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Productive Failure

Principle · All principles
Evidence · 49 claims (19 for, 23 mixed, 7 against) · 29 studies (17 causal, 6 review, 4 theoretical, 2 quant-synthesis), q1–q4 · 12 of 29 report an effect size · 46 claims rest on one study

Conditional relationship

This page owns the decision of whether a new concept is taught first or attempted first. When the goal is conceptual understanding of a new concept and transfer to problems not yet seen, and learners already have enough prior knowledge to generate several partial or wrong solutions of their own, letting them first attempt problems the concept solves (problem solving followed by instruction, PS-I), and then teaching the concept by comparing their attempts with the canonical solution, is expected to improve conceptual knowledge and transfer over teaching first and practising after (I-PS). Pooled across studies, it is not expected to improve procedural skill; one trial of a brief, repeated variant for a multi-step procedure is the exception recorded in the wiki (see the procedure rows below).

The relationship is conditional on five things, each from the evidence below:

  • The outcome. Across 53 studies and 166 comparisons the advantage was g = 0.36 on conceptual knowledge and transfer, and g = −0.03, no difference, on procedural knowledge (Sinha & Kapur 2021).
  • How the attempt and the teaching are designed. The advantage grew with fidelity to the productive-failure design: problems that admit several solution methods, learners actually generating several, group work, and, most of all, instruction that builds on the learners' own solutions (g = 0.56 where it did, 0.20 where it did not). A theory-building review (Loibl, Roll & Rummel 2017) reached the same point from the other side: problem solving before instruction helped only where the instruction built on student solutions or used contrasting cases. Group work is the weakest of these features: one randomised trial with tenth-graders found no difference in conceptual knowledge between attempting alone and in groups (Brand et al. 2023).
  • Who the learners are. The effect was negative for second to fifth graders and rose with grade level. Young learners may not have enough prior knowledge to generate several solutions.
  • What is being learned. For domain-general skills, such as the control-of-variables strategy, the instruction-first order did better.
  • How long the intervention runs. In the meta-regression, the fidelity benefit tended to shrink for interventions spanning only a few hours (a marginal interaction, p = .055); longer interventions also had higher fidelity.

How this sits beside its neighbours: Guided Discovery Learning and the evidence against minimal guidance concern learning without the instruction that follows; productive failure always ends with full instruction, and the question is only its order. Worked Examples and Cognitive Load Management argue for teaching first, especially for novices learning procedures; the evidence here agrees for procedural outcomes and for young learners, and differs for conceptual outcomes in learners old enough to generate solutions. Pretesting is a smaller cousin: an attempt before study, without the generation of methods.

Default design, while the dose is untested

The meta-analysis establishes the direction, the outcomes it holds for and which design features go with larger effects; it does not set a dose. This default is a labelled proposal: the two phases and the features follow the evidence, the timings are untested choices.

  1. Check the condition. Is the target a concept with an underlying structure (variance, ratio, a physical law, a statistical idea), and is the outcome conceptual understanding or transfer rather than fluent execution of a procedure? Are learners past the early primary years, with the prior knowledge to attempt the problem in several ways? If not, teach first.
  2. Choose one rich problem the concept is the answer to: one that admits several reasonable methods, most of them partial or wrong (for variance: which of three players is the most consistent scorer?). Give it a story or a reason to care. Pilot it with a few learners first where you can: the sign of the right problem is that they produce several ideas containing the errors the instruction will address, and do not reach the canonical method; a problem almost nobody makes any headway on is too hard (studies with very low solution rates in the attempt phase tended not to find the benefit). Where the time allows a second problem, set it in a different context from the first: in two studies of the same design, one short problem before instruction did worse for transfer than explaining a worked solution, and two problems did better.
  3. Problem-solving phase, 30–60 minutes, in small groups or individually. Groups are optional: one trial found no conceptual difference between attempting alone and in groups. Where groups are used, mix prior attainment so each group has at least one member able to drive several methods. Ask for as many ways of solving it as they can find. Do not teach, give hints toward the canonical method, or grade correctness; content-general prompts that help without telling the content ("what else could you try?", "what does your method leave out?", or a think-ask-explain role script for pairs) are compatible with the attempt. Say plainly that not solving it is expected and that trying several ways is the task.
  4. Collect the attempts. Note the three or four most common or most instructive methods, including wrong ones.
  5. Instruction phase, building on the attempts. Present the learners' methods, ask what each captures and misses, compare them with each other and then with the canonical method, and show which features of the problem the canonical method handles that theirs did not. Where the learners' own attempts cannot be collected (a self-paced course, no time to sort them), set prepared typical student solutions, or contrasting cases, side by side instead: the review evidence counts either as doing the job, and an attempt followed by instruction that does neither is the version that did not help. Contrasting cases have to be used, not just present: ask learners to compare them and say what differs; in one trial, cases placed in the problem material without guidance on their use did not help. Then teach the concept in full.
  6. Then practise the procedure, as you would after instruction-first teaching: the attempt phase does not replace it. (For a multi-step procedure whose fluency is the goal, the default stays teach first; brief attempts before each step are a recorded alternative, on one trial, in the procedure rows below.)
  7. Across sessions, run the attempt and the instruction on different days or at least with a break between them where the course allows; do not compress the whole design into one short lesson. Over a unit, use a full attempt for each foundational concept rather than every topic; where a content-general script is used, expect the first session to go no better than teaching first (in one four-week study the scripted group pulled ahead only from week two, as students internalised the script).
  8. Judge it on a conceptual or transfer test, not on the attempt phase, which will look like failure (learners taught first produce fewer but better attempts, and in one trial almost all of them solved the practice sheets while the attempt-first learners mostly did not), and not on a procedural test alone, where no difference is expected.

