Worked Examples

Pattern · All patterns
Evidence · 28 claims (11 for, 15 mixed, 2 against) · 23 studies (11 causal, 6 review, 4 theoretical, 1 quant-synthesis, 1 design), q1–q3 · 1 of 23 report an effect size · 26 claims rest on one study

Description and scope

A reusable policy for selecting and adapting correct solution models on structured tasks. It instantiates the conditional principle. The study configurations below are evidence; the response-dependent policy is an untested design proposal. Use it to gather better evidence, not to certify a latent learner state.

Inputs: establish the design brief

Field	Record or elicit
Learner and starting observation	Task-specific experience; an independent response and reasoning; errors, confidence and uncertainty. Preserve unknowns.
Context and activities	Representation, language/access conditions, available time, tools, prompts, earlier exposures and exact help.
Learner-valued goal	Ask what the learner wants and why. Record disagreement with the designer objective; negotiate rather than assume agreement.
Designer objective	Intended capability and representative task; identify what must be independent and which aids are permitted.
Outcome	Scoring instrument, locally chosen criterion, immediate/delayed horizon, and any distinct use or safety outcome.

A request for “better learning” does not specify these inputs. Ask for them before prescribing dose, a fading threshold or a predicted gain. Check the solution and scoring key for correctness and alignment first. Incorrect-example learning is a different configuration with its own evidence; accurate copying of an error is not readiness.

Sequence and conditional policy

1. Elicit briefly. Ask for a first decision and justification without showing the worked answer. Avoid turning a diagnostic attempt into a long unguided treatment. Record its learning exposure.
2. Select a bounded candidate. If task-specific reasoning is weak and the task is structured, consider a correct example with visible decision rationale. If varied independent performance is already available, consider independent work or targeted help; the novice contrast does not require a full example for every learner.
3. Observe the process. Ask which relation licenses a step or how a relevant condition would change it. A completion problem removes steps inside a solution; an example→problem pair presents a separate complete problem. Record which was actually delivered.
4. Choose the next activity provisionally. Use the table below. Repeat matched probes where feasible; task, representation, assistance and practice history can confound their interpretation.
5. Reobserve. Use a new representative task under the agreed aids, rubric and horizon. Retain unresolved explanations. If the response disagrees with the expectation, revise the interpretation or configuration.

Observation	Discriminating probe	Proposed action, with its uncertainty
Cannot start independently	Compare first-step reasoning in matched familiar and changed representations; permit an accessible response mode without supplying the reasoning.	If reasoning remains weak, model the relevant relation and invite another attempt. If only recognition/access fails, compare representations or improve access. Neither branch is a validated diagnosis.
Correct with hints or tools only	Vary one named aid while keeping the reasoning demand similar.	Retain necessary access tools; reduce solution hints only provisionally. Do not remove tools that the intended capability permits simply to make the task harder.
Correct routine answer and explanation	Change a relevant condition as well as surface details; ask what changes and why.	Offer less solution support after representative independent success, then check again. One success is insufficient to establish an optimal fading threshold.
Fluent explanation but weak integrated performance	Compare component and whole-task demands; record time/memory and omitted information.	Offer targeted integration practice or support rather than repeat the whole explanation automatically.
Low effort or little participation	Ask about purpose and barriers; compare accuracy/reasoning under accessible, meaningful conditions.	Negotiate purpose or conditions when warranted. Neither effort nor participation alone establishes learning.

Choosing configurations from evidence

• For a comparable initial circuit task, the four-arm contrast [+W] supports an example-first candidate. Calculators/formula sheets were permitted; solution access was restricted. “Independent” must preserve that distinction.
• If examples/problems repeat the identical task, the qualification [~W] prevents a universal final-test ordering claim. Lack of a detected difference is not equivalence.
• For a transition to more independent probability reasoning, backward fading and principle prompts [+W] provide a candidate configuration. Their study does not validate this table's adaptive branches or a special synergy.

Do not convert reported partial η² into a probability, rank unlike comparators using Cohen/Kraft labels, or predict delayed repair from immediate paper-task scores. A precise abstention names the missing comparison, target or observation and the next way to resolve it.

Fitting the design to a situation

Ask for three facts when the brief omits them: what a learner does on a first attempt at this problem type without help, how many example–problem pairs the time allows, and which outcome is checked, and when (the practised procedure, a changed problem, a delayed test).

If the brief says…	Then change…	Basis
A first lesson on a structured procedure for learners who have not met it	Open with a fully worked example with the reasoning for each step visible, then a comparable problem	Example-based sequences outperform problem-only practice for novices [+M]; Example–problem sequences reduce cognitive load [+M]
One lesson with room for about four pairs	Sequence example → problem in each pair, never problem → example	Example-first beat problem-first on an immediate test [+M]
The paired problem is identical to the example	Vary the paired problem's surface or numbers, and do not expect an order effect to last to a final test	Order advantage not detected at the final test [~M]
A unit of several lessons	Move from full examples to examples with the last step left out, then two steps, then bare problems	Fading worked steps eases the move to problem solving [+M]
Learners will be tested on the principles, not only the procedure	Fade the steps that apply the principles to be learned, and prompt learners to name the principle at each step	Learners learned most about the faded principles [+M]; Backward fading and principle prompts supported transfer [+M]
The first attempt shows learners can already solve and explain the problem	Skip to completion or independent problems for those learners, and check again on a changed problem	Worked examples become less effective as expertise grows [~M]
The first attempt shows little task knowledge	Give full, not completion, examples to these learners	Lower-prior-knowledge learners did better with full than completion examples [+M]
Examples come as a diagram plus separate text, or as narrated slides	Integrate the text into the diagram; if narration is used, add cues that direct attention when the visual search is heavy	Split-attention examples lose their advantage [~M]; Dual-mode presentation helps, except under high visual search without cues [~W]
The practice set uses widely varied problems	Pair varied problems with worked examples rather than with conventional problem solving	High variability aids learning from examples but harms learning from problems [~W]
An AI tutor or retrieval system is meant to supply worked examples	Check that examples are actually delivered; one system included them in about 42% of responses despite a large problem bank	Worked examples appeared in only about 42% of responses [-W]

