Memory & Cognition

, Volume 42, Issue 5, pp 729–741 | Cite as

Contracting, equal, and expanding learning schedules: The optimal distribution of learning sessions depends on retention interval

  • Carolina E. Küpper-TetzelEmail author
  • Irina V. Kapler
  • Melody Wiseheart


In laboratory and applied learning experiments, researchers have extensively investigated the optimal distribution of two learning sessions (i.e., initial learning and one relearning session) for the learning of verbatim materials. However, research has not yet provided a satisfying and conclusive answer to the optimal scheduling of three learning sessions (i.e., initial learning and two relearning sessions) across educationally relevant time intervals. Should the to-be-learned material be repeated at decreasing intervals (contracting schedule), constant intervals (equal schedule), or increasing intervals (expanding schedule) between learning sessions? Different theories and memory models (e.g., study-phase retrieval theory, contextual variability theory, ACT-R, and the Multiscale Context Model) make distinct predictions about the optimal learning schedule. We discuss the extant theories and derive clear predictions from each of them. To test these predictions empirically, we conducted an experiment in which participants studied and restudied paired associates with a contracting, equal, or expanding learning schedule. Memory performance was assessed immediately, 1 day, 7 days, or 35 days later with free- and cued-recall tests. Our results revealed that the optimal learning schedule is conditional on the length of the retention interval: A contracting learning schedule was beneficial for retention intervals up to 7 days, but both equal and expanding learning schedules were better for a long retention interval of 35 days. Our findings can be accommodated best by the contextual variability theory and indicate that revisions are needed to existing memory models. Our results are practically relevant, and their implications for real-world learning are discussed.


Memory Memory models Long-term retention Distributed practice Learning schedule Theory evaluation 


Author Note

The first author acknowledges support from the Ontario/Baden-Württemberg Faculty Mobility Program of the Ministry for Science, Research, and Arts of Baden-Württemberg, Germany, and from a postdoc fellowship from the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG). We are grateful to the Faculty of Health at York University in Toronto, Canada, for supporting this project with a Minor Research Grant and an SSHRC Small Grant. We thank Masa Calic, Suzette Fernandez, and Ariella Winter for their assistance with data collection, and Tina Weston for helpful comments on a previous draft of this article.


