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Productive Failure in Learning Math

Dados Bibliográficos

ID23348656
AutoresManu Kapur (0000-0002-2232-6111, National Institute of Education Nanyang Technological University, autor correspondente)
Ano2014
Volume38
Fascículo5
Páginas1008-1022
Data de publicação2014-06-01
Peer ReviewedSim
Open AccessSim
TipoARTICLE
PeriódicoCognitive Science (JOURNAL)
Identificadores do periódicoISSN: 0364-0213 • E-ISSN: 1551-6709
EditoraWiley (PUBLISHER • GB)
DOI10.1111/cogs.12107
PMID24628487
OpenAlexW2143991504
IdiomaEN
Citações recebidas94
Referências citadas21

When learning a new math concept, should learners be first taught the concept and its associated procedures and then solve problems, or solve problems first even if it leads to failure and then be taught the concept and the procedures? Two randomized‐controlled studies found that both methods lead to high levels of procedural knowledge. However, students who engaged in problem solving before being taught demonstrated significantly greater conceptual understanding and ability to transfer to novel problems than those who were taught first. The second study further showed that when given an opportunity to learn from the failed problem‐solving attempts of their peers, students outperformed those who were taught first, but not those who engaged in problem solving first. Process findings showed that the number of student‐generated solutions significantly predicted learning outcomes. These results challenge the conventional practice of direct instruction to teach new math concepts and procedures, and propose the possibility of learning from one's own failed problem‐solving attempts or those of others before receiving instruction as alternatives for better math learning.

Concept learning · Mathematics education · Process (computing) · Computer Science · Innovative Teaching and Learning Methods · Mathematics · Science Education and Pedagogy · Visual and Cognitive Learning Processes

  • An Exploratory Analysis of Transactive Interaction Patterns in Cooperative Learning Using Sequential Analysis

    Open Access•Lea Nemeth, Tim Blumenfeld et al.•Education Sciences•2023

  • Examining Productive Failure, Productive Success, Unproductive Failure, and Unproductive Success in Learning

    Manu Kapur•Educational Psychologist•2016

  • The relative effectiveness of different active learning implementations in teaching elementary school students how to design simple experiments

    Open Access•Amedee Marchand Martella, David Klahr et al.•Journal of Educational Psychology•2020

  • The Cambridge Handbook of Computing Education Research

    Open Access•Sally A Fincher, Anthony V Robins•Cambridge Handbook of Computing…•2019

  • Towards a Theory of When and How Problem Solving Followed by Instruction Supports Learning

    Open Access•Katharina Loibl, Ido Roll et al.•Educational Psychology Review•2017

  • Rethinking the Boundaries of Cognitive Load Theory in Complex Learning

    Open Access•Slava Kalyuga, Anne‐marie Singh et al.•Educational Psychology Review•2016

  • Managing uncertainty in scientific argumentation

    Open Access•Ying-Chih Chen, Matthew J Benus et al.•Science Education•2019

  • The changes we need

    Open Access•Yong Zhao, Jim Watterston•Journal of Educational Change•2021

  • Understanding student experiences in a mentorship-driven summer research program

    Open Access•Chwan-Li Shen, Stephanie Stroever et al.•Frontiers in Education•2026

  • Making failure desired during learning – A quasi-experimental study

    Open Access•Tanmay Sinha•Thinking Skills and Creativity•2026

  • Improving the transfer of inquiry strategies by using short instructional videos

    Open Access•Ana Saavedra, Daniel L Schwartz et al.•Educational Technology Research…•2026

  • Instructional Implications of Evolutionary Perspective on Human Cognitive Architecture as an Intelligent Natural Information Processing System

    Open Access•Slava Kalyuga•Educational Psychology Review•2026

  • Optimizing learning conditions for self-determination in primary mathematics education

    Open Access•Jane Hubbard, James Russo et al.•Mathematics Education Research…•2026

  • Effects of instructional design, instructional preferences, and cognitive load on problem solving and knowledge acquisition in a computer-based office simulation

    Open Access•Sabrina Ludwig, Andreas Rausch et al.•Learning and Instruction•2026

  • Mechanisms to prepare for future learning

    Open Access•Katharina Ockl, Inga Glogger-Frey•Learning and Instruction•2026

  • Deliberate errors vs. induced errors

    Open Access•Xing Li, Han Bai et al.•Learning and Instruction•2026

  • Training future primary teachers in historical thinking through error-based learning and learning analytics

    Open Access•Sergio Tirado‐Olivares, Roberto C Gutierrez et al.•Humanities and Social Sciences…•2023

