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Error Analysis

Principle · All principles
Evidence · 22 claims (14 for, 7 mixed, 1 against) · 24 studies (9 causal, 5 theoretical, 4 quant-synthesis, 3 review, 2 associational, 1 qualitative), q1–q4 · 5 of 24 report an effect size · 17 claims rest on one study

Conditional relationship

This page covers using an error as the object of study: the learner's own error, or an incorrect solution presented as a hypothetical peer's (erroneous examples), set beside a correct one, with the learner asked to find what is wrong, say why, and fix it, and with the correct answer made available. The relationship it proposes is conditional. For a learner who already has a partial grasp of a concept or principle (they can follow a correct solution but hold, or are at risk of, a specific misconception), comparing incorrect with correct examples and explaining the difference is expected to improve conceptual-understanding and correct procedures more than studying correct examples alone, at least on an immediate test. Separately, for verbal-association and recall items, an error that is followed by the correct answer is expected to be corrected more durably than an error left uncorrected, and errors made with high confidence are expected to be corrected more durably than low-confidence ones. Neither expectation has been tested here at a delayed horizon for conceptual outcomes, in adult or workplace settings, or outside mathematics and word lists.

Three things fall outside it. When the correction arrives (during the attempt, at the end of the set, or later) belongs to the Immediate Feedback principle, whose model says presence and content of correction are the better-supported levers and that timing is a local choice; this page assumes a correction comes before the error is practised again and does not re-argue timing. Letting learners fail on a problem before instruction is a neighbouring design (productive failure [~M], below), in which the learner's own failed attempts are later compared with the canonical solution; this page treats it as one configuration of error analysis, with its own age boundary. And the teacher's analysis of learner language in second-language teaching, also called error analysis, is a diagnostic method for the designer, not a learning activity; its stated limitations (attention to errors can hide correct use, and a learner who avoids a structure shows no error in it) are recorded in a theoretical article [~W] and are a caution for the observation table below, not evidence for this relationship.

Worked Examples holds the model for studying correct solutions first; erroneous examples are a later step in that sequence, not a replacement for it. No pattern page instantiates this principle; the strategies self-correction routines, exam wrappers and confidence-based quizzing are recipes that use parts of it, not tested models.

Default design, while the relationship is untested

The page's earlier guidance, kept as a concrete default a designer can act on and revise. Each step is a design proposal; the evidence status is stated beside it.

  1. Make sure a correct model comes first. Before showing errors, the learner should be able to follow at least one correct solution of the same kind (from a worked example or instruction). Untested; from the earlier page. The erroneous-examples claim's Discussion says novices can be confused by errors, but its one primary study's abstract reports no interaction with prior knowledge, so this step is a precaution, not a finding.
  2. Choose the error deliberately. Build each erroneous example around one misconception the learners are known or likely to hold (for example, a rule over-applied from a simpler case the learner already knows), not a random slip. Untested; from the earlier page ("learners with deep-seated misconceptions").
  3. Show the incorrect solution beside a correct one, of the same problem or a matched one, and ask the learner to compare them. One pair per misconception is the unit; in the one study recorded, the whole treatment fitted in a brief tutoring session. Evidence: correct and incorrect examples compared, against correct examples only [+M], 74 children in grades 4 and 5, decimal magnitude.
  4. Prompt the learner to explain why the incorrect step is wrong and how to fix it, with a "why" prompt rather than only "find the mistake". Evidence carried from self-explanation in general: prompted self-explanation in mathematics [+W]; the claim does not separate prompts on errors from prompts on correct examples.
  5. Always supply the correct answer after an error, and on multiple-choice practice always give feedback, so the chosen wrong answer is not learned. Evidence: corrective feedback after failed retrieval [+M] and feedback after multiple-choice tests [+M], both on recall of facts or word pairs.
  6. Ask for a confidence rating before revealing the answer, and spend correction time on confident errors first. Evidence: high-confidence errors are corrected more durably [+M], a review and one experiment on recall; how much more, and at what delay, is not reported on the claim page.
  7. Watch for strings of errors with confusion, and switch to a correct worked example when you see one. Proposal; the only bearing evidence is an exploratory model in which confusion was more harmful when most practice attempts were wrong: confusion and prior incorrect trials [~W]. A threshold (for example, three wrong attempts in a row on the same item type) is an untested local choice.
  8. Frame errors as information, privately by default. Use a hypothetical peer's work rather than a named classmate's, and do not grade the analysis. Untested; from the earlier page ("non-punitive", "cultural barriers").
  9. Build the examples from the learners' own diagnostic errors. Sort the errors on a diagnostic by the step where each goes wrong (in solving equations, for example: moving a term across the equals sign, multiplying out a negative, dividing by a negative), and write one incorrect/correct pair per step, starting with the most common. Untested; from the earlier page ("learners with deep-seated misconceptions").
  10. Plan the dose and progression across sessions. A default for a course of several weeks: short error-analysis segments (about 20–30 minutes) inside longer sessions, alternated with practice on correct solutions, rather than one long block; and a progression from a hypothetical peer's errors, to anonymised errors from the group, to each learner keeping a log of their own errors, once treating errors as information is routine. Untested proposals; the one study recorded used a single brief session.