  1. Bahrick, H. P., & Hall, L. K. (1991). Lifetime maintenance of high school mathematics content. Journal of Experimental Psychology: General, 120, 20–33. doi: 10.1037/0096-3445.120.1.20 CrossRefGoogle Scholar
  2. Balota, D. A., Duchek, J. M., & Logan, J. M. (2007). Is expanded retrieval practice a superior form of spaced retrieval? A critical review of the extant literature. In J. S. Nairne (Ed.), The foundations of remembering: Essays in honor of Henry L. Roediger III (pp. 83–105). New York, NY: Psychology Press.Google Scholar
  3. Bellezza, F. S., & Young, D. R. (1989). Chunking of repeated events in memory. Journal of Experimental Psychology: Learning, Memory, and Cognition, 15, 990–997. doi: 10.1037/0278-7393.15.5.990 Google Scholar
  4. Braun, K., & Rubin, D. C. (1998). The spacing effect depends on an encoding deficit, retrieval, and time in working memory: Evidence from once-presented words. Memory, 6, 37–65. doi: 10.1080/741941599 PubMedCrossRefGoogle Scholar
  5. Carpenter, S. K., & DeLosh, E. L. (2005). Application of the testing and spacing effects to name learning. Applied Cognitive Psychology, 19, 619–636. doi: 10.1002/acp.1101 CrossRefGoogle Scholar
  6. Cepeda, N. J., Coburn, N., Rohrer, D., Wixted, J. T., Mozer, M. C., & Pashler, H. (2009). Optimizing distributed practice: Theoretical analysis and practical implications. Experimental Psychology, 56, 236–246. doi: 10.1027/1618-3169.56.4.236 PubMedCrossRefGoogle Scholar
  7. Cepeda, N. J., Pashler, H., Vul, E., Wixted, J. T., & Rohrer, D. (2006). Distributed practice in verbal recall tasks: A review and quantitative synthesis. Psychological Bulletin, 132, 354–380. doi: 10.1037/0033-2909.132.3.354 PubMedCrossRefGoogle Scholar
  8. Cepeda, N. J., Vul, E., Rohrer, D., Wixted, J. T., & Pashler, H. (2008). Spacing effects in learning: A temporal ridgeline of optimal retention. Psychological Science, 19, 1095–1102. doi: 10.1111/j.1467-9280.2008.02209.x PubMedCrossRefGoogle Scholar
  9. Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum.Google Scholar
  10. Cull, W. L. (2000). Untangling the benefits of multiple study opportunities and repeated testing for cued recall. Applied Cognitive Psychology, 14, 215–235. doi: 10.1002/(SICI)1099-0720(200005/06)14:3<215::AID-ACP640>3.0.CO;2-1 CrossRefGoogle Scholar
  11. Cull, W. L., Shaughnessy, J. J., & Zechmeister, E. B. (1996). Expanding understanding of the expanding-pattern-of-retrieval mnemonic: Toward confidence in applicability. Journal of Experimental Psychology: Applied, 2, 365–378. doi: 10.1037/1076-898X.2.4.365 Google Scholar
  12. Ebbinghaus, H. (1964). Memory: A contribution to experimental psychology. Oxford, UK: Dover. Original work published 1885.Google Scholar
  13. Estes, W. K. (1955). Statistical theory of distributional phenomena in learning. Psychological Review, 62, 369–377. doi: 10.1037/h0046888 PubMedCrossRefGoogle Scholar
  14. Gerbier, E., & Koenig, O. (2012). Influence of multiple-day temporal distribution of repetitions on memory: A comparison of uniform, expanding, and contracting schedules. The Quarterly Journal of Experimental Psychology, 65, 514–525. doi: 10.1080/17470218.2011.600806 PubMedCrossRefGoogle Scholar
  15. Glenberg, A. M. (1979). Component-levels theory of the effects of spacing of repetitions on recall and recognition. Memory & Cognition, 7, 95–112. doi: 10.3758/BF03197590 CrossRefGoogle Scholar
  16. Glenberg, A. M., & Lehmann, T. S. (1980). Spacing repetitions over 1 week. Memory & Cognition, 8, 528–538. doi: 10.3758/BF03213772 CrossRefGoogle Scholar
  17. Henrich, J., Heine, S. J., & Norenzayan, A. (2010). The weirdest people in the world? Behavioral and Brain Sciences, 33, 61–83. doi: 10.1017/S0140525X0999152X PubMedCrossRefGoogle Scholar
  18. Karpicke, J. D., & Bauernschmidt, A. (2011). Spaced retrieval: Absolute spacing enhances learning regardless of relative spacing. Journal of Experimental Psychology: Learning, Memory, and Cognition, 37, 1250–1257. doi: 10.1037/a0023436 PubMedGoogle Scholar
  19. Karpicke, J. D., Butler, A. C., & Roediger, H. L., III. (2009). Metacognitive strategies in student learning: Do students practise retrieval when they study on their own? Memory, 17, 471–479. doi: 10.1080/09658210802647009 PubMedCrossRefGoogle Scholar
