Methods · Generative practice & retrieval
B6
Far-transfer problems
Solve problems that need the same principle in an unfamiliar dress, so you can recognise the idea outside the textbook costume.
When to use it
- Near variants feel easy, but a word problem in a new setting still blindsides you.
- The exam loves unusual contexts for the same underlying rule.
- You can execute a method in the chapter’s examples and fail when the story changes.
- You want to test whether you understand the principle or only the costume.
What to ask AI
Type something like: “Principle I think I know: [principle]. Give me a far-transfer problem in a different context. Do not hint which chapter it came from. Wait for my attempt.”
Ask it to change surface story, domain, or representation, not the underlying rule.
After you solve, ask: “What in my solution shows I used the principle, or failed to?”
How it helps
Far transfer means the same idea wearing clothes you did not study in.
Exams and real work rarely announce which example you are supposed to copy.
Practising far transfer trains recognition of the principle, not rehearsal of a storyline.
If far problems crush you, step back to near variants, that is information, not failure.
How to run it
- State the principle you believe you understand in one or two sentences.
- Ask for a problem that needs that principle in a new context or representation.
- Attempt without asking which lesson it matches.
- Explain which principle you used and why the new dress still fits.
- If you cannot see the link, ask for a hint that names the bridge, not the full solution.
Example exchange
I understand conservation of energy from the roller-coaster examples. Can you give me a far-transfer problem that does not look like those, and wait for my attempt before any solution?
A spring launches a block up a rough incline. You know the spring constant, compression, mass, friction coefficient, and angle. Does the block reach a marked height? Attempt it with a clear energy account.
I wrote ½kx² = mgh plus work against friction. I am unsure what distance to use for friction, the height or the path along the incline.
Good principle choice. Before more maths: is friction’s path the vertical height or the distance along the slope? Answer that, then finish.
Copyable prompt
Principle I think I know: [PRINCIPLE].
Give me ONE far-transfer problem in an unfamiliar context or representation.
Do not label the chapter or give hints until I submit an attempt and say which
principle I used.
The Tell
You will know the method has flipped when the AI labels the principle in the problem statement, or you ask “which method is this?” before trying.
Then you never practised recognising the idea in disguise.
Hide the chapter tag, attempt a path, and only then check whether the principle you named was the right one.
Principle evidence
Strength of the underlying learning idea, not a claim about AI products.
Far transfer is harder and less automatic than near transfer. Practice that varies context while holding the principle fixed is a standard recommendation when the goal is flexible use, not only fluent copying.
AI delivery evidence
Whether an AI tutor delivers this method well is a separate question.
AI-generated “far” problems sometimes sneak in extra principles or stay oddly near. Judge distance yourself; reject items that need ideas you have not learned yet.