How far each neighbouring claim may be carried: the erroneous-examples evidence is one brief study with children on one mathematics concept plus a meta-analysis of self-explanation in mathematics, both without effect sizes on the claim page and not yet checked against their sources; the hypercorrection and feedback claims are about recall of facts and word pairs, mostly with university students or unstated samples; the confusion claim is one exploratory model. None tests error analysis in writing, clinical practice, adult professional training or at a delayed conceptual horizon.

Fitting the design to a situation

The three facts that most change the decision:

  1. Whether the learner can already follow a correct solution of this kind. Error analysis presupposes a correct model to compare against; without one, an incorrect example has nothing to be contrasted with. If unstated, ask: can they solve or explain one standard item of this kind unaided?
  2. The kind of goal: recall of facts, or understanding of a concept or principle. For verbal-association the evidence supports attempt, confidence, correct answer; comparing and explaining erroneous solutions has been tested only for a concept in mathematics. If unstated, ask: will the learner need to explain or apply this to a new case, or recall it?
  3. The learner's age and the setting's tolerance of visible error. The problem-first reversal for young children and the affective cost of public error change what is safe to ask. If unstated, ask: how old are the learners, and will anyone else see their errors?
If the brief says… Then change… Basis
novice: no correct model of this task yet Do not open with errors. Teach or show one or two correct worked examples first; add one erroneous example per misconception only once the learner can follow a correct one. untested; from the earlier page
child (primary school) Keep correction overt (show the correct answer and how, not only right/wrong); use constructed peer errors after instruction rather than problem-first failure, which reversed for second to fifth graders. productive failure [~M]; overt correction for young children [~W] (second-hand, 1962 study)
adult or professional, intermediate Collect a confidence rating on each answer; review confident errors first and in most depth; low-confidence errors may need re-teaching, not analysis. high-confidence errors [+M]; tested on recall, untested on professional judgement
goal is verbal-association (facts, vocabulary, terms) Skip erroneous-example analysis. Use retrieval attempts followed by the correct answer after every error; always give feedback on multiple-choice items. corrective feedback after failed retrieval [+M]; multiple-choice feedback [+M]
goal is a concept or principle with a known misconception Build one incorrect/correct pair around the misconception, require a written "why" explanation, and test with changed problems, not only the practised procedure. erroneous examples [+M] (children, decimals, one session); productive failure [~M] (gain on conceptual, not procedural, outcomes)
goal is a complex-skill (writing, a whole clinical or technical task) Ask learners to look for one or two named error types in their own draft or performance, then revise; do not mark every error at once. noticing particular errors in writing [+W] (one study, reported in a review, EFL college writing)
goal is an attitude-motivation (comfort with error, persistence) Make error analysis routine and ungraded; use peer-anonymous errors; measure willingness to attempt, not only accuracy. untested proposal
online-self-paced, no teacher present The system must supply the correct solution and the explanation; log error streaks and self-reported confusion, and switch to a worked example after repeated errors on one item type. confusion with prior incorrect trials [~W] (exploratory); the switch rule is an untested proposal
single-session: one lesson or less Use one comparison set per target misconception with explanation prompts and a short immediate check; do not expect the delayed effect to be shown. erroneous examples [+M] (brief session, immediate outcome)
high stakes, public setting, or workplace-clinical where real errors are unsafe Use constructed erroneous examples or simulation rather than live errors; analyse errors privately or in writing; keep error analysis out of graded assessment. untested; from the earlier page

Seven rows rest on a claim, each tested only with the learners and tasks named in its cell; the novice, attitude and high-stakes rows are untested proposals.

