Pairing Non-examples with Examples¶

Principle · All principles
Evidence · 15 claims (8 for, 7 mixed) · 22 studies (9 causal, 7 review, 3 quant-synthesis, 2 theoretical, 1 design), q1–q4 · 2 of 22 report an effect size · 10 claims rest on one study

Conditional relationship¶

This page owns one design move: setting a matched non-example beside a correct example and asking the learner to say what separates them. A non-example here is either a case that falls just outside a category (a near miss that lacks one deciding attribute) or an incorrect solution or step set beside a correct one. The relationship it proposes is conditional. For a learner who can already follow or recognise at least one correct example of a concept, procedure or principle, but whose classifications or solutions show a plausible boundary error (a surface-feature rule, a known misconception), studying a correct case beside a matched non-example and explaining the difference is expected to improve conceptual-understanding and correct procedures (immediate-performance, near-transfer) more than studying correct examples alone. The expectation is weaker or reversed for a learner who cannot yet recognise a correct case, and for a learner who already discriminates the boundary.

One claim in the wiki tests the relationship, for one form of it: in a brief tutoring session, 74 fourth- and fifth-graders who compared correct with incorrect examples of decimal magnitude gained more correct procedures and key concepts than those who compared correct examples only (erroneous examples [+M]). That is one primary study, with children, in mathematics, on an immediate test; the same claim's meta-analytic entry (prompted self-explanation) prints no effect size. No claim in the wiki tests category non-examples (a near-miss instance that does not belong) against examples alone, and none tests either form with adults, outside mathematics, or at a delay. The nearest evidence for the category form is case comparison in general (analogous cases, not examples against non-examples) and interleaving labelled examples of confusable categories; both are carried here by extrapolation, and the page says so where it uses them.

How this sits beside the converted pages: Error Analysis owns using an error as the object of study (find, explain, fix) and its timing questions; this page uses its evidence for the incorrect-solution form and does not repeat its model. The Concept Attainment pattern owns inducing a concept from labelled "yes" and "no" instances; pairing non-examples also works inside definition-first or example-first teaching, where the rule is stated and the pair sharpens it. Analogical Reasoning owns comparing cases that share a structure; this page owns comparing cases that differ on the one feature that decides. Worked Examples owns the correct model that comes first.

Default design, while the relationship is untested¶

The earlier page's guidance, kept as a concrete default a designer can use and revise. Only step 3 has a claim that tests it (for incorrect solutions in mathematics, with children); the other steps are proposals or carry a neighbouring finding, and each says which.

Anchor with correct examples first (about 3 minutes per concept). Show and explain one or two clear correct examples (a worked solution, a prototypical instance) before any non-example, so the non-example is never the learner's first model. Evidence status: carried from example-first sequences [~M] (secondary-school novices, circuit troubleshooting: starting with an example beat starting with a problem; not a test of non-examples). The erroneous-examples claim's own Discussion records this as a precaution, not a finding: its primary study reports no interaction with prior knowledge.
Build each non-example as a near miss on one deciding feature. Change one attribute or one step of a correct example, and take the change from an error these learners actually make (a reported error, a common wrong answer, a frequent misclassification). A non-example that differs in many ways teaches little. Untested proposal; from the earlier page ("well-matched contrasts").
Show the pair side by side, labelled, and ask for the difference (2–3 minutes a pair, two or three pairs per concept). Ask "which feature makes this one fit and that one not?" and have the learner answer, in words or by pointing, before anyone confirms. Evidence: comparing correct with incorrect examples, against correct examples only [+M] (grades 4–5, decimal magnitude, brief tutoring session, immediate test).
State the deciding feature after the comparison. Once learners have tried, the teacher or system names the attribute or step that decides membership or correctness, and corrects a wrong account. Evidence status: carried from case comparison [+M], whose meta-analysis found larger gains when the principle was given after the comparison and when learners were asked to find similarities; those studies compared analogous cases, not examples with non-examples.
Ask for a prediction first when the misconception is confidently held. Before showing the pair, ask learners to classify the non-example and say how sure they are; then show the pair and the correction. Evidence status: carried from the hypercorrection effect [~S] (errors made with high confidence were corrected more durably than low-confidence ones, in recall research; it depends on clear correction following the error). Not tested with concept pairs.
Classify new, unlabelled items with feedback on each (5–8 minutes, 6–10 items). Mix correct cases, near misses and instances of the concept most often confused with it; include at least two near misses. Evidence status: carried from interleaving labelled category examples [~M] (benefit for paintings, photographs and mathematical tasks; reversed for word-based categories, where examples of each category should first be seen together).
Have the learner make one example and one non-example of their own (about 3 minutes), and say which feature they changed. Untested proposal; from the earlier page ("category boundary sort", "stronger explanation").