  • Fail, flip, fix, and feed – Rethinking flipped learning

    Open Access•Manu Kapur, John Hattie et al.•Frontiers in Education•2022

  • College algebra students’ perceptions of exam errors and the problem-solving process

    Open Access•Mary E Pilgrim, Linda C Burks et al.•Frontiers in Education•2025

  • Fail, flip, fix, feed

    Open Access•Richard Conrardy, Christian Spannagel et al.•Frontiers in Education•2026

  • Generating mathematical strategies shows evidence of a serial order effect

    Open Access•Stacy T Shaw, Anahit A Yeghyayan et al.•Frontiers in Education•2024

  • Promoting the construction of intelligent knowledge with the help of various methods of cognitively activating instruction

    Open Access•Ralph Schumacher, Elsbeth Stern•Frontiers in Education•2023

  • The safety gap

    Open Access•Hong Wang, Wenhui Shan•Frontiers in Education•2026

  • Promoting future teachers’ evidence-informed reasoning scripts

    Open Access•Theresa Krause-Wichmann, Martin Greisel et al.•Frontiers in Education•2023

  • Impact of a Short-Term Professional Development Teacher Training on Students’ Perceptions and Use of Errors in Mathematics Learning

    Open Access•Florence Kyaruzi, Jan-Willem Strijbos et al.•Frontiers in Education•2020

  • The effects of mathematical ability and motivational beliefs on students’ perceptions of feedback usefulness

    Open Access•Sharmin Söderström, Torulf Palm et al.•Frontiers in Education•2024

  • Engineering and humanitarian intervention

    Open Access•Adeela Arshad‐ayaz, M Ayaz Naseem et al.•Journal of International…•2020

  • Distinguishing between Grit, Persistence, and Perseverance for Learning Mathematics with Understanding

    Open Access•Joseph DiNapoli•Education Sciences•2023

  • A Model of Scientific Data Reasoning

    Open Access•Amy M Masnick, Amy Masnick et al.•Education Sciences•2022

  • Exploring Education as a Complex System

    Open Access•John Vulic, M J Jacobson et al.•Education Sciences•2024

  • Factors Influencing Students’ Performance in University Mathematics Courses

    Open Access•Moeketsi Mosia, Egara Felix Oromena et al.•Education Sciences•2025

  • Describing and Interpreting the Space of Classroom Learning in Problem-Solving-Based Mathematics Instruction

    Open Access•Berie Getie Kassa, Liping Ding et al.•Education Sciences•2023

  • A Lecture-Specific AI-Based Tutor for Higher Education

    Open Access•Samuel Tobler, Katja Köhler•Education Sciences•2026

  • When is a performance-approach goal unhelpful? Performance goal structure, task difficulty as moderators

    Open Access•Jong-Baeg Kim, Kyoung-Suk Moon et al.•Asia Pacific Education Review•2021

  • On Technology and the Ecology of Thinking

    Open Access•Mustafa Selek•International Journal of Applied…•2026

  • The role of individual preparation before collaboration

    Wenli Chen, Qianru Lyu et al.•Journal of the Learning Sciences•2024

  • Self-study enhances the learning effect of discussions

    Jaeseo Lim, Jooyong Park•Journal of the Learning Sciences•2023

  • Exploring the use of productive failure to learn ecology in a virtual world

    Lu Cao, Jingjing Zhang•Interactive Learning Environments•2025

  • The trade-off between complexity and accuracy. Preparing for computer-based adaptive instruction on fractions

    Antje Boomgaarden, Katharina Loibl et al.•Interactive Learning Environments•2023

  • Using failure cases to promote veterinary students’ problem-solving abilities

    Open Access•Hui Rong, Ikseon Choi et al.•Educational Technology Research…•2020

  • Using Learning Curves to Identify and Explain Growth Patterns of Learners in Bronchoscopy Simulation

    Briseida Mema, Maria Mylopoulos et al.•Academic Medicine•2020

  • The Benefits of Tying Yourself in Knots

    Andreas Höier Aagesen, Rune Dall Jensen et al.•Academic Medicine•2020

  • How do students become experts? An in-depth study on the development of domain-specific awareness in a materials chemistry course

    Stefanie Lenzer, Bernd Smarsly et al.•International Journal of Science…•2020

  • Sequencing problem solving and worked examples

    Open Access•Ines Zeitlhofer, Joerg Zumbach•International Journal of…•2026

  • Designing for fake news literacy training

    Open Access•Christian Scheibenzuber, Scott Hofer et al.•Computers in Human Behavior•2021

