Example Problem Pairs

Element · All elements
Evidence · 7 claims (3 for, 3 mixed, 1 against) · 7 studies (3 review, 2 causal, 2 theoretical), q1–q3 · 0 of 7 report an effect size · 5 claims rest on one study

Description

An example problem pair pairs a fully worked example with a structurally identical (isomorphic) problem that the learner must solve immediately afterward. The learner studies the expert solution, then applies the same procedure to a near-transfer task, alternating example study and problem solving across a sequence.

Design Implications

Example problem pairs reduce unguided search during early skill acquisition while guaranteeing that every example is followed by active application Example–problem pairs lower cognitive load compared with solving all problems independently. [+M]. The pairing is the critical design feature: examples alone produce passive study and illusions of competence, while problems alone impose search costs on novices; the alternation captures the benefit of both Example-based sequences outperform problem-only practice for novices, and fading support is argued to aid transfer [+S]. Pairs should be structurally similar but superficially varied so learners abstract the underlying procedure rather than surface features.

Context

Requirements

• A fully worked example with clear step-by-step reasoning (Worked Examples)
• An isomorphic follow-up problem matched in solution structure
• Successive pairs that vary surface features while holding solution structure constant, to support schema abstraction
• Learner accountability for studying the example (e.g., self-explanation prompts or completion problems), since unexamined copying defeats the design

Constraints

• For learners with substantial prior knowledge, studying a full example is redundant and slows them relative to plain problem solving Worked-example guidance becomes less effective as learner expertise increases. [~M] — the expertise reversal effect applies directly to pair sequences
• If the follow-up problem is too dissimilar, learners cannot map the example onto it and revert to guessing
• Long uninterrupted example sequences without problems reduce engagement and processing depth Example-based sequences outperform problem-only practice for novices, and fading support is argued to aid transfer [-S]
• Less suited to ill-structured domains where no single solution procedure transfers across problems

Target Learners

• Novices in a structured domain (algebra, physics, programming, statistics) who lack schemas for the task type Example–problem pairs lower cognitive load compared with solving all problems independently. [+M]
• Learners prone to ineffective trial-and-error strategies under conventional problem sets
• Less beneficial for advanced learners, who should receive faded or problem-only sequences Worked-example guidance becomes less effective as learner expertise increases. [~M]

Target Learning Goals

• Procedural fluency: acquiring and automating a solution procedure
• Schema construction: recognizing which problem type a new problem belongs to
• Near transfer: applying a learned procedure to structurally identical problems

Affordances

• Worked Examples — the example half of the pair is a worked example; the pair format is the canonical way of embedding worked examples in a practice sequence
• Cognitive Load Management — the example eliminates means-ends search on the first task, freeing working memory for schema construction; the paired problem then consolidates it under moderate load
• Scaffolding — pairs are a starting point for a fading sequence: full example + problem → completion problem + problem → problem + problem as expertise grows (Fading)
• Cognitive Apprenticeship — the worked example functions as a model of expert solution behavior that learners immediately imitate in the paired task

Claims

• Worked examples did not improve application of CDR strategy knowledge relative to problem-solving [-W]
• Alternating example-practice pairs produce faster and more accurate near-transfer solutions than blocked presentation of examples followed by practice [+W]
• The worked example effect holds for the schema-acquisition goal, but other instructional goals may be better served by other means [~W]
• Solving an isomorphic practice problem after studying a worked example improves prospective monitoring accuracy, with mixed effects on regulation accuracy [~W]

Related Elements

• Worked Examples — the example component of the pair
• Fading — the natural next step once pairs have built initial competence
• Practice — the problem component; pairs guarantee practice follows every example
• Non-Examples — can replace the example in a pair to sharpen conceptual discrimination
• Erroneous Examples — a variant where the example contains an error for learners to diagnose

Patterns That Use This Element

• Cognitive Load Theory — the canonical example-based instruction sequence
• Four-Component Instructional Design — supportive information and task classes built from example–task alternation
• Direct Instruction — model–guide–test structure mirrors example → pair → independent problems

Examples

Use Worked Examples — The general strategy of alternating fully solved problems with isomorphic practice problems; example problem pairs are its core unit.

Sweller & Cooper's algebra studies — The original experimental paradigm: students studied a worked algebra example then solved a matched problem, outperforming problem-only peers on subsequent tests.

Khan Academy — Narrated example videos followed immediately by practice exercises of the same type, with on-demand hints that decompose the problem into completion steps.

Codecademy — Annotated example code shown alongside an exercise where learners write structurally similar code, an example problem pair in a programming context.

Key Sources

• Sweller, J., & Cooper, G. A. (1985). The use of worked examples as a substitute for problem solving in learning algebra. Cognition and Instruction, 2(1), 59–89. doi:10.1207/s1532690xci0201_3
• Cooper, G., & Sweller, J. (1987). Effects of schema acquisition and rule automation on mathematical problem-solving transfer. Journal of Educational Psychology, 79(4), 347–362. doi:10.1037/0022-0663.79.4.347
• van Gog, T., & Rummel, N. (2010). Example-based learning: Integrating cognitive and social-cognitive research perspectives. Educational Psychology Review, 22(2), 155–174. doi:10.1007/s10648-010-9134-7
• Kalyuga, S., Ayres, P., Chandler, P., & Sweller, J. (2003). The expertise reversal effect. Educational Psychologist, 38(1), 23–31. doi:10.1207/S15326985EP3801_4
• Renkl, A. (2014). Toward an instructionally oriented theory of example-based learning. Cognitive Science, 38(1), 1–37. doi:10.1111/cogs.12086

Page metadata

Field	Value
type	element
id	example-problem-pairs
title	Example Problem Pairs
description	An example problem pair presents a fully worked solution followed immediately by a similar problem for the learner to solve, alternating study of an example with practice on an isomorphic task.
status	review
canonical	True
generated	by claude/unspecified on 2026-08-29
trust	unverified — no one has confirmed this page's content

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