Dose and progression across sessions (all quantities are untested proposals). One concept takes about 20–25 minutes in the first session. Early sessions: the designer builds the pairs, labels stay visible, the deciding feature is named right after each comparison. Middle sessions: open with two or three unlabelled items from the previous concept; pairs are drawn from errors this group actually made (shown without names), and learners name the deciding feature before the teacher does. Late sessions: unlabelled mixed sets that include neighbouring concepts, learner-built pairs exchanged with a partner, and borderline cases the class argues over. A learner moves on from pairs to independent practice or richer tasks when they classify about 8 of 10 new items correctly, including the near misses, and name the deciding feature, on two consecutive checks. A learner who already does this on the first check skips the pairs (expertise reversal [~S], carried from cognitive-load studies of guidance in general).

When a condition is not met: if learners cannot recognise a correct case yet, stay with correct examples and add the pairs later; if the target is a single procedure with no plausible wrong version, model it and practise it instead.

Fitting the design to a situation¶

The three facts that most change the decision:

Whether learners can already recognise or follow a correct case. Pairs sharpen a boundary the learner partly holds; they can confuse a learner with no anchor. If unstated, ask: shown one correct example, can they say why it is correct, and do they misclassify a near miss?
What the non-example is: an incorrect solution or a near-miss instance of a category, and in what material. The tested evidence is for incorrect solutions in mathematics; for categories, the evidence is borrowed and depends on whether instances are visual, symbolic or verbal. If unstated, ask: what is the commonest wrong answer or wrong classification, and are the cases pictures, symbols or sentences?
Which outcome counts. Classifying new cases, explaining the deciding feature, and using the right procedure need different checks; comparison has raised procedural knowledge without raising conceptual knowledge. If unstated, ask: on what task, with what aids, and when will the learner show they have the boundary?