Observation, state and explanation

What can be observed is the error itself (which step, which wrong answer), the learner's stated confidence, what they say when asked to explain it, and their next response on the same and a changed item. "Holds a misconception" or "was surprised into attention" are inferred states. Record the item, the confidence, the correction given and the later response; do not record "careless" or "doesn't get it".

Response Plausible explanations Observation that could change the interpretation
Spots the error in a peer's example, then makes the same error on their own problem Recognition without production; matched surface features of the example rather than the principle; the example's error was not the learner's misconception Give a changed problem with no example in view; ask the learner to state the rule they used; compare with an error built on a different misconception.
Corrects an error at once, repeats it a week later Correction held only briefly; the original guess was low-confidence, not a belief; later material interfered; the correction was copied, not understood Check the confidence recorded at the time; probe with a reworded item; ask the learner to explain the correction before reshowing it.
Confident errors are corrected and kept; low-confidence errors persist Hypercorrection as the claim describes; low-confidence errors reflect absent knowledge that needs teaching, not correcting Re-teach the low-confidence items with a correct example and compare with correction alone on matched items.
Explains the error fluently but with a wrong reason Misconception carried into the explanation; prompt too open; explaining in the language of instruction is the barrier Ask a forced-choice "which of these reasons" probe; let the learner explain in a first language or with a diagram.
Many errors in a row, rising confusion, then stops Task beyond current knowledge; public or graded error is threatening; productive struggle that needs a consolidation step Offer a correct worked example and see whether attempts resume; move the analysis to private or ungraded; ask how the learner feels about being wrong here.

These are proposals, untested with learners. A probe can shift confidence between explanations; it does not identify a cause, and analysing an error is itself an intervention. An absence of errors is not evidence of understanding: a learner may avoid a structure or item type they find hard, which an error count cannot see.

Evidence and qualifications

No claim in the wiki tests the page's original general statement, that treating errors as learning opportunities improves conceptual understanding and retention, as a whole. The claims below test parts of it.

  • Erroneous examples improve conceptual understanding by forcing comparison with correct models. [+M]: the closest test of the relationship. In one experiment, 74 fourth- and fifth-grade students learning decimal magnitude in a brief tutoring session who compared correct and incorrect examples improved correct procedures and key concepts more than those comparing correct examples only; the abstract reports no interaction with prior knowledge. A mathematics meta-analysis of prompted self-explanation names erroneous examples as a key tool, especially for conceptual understanding and transfer. Both causal/quant-synthesis, q3, no effect size on the claim page, not yet checked against their sources. The comparator is correct examples only, not errors studied alone; the horizon is not reported. The claim's Discussion (novices confused by errors) is not supported by its own entries, and one subclaim calls the participants "middle-school students", which the entry contradicts.
  • High-confidence errors are more likely than low-confidence errors to be corrected on a later test after feedback. [+M]: a narrative review reports the hypercorrection effect as robust across domains and age groups, and an experiment finds feedback that contradicts a high-confidence prediction is better remembered. No effect sizes, samples or delays are given on the claim page, and its entries could not be confirmed from the abstract available; marked M, below its cap, for that reason. It bears on which errors to prioritise, not on comparing examples.
  • Feedback Enhances Retrieval Practice [+M]: in a laboratory study of 258 participants learning Luganda–English word pairs, giving the correct answer after an incorrect response raised one-week retention by 494%, while feedback after correct responses made little difference; a classroom meta-analysis found quizzes with feedback gave g = 0.537 against 0.374 without, a between-study comparison that an earlier meta-analysis did not reproduce. It supports correcting errors after an attempt, for verbal-association; one of two entries checked, on an abstract.
  • Providing feedback after initial multiple-choice tests cut lure intrusions on final short-answer tests roughly in half [+M]: a review chapter reports that feedback cut wrong-lure answers on a final short-answer test from 20% to roughly 10% in one study. Uncorrected errors persist; this is the cost of skipping correction. Second-hand, learners and horizon not reported, not yet checked.
  • Productive Failure Improves Conceptual Learning [~M]: a meta-analysis of 53 studies (166 comparisons) found problem solving before instruction beat instruction first on conceptual knowledge and transfer (g = 0.36), not on procedural knowledge (g = −0.03), with larger effects when instruction built on students' own solutions, and a reversal for second to fifth graders and for domain-general skills. In one of two randomised studies, students who studied peers' failed attempts before instruction beat instruction first but not students who generated the attempts themselves. It extends error analysis to self-generated failure and limits it by age; mostly mathematics and physics. One of two entries checked, on an abstract.
  • Higher self-reported confusion predicts a much larger negative effect on future performance when learners answer more questions incorrectly [~W]: an exploratory model of retrieval-practice data in which confusion was more detrimental when practice was mostly unsuccessful (interaction estimate −0.18). It limits the relationship: many errors with confusion are not productive. One study, which its authors call exploratory; not yet checked.