Fitting the design to a situation

Four facts change the decision most. Ask for them when the brief omits them: is the outcome conceptual and transfer, or procedural?; how old are the learners and what do they already know?; is the target a domain concept or a domain-general skill?; and how much time is there?

If the brief says… Then change… Basis
The goal is conceptual understanding or transfer of a new concept (mathematics, science, statistics) Use the attempt-first design above Productive failure improves conceptual learning [+M] (g = 0.36 over 53 studies)
The goal is fluent execution of a procedure (procedure) Teach first; pooled, a full attempt phase adds time without a procedural gain PS-I shows no pooled benefit for procedural knowledge [~M] (g = −0.03)
The goal is a multi-step procedure (an algebraic method, a worked calculation), and the teacher wants learners to understand why each step is there Teach first remains the default; an alternative is "micro" attempts: a few minutes' attempt before each step is taught, repeated step by step, rather than one long attempt. Do not expect a conceptual gain from it Micro productive failure improved sixth-graders' isomorphic algebraic procedural problem solving [+M] (η²p = 0.06, held at one week); Micro productive failure showed no effect on conceptual explanation [~M]; one trial, against the pooled null above
Learners are in the early primary years (roughly ages 7–11) Teach first PS-I effects are negative for 2nd–5th graders and increase with age [-M]
The target is a domain-general skill (the control-of-variables strategy, a general reasoning heuristic) Teach first For domain-general skills, one meta-analysis finds a negligible effect (g = −0.17) in favour of I-PS over PS-I [-M]; one exception reported secondhand: with a virus-transmission simulation, learners who attempted first did no better at the end of the unit but transferred multivariable causal reasoning better to a new context (PS-I with a virus transmission simulation showed better transfer of multivariable causality [+W], an editorial's summary, no effect size)
The target is outside mathematics and science (a social-science method, a humanities concept) Do not assume the advantage carries over; teach first, or run the attempt-first design as a trial against teaching first with a conceptual test PF students did not outperform DI students when learning social science research methods [-W] (two quasi-experiments, 364 tenth-graders, even though the pilots showed the attempt phase worked as designed: the problem met the sweet spot of complexity [+W]); of eight PF-similar studies in non-STEM or domain-general settings, only one found a positive effect [-W] (narrative overview)
The teacher cannot or will not build the instruction on the learners' own attempts Build it on prepared typical student solutions or contrasting cases instead, and have learners compare the cases explicitly; if the instruction uses neither, expect a much smaller effect or none, and consider teaching first: delaying the instruction is not by itself the active ingredient PF design fidelity predicts larger PS-I effects [+M] (0.56 when instruction built on student solutions, 0.20 when not); PS-I fosters learning only if contrasting cases or instruction built on student solutions are implemented [+W] (review, no pooled effect); PS-I outperforms I-PS on conceptual knowledge only when instruction builds on student solutions [+W] (Loibl & Rummel 2014, as summarised in a 2025 framework article); Merely delaying instruction does not improve conceptual understanding [~W] and contrasting cases without explicit guidance on their use do not improve conceptual understanding [~W] (one randomised trial, 181 students; non-significant differences, not shown equivalent)
Only a single short session is available Keep the design simple, or teach first; do not cram every feature into a few hours. A single short problem is the weakest version: if the attempt cannot include two problems in different contexts, explaining a worked solution before instruction may serve transfer better In one meta-regression, the PS-I fidelity benefit tended to shrink for interventions spanning only a few hours [~M] (marginal, p = .055); Across two studies that differed in the duration of the initial problem-solving phase, the PS-I versus WS-I transfer advantage reversed [~W] (two studies of density and ratio, one problem against two, as summarised in a framework article; the comparison is with a worked solution, not with teaching first)