If the brief says…	Then change…	Basis
Learners are `novice` and cannot yet recognise a correct case	Teach with correct examples only for the first session; add one near-miss pair at the end only if they can explain a correct case; name the deciding feature for them rather than waiting	Example-first sequences [~M] (secondary-school novices, circuits; carried, not a test of non-examples); the novice caution is a precaution on the erroneous-examples claim [~M], not a finding
Learners are `advanced`, or already discriminate the boundary on a check	Skip anchors and labelled pairs; give only borderline cases, or have them build non-examples for others and defend them	Expertise reversal [~S] (guidance in general, cognitive-load studies; gives no crossover point)
Learners are `child` (primary age)	One deciding feature per pair, concrete or pictured cases, oral or pointing answers, pairs run with the teacher in a small group	Correct against incorrect examples [+M] (grades 4–5, brief tutoring session); the group format is untested
The goal is a `procedure` (choosing or carrying out a method)	Pair a correct method with a plausible wrong one, or two correct methods, and ask which works here and why; check method choice on new problems	Comparing cases [~S] (seventh-graders comparing algebra methods gained procedural knowledge and flexibility)
The goal is `conceptual-understanding`, an explanation of why	Score the explanation of the deciding feature separately from classification; add the make-your-own non-example task	Comparing cases [~S]: in the algebra study comparison did not raise conceptual knowledge, so classification alone may hide it
Instances are verbal (word categories, sentence types, genres) rather than visual or mathematical	Show each category's examples together first, then near-miss pairs one feature at a time; mix categories only after that; keep labels visible	Interleaving labelled category examples [~M] (mixing reversed for word-based categories; ages and settings not on the claim page)
The target is a fact, a simple association or a precise response, not a concept	Do not build non-examples; teach the correct form directly and practise it, so errors are not rehearsed	Task-type argument [~W] (a 1966 conceptual analysis, not a test)
The brief wants learners to attempt a problem before instruction	Use the pair in the instruction that follows: set learners' own failed attempts or a prepared incorrect solution beside the canonical one	PS-I review [+M] (benefits only where contrasting cases or instruction built on student solutions were part of the design)
The concept is source credibility, or checking AI or other generated output	Model the check on a credible and a misleading item side by side, thinking aloud; then have learners check a fresh pair and agree a cross-checking routine	Teacher modelling with contrasting cases [+W] (preparatory students' reflective essays; self-report, no comparison group)
`classroom`, one teacher and a large group	Project one pair; every learner commits an answer at once (cards, mini-whiteboards, a poll), then pairs of learners explain; the teacher names the feature and goes to those who still miss it	Untested proposal; the tested study was one-to-one tutoring
`online-self-paced`, no teacher	The system shows the pair, the learner selects or types the deciding feature before feedback; a wrong quiz answer triggers a pair built on that wrong answer; end with mixed unlabelled items	Untested proposal (see the contrastive remediation videos strategy, itself untested here)
Mixed modes: some learners remote, some in the room, or phone-only	Put each pair in one shared image or document with the two cases stacked vertically and labelled A and B, so a phone screen shows both; collect answers in the same channel for everyone	Untested proposal
A single session only, or a fixed short time budget (e.g. 15 minutes)	One concept: one anchor (3 min), two pairs (6 min), five mixed items with feedback (5 min), one-line explanation of the deciding feature (1 min); record what the items show and do not claim retention	Untested proposal
Scarce facilitator time (volunteers, a busy shift, one tutor checking in briefly)	Prepare pair cards with the answer and the deciding feature on the back; learners self-check and the facilitator looks only at the explanation line	Untested proposal
The brief names its own routine, template or categories (a Frayer model, its own rubric, the job's own fault categories)	Keep it; fill its non-example part with near misses on one deciding feature, and use the brief's categories as the labels; change nothing else	Untested proposal
The brief reports an error learners actually made	Use that error, unchanged, as the non-example in the first pair	Untested proposal; consistent with the tested study, which used plausible incorrect examples
Learners have low confidence or low literacy, or are working in a second language	Use pictured or concrete cases, keep labels visible, accept pointing answers; never use an identifiable learner's error as a public non-example	Untested proposal
Adults in a work setting	Draw non-examples from real near misses on the job (a rejected claim form, a near-miss incident report), anonymised; check on a fresh case from their work	Untested proposal; no claim here tests adults
Private or sensitive material (learners' own work, patient or client cases)	The learner decides whether their own error becomes a pair; otherwise build a synthetic pair with the same error	Untested proposal
The brief wants a whole performance kept whole (a presentation, a procedure on the job, a piece of writing)	Pair two whole performances, one with the flaw, rather than splitting it into items; ask where they differ and why it matters	Untested proposal
A product or performance for a real audience	Take non-examples from published or professional work that misses the mark, not from classmates' drafts	Untested proposal
High stakes, or the assessment is weeks later	Test on new, unlabelled cases including near misses, at that delay, not on practice items	Untested proposal (the case-comparison benefit was larger on immediate tests, a reason to test late)

Nine of the twenty-two rows cite a claim that bears on them; one (children, incorrect examples in mathematics) is close to the tested setting, and the others carry a neighbouring finding and say so. The rest are untested proposals.

Observation, state and explanation¶

What can be observed is a response to a pair under stated conditions: which case the learner chose, the feature they named, their confidence, whether labels were visible, and how they classified the next unlabelled item. "Holds the misconception", "sees the boundary" and "is matching on surface features" are inferred states.

Response	Plausible explanations	Observation that could change the interpretation
Picks the correct case but names an irrelevant feature	Matching on a surface feature that happens to co-occur; guessing; cannot put the deciding feature into words	Show a pair where the surface feature is on the wrong side; ask the learner to point to the difference instead of naming it.
Accepts the non-example as correct	Holds the misconception; did not look closely; the near miss is too subtle for the material	Ask for a confidence rating before revealing; show the same pair with the deciding feature highlighted. High confidence plus a later correct answer suggests the misconception was addressed.
Correct on labelled pairs, wrong on unlabelled mixed items	The labels carried the decision; cannot tell the concept from its neighbour; the mixed items differ more than intended	Give an unlabelled pair with only one difference, then one with a neighbouring concept; compare.
Reproduces the non-example's error later	The non-example became the model (no anchor, or the correction was not seen); the error was practised	Ask the learner what the correct case was; check whether an anchor preceded the pair and whether the correction was stated.
Explains the difference well but still uses the wrong procedure	Knowledge of the boundary without fluent use; the practice was too close to the pairs	Give a new problem without any pair present and watch the steps.

These rows are untested with learners as diagnostics. A probe is itself practice, so record each one, and keep open the explanations the observations have not ruled out.

