Worked Examples¶

Principle · All principles
Evidence · 35 claims (18 for, 14 mixed, 3 against) · 30 studies (21 causal, 4 theoretical, 3 quant-synthesis, 2 review), q1–q4 · 7 of 30 report an effect size · 30 claims rest on one study

Conditional relationship¶

For an initial structured task, a learner without an applicable solution schema may benefit from studying a correct solution before attempting a comparable problem. Available task knowledge, representation, help conditions, example/problem identity, intended capability and assessment horizon constrain this relationship. Most of the wiki's evidence comes from well-structured tasks (algebra, circuits, probability); one experiment extends example-first preparation to an ill-structured assessment task for pre-service teachers, so "structured" marks where the evidence is dense, not a tested boundary. The relationship is weakest where the goal is conceptual understanding of a new mathematics concept and a designed problem-solving phase precedes instruction (productive failure), where a meta-analysis favours the problem-first order. The pattern specifies a reusable design policy; its local diagnostic branches remain proposals.

Fitting the design to a situation¶

Ask for three facts when the brief omits them: can these learners already start this kind of problem on their own?, is the task well structured (a procedure with a correct solution)?, and is the goal the practised procedure, transfer to new problems, or a delayed test?

If the brief says…	Then change…	Basis
Learners are new to this task type, and it is a structured problem (algebra, circuits, probability)	Replace some early practice problems with fully worked examples to study, before asking for unaided solutions; expect the gain on problems with the same structure as the examples, since in the original algebra experiments it did not reach differently structured problems	Worked examples improve mathematics performance [+M]; Worked examples reduce novice search [+M]
The lesson was planned as unaided discovery	Give worked examples rather than leaving novices to discover the method; in the meta-analysis they were the strongest comparison against unassisted discovery	Worked examples beat unassisted discovery by the widest margin [+M]
Examples and practice problems alternate	Put each example before its paired problem, not after; judge the order on an immediate test, since with identical pairs the early advantage was not detected at the final test. With primary pupils, gifted and nongifted alike, example-first reached the same test score for less reported effort: an efficiency gain, not a higher score	Example-first beat problem-first on an immediate test [+M]; Order advantage not detected at the final test [~M]; Example–problem pairs more efficient for gifted and nongifted pupils [+M]
Learners already solve these problems reliably	Replace full examples with completion problems or independent practice; check first with an unsupported changed problem	Worked examples become less effective as expertise grows [~M]; With experience, examples became redundant [~M]
Prior knowledge varies widely in the class	Give full worked examples to the learners with less prior knowledge; completion examples can go to those with more, but the higher-prior-knowledge advantage for completion examples was not significant, and the pattern depended on task difficulty, so check with a pretest and an unsupported problem rather than assuming the switch	Lower-prior-knowledge learners did better with full than completion examples [+M]; Prior knowledge, example type and task difficulty interact on the posttest [~M]
The goal is conceptual understanding in a new university subject (statistics), and learners start with little prior knowledge	Open with worked-out examples; move to open questions and argument once learners have the prior knowledge to use them, since for low-prior-knowledge students questions plus arguments was the weakest condition	Low-prior-knowledge students learned most conceptual understanding from worked-out examples [+M]
Learners prepare for later instruction in an ill-structured task (pre-service teachers judging the quality of learning strategies)	Prepare with a worked example of the judgement rather than an open inventing problem; during the later lesson, look for learners applying the canonical criteria, which was the process that carried the transfer gain	Worked-example preparation beat inventing on transfer [+M]; Applying canonical criteria mediated the transfer advantage [+M]
The goal is conceptual understanding of a new mathematics concept, and there is time for a designed problem-solving phase before instruction	Example-first is not the only defensible order here: a designed problem-solving attempt followed by instruction did better on conceptual knowledge and transfer in a meta-analysis (not for procedural knowledge, and not for grades 2–5). Use worked examples first for procedural goals and young pupils	Productive failure improves conceptual learning [~M]
Adult learners revise their own explanations (pre-service teachers explaining fraction comparisons)	Give a correct and complete exemplar to compare against their own explanation, rather than examples built from common errors	Correct exemplars improved explanations more than error-displaying examples [+M]
Several sessions should move learners to solving alone	Fade the worked steps one at a time across examples, rather than jumping from a full example to a bare problem	Fading worked steps eases the move to problem solving [+M]; Backward fading and principle prompts supported transfer [+M]
The goal is transfer to problems that look different	Ask learners to name the principle behind each step, and label the subgoals in the example	Backward fading and principle prompts supported transfer [+M]; Subgoal labels enhance transfer [+W]
The example uses a diagram with its explanation printed separately	Put the explanation on the diagram, next to the part it refers to; split-source examples lost their advantage over practice	Split-attention examples lose their advantage [~M]
The goal is conceptual understanding where learners hold known misconceptions	Add incorrect examples for learners to compare with correct ones, alongside a correct model; when learners are revising their own explanations, examples made only of errors did worse than a correct and complete exemplar	Erroneous examples build conceptual knowledge [+M]; Correct exemplars improved explanations more than error-displaying examples [~M]
Training uses a game or simulation	Insert worked examples between rounds of play; expect gains to remain far below expert performance	Worked examples between game rounds improved understanding [+M]; Gains stayed small relative to experts [~M]
Middle or high school algebra classes	Use solved problems with questions about the reasoning, but treat the evidence as thin; one study found solved problems worse than reflective questioning	Solved problems improve algebra achievement, on minimal evidence [~W]