Learners work alone (online-self-paced) Individual attempts are acceptable; in the instruction, show learners a set of typical attempts (other learners' or prepared ones) beside the canonical solution. Watch persistence: keep the attempt short, ungraded and visibly expected to fail. Where attempting is impractical, let learners watch a modelled learner work through several different failed methods before the instruction (vicarious failure); the methods shown must be diverse, since a model showing few did no better than teaching first Collaborative and individual problem solving in traditional PF do not differ in conceptual knowledge after instruction [~M] (tenth-graders, a non-significant difference, not shown equivalent); Learning the CVS with self-generated, vicarious, combined, or no errors during PS-I does not differentially affect posttest performance [~W] (others' errors did as well as one's own, on a domain-general skill); Pre-tests reduced adult learners' persistence in a MOOC [-W] (pretests, not PS-I); Vicarious failure with high solution diversity is as effective as engaging in productive failure oneself [~W] and outperforms low-diversity vicarious failure and direct instruction [+M] (one randomised trial, 152 secondary students, d ≈ 0.65 over teaching first; equal to attempting, not shown equivalent); observing the whole problem-solving-and-failing process beat generating one's own attempts [+M], more so for learners with more prior knowledge (prior knowledge moderated the VF-process advantage [~M]; one trial, 173 secondary students); both trials were in classrooms, so the self-paced PS-I design as a whole is an untested proposal
The teacher forms the groups for the attempt Mix prior attainment in mathematics or the domain, so each group has at least one member who can drive several methods; avoid all-low and all-high groups Mixed-ability groups generated a broader range of solution methods than all-low and all-high groups [+W] (two undergraduate studies, reported in an editorial; method range and uptake of the formula, not a learning test)
The question is whether to help learners succeed during the attempt (hints, guidance toward the method) Do not steer toward the canonical method during the attempt; guidance raised solution quality but not later learning. Content-general support (a role script that prompts learners to think, ask and explain, without telling the content) is compatible Guidance during initial problem solving does not improve learning from subsequent instruction [~M]; Role-script support during generation led university relearning students to outperform direct instruction in all weeks but the first [+W]
Learners are relearning material they met before (revision for an exam, a refresher course) Generation with a content-general script before re-teaching is an option; run it across several sessions, since the first session showed no advantage Role-script support during generation led university relearning students to outperform direct instruction in all weeks but the first [+W] (76 university students, mathematical analysis, four weeks; reported secondhand in an editorial, no effect size)
Learners will meet later material that builds on the concept (a course, not a lesson) Use the attempt-first design for the foundational concepts; its benefit shows when learners later learn from new resources. In a university course, repeated attempt-first tasks across the year are a recorded option Invention tasks prepare future learning [+M]; PS-I over a year in a university linear algebra course was followed by higher final exam performance than baseline cohorts [+W] (four iterations against earlier cohorts, not randomised; reported in an editorial, no effect size)
Learners are novices with little prior knowledge of the domain, and the problem cannot be attempted without it Teach first, or give the minimum prior knowledge before the attempt; an attempt with nothing to generate from is minimal guidance, not productive failure Minimal guidance is less effective for novices than explicit instruction [-M]; Expertise reversal [~W] (the balance between generating and being told shifts with prior knowledge; a narrative review)
Learners are anxious about failure or the setting grades every attempt State that the attempt is not graded and that not solving it is expected; keep the attempt phase out of the grade Pre-tests reduced adult learners' persistence in a MOOC [-W] shows a cost of failing first on a pretest, not on a PS-I attempt; the framing is an untested proposal
One teacher for a large class Collect attempts from a sample of groups (or a quick poll of methods) and build the instruction on the three or four most common untested proposal

Observation, state and explanation

These rows are proposals, untested with learners as diagnostics.

