Erroneous examples improve conceptual understanding by forcing comparison with correct models.¶

Claim · All claims
Evidence · 2 studies · 1 causal r?, 1 quant-synthesis r? · q3
Currency · newest study 2017 · not yet checked against its sources · not reviewed by a person

Studying a hypothetical peer's incorrect solution and being prompted to find, explain, and fix the error leads to deeper conceptual understanding, as it requires learners to discriminate between correct and incorrect features of a problem.

Subclaims¶

q3 i? Analyzing and explaining errors in erroneous examples improves conceptual knowledge and procedural transfer more than studying correct examples alone. → Rittle-Johnson 2017 q3 i? In a brief tutoring session, comparing correct and incorrect examples improved fourth- and fifth-grade students' (N = 74) correct procedures and key concepts for decimal magnitude more than comparing correct examples only. → Durkin & Rittle-Johnson 2012

Evidence¶

Primary evidence link: https://doi.org/10.1007/s11858-017-0834-z

Rittle-Johnson 2017¶

Rittle-Johnson, B. (2017). Promoting self-explanation to improve mathematics learning: A meta-analysis and instructional design principles. ZDM Mathematics Education, 49(4), 599–611. https://doi.org/10.1007/s11858-017-0834-z

q3 · meta-analysis · i? · no source text available to check; the entry prints no effect size · n=N/A · quant-synthesis · r?

The meta-analysis highlights erroneous examples as a key instructional tool for prompted self-explanation, finding that it is particularly effective for improving conceptual understanding and transfer.

Durkin & Rittle-Johnson 2012¶

Durkin, K., & Rittle-Johnson, B. (2012). The effectiveness of using incorrect examples to support learning about decimal magnitude. Learning and Instruction, 22(3), 206–214. https://doi.org/10.1016/j.learninstruc.2011.11.001

q3 · peer-reviewed experimental study · i? · no effect size in the abstract · n=74 fourth- and fifth-grade students · causal · r?

Fourth- and fifth-grade students (N=74) learned decimal magnitude in a brief tutoring session. Comparing correct and incorrect examples improved correct procedures and key concepts relative to comparing correct examples only; the published abstract reports no interaction with prior knowledge. This page's earlier n=116 and “middle-schoolers” descriptions do not match the source abstract.

Studies bearing on this claim¶

Does setting an incorrect or non-matching case beside a correct one help learners more than correct examples alone? This table gathers the studies behind this claim and the 5 narrower claims that bear on it: 9 distinct studies (4 causal, 2 quant-synthesis, 1 review, 1 design, 1 qualitative), q2–q4, 1 of 9 with an effect size coded. One row per study, codes as each entry records them; no effect is averaged and no verdict is drawn. Built by scripts/synthesize_claim.py from eval/synthesis/; a row that looks wrong is fixed on the claim it comes from.

Discussion¶

A design precaution, not a finding of the studies recorded here: erroneous examples may be confusing or overloading for learners with no prior knowledge of the topic, so some designers reserve them for learners with at least some prior knowledge. Neither entry tests this: the Durkin & Rittle-Johnson (2012) abstract reports no interaction with prior knowledge.

Related Claims¶

• 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 — the general claim this finding bears on, with the studies behind it
• High-confidence errors are more likely than low-confidence errors to be corrected on a later test after feedback.
• Prompting learners to self-explain improves understanding and problem solving on immediate tests by a moderate average amount, with little evidence yet on delayed or classroom gains.
• Studying worked examples improves novices' algebra performance on problems with the same structure as the examples — related
• Productive Failure Improves Conceptual Learning — related
• Providing worked examples of journal entries early (rather than delayed) yields better early journal quality and more conceptual knowledge — related
• Erroneous examples produce significantly higher delayed-test learning gains than problem solving for decimal learning — a narrower finding that bears on this claim
• Erroneous examples benefit learners with more prior knowledge, while correct-only solutions better serve low-prior-knowledge learners — related
• Low prior knowledge students learned most conceptual understanding from worked-out examples, and least from questions plus arguments — related
• Correct and complete exemplar supports produced greater improvement in preservice teachers' fraction comparison explanations than supports displaying common misconceptions and errors — a narrower finding that bears on this claim
• Assisting self-explanation prompts particularly foster conceptual knowledge, an effect mediated by self-explanations on the rationale of a principle — related
• Intelligent Novice error-correction tutoring produced better delayed transfer and immediate isomorphic performance than the Expert tutor in spreadsheet learning — related
• Prior knowledge moderates the effectiveness of erroneous and contrasting erroneous examples, with low-prior-knowledge learners benefiting in several studies but findings contradictory — related
• PS-I fosters learning only if specific design features (contrasting cases or building instruction on student solutions) are implemented — related