Methods · Creation, transfer & long horizon · Short guide

Analogical problem solving

Solve a new problem by finding a structurally similar solved one, mapping roles deliberately, then transferring the solution method without copying surface features.

When to use this: While you practise
Learning impact: Strong change
Learning evidence: Credible with caveats
Where you are with the topic: Applying in new contexts
How often to use it: Worth repeating often

When to use it

A new problem looks unfamiliar, but you suspect you have solved something with the same structure before.
You keep copying surface details from a worked example and the next problem still fails.
You want practice mapping roles, not just reading another solution.

What to ask AI

Type something like: “Target problem: [ ]. Help me find a structurally similar solved problem. Do not solve the target. Make me build a mapping table first.”

Ask it to critique only your mapping errors after you adapt the method yourself.

Keep the hard part on your side: you map roles and transfer steps; the AI does not hand you the finished solution.

How it helps

Experts look for structural twins. Novices look for similar stories. The difference is what you map, not how the problem is dressed.

Analogical problem solving trains the map: what plays the role of what, then which solution steps transfer.

If you skip the mapping table, you only practised reading solutions, and the next cover story will defeat you again.

How to run it

State the target problem without solving it yet.
Recall or request a solved analogue with similar structure, not a similar cover story.
Build a mapping table: each target element ↔ source element.
Transfer the method step by step into the target.
Stress-test the map: where does the analogy break?
Solve a third problem with the same structure cold, without looking at the table.

Example exchange

You

I have a river-crossing puzzle with boat-size limits. Help me find a problem with the same structure. Please don't solve the crossing for me.

Before I suggest anything, write what counts as the load, the capacity, and the forbidden combinations in your problem. Then we can hunt for a twin.

You

The load is the people and animals to move. The boat holds two. Forbidden combinations include the wolf alone with the goat, and similar pairs.

Good. Now propose your own mapping to a puzzle you already know, or say you need a source first. I will only critique the map, not finish the crossing.

Copyable prompt

Target problem: [ ].
Help me find a structurally similar solved problem (or use this source: [ ]).
Do not solve the target. Ask me to produce a mapping table first. Then let me
adapt the solution. Critique only my mapping errors.

The Tell

If you “used an analogy” but cannot show the mapping table, the AI or the worked example did the thinking.

Recognising a similar story is not transfer until you can name the roles and adapt the steps.

Principle evidence

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

The underlying learning idea is rated moderate. Analogical problem solving, retrieving a structural source analogue and mapping it, is a major cognitive-science tradition. Structure beats surface similarity for transfer.

AI delivery evidence

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

AI retrieval of clever analogues is convenient and unproven as a tutoring method on its own. The learning event is your mapping and adaptation. If the AI solves the target, delivery failed even when the answer is right.