How the amount and spacing of retrieval practice affect the short- and long-term retention of mathematics knowledge
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Non-randomized interventions, assessed using ROBINS-I, showed moderate to low risks, particularly regarding participant selection and confounding variables.
“Non-randomized interventions, assessed using ROBINS-I, showed moderate to low risks, particularly regarding participant selection and confounding variables (Lyle et al., 2020;Taveira-Gomes et al., 2015).”
From Systematic Review of the Effectiveness of Neurodidactic Spaced Learning Strategies in Long-Term Memory (2026) · cites this paper as Lyle et al., 2020
Several studies employed within-subject designs to control for individual student variability.
“Furthermore, several studies employed within-subject designs to control for individual student variability, effectively comparing massed versus distributed retrieval practice within the same cohorts of engineering, medicine, and language students”
From Systematic Review of the Effectiveness of Neurodidactic Spaced Learning Strategies in Long-Term Memory (2026) · cites this paper as Lyle et al., 2020
In studies such as Lyle et al. (2020) and Taveira-Gomes et al. (2015), the lack of formal randomization introduced potential confounding variables-such as prior knowledge or varying levels of baseline cognitive load-which may have interacted with the spacing effect.
“In studies such as those of Lyle et al. (2020) and Taveira-Gomes et al. (2015), the lack of formal randomization introduced potential confounding variables-such as prior knowledge or varying levels of baseline cognitive load-which may have interacted with the spacing effect.”
From Systematic Review of the Effectiveness of Neurodidactic Spaced Learning Strategies in Long-Term Memory (2026) · cites this paper as Lyle et al., 2020
Cites
Dunlosky, J., Rawson, K. A., Marsh, E. J., Nathan, M. J., & Willingham, D. T. (2013) · Psychological Science in the Public Interest · doi:10.1177/1529100612453266 · Cited by 3,138 · see citing works
Test-Enhanced Learning: Taking Memory Tests Improves Long-Term Retention
Roediger, H. L., & Karpicke, J. D. (2006) · Psychological Science · doi:10.1111/j.1467-9280.2006.01693.x · Cited by 2,867 · see citing works
The power of testing memory: Basic research and implications for educational practice
Roediger, H. L., & Karpicke, J. D. (2006) · Perspectives on Psychological Science · doi:10.1111/j.1745-6916.2006.00012.x · Cited by 2,037 · see citing works
Distributed practice in verbal recall tasks: A review and quantitative synthesis.
Cepeda, N. J., Pashler, H., Vul, E., Wixted, J. T., & Rohrer, D. (2006) · Psychological Bulletin · doi:10.1037/0033-2909.132.3.354 · Cited by 1,888 · see citing works
The effect of testing versus restudy on retention: A meta-analytic review of the testing effect.
Rowland, C. A. (2014) · Psychological Bulletin · doi:10.1037/a0037559 · Cited by 1,066 · see citing works
(2011) · Cited by 725 · see citing works
Learning Versus Performance: An Integrative Review
Soderstrom, N. C., & Bjork, R. A. (2015) · Perspectives on Psychological Science · doi:10.1177/1745691615569000 · Cited by 651 · see citing works
Spacing Effects in Learning: A Temporal Ridgeline of Optimal Retention
Cepeda, N. J., Vul, E., Rohrer, D., Wixted, J. T., & Pashler, H. (2008) · Psychological Science · doi:10.1111/j.1467-9280.2008.02209.x · Cited by 631 · see citing works
Testing the testing effect in the classroom
McDaniel, M. A., Anderson, J. L., Derbish, M. H., & Morrisette, N. (2007) · European Journal of Cognitive Psychology · doi:10.1080/09541440701326154 · Cited by 563 · see citing works
Pyc, M. A., & Rawson, K. A. (2009) · Journal of Memory and Language · doi:10.1016/j.jml.2009.01.004 · Cited by 551 · see citing works
Rethinking the Use of Tests: A Meta-Analysis of Practice Testing
