Compare two examples side-by-side to extract the underlying principle

Place two worked examples next to each other and find exactly what is the same, structurally, beneath the surface differences.

Why it works

Structural alignment — comparing two cases to find their deep relational match — is the primary mechanism through which schema abstraction occurs. When two examples are compared simultaneously, the brain performs a mapping operation that highlights invariant structure and suppresses surface noise. Gentner’s work on analogical encoding shows this process is far more effective than studying examples sequentially without explicit comparison.

How to do it

1. Place two worked examples of the same principle side by side (or on two pages you can flip between).
2. Identify every step and ask: "What is the corresponding step in the other example?"
3. Write one sentence naming the structural principle that appears in both (not the surface features).
4. Attempt a problem from a third context, applying the named principle.

Evidence

Gentner et al. (2003) demonstrated that analogical comparison — studying two examples simultaneously with explicit mapping — produced better schema abstraction and transfer than studying examples sequentially, even when total time was equated. (rct)

Comparison requires enough working memory capacity to hold both examples simultaneously; for very complex material, presenting the comparison after initial individual study may be needed.

Sources

• Gentner, Loewenstein & Thompson (2003), Learning and transfer: A general role for analogical encoding, Journal of Educational Psychology

Common mistake

Comparing examples based on surface features ("both involve circles") rather than structural ones ("both require equating rates of change"), which confirms superficial pattern-matching rather than building the actual principle.