Response Plausible explanations Observation that could change the interpretation
Learners produce one method, or none, during the attempt The problem admits too few methods; learners lack the prior knowledge to generate; they are waiting to be told Ask what they would try if the first method were not allowed; check the prior knowledge the problem assumes. Do not treat the count of methods as the measure of success: one study found it predicted learning, two did not (see the evidence list).
Almost nobody gets any part of the way, even to a partial method The problem is too hard for this group; the prior knowledge it assumes is missing Look at how much of the canonical solution the best attempts contain; simplify the problem or teach the prerequisite first, since attempt phases with very low solution rates went with no benefit.
A group settles on one method within minutes, or one member does all the generating The group is all high-attaining (someone already knows a method) or all low-attaining (nobody can start); the problem admits too few methods Look at the group's composition and at the methods other groups found; regroup to mix prior attainment, or ask each member to write a method before the group discusses.
Learners disengage or say the task is unfair The failure is not framed as expected; the attempt is too long; the attempt is graded Ask how they understood the task; shorten the attempt and restate that it is not graded.
Conceptual test no better than with teaching first The instruction did not build on the attempts; the learners were too young or too new to the domain; the test measured procedure Check whether the instruction compared their methods with the canonical one; check what the test asked.
Procedural test worse than with teaching first Practice time was lost to the attempt phase Give the same amount of practice after instruction in both designs before comparing.

Evidence and qualifications

Taken together: for conceptual understanding and transfer in learners past the early primary years, attempting first and being taught second, with the teaching built on the attempts, beats teaching first by about a third of a standard deviation; for procedures, for young children and for domain-general skills it does not, pooled, though one trial of brief repeated attempts found a procedural gain in sixth-graders. Group work helps less than the fidelity coding suggested; building the instruction on solutions (the learners' own or typical ones) matters most, and delaying the instruction without it did not help. Watching a modelled learner fail in several different ways did as well as failing oneself in two classroom trials. Outside mathematics and science, the wiki records no advantage. No claim in the wiki tests a dose directly (how long the attempt), beyond two studies in which two problems beat one, or the full design in a self-paced online course.

The evidence by question

Further evidence, not yet read against this model

Read 2026-10-19; the rest of what was listed here moved into the model above (the procedure, alone, groups, guidance, relearning, anxious-learner and novice rows, and the evidence list).

  • Pretesting enhances learning [+M]: an attempt before study, without the generation of methods; a cousin of this design, named in the conditional relationship. Its studies are laboratory retention tests with undergraduates, not tests of conceptual transfer, so it does not change the model.
  • Giftedness interacts significantly with instruction type on the learning and recall outcomes in the 2×2×2 study [~M] — attached 2026-10-18 from Lim et al. (2023), invention-first against example-first with 199 seventh-graders. The claim records that the effect of the order differed between gifted and other students (η²p = .077) but not which way, so it cannot yet set a row; reading the article for the direction is the next step.

Read 2026-10-19 (second pass, claims linked overnight); the others linked then moved into the model above (the vicarious-failure, non-STEM, fidelity, short-session, course and domain-general rows, the attempt-phase observation rows and the evidence list).

Objective and learner-valued goal

The designer's objective is understanding deep enough to use a concept on problems not yet seen. Ask separately what the learner wants: a learner who must pass a procedural test next week is not served by an attempt phase that costs practice time, and a learner who reads failure as a verdict on ability needs the framing in step 3 before anything else.

What would revise this model?

The expectation should weaken if new comparisons with comparable learners, holding total time and practice equal, find no conceptual or transfer advantage for attempting first; or if the advantage disappears when the instruction-first condition also builds on typical student errors, which would locate the effect in the instruction rather than the order. It should be extended, not reversed, by studies of self-paced online versions. The non-STEM row should change if randomised trials outside mathematics and science find the advantage the two quasi-experiments recorded here did not; the vicarious-failure option should be dropped if trials by other research groups find watching diverse failed attempts worse than making them. The procedure rows should change if further trials of brief repeated attempts replicate, or fail to replicate, the one procedural gain recorded here, and the group rows if a powered trial shows attempting alone equivalent to, or worse than, attempting in groups.