Evidence and qualifications¶

Erroneous examples improve conceptual understanding by forcing comparison with correct models. [+M]: 74 fourth- and fifth-grade students learning decimal magnitude in a brief tutoring session; comparing correct and incorrect examples improved correct procedures and key concepts more than comparing correct examples only (randomised, causal, q3, no effect size in the abstract). A second entry, a meta-analysis of prompted self-explanation in mathematics, is described as finding erroneous examples useful for conceptual understanding and transfer, with no effect size on the page. This is the claim that tests this page's relationship, for incorrect solutions only. Its Discussion records that the abstract reports no interaction with prior knowledge, so the novice precaution in the default design is not from this study. Its claim page is the hub of the question below; it carries no studies table yet.
Comparing cases side by side improves learning and transfer by a moderate average amount, though in one algebra study it raised procedural knowledge and flexibility but not conceptual knowledge [~S]: a meta-analysis of 57 experiments (d = .50) found comparison activities beat single, sequential or non-analogous case study, with larger gains when learners looked for similarities, when the principle came after the comparison, for perceptual content and on immediate tests; undergraduates comparing two negotiation cases on one page transferred the principle more often (48% vs 19%); seventh-graders comparing algebra methods gained procedural knowledge and flexibility but not conceptual knowledge. The compared cases were mostly analogous, not examples against non-examples, so it supports the side-by-side format and the order (feature named after the comparison) by extrapolation, and qualifies the conceptual-outcome expectation.
Example–problem sequences reduce cognitive load and improve learning outcomes [~M]: 96 Dutch secondary-school novices in circuit troubleshooting; starting with a worked example beat starting with a problem on test performance and invested effort. One experiment, immediate test. It is the basis, carried, for putting a correct anchor before any non-example; it does not test non-examples.
High-confidence errors are more likely than low-confidence errors to be corrected on a later test after feedback. [~S]: a narrative review and one experiment on the hypercorrection effect, in recall research; the claim's Discussion says it depends on immediate, clear correction and that uncorrected errors can be reinforced. It supports asking for a prediction before showing a pair, and qualifies the design: a non-example left without a correction risks the error.
Interleaving category examples improves inductive category learning for visual and mathematical materials, but not for expository texts or word categories [~M]: a meta-analysis of 59 studies (g = 0.42) comparing interleaved with blocked presentation of labelled category examples, stronger where categories were similar to each other; reversed for word-based categories (g = −0.39). It bears on mixing neighbouring concepts in later practice, and limits it for verbal material.
PS-I fosters learning only if specific design features (contrasting cases or building instruction on student solutions) are implemented [+M]: a review of problem-solving-before-instruction designs; positive outcomes occurred only when contrasting cases or instruction built on students' own solutions were part of the design. No pooled effect size. It supports pairing in that one configuration.
Students perceived the teacher’s modeling with contrasting cases as a turning point that repositioned them as active gatekeepers of AI-generated content [+W]: thematic analysis of preparatory students' reflective essays after a GenAI prompt-engineering intervention; students described the teacher's modelling with contrasting cases as a turning point toward cross-checking AI output. Self-report, one design study, no comparison condition.
Limits. The usefulness of induction and errorful learning varies with the type of terminal task being taught [~W]: a 1966 conceptual analysis arguing that response precision and simple associations do not need errorful learning, and that induction may suit concepts. Instructional guidance that helps novices can become redundant or counterproductive as expertise grows. [~S]: guidance that helps novices loses value or harms once learners hold the schema; it is why pairs are dropped for learners who already discriminate the boundary.

Learners, materials and outcomes differ across these claims (children with decimals, undergraduates with negotiations, art and photographs, recall items), so do not rank them by effect label. None measures a delayed outcome of example–non-example pairs.

The evidence by question¶

Does setting an incorrect or non-matching case beside a correct one help learners more than correct examples alone? Erroneous examples improve conceptual understanding by forcing comparison with correct models. [+M]

Further evidence, not yet read against this model¶

Claims read for this page that bear on it less directly; none is part of the model above.