The evidence by question

• Do novices learn more from studying worked examples than from solving the same problems unaided? Example-based sequences outperform problem-only practice for novices, and fading support is argued to aid transfer [+M]
• For whom: how does the benefit change with prior knowledge? Worked-example guidance becomes less effective as learner expertise increases. [~M]
• How should learners move from studying examples to solving problems alone? Successively fading out worked solution steps is effective for facilitating the transition from learning from worked examples to problem solving, compared to example-problem pairs [+M]

Further evidence, not yet read against this model

Claims this page cited before it was rewritten as a conditional model. They are evidence about the relationship, but none has yet been re-read against the model above; each says how far its own sources have been checked.

• Worked examples reduce unnecessary search for novices. [+W] — not settled: the abstract available could not confirm the entries
• Example–problem sequences reduce cognitive load and improve learning outcomes [+W] — not yet checked against its sources

Illustrative design instance and observation record

A learner wants to explain equipment faults; the designer initially requests speed. Elicit the difference, agree whether explanation and/or timing matter, and choose a representative simulated diagnosis. Define an agreed reasoning rubric and permitted aids; assess delayed application separately if it is a target. This is an illustrative proposal, not a tested repair lesson.

Record: prompt/task → permitted and actual help → response/reasoning → candidate interpretations and confidence basis → distinguishing probe → chosen activity and justification → next observation at the stated horizon. Preserve the learner's stated purpose and any change in it. An agent may summarize this record, but must not fabricate missing inputs or assign numerical state probabilities without a calibrated model.

Elements and limits

Worked examples, demonstration, fading, and practice.

This pattern is scoped to selecting solution support for structured tasks. Open-ended generation, incorrect examples, productive-failure lessons and competency certification need distinct configurations and evidence. The present policy supports observation and design reasoning; predictive accuracy and the learner-significance mechanism remain to be tested with actual learners.

Claims

• Pedagogical-criterion breakdown shows worked examples in only about 42% of responses, the weakest criterion despite 312 practice problems in the knowledge base [-W]
• Prior knowledge and working memory capacity did not moderate the worked example effect [~W]
• Worked examples improved the exchange of relevant information in the CDR process, driven by the initial-situation step [+W]
• Across two studies that differed in the duration of the initial problem-solving phase, the PS-I versus WS-I transfer advantage reversed [~W]
• 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]
• Erroneous examples and problem solving do not differ significantly on an immediate posttest [~W]
• Students like problem solving more than erroneous examples and find its interface easier, though it yields weaker delayed learning [~W]
• Students using a worked-example revised probability textbook improved more in probabilistic reasoning than students using the standard textbook [+W]
• The worked example effect failed to replicate for geometry and kinematics problems, and was reinstated when worked examples were restructured to reduce split attention [~W]
• Combining tracing with imagining (tracing with closed eyes) reduced problem-solving times compared to no tracing and imagining in worked-example mathematics learning [~W]
• Restudy of worked examples invested much less mental effort than testing after four examples, but this difference was not replicated with vocational students [~W]
• Worked examples benefit learning even compared to tutored problem solving with on-demand guidance, indicating the effect is not an artefact of weak control conditions [+W]
• Type of mathematics assessed (Numerical Operations vs Mathematical Reasoning) does not significantly influence effect sizes [~W]
• Problem solving after acquisition outperformed example study at a one-week delayed posttest but not immediately [~W]
• Worked examples result in better performance than conventional problem solving with no guidance, per prior work cited in the thesis [+W]

Key Sources

• van Gog, T., Kester, L., & Paas, F. (2011). Effects of worked examples, example-problem, and problem-example pairs on novices' learning. Contemporary Educational Psychology, 36(3), 212–218. doi:10.1016/j.cedpsych.2010.10.004
• van Gog, T. (2011). Effects of identical example–problem and problem–example pairs on learning. Computers & Education, 57(2), 1775–1779. doi:10.1016/j.compedu.2011.03.019
• Atkinson, R. K., Renkl, A., & Merrill, M. M. (2003). Transitioning from studying examples to solving problems: Effects of self-explanation prompts and fading worked-out steps. Journal of Educational Psychology, 95(4), 774–783. doi:10.1037/0022-0663.95.4.774
• Renkl, A., Atkinson, R.K. & Große, C.S. (2004). How Fading Worked Solution Steps Works – A Cognitive Load Perspective. Instructional Science. https://doi.org/10.1023/B:TRUC.0000021815.74806.f6
• 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. https://doi.org/10.1207/s1532690xci0201_3
• Gupta, U., & Zheng, R. Z. (2020). Cognitive Load in Solving Mathematics Problems: Validating the Role of Motivation and the Interaction Among Prior Knowledge, Worked Examples, and Task Difficulty. European Journal of STEM Education, 5(1), 05. https://doi.org/10.20897/ejsteme/9252

Page metadata

Field	Value
type	pattern
id	worked-examples
title	Worked Examples
description	A reusable example-first policy for a structured task, qualified by task-specific knowledge, representation and intended outcome.
status	review
grain_size	lesson
canonical	True
generated	by codex/unspecified on 2026-09-30
trust	unverified — no one has confirmed this page's content

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