Study multiple varied examples of the same principle before generalizing

Comparing examples that share a deep principle but differ on surface features builds transferable knowledge faster than repetition of similar examples.

Why it works

A single worked example builds a schema that may be over-fitted to the surface features of that specific example — a form of overfitting analogous to machine learning. Comparing multiple examples that share the same underlying principle but differ in context, numbers, or surface presentation forces the learner to abstract the principle from its context, which is what produces transferable schemas. Analogy-making between examples is the mechanism: shared deep structure across varied surfaces reveals the invariant principle.

How to do it

1. For each principle you want to learn, gather at least three worked examples that differ in surface features but share the same solution structure.
2. After studying each example, identify: "What is the same across all of them? What is the structural pattern?"
3. Write that structural pattern in a sentence before moving on.
4. Test your schema by generating a novel example yourself and solving it.

Evidence

Catrambone and Holyoak (1989) showed that students who compared two analogous examples before solving problems showed better far transfer than those who only studied one example, directly supporting the multiple-example-variation approach. (rct)

Comparison is effortful for novices; the benefit depends on the learner having enough prior knowledge to recognize the shared structure — completely novel domains may require a simpler start.

Sources

• Catrambone & Holyoak (1989), Overcoming contextual limitations on problem-solving transfer, Journal of Experimental Psychology: Learning, Memory, and Cognition

Common mistake

Studying multiple examples that differ in surface features but also in principle, which fragments rather than consolidates the schema by confusing variation that matters with variation that doesn’t.