Studying worked examples improves novices' algebra performance on problems with the same structure as the examples [+M]: its Barbieri & Booth (2016) entry reports that worked-example variants including incorrect worked examples supported struggling algebra students; no source text was available to check it, and it is a different paper from the Barbieri & Booth (2020) study in Key Sources.
Invention Tasks Prepare Future Learning [~M]: ninth-graders who invented a statistics procedure before instruction later learned more from a worked-example resource; its Discussion says pairing invention with contrasting cases is the standard design, which the entry does not test.
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]: a review reporting that self-explaining examples, and explaining their deep structure, went with better problem solving; it bears on step 3's explanation prompt, not on non-examples.
Contrasting erroneous examples were more often effective than correct examples and problem-solving, sometimes equally or more effective than erroneous examples [+W] — attached 2026-10-19 from Sonja Dieterich et al. (2025), which proposed "Use contrasting erroneous examples rather than erroneous examples alone when the goal is comparing incorrect and correct solutions"; tests this page's relationship.

Objective and learner-valued goal¶

The designer's objective is usually that the learner classifies new cases correctly at the boundary, or uses the correct procedure, and can say which feature decides. Elicit separately what the learner wants: to stop making a mistake that has cost them marks or work, to recognise a fake source before sharing it, to pass a test. Agreement and divergence are both observations. A learner who wants to avoid being seen as wrong may resist having their own error shown as a non-example even anonymously; one who wants a quick rule may skip the explanation. For example, a trainee who wants to stop having claim forms rejected values the near misses from their own rejected forms; the designer's objective, the category boundary in the policy, is served by the same pairs if they are built from those forms. Record both, so that success on designer-built pairs is not read as the capability the learner came for.

What would revise this model?¶

The expectation should weaken if studies comparing example–non-example pairs with correct examples alone, with comparable learners and new-case outcomes, show no advantage for category concepts or outside mathematics, or if a gain on the immediate test disappears at a delay. If comparison keeps raising procedural knowledge without conceptual knowledge, the model should promise better method choice, not better explanation. If learners with no prior knowledge do as well with pairs as with correct examples alone, drop the anchor-first step. If confidence ratings before a pair make no difference to correction, drop step 5. Do not protect the model by calling each failure "a poorly matched non-example" after the fact; record the pair used before the result is known.

Classification of labelled pairs, classification of new unlabelled cases, explanation of the deciding feature, delayed retention and use in the learner's own setting are separate claims. The present evidence sets no number of pairs and no move-on threshold.

Claims¶

Error Analysis — pairing examples with non-examples is one concrete way to analyze and correct misconceptions.
Worked Examples — correct worked examples often provide the comparison anchor.
Explicit Instruction: Math Strategies — contrastive cases can clarify when and why a strategy applies.
Evaluating Sources — source evaluation often relies on distinguishing valid from invalid or misleading examples.
Analogical Reasoning — comparing cases that share a structure; this page compares cases that differ on the one feature that decides.
Concept Attainment (pattern) — induction of a concept from labelled examples and non-examples.

Examples¶

Incorrect worked examples in algebra: Learners compare a correct solution with a plausible but wrong one and explain the difference.
Real versus fake source comparison: Learners identify which source characteristics make one text credible and another misleading.
Category boundary sort: Learners sort cases into examples and non-examples, then justify the classification.
Procedure contrast: Learners compare a correct sequence of steps with an incorrect or incomplete one.
Misconception-aware contrastive remediation videos triggered by incorrect quiz answers
Contrasting examples as a generative-processing instructional method whose preconditions for critical-thinking transfer are questioned
Use a pupil-plays-teacher error-correction game format for language testing

Key Sources¶

Barbieri, C. A., & Booth, J. L. (2020). Mistakes on display: Incorrect examples refine equation solving and algebraic feature knowledge. Applied Cognitive Psychology, 34(4), 862-878. https://doi.org/10.1002/acp.3663
Bowe, B. J. (2019). Separating real from fake: Building news literacy with the Frayer Model. Communication Teacher, 33(4), 246-252. https://doi.org/10.1080/17404622.2019.1575971

Page metadata

Field	Value
`type`	`principle`
`id`	`pairing-non-examples-with-examples`
`title`	`Pairing Non-examples with Examples`
`description`	`For a learner who can already follow a correct example but makes a plausible boundary error, studying a matched non-example or incorrect case beside the correct one and explaining the difference is expected to improve conceptual understanding and correct procedures more than correct examples alone; one claim tests this for incorrect solutions in mathematics with children, and none tests category non-examples.`
`status`	`review`
`canonical`	`True`
`generated`	by `claude/unspecified` on `2026-10-15`
`trust`	unverified — no one has confirmed this page's content
`sources`	2 — `barbieri-2020`, `bowe-2019`

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