Mathematics: Contingent hinting
Get unstuck on a problem without getting rescued from it, which matters more in mathematics than anywhere else.
What you'll be able to do: Get unstuck on a problem without getting rescued from it, which matters more in mathematics than anywhere else.
The failure this prevents
A student is stuck. They paste the problem. They get back a clean, correct, well-structured solution. They read it, follow every line, and think yes, obviously.
Then the next problem, and they're stuck in exactly the same place.
This is the single most common way AI makes mathematics worse, and it's invisible from the inside because reading a good solution is pleasant and feels like progress. Something did happen, you now understand that solution. What didn't happen is the thing that would let you start the next one.
The mechanism you skipped is being stuck. In mathematics more than any other subject, the ten minutes of not knowing what to try is where the learning is, because the difficulty is nearly always recognition: which method, which substitution, which first move, and recognition is built by searching, not by being shown the result of someone else's search.
The ladder, with mathematics rungs
| Rung | Ask for | What it costs you |
|---|---|---|
| 1 | "Is my approach reasonable?" | Nothing |
| 2 | "What type of problem is this?" | The category only |
| 3 | "What should I look at first?" | Direction |
| 4 | "First step only, then stop." | One step |
| 5 | "Show me a similar problem worked fully." | A model, not your answer |
Rung 1 resolves roughly half of student stuckness in mathematics, because half the time you were on the right track and stalled on confidence rather than method. It costs you no content at all, which makes it close to free.
Rung 2 is unusually powerful here and is the one to reach for next. "This is a related-rates problem" or "this needs partial fractions" is often the entire obstacle. Once named, execution is routine, which is exactly the property that makes blocked practice so misleading (article 04).
Rung 5 is deliberately a different problem. You get a complete model and still have to do the transfer yourself, which is where the learning lives.
Notice what's absent from the ladder: solve this for me. If you need that, you're not stuck, you're past the material, go down a level (article 03) rather than borrowing an answer.
The setup, once per session
I'm working on problems and I want contingent hints, not solutions. Rules: never give me a complete solution; give the smallest hint that would unstick me and then stop; if I haven't shown you an attempt, ask for one first. If I ask for the answer, remind me of these rules and give me a hint instead.You will need to re-issue this. Helpfulness is the default and it drifts back within a few exchanges.
Across the syllabus
Integration. Rung 2 is the whole game: naming the method resolves most stuckness. Resist rung 4, being given the substitution removes the only decision in the problem.
Geometry proofs. Rung 3: "which pair of triangles would be worth looking at?": without saying why.
Word problems. Rung 1 first, because the usual failure is confidence in the setup rather than the algebra. "Is my equation capturing the situation?" is often sufficient.
Induction. Rung 3: "look at what you're allowed to assume." Students routinely write the assumption and never use it.
Related rates. Rung 2 plus "what's changing and what's fixed?": the classification is the difficulty.
Linear algebra. Rung 1 matters most; a wrong approach here costs twenty minutes of correct arithmetic.
Probability word problems. Rung 2, conditional, independent, or complementary, because the wording deliberately obscures it.
Series convergence. Rung 2 is which test, and being told is fatal because choosing the test is the exercise.
Withdrawing the help
The half everyone skips. Hints on the first two problems of a set, none after. Schedule it explicitly:
I've done three of these with hints. Give me the next one with no help at all, and don't respond until I've finished.Without this you have a crutch with good branding. Fading is what makes scaffolding scaffolding.
Log which rung you needed
Over a fortnight, the pattern is a precise map of your weaknesses. Consistently needing rung 4 on integration and rung 1 on differentiation says something specific and actionable that no score would tell you.
Pitfalls
- Asking before attempting. Voids the method entirely.
- Climbing without attempting between rungs. Five hints delivered slowly is a solution.
- Taking rung 5 on your own problem. It must be a similar one.
- Never withdrawing. Schedule the unaided problems.
- Taking hints you didn't need. Processing help you'd have got past costs you the search.
- The tell: you finished the problem set having been unstuck every time and couldn't start any of them tomorrow.
Try this today
Next time you're stuck: don't paste the problem. Paste the problem and your attempt, and ask only "is my approach reasonable?"
Keep count this week of how often that was enough. For most people it's about half, which means half the solutions they'd have read were never needed.