concrete-examples

Concrete Examples

Overview

Students grasp an abstraction faster when it's anchored in something familiar — but the technique is more than "give an example." Two failure modes sink the naive version: one example (the student learns that example, not the principle) and surface-similar examples that look related but don't share the concept's structure (they learn the surface). (Weinstein & Sumeracki's six strategies; concreteness fading: Fyfe et al. 2014; Goldstone & Son 2005.)

The discipline

• Multiple, varied examples — not one. Two or three from different surfaces let students extract the shared principle (transfer). A shuffled deck, a dart hitting wall-not-bullseye, and ink spreading in water are the same counting logic on three surfaces.
• Structural, not surface, match. The example must map to the concept's structure, not merely feel related — and state the mapping ("here's how this lines up"). A surface-similar example that breaks the mapping teaches the wrong thing.
• Concreteness fading — concrete → abstract. Start concrete (the deck), build the abstraction on it (counting microstates), and end on the abstraction itself (the formal statement / equation), naming the transition. Students who only ever see the concrete can't transfer to formal problems; fading is what carries them across.
• Pick examples that disarm the misconception the abstract term invites ("disorder" → counting arrangements), not ones that reinforce it.

Example

• ❌ One-and-done: "Entropy is like a messy room." (one example, and surface-similar — "messy" is the disorder misconception, and it never fades to the real idea.)
• ✅ Faded + varied: deck → dart → ink (same counting logic, varied surfaces) → "entropy counts the microstates consistent with the macrostate" (the abstraction, named).

Red flags — STOP

• A single example carrying the whole concept.
• Examples that are surface-similar but structurally different (mislead).
• Staying concrete — never fading to the abstraction students must use.
• A familiar analogy that reinforces the misconception.

See also elaboration-and-self-explanation (prompt students to explain the mapping) and dual-coding (pair the example with a visual).

Eval-side companion: no dedicated scored dimension yet; cite Fyfe et al. 2014 / Weinstein & Sumeracki directly. docs/website/reference/evidence-based-pedagogy-rubric.md.