  • Adaptive guidance for uncertainty

    Open Access•N L Bohm, Renate G Klaassen et al.•Higher Education Research &…•2025

  • False certainty as an unwanted side effect of knowledge acquisition in computer-based online search and content learning

    Open Access•Johannes F von Hoyer, Joachim Kimmerle et al.•Computers & Education•2024

  • Comparing the productive failure and directive instruction for declarative safety knowledge training using virtual reality

    Open Access•Lu Song, Song Lu et al.•Journal of Computer Assisted…•2024

  • Comparing effects of different goal type orders on collaborative simulation‐based inquiry in engineering problem solving

    Open Access•Yanyan Sun, Chengjun Feng et al.•Journal of Computer Assisted…•2024

  • The benefit of combining teacher-direction with contrasted presentation of algebra principles

    Open Access•Esther Ziegler, Peter A Edelsbrunner et al.•European Journal of Psychology of…•2021

  • Teaching for transfer of learning in health professions education

    Open Access•Dario Cecilio-Fernandes, John Sandars et al.•Medical Teacher•2025

  • Twelve tips for fostering productive struggle in the clinical learning environment

    Tim Mickleborough, Timothy Mickleborough et al.•Medical Teacher•2025

  • A change of mind

    Liv Dyre Rasmussen, Lawrence Grierson et al.•Medical Teacher•2025

  • From struggle to strength

    Maria Mylopoulos, Naomi Steenhof et al.•Medical Teacher•2025

  • When Problem Solving Followed by Instruction Works

    Open Access•Tanmay Sinha, Manu Kapur•Review of Educational Research•2021

  • A Framework for Learning From Erroneous Examples and Meta-Analysis of Empirical Research

    Open Access•Ecenaz Alemdag, Anja Eichelmann et al.•Review of Educational Research•2025

  • Build back better

    Open Access•Yong Zhao•Prospects•2022

  • Split up, but stay together

    Open Access•Rotem Abdu, Baruch B Schwarz et al.•Instructional Science•2020

  • Assistance that fades in improves learning better than assistance that fades out

    Open Access•Jay Jennings, Kasia Müldner•Instructional Science•2020

  • Effectiveness of invention tasks and explicit instruction in preparing intellectually gifted adolescents for learning

    Open Access•Sue-ann Lim, Jae Yup Jung et al.•Instructional Science•2023

  • When failure fails to be productive

    Open Access•Valentina Nachtigall, Katja Serova et al.•Instructional Science•2020

  • Preparatory effects of problem solving versus studying examples prior to instruction

    Open Access•Christian Hartmann, Tamara Van Gog et al.•Instructional Science•2021

  • Uncertain instruction

    Open Access•Marianna Lamnina, Catherine C Chase•Instructional Science•2021

  • Learning from erroneous examples in the mathematics classroom

    Open Access•Rafi’ Safadi, Nadera Hawa•Instructional Science•2024

  • Micro productive failure and the acquisition of algebraic procedural knowledge

    Open Access•Esther Ziegler, Dragan Trninic et al.•Instructional Science•2021

  • Using productive failure to learn genetics in a game-based environment

    Open Access•Lu Cao, Polly K Lai et al.•Instructional Science•2024

  • Making the productive failure in PS-I more productive

    Open Access•Rafi’ Safadi, Ali Diab•Instructional Science•2026

  • The effect of contrasting cases during problem solving prior to and after instruction

    Open Access•Katharina Loibl, Marcel Tillema et al.•Instructional Science•2020

  • Do students learn more from failing alone or in groups? Insights into the effects of collaborative versus individual problem solving in productive failure

    Open Access•Charleen Brand, Christian Hartmann et al.•Instructional Science•2023

  • How preparation-for-learning with a worked versus an open inventing problem affect subsequent learning processes in pre-service teachers

    Open Access•Inga Glogger-Frey, Anne‐Katrin Treier et al.•Instructional Science•2022

  • Pre-Service Mathematics Teachers’ Experience with Productive Struggle

    Zareen Gul Rahman, Zareen Rahman•The Educational Forum•2023

  • Students’ Mathematical Learning Behaviour in Teaching-for-Understanding Classes

    Joke H Van Velzen•The Educational Forum•2021

  • Investigating the motivational and knowledge affordances of conversational AI using induction, concretization and exemplification in math learning