Claims

Examples

Key Sources

  • 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
  • Kapur, M. (2016). Examining productive failure, productive success, unproductive failure, and unproductive success in learning. Educational Psychologist, 51(2), 289–299. doi:10.1080/00461520.2016.1155457
  • Kapur, M. (2014). Productive failure in learning math. Cognitive Science, 38(5), 1008–1022. doi:10.1111/cogs.12107
  • Schwartz, D. L., & Martin, T. (2004). Inventing to prepare for future learning: The hidden efficiency of encouraging original student production in statistics instruction. Cognition and Instruction, 22(2), 129–184. doi:10.1207/s1532690xci2202_1
  • Loibl, K., Roll, I., & Rummel, N. (2017). Towards a theory of when and how problem solving followed by instruction supports learning. Educational Psychology Review, 29, 693–715. doi:10.1007/s10648-016-9379-x
  • Ziegler, E., Trninic, D., & Kapur, M. (2021). Micro productive failure and the acquisition of algebraic procedural knowledge. Instructional Science, 49, 313–336. doi:10.1007/s11251-021-09544-7
  • Brand, C., Hartmann, C., Loibl, K., & Rummel, N. (2023). Do students learn more from failing alone or in groups? Insights into the effects of collaborative versus individual problem solving in productive failure. Instructional Science. doi:10.1007/s11251-023-09619-7
  • Kapur, M., & Rummel, N. (2012). Productive failure in learning from generation and invention activities. Instructional Science, 40, 645–650. doi:10.1007/s11251-012-9235-4
  • Janelli, M., & Lipnevich, A. A. (2021). Effects of pre-tests and feedback on performance outcomes and persistence in Massive Open Online Courses. Computers & Education, 161, 104076. doi:10.1016/j.compedu.2020.104076
  • Hämmerle, L., Kuhlmann, S. L., Krause-Wichmann, T., & Möller, A. (2026). Learning the control-of-variables strategy through self-generated and vicarious errors: the mediating roles of affect, motivation, cognitive load, and error awareness. Instructional Science. doi:10.1007/s11251-026-09822-2
  • Braas, T. C., Hartmann, C., Hoogerheide, V., Rummel, N., & van Gog, T. (2025). When is observing failure productive? Investigating the role of solution diversity in vicarious failure. Instructional Science. doi:10.1007/s11251-025-09706-x
  • Hartmann, C., van Gog, T., & Rummel, N. (2021). Preparatory effects of problem solving versus studying examples prior to instruction. Instructional Science. doi:10.1007/s11251-020-09528-z
  • Loibl, K., Tillema, M., Rummel, N., & van Gog, T. (2020). The effect of contrasting cases during problem solving prior to and after instruction. Instructional Science. doi:10.1007/s11251-020-09504-7
  • Nachtigall, V., Serova, K., & Rummel, N. (2020). When failure fails to be productive: probing the effectiveness of productive failure for learning beyond STEM domains. Instructional Science. doi:10.1007/s11251-020-09525-2
  • Loibl, K., Leuders, T., Glogger-Frey, I., & Rummel, N. (2025). CID: a framework for the cognitive analysis of composite instructional designs. Instructional Science. doi:10.1007/s11251-024-09665-9
  • Loibl, K., Nachtigall, V., & Leuders, T. (2025). Advances in research on composite instructional designs – investigating intermediate knowledge and preparation effects. Instructional Science. doi:10.1007/s11251-025-09751-6
Page metadata
Field Value
type principle
id productive-failure
aliases problem-solving-before-instruction, ps-i, invention-before-instruction
title Productive Failure
description When the goal is conceptual understanding and transfer of a new concept, having learners first attempt problems that the concept solves, before they are taught it, and then teaching it by building on their attempts, is expected to improve conceptual knowledge and transfer over teaching first, with no pooled gain on procedural skill.
status review
canonical True
generated by claude/unspecified on 2026-10-19
trust unverified — no one has confirmed this page's content
sources 16 — sinha-kapur-2021, kapur-2016, kapur-2014, schwartz-martin-2004, loibl-roll-rummel-2017, ziegler-trninic-kapur-2021, brand-et-al-2023, kapur-rummel-2012, janelli-lipnevich-2021, hammerle-et-al-2026, braas-et-al-2025, hartmann-van-gog-rummel-2021 … and 4 more

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