students attempt to use GPT-4 as a "crutch" during practice.
Many students also find it hard to watch their own thinking while they solve. A 2025 think-aloud study of 30 Grade 11 students solving physics problems, in Physical Review Physics Education Research, classed most of them as novices who struggled to apply metacognitive knowledge and skills, and noted that assessment focused heavily on final results may hold back deeper problem solving.
What goes in a three-line plan?
The idea is old. George Polya's four steps for problem solving are understand the problem, design a plan, carry out the plan, and look back, as summarised in this University of Kentucky course page. Three lines is enough to capture the first, second and fourth steps before you touch the third:
Find: what exactly is unknown, and what is given.
Method: which law, idea or trick links the data to the unknown, and why it applies here.
Check: how you will know the answer is right (units, a rough estimate, a limiting case).
Our walk-through of Polya's four steps on a real physics problem shows the full method. If you cannot write line 2, you have found the real doubt: ask about the idea itself rather than the problem. Our guide on asking AI for only the first step covers that case.
How do you ask an AI to critique a plan without solving it?
Paste the problem and your plan, then add this script word for word:
"Do not solve this problem and do not give any numbers or final expressions. Critique only my plan. For each line, say whether it is sound. If a line has a flaw, ask me one question that points at it instead of correcting it. If the whole plan works, say so and suggest one extra check."
Revise the plan yourself after the critique, and only then pick up your pen to solve.
What does a plan critique look like in practice?
Take a Class 11 kinematics question: a ball is thrown horizontally at 10 m/s from the top of a 20 m building. How far from the base does it land? Take g = 10 m/s².
A first plan many students write:
Find: the range R.
Method: use R = u² sin 2θ / g.
Check: the answer should come out in metres.
A good critique does not fix this. It asks: "The range formula assumes the ball lands at the same height it was thrown from. Is that true here? And what does it give when θ = 0?"
The revised plan:
Find: horizontal distance travelled by the time the ball reaches the ground.
Method: treat the two directions separately; the vertical fall of 20 m from zero vertical speed gives the time from h = ½gt², and the steady 10 m/s horizontal speed gives x = ut.
Check: the same time must be used in both directions, and a taller building should give a longer distance.
Now you solve it yourself: t = 2 s, so x = 20 m. The method is now yours, and you will recognise the "different landing height" trap the next time it appears in a mock test.
What if the AI solves it anyway?
Chat tools often drift back to answering. Three rules help:
If the reply contains the answer, close the chat and rewrite the plan from memory.
Repeat the script for every new problem; do not rely on the chat remembering it.
If you are stuck on line 2, ask for a hint, not a method. Our hint ladder for hard problems sets out the steps.
If you do not know where to start a plan at all, Fermi's AI tutor works out what you already know, builds a plan for the session, and decides whether to explain, ask or show, so the reasoning stays with you. After you have solved a problem, you can compare your route with the Fermi Problem Library, whose step-by-step solver explains the reasoning rather than printing an answer.
Try it on the next three problems you sit down with tonight: three lines, one critique, then solve.