Taken together: correcting errors has the best evidence, for recall items; prioritising confident errors and comparing incorrect with correct examples each rest on one or two studies without effect sizes on the claim pages; and generating errors before instruction helps conceptual outcomes on average but not for young children. Do not rank these by effect label: learners, tasks and outcomes differ, and none measures conceptual understanding at a delay after erroneous-example study.

The evidence by question

Further evidence, not yet read against this model

Claims this page cited before it was rewritten as a conditional model. Both are now read above as core evidence; their earlier markers, capped, and how far their sources have been checked are recorded here so the change is visible.

The earlier page also cited the erroneous-examples claim [-M] for novice overload and the high-confidence claim [~M] for low-confidence errors; both readings are kept in the model above, with the first marked as not supported by the claim's own entries. - Students report code understanding, debugging, and AI-limitation awareness as primary learning benefits of buggy GenAI programming tasks [+M] — attached 2026-10-10 from When AI Is Wrong on Purpose: How Students Respond to Buggy GenAI Code, which proposed "Deliberate bug injection into correct GenAI code to create code review opportunities". - Erroneous examples produce significantly higher delayed-test learning gains than problem solving for decimal learning [+W] — attached 2026-10-16 from Bruce M. McLaren et al. (2015), which proposed "Pair erroneous examples with correctness feedback so students cannot proceed with incorrect solutions"; tests this page's relationship.

Objective and learner-valued goal

The designer's objective fixes what the error analysis is for: correct recall of an item, a changed misconception shown on new problems, or fewer errors of one type in real work, each at a stated horizon. Name the outcome before choosing the activity, because a drop in errors on practised items says nothing about understanding on changed ones. Elicit separately what the learner wants: to get the answer right and move on, to understand why, or not to be seen getting it wrong. Agreement and divergence are both observations.

For example, nursing students practising drug-dose calculations may want to pass the calculation test and avoid being corrected in front of peers, while the designer's objective is that they recognise a decimal-place or unit-conversion error in an unfamiliar order. Private, ungraded analysis of a hypothetical colleague's miscalculation serves the learner's wish and gives the designer evidence on the objective; a fast correctness-only quiz serves the test but not the objective. Recording both lets the designer check whether the learners' own errors on the test match the misconceptions the examples were built around.

What would revise this model?

The erroneous-example expectation should be strengthened if comparisons with older learners, other domains and delayed conceptual tests reproduce it against correct-examples-only, and weakened if they do not. If studies find erroneous examples harm learners without a correct model, step 1 of the default design becomes a finding rather than a precaution; if they find no such harm, it can be relaxed. If hypercorrection is shown not to hold for conceptual errors or professional judgements, the confidence-first step should be confined to recall. If more data link strings of errors with confusion to lower later performance, the switch rule in step 7 needs a tested threshold. Do not protect the model by calling every failure a learner who was not ready.

Correct procedures, conceptual understanding, recall of a correction and comfort with error are separate claims. The present evidence does not establish how many erroneous examples to use, when in a unit to introduce them, or that error analysis works the same for children, adults and professionals.

Claims

Examples

Key Sources

Page metadata
Field Value
type principle
id error-analysis
title Error Analysis
description For a learner who can already follow a correct solution, comparing an incorrect solution with a correct one, explaining the error and seeing the correction is expected to improve conceptual understanding, and correcting errors (confident ones first) to improve later recall, but the evidence is a few short studies, mostly children in mathematics and adults on recall items.
status review
canonical True
generated by claude/unspecified on 2026-10-02
trust unverified — no one has confirmed this page's content
sources 3 — metcalfe-2017, durkin-2012, fazio-2009

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