Error-first practice

Deliberately attempt problems a bit above your level so informative failures show you what to learn next.

When to use this: While you practise
Learning impact: Reliable gain
Learning evidence: Credible with caveats
Where you are with the topic: Building understanding
How often to use it: Worth repeating often

When to use it

Comfortable drills feel smooth and teach you little new.
You want failures that diagnose, not random overwhelm.
You have time to attempt hard items before a targeted micro-lesson.

What to ask AI

Type something like: “Give me one problem slightly above my level on [skill]. I’ll attempt it expecting to fail usefully. Then diagnose the first break, no full solution yet.”

Ask for productive difficulty, not sadism, one notch up, not three.

Keep the attempt before any teaching.

How it helps

A carefully chosen hard attempt can reveal the exact missing piece faster than more easy reps.

The point is an informative failure, not humiliation.

After the fail, switch into targeted feedback or remediation, do not grind blind.

If every attempt is impossible, you aimed too high; adjust the notch.

How to run it

Name your current comfortable level on a skill.
Request one item slightly harder.
Attempt fully, expecting friction.
Ask for first-error diagnosis, then a micro-remediation if needed.
Retry a near variant to see whether the failure taught you.

Example exchange

You

I am comfortable with basic chain rule. Give me one notch harder, nested trig compositions. I will attempt it expecting a useful fail. Afterward, tell me only the first error.

Differentiate y = sin(cos(3x)). Attempt it fully.

You

I got cos(cos(3x)) times (−sin(3x)), and then I stalled on what to do with the 3.

First break: the innermost derivative. You started the chain and then dropped a layer. Repair that factor, then try a cousin problem.

Copyable prompt

Skill: [ ]. My comfortable level: [ ].
Give me ONE problem slightly above that level. I will attempt it expecting an
informative failure. Afterward: first wrong step and likely misconception only, no full solution unless I ask.

The Tell

You will know the method has flipped when “hard practice” means watching the AI solve olympiad problems while you follow along.

Then you never failed productively; you spectated.

Put an attempt on paper first, even if it is messy and wrong.

Principle evidence

Strength of the underlying learning idea, not a claim about AI products.

Desirable difficulties and productive failure traditions suggest that well-pitched challenge can improve learning when followed by good feedback, not when difficulty is pure confusion without a repair path.

AI delivery evidence

Whether an AI tutor delivers this method well is a separate question.

Difficulty calibration by AI is imperfect. Say when an item is wildly out of range; the method needs a near miss, not a brick wall.