Observation, state and explanation¶

Record a response under stated conditions, not a context-free learner trait. Copying, choosing a step, explaining a relation and adapting it are different performances. “Novice” refers to the particular task; experience in the wider domain does not settle it. A formula sheet or calculator may be compatible with independence from a worked solution, but not with unaided recall. Define which capability matters before interpreting help dependence.

Reduced search and schema acquisition are explanatory hypotheses. Accuracy, reported effort, response time and confidence are observations; none directly measures the schema. Lower effort could also reflect disengagement. A learner's goal and its significance may alter participation and interpretation, but the studies linked here do not validate that causal mechanism.

Response	Plausible explanations	Observation that could change the interpretation
Copies accurately, cannot start a changed problem	Missing task relation; failure to recognize it; inaccessible prompt	Elicit first-step reasoning on matched familiar/changed representations and accessible response modes, recording every hint.
Succeeds with an aid, fails without it	Tool-supported capability; aid dependence; increased memory demand	Hold the target reasoning constant and vary the named aid. Decide whether aid removal belongs to the objective.
Explains correctly but fails in a whole task	Local relation available; integration/working-memory demand; task change	Compare a component probe and a representative whole task, including the omitted conditions.
Studied the example but applies none of its criteria to a new case	Example read as an answer, not as a set of criteria; criteria not yet understood; new case looks unrelated	Ask the learner to say which criterion each step of a new case meets (think-aloud or written), as the process that carried transfer in one preparation study.
Improves after instruction and repeated probes	Learning from example, from probes, from feedback, or their combination	Preserve all exposures. Only a defensible comparison can attribute the gain to one component.

These probes can shift confidence among hypotheses; a single contrast does not identify a cause. Match demands and repeat where feasible. Probe exposure itself can change the state. Record what remains unresolved rather than selecting an explanation because its name fits.

Evidence and qualifications¶

Initial circuit-task ordering [+W]: example-first conditions supported better immediate performance in a bounded novice comparison. Its full manuscript is checked; the aligned paper test is not evidence of delayed safe repair.
Identical-pair qualification [~W]: an early order advantage did not persist detectably at the final test. Abstract checked; no equivalence or fully verified method claim follows.
Transition configuration [+W]: backward fading and principle prompts have evidence in probability learning. This supplies a distinct candidate configuration, not a universal individual readiness threshold or proven combined synergy.
Full versus completion examples by prior knowledge [~M]: in one college algebra factorial experiment the prior-knowledge by example-type interaction appeared on self-reported germane load (partial η² = .04) and not on intrinsic or extraneous load; on the posttest it appeared only in a three-way interaction with task difficulty. Self-reported load is an observation, not a measure of schema construction, and the posttest follow-ups were p = .05 for low-prior-knowledge learners and non-significant for high.
Preparation processes [+M]: in the pre-service teacher experiment (n = 45), think-aloud coding showed more elaboration (d = .68) and more application of canonical criteria (d = .71) after worked-example preparation; only the canonical-criteria path mediated transfer, in an exploratory analysis. These process observations are candidate probes for the table above, not established diagnostics.
Grain: the Coppens order study was quasi-randomised (matched by gender and maths score), and the Leppink and Glogger-Frey contrasts rest on small subgroups (low prior knowledge t(25); 45 participants in all), so their large effects (d = 0.96, d = 1.24) are single-study estimates.

Retain learner/sample, assignment, exclusions, baseline assessment, help, dose, comparator, instrument alignment, score range and horizon when transporting these observations. Random assignment is not proof that the realized groups were equal. An omnibus partial η² is neither a pairwise d nor a learner's probability of success. Do not rank these studies by an effect label while their comparisons differ.

The evidence by question¶

Each question below links a general claim that gathers the studies behind it into one table, one row per distinct study, with each study's design and effect as recorded and no averaged verdict (eval/synthesis/worked-examples.json, scripts/synthesize_claim.py). The count is of distinct studies across the claim and the narrower claims that bear on it.

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 [+S]: 7 distinct studies.
Should the example come before or after the practice problem? Example-first conditions outperformed problem-first conditions on an immediate circuit test [~M]: 3 distinct studies.
For whom: how does the benefit change with prior knowledge? Worked-example guidance becomes less effective as learner expertise increases. [~S]: 3 distinct studies.
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]: 2 distinct studies.
What should learners do while studying an example, and which examples should they see? Students who self-explain worked examples learn more effectively than those who do not, and the quality of self-explanations relates to explaining deep structure [~M]: 3 distinct studies.
How should a worked example be presented? Split-attention worked examples lose their advantage over conventional practice, while integrated formats restore it [~M]: 2 distinct studies.