Adesope, O. O., Trevisan, D. A., & Sundararajan, N. (2017) · Review of Educational Research · doi:10.3102/0034654316689306 · Cited by 544 · see citing works
Carpenter, S. K., Cepeda, N. J., Rohrer, D., Kang, S. H. K., & Pashler, H. (2012) · Educational Psychology Review · doi:10.1007/s10648-012-9205-z · Cited by 469 · see citing works
(1992) · Cited by 464 · see citing works
Karpicke, J. D., & Roediger, H. L. (2007) · Journal of Experimental Psychology: Learning, Memory, and Cognition · doi:10.1037/0278-7393.33.4.704 · Cited by 421 · see citing works
Spaced Repetition Promotes Efficient and Effective Learning: Policy Implications for Instruction
Kang, S. H. K. (2016) · Policy Insights from the Behavioral and Brain Sciences · doi:10.1177/2372732215624708 · Cited by 408 · see citing works
Hintzman, D. L. (1976) · Psychology of Learning and Motivation · doi:10.1016/s0079-7421(08)60464-8 · Cited by 388 · see citing works
McDaniel, M. A., Agarwal, P. K., Huelser, B. J., McDermott, K. B., & Roediger, H. L. (2011) · Journal of Educational Psychology · doi:10.1037/a0021782 · Cited by 360 · see citing works
Roediger, H. L., III, & Pyc, M. A. (2012) · Journal of Applied Research in Memory and Cognition · doi:10.1016/j.jarmac.2012.09.002 · Cited by 310 · see citing works
Optimizing schedules of retrieval practice for durable and efficient learning: How much is enough?
Rawson, K. A., & Dunlosky, J. T. (2011) · Journal of Experimental Psychology General · doi:10.1037/a0023956 · Cited by 307 · see citing works
Optimizing distributed practice
Cepeda, N. J., Coburn, N., Rohrer, D., Wixted, J. T., Mozer, M. C., & Pashler, H. (2009) · Experimental Psychology · doi:10.1027/1618-3169.56.4.236 · Cited by 296 · see citing works
Karpicke, J. D. (2012) · Current Directions in Psychological Science · doi:10.1177/0963721412443552 · Cited by 286 · see citing works
Retrieval-Based Learning: An Episodic Context Account
Karpicke, J. D., Lehman, M. S., & Aue, W. R. (2012) · Current Directions in Psychological Science · Cited by 276 · see citing works
Spaced retrieval: Absolute spacing enhances learning regardless of relative spacing.
Karpicke, J. D., & Kaminske, A. N. (2011) · Journal of Experimental Psychology Learning Memory and Cognition · doi:10.1037/a0023436 · Cited by 263 · see citing works
The effects of overlearning and distributed practise on the retention of mathematics knowledge
Rohrer, D., & Taylor, K. (2006) · Applied Cognitive Psychology · doi:10.1002/acp.1266 · Cited by 250 · see citing works
Bloom, K. C., & Shuell, T. J. (1981) · The Journal of Educational Research · doi:10.1080/00220671.1981.10885317 · Cited by 243 · see citing works
Testing Enhances the Transfer of Learning
Carpenter, S. K. (2012) · Current Directions in Psychological Science · doi:10.1177/0963721412452728 · Cited by 230 · see citing works
The Exam-A-Day Procedure Improves Performance in Psychology Classes
Leeming, F. C. (2002) · Teaching of Psychology · doi:10.1207/s15328023top2903_06 · Cited by 222 · see citing works
Retrieval-Based Learning: Active Retrieval Promotes Meaningful Learning
Karpicke, J. D. (2012) · Current Directions in Psychological Science · Cited by 198 · see citing works
Retrieving Essential Material at the End of Lectures Improves Performance on Statistics Exams
Lyle, K. B., & Crawford, N. A. (2011) · Teaching of Psychology · doi:10.1177/0098628311401587 · Cited by 180 · see citing works
Self-citationMcDaniel, M. A., Wildman, K. M., & Anderson, J. L. (2012) · Journal of Applied Research in Memory and Cognition · doi:10.1016/j.jarmac.2011.10.001 · Cited by 177 · see citing works
Effects of repetition as a function of study-phase retrieval
Thios, S. J., & D'Agostino, P. R. (1976) · Journal of Verbal Learning and Verbal Behavior · doi:10.1016/0022-5371(76)90047-5 · Cited by 171 · see citing works
Interleaved practice improves mathematics learning.