    Open Access•Chenglu Li, Bailing Lyu•British Journal of Educational…•2025

  • Mirror, mirror

    Open Access•Betül Sağlam, Ayşe Elif Yavuz Sever et al.•AI & Society•2026

  • Breaking Free

    Open Access•Michael Mills, J H Watson•TechTrends•2021

  • K12 Practitioners’ Perceptions of Learning from Failure, Creativity, and Systems Thinking

    Open Access•T Logan Arrington, Alan L Moore et al.•TechTrends•2021

  • Normalising vulnerability, humanising learning

    Open Access•Javeed Sukhera, Mario Fahed•Medical Education•2026

  • Aesthetic Learning, Creative Writing and English Teaching

    Francis Gilbert•Changing English•2016

  • Co-Construction of Iteration Through Failure Moments

    Amber Simpson, Andrew Osterhout et al.•Visitor Studies•2024

  • The Use of Communication Strategies by Second Language Learners of Chinese in a Virtual Reality Learning Environment

    Open Access•Hongzhi Yang, Linda Tsung et al.•SAGE Open•2022

  • Voice to validation

    Open Access•João Akio Ribeiro Yamaguchi•Policy Futures in Education•2025

  • Learning by Invention

    Andrew F Jarosz, Olga Goldenberg et al.•Discourse Processes•2017

  • Advances in research on composite instructional designs – investigating intermediate knowledge and preparation effects

    Open Access•Katharina Loibl, Valentina Nachtigall et al.•Instructional Science•2025

  • Flipping a simulation before instruction can improve students' learning, interest and perceived competence

    Open Access•Marci S Decaro, Derek K McClellan et al.•British Journal of Educational…•2025

  • Prior knowledge activation as preparation prior to instruction

    Open Access•Charleen Brand, Katharina Loibl et al.•Instructional Science•2025

  • When is observing failure productive? Investigating the role of solution diversity in vicarious failure

    Open Access•Thomas C Braas, Christian Hartmann et al.•Instructional Science•2025

  • Problem-solving before instruction for learning linear algebra in university mathematics

    Open Access•Vera Baumgartner, Simona Daguati et al.•Instructional Science•2025

  • Problem-solving prior to instructional explanations when learning javelin throwing in primary school

    Open Access•Christian Leukel, Katharina Loibl•Instructional Science•2025

  • Increasing contrasting cases during exploration or practice problems given before or after instruction

    Open Access•Marci S Decaro, Campbell R Bego et al.•Instructional Science•2025

  • Comparing effectiveness of exploratory learning activities given before instruction

    Open Access•Lianda Velić, Marci S Decaro•Instructional Science•2025

  • Supportive error feedback fosters students' adaptive reactions towards errors

    Open Access•Annalisa Soncini, Maria Cristina Matteucci et al.•British Journal of Educational…•2025

  • Designing novel activities before instruction

    Open Access•Campbell R Bego, Raymond J Chastain et al.•British Journal of Educational…•2023

  • Element interactivity as a factor influencing the effectiveness of worked example-problem solving and problem solving-worked example sequences

    Open Access•Olivia Chen, Endah Retnowati et al.•British Journal of Educational…•2020

  • Learning from errors and failure in educational contexts

    Open Access•Susanne Narci, Ecenaz Alemdag•British Journal of Educational…•2025

  • Inventing to Prepare for Future Learning

    Daniel L Schwartz, Taylor Martin•Cognition and Instruction•2004

  • The Expertise Reversal Effect

    Slava Kalyuga, Paul Ayres et al.•Educational Psychologist•2003

  • Training strategies for attaining transfer of problem-solving skill in statistics

    Fred Paas, Fred G W C Paas•Journal of Educational Psychology•1992

  • New Conceptualizations of Practice

    Open Access•Richard A Schmidt, Robert A Bjork•Psychological Science•1992

  • Practicing versus inventing with contrasting cases

    Daniel L Schwartz, Catherine C Chase et al.•Journal of Educational Psychology•2011

  • The double-edged sword of pedagogy

    Open Access•Elizabeth Bonawitz, Patrick Shafto et al.•Cognition•2011

  • The Equivalence of Learning Paths in Early Science Instruction

    Open Access•David Klahr, Milena Nigam et al.•Psychological Science•2004

  • Designing for Productive Failure

    Manu Kapur, Katerine Bielaczyc•Journal of the Learning Sciences•2012

  • Why Minimal Guidance During Instruction Does Not Work

    Paul A Kirschner, John Sweller et al.•Educational Psychologist•2006

Obras citantes distintas94
Citações por ano9,4
Intervalo de citações2016 - 2026 (11)
Velocidade de citaçãocurrent
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