Further evidence, not yet read against this model¶

Every claim previously listed here has been read against the model above and moved into it. Claims linked later appear below until they are read.

Objective and learner-valued goal¶

Ask what the learner wants to accomplish and why, separately from the designer's objective. Agreement, divergence and uncertainty are observations. Negotiate a meaningful task when possible; do not infer motivation from compliance. Choose a representative instrument, local criterion, permitted aids and horizon. Speed, explanation, recall, transfer and safety require different evidence.

For example, a learner may value explaining an equipment fault while a designer seeks fast routine diagnosis. A timed score alone cannot establish agreement or explanatory competence. The pattern shows how to preserve both aims and test the intended capability.

What would revise this model?¶

A bounded example-first expectation should weaken if comparable learners, configurations and aligned outcomes fail to reproduce it under defensible comparisons. If matched access changes explain performance better than schema support, revise the local state interpretation. If independent procedural success fails to predict later conceptual application, retain that distinction rather than calling both mastery. Do not protect the model by retrospectively relabelling every failure as low motivation or insufficient prior knowledge.

A learning-phase advantage, immediate changed-task success, delayed retention and valued real-world use are separate claims. The present evidence does not establish an optimal fading policy, a numerical individual forecast or universal benefit across domains.

Claims¶

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. https://doi.org/10.1207/s1532690xci0201_3
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. (2003). Structuring the transition from example study to problem solving in cognitive skill acquisition: A cognitive load perspective. Educational Psychologist, 38(1), 15-22. https://doi.org/10.1207/S15326985EP3801_3
Kalyuga, S., Ayres, P., Chandler, P., & Sweller, J. (2003). The expertise reversal effect. Educational Psychologist, 38(1), 23-31. https://doi.org/10.1207/S15326985EP3801_4
Barbieri, C. A., Miller-Cotto, D., Clerjuste, S. N., & Chawla, K. (2023). A meta-analysis of the worked examples effect on mathematics performance. Educational Psychology Review, 35(1), 11. doi:10.1007/s10648-023-09745-1
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
Star, J. R., Caronongan, P., Foegen, A., Furgeson, J., Keating, B., Larson, M. R., Lyskawa, J., McCallum, W. G., Porath, J., & Zbiek, R. M. (2015). Teaching strategies for improving algebra knowledge in middle and high school students (NCEE 2015-4010). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. https://ies.ed.gov/ncee/wwc/PracticeGuide/20
Leppink, J., Broers, N. J., Imbos, T., van der Vleuten, C. P. M., & Berger, M. P. F. (2012). Self-explanation in the domain of statistics: an expertise reversal effect. Higher Education, 63, 771–785. doi:10.1007/s10734-011-9476-1
Glogger-Frey, I., Treier, A.-K., & Renkl, A. (2022). How preparation-for-learning with a worked versus an open inventing problem affect subsequent learning processes in pre-service teachers. Instructional Science. doi:10.1007/s11251-022-09577-6
Guba, T.-P., Barbieri, C. A., Jansen, A., & Morris, A. (2026). Supports for preservice teachers' metacognitive monitoring and explanations of fraction comparisons. Instructional Science, 54, 18. doi:10.1007/s11251-025-09773-0
Coppens, L. C., Hoogerheide, V., Snippe, E. M., Flunger, B., & van Gog, T. (2019). Effects of problem–example and example–problem pairs on gifted and nongifted primary school students' learning. Instructional Science, 47, 279–297. doi:10.1007/s11251-019-09484-3
Sinha, T., & Kapur, M. (2021). When problem solving followed by instruction works: Evidence for productive failure. Review of Educational Research, 91(5), 761–798. doi:10.3102/00346543211019105
Shen, C.-Y., & O'Neil, H. (2006). The Effectiveness of Worked Examples in a Game-Based Learning Environment. Paper presented at the annual meeting of the American Educational Research Association, San Francisco, CA. https://eric.ed.gov/?id=ED491961

Page metadata

Field	Value
`type`	`principle`
`id`	`worked-examples`
`aliases`	`match-worked-example-type-to-learner-prior-knowledge`
`title`	`Worked Examples`
`description`	`An example-first relationship qualified by task knowledge, representation, configuration and assessment horizon.`
`status`	`review`
`canonical`	`True`
`generated`	by `claude/unspecified` on `2026-10-19`
`trust`	unverified — no one has confirmed this page's content
`sources`	4 — `van-gog-2011`, `van-gog-identical-2011`, `atkinson-renkl-merrill-2003`, `gupta-2020`

Frontmatter is the page's machine-readable record — see the Schema & Guide.