Rohrer, D., Dedrick, R. F., & Stershic, S. (2015) · Journal of Educational Psychology · doi:10.1037/edu0000001 · Cited by 164 · see citing works
The Power of Successive Relearning: Improving Performance on Course Exams and Long-Term Retention
Rawson, K. A., Dunlosky, J., & Sciartelli, S. M. (2013) · Educational Psychology Review · doi:10.1007/s10648-013-9240-4 · Cited by 148 · see citing works
Five Popular Study Strategies: Their Pitfalls and Optimal Implementations
Miyatsu, T., Nguyen, K., & McDaniel, M. A. (2018) · Perspectives on Psychological Science · doi:10.1177/1745691617710510 · Cited by 145 · see citing works
Hopkins, R. F., Lyle, K. B., Hieb, J. L., & Ralston, P. A. S. (2016) · Educational Psychology Review · doi:10.1007/s10648-015-9349-8 · Cited by 136 · see citing works
Self-citationEffects of Repetition as a Function of Study-Phase Retrieval
Thios, S. J., D’Agostino, P. R., & Lovelace, E. A. (1975) · PsycEXTRA Dataset · doi:10.1037/e666602011-347 · Cited by 136 · see citing works
Rohrer, D., Dedrick, R. F., & Burgess, K. (2014) · Psychonomic Bulletin & Review · doi:10.3758/s13423-014-0588-3 · Cited by 122 · see citing works
Toppino, T. C., & Gerbier, É. (2013) · The Psychology of learning and motivation/The psychology of learning and motivation · doi:10.1016/b978-0-12-800090-8.00004-4 · Cited by 116 · see citing works
Kapler, I. V., Weston, T., & Wiseheart, M. (2015) · Learning and Instruction · doi:10.1016/j.learninstruc.2014.11.001 · Cited by 101 · see citing works
The effect of overlearning on long‐term retention
Rohrer, D., Taylor, K., Pashler, H., Wixted, J. T., & Cepeda, N. J. (2004) · Applied Cognitive Psychology · doi:10.1002/acp.1083 · Cited by 100 · see citing works
Student Instruction Should Be Distributed Over Long Time Periods
Rohrer, D. (2015) · Educational Psychology Review · doi:10.1007/s10648-015-9332-4 · Cited by 97 · see citing works
Massed versus distributed practice in computerized spelling drills.
Fishman, E. J., Keller, L., & Atkinson, R. C. (1968) · Journal of Educational Psychology · doi:10.1037/h0020055 · Cited by 65 · see citing works
Diagnosing Criterion-Level Effects on Memory
Vaughn, K. E., & Rawson, K. A. (2011) · Psychological Science · doi:10.1177/0956797611417724 · Cited by 65 · see citing works
Practice versus Review Exams and Final Exam Performance
Balch, W. R. (1998) · Teaching of Psychology · doi:10.1207/s15328023top2503_3 · Cited by 59 · see citing works
Spreading the words: A spacing effect in vocabulary learning
Goossens, N. A. M. C., Camp, G., Verkoeijen, P. P. J. L., Tabbers, H. K., & Zwaan, R. A. (2012) · Journal of Cognitive Psychology · doi:10.1080/20445911.2012.722617 · Cited by 45 · see citing works
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The science of effective learning with spacing and retrieval practice
Carpenter, S. K., Pan, S. C., & Butler, A. C. (2022) · Nature Reviews Psychology · doi:10.1038/s44159-022-00089-1 · Cited by 184 · see citing works
Spaced Retrieval Practice Imposes Desirable Difficulty in Calculus Learning
Lyle, K. B., Bego, C. R., Ralston, P. A. S., & Immekus, J. C. (2022) · Educational Psychology Review · doi:10.1007/s10648-022-09677-2 · Cited by 31 · see citing works
“This is consistent with the idea that spacing induces desirable difficulty, as argued in a prior study of precalculus (Lyle et al., 2020; see also Rohrer & Taylor, 2006).”
BackgroundResultInfluentialSelf-citationThe benefits of successive relearning on multiple learning outcomes.
Higham, P. A., Zengel, B., Bartlett, L. K., & Hadwin, J. A. (2022) · Journal of Educational Psychology · doi:10.1037/edu0000693 · Cited by 23 · see citing works
Vemu, S., Denaro, K., Sato, B. K., & Williams, A. E. (2022) · CBE—Life Sciences Education · doi:10.1187/cbe.21-08-0216 · Cited by 15 · see citing works
“College students in a pre-calculus course showed a significant improvement in an exam the next semester when quiz questions also contained questions from past learning objectives rather than focusing on only the current objectives (Hopkins et al. , 2016; Lyle et al. , 2020).”
Using Spacing to Promote Lasting Learning in Educational Contexts: Promises and Challenges
Ebersbach, M., Lachner, A., Scheiter, K., & Richter, T. (2022) · Zeitschrift für Entwicklungspsychologie und Pädagogische Psychologie · doi:10.1026/0049-8637/a000259 · Cited by 14 · see citing works
The Distributed Practice Effect on Classroom Learning: A Meta-Analytic Review of Applied Research
Mawson, R. D., & Kang, S. H. K. (2025) · Behavioral Sciences · doi:10.3390/bs15060771 · Cited by 14 · see citing works
“…preceding 10 years likely add valuable information relevant to the application of distributed practice to classroom learning (e.g., Barzagar Nazari & Ebersbach, 2019a; Barzagar Nazari & Ebersbach, 2019b; Foot-Seymour et al., 2019; Greving & Richter, 2021; Lyle et al., 2019; Svihla et al., 2017).”
Bego, C. R., Lyle, K. B., Ralston, P. A. S., Immekus, J. C., Chastain, R. J., Haynes, L. D., Hoyt, L. K., Pigg, R. M., Rabin, S. D., Scobee, M. W., et al. (2024) · International Journal of STEM Education · doi:10.1186/s40594-024-00468-5 · Cited by 12 · see citing works
Self-citationMurray, E., Horner, A. J., & Göbel, S. M. (2025) · Educational Psychology Review · doi:10.1007/s10648-025-10035-1 · Cited by 4 · see citing works
Testing the testing effect with advanced materials while accounting for individual differences
Redifer, J. L., Myers, S. J., Bae, C. L., Naas, A., & Scott, A. (2026) · Instructional Science · doi:10.1007/s11251-025-09758-z · Cited by 2 · see citing works
Silva Sánchez, M., Lainez Quinde, G. A., & Zambrano Vélez, W. A. (2026) · Education Sciences · doi:10.3390/educsci16060962
“Non-randomized interventions, assessed using ROBINS-I, showed moderate to low risks, particularly regarding participant selection and confounding variables (Lyle et al., 2020; Taveira-Gomes et al., 2015).”
Influential
- Authors
- Lyle, K. B., Bego, C. R., Hopkins, R. F., Hieb, J. L., & Ralston, P. A. S.
- Affiliations
- University of Louisville (US)
- Corresponding author
- Lyle, Keith B.
- Venue
- Educational Psychology Review
- Published
- 2019-06-06
- Volume
- 32
- Issue
- 1
- Pages
- 277-295
- ISSN
- 1040-726X (ISSN-L)
- 1573-336X
- OpenAlex
- W2949036105
- Cited by
- 103
- References
- 45
- Citations by year
- 2026: 9 · 2025: 22 · 2024: 29 · 2023: 10 · 2022: 14 · 2021: 8 · 2020: 9 · 2019: 2
- FWCI
- 4.78
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Educational Psychology Review (publishedVersion)
- Funders
- National Science Foundation (NSF DUE-IUSE 1609290)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Memory Processes and Influences
- Physical Sciences › Mathematics › Applied Mathematics › Mathematics Education and Pedagogy
- Social Sciences › Education › Mathematics Education and Teaching Techniques
- Keywords
- retrieval practice, spacing effect, memory retention, mathematics learning, precalculus, engineering students, long-term retention
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