  20. Karpicke, J. D., & Roediger, H. L., III. (2007). Expanding retrieval practice promotes short-term retention, but equally spaced retrieval enhances long-term retention. Journal of Experimental Psychology: Learning, Memory, and Cognition, 33, 704–719. doi: 10.1037/0278-7393.33.4.704 PubMedGoogle Scholar
  21. Karpicke, J. D., & Roediger, H. L., III. (2010). Is expanding retrieval a superior method for learning text materials? Memory & Cognition, 38, 116–124. doi: 10.3758/MC.38.1.116 CrossRefGoogle Scholar
  22. Küpper-Tetzel, C. E., & Erdfelder, E. (2012). Encoding, maintenance, and retrieval processes in the lag effect: A multinomial processing tree analysis. Memory, 20, 37–47. doi: 10.1080/09658211.2011.631550 PubMedCrossRefGoogle Scholar
  23. Küpper-Tetzel, C. E., Erdfelder, E., & Dickhäuser, O. (2013). The lag effect in secondary school classrooms: Enhancing students’ memory for vocabulary. Instructional Science. Advance online publication. doi: 10.1007/s11251-013-9285-2
  24. Landauer, T. K., & Bjork, R. A. (1978). Optimum rehearsal patterns and name learning. In M. M. Gruneberg, P. E. Morris, R. N. Sykes, & the British Psychological Society (Eds.), Practical aspects of memory (pp. 625–632). London, UK: Academic Press.Google Scholar
  25. Lindsey, R., Mozer, M. C., Cepeda, N. J., & Pashler, H. (2009). Optimizing memory retention with cognitive models. In A. Howes, D. Peebles, & R. Cooper (Eds.), Proceedings of the Ninth International Conference on Cognitive Modeling (ICCM 2009) (pp. 74–79). Manchester, UK: ICCM.Google Scholar
  26. Logan, J. M., & Balota, D. A. (2008). Expanded vs. equal interval spaced retrieval practice: Exploring different schedules of spacing and retention interval in younger and older adults. Aging, Neuropsychology, and Cognition, 15, 257–280. doi: 10.1080/13825580701322171 CrossRefGoogle Scholar
  27. Mozer, M. C., Pashler, H., Cepeda, N. J., Lindsey, R., & Vul, E. (2009). Predicting the optimal spacing of study: A multiscale context model of memory. In Y. Bengio, D. Schuurmans, J. Lafferty, C. K. I. Williams, & A. Culotta (Eds.), Advances in neural information processing systems (pp. 1321–1329). La Jolla, CA: NIPS Foundation.Google Scholar
  28. Pashler, H., Cepeda, N. J., Wixted, J. T., & Rohrer, D. (2005). When does feedback facilitate learning of words? Journal of Experimental Psychology: Learning, Memory, and Cognition, 31, 3–8. doi: 10.1037/0278-7393.31.1.3 PubMedGoogle Scholar
  29. Pashler, H., Rohrer, D., Cepeda, N. J., & Carpenter, S. K. (2007). Enhancing learning and retarding forgetting: Choices and consequences. Psychonomic Bulletin & Review, 14, 187–193. doi: 10.3758/BF03194050 CrossRefGoogle Scholar
  30. Pavlik, P. I., & Anderson, J. R. (2008). Using a model to compute the optimal schedule of practice. Journal of Experimental Psychology: Applied, 14, 101–117. doi: 10.1037/1076-898X.14.2.101 PubMedGoogle Scholar
  31. Raaijmakers, J. G. (2003). Spacing and repetition effects in human memory: Application of the SAM model. Cognitive Science, 27, 431–452. doi: 10.1207/s15516709cog2703_5 CrossRefGoogle Scholar
  32. Staddon, J. E. R., Chelaru, I. M., & Higa, J. J. (2002). Habituation, memory and the brain: The dynamics of interval timing. Behavioural Processes, 57, 71–88. doi: 10.1016/S0376-6357(02)00006-2 PubMedCrossRefGoogle Scholar
  33. Thios, S. J., & D’Agostino, P. R. (1976). Effects of repetition as a function of study-phase retrieval. Journal of Verbal Learning & Verbal Behavior, 15, 529–536. doi: 10.1016/0022-5371(76)90047-5 CrossRefGoogle Scholar
  34. Toppino, T. C., Hara, Y., & Hackman, J. (2002). The spacing effect in the free recall of homogeneous lists: Present and accounted for. Memory & Cognition, 30, 601–606. doi: 10.3758/BF03194961 CrossRefGoogle Scholar
  35. Tsai, L. S. (1927). The relation of retention to the distribution of relearning. Journal of Experimental Psychology, 10, 30–39. doi: 10.1037/h0071614 CrossRefGoogle Scholar

Copyright information

© Psychonomic Society, Inc. 2014

Authors and Affiliations

  • Carolina E. Küpper-Tetzel
    • 1
    • 2
    Email author
  • Irina V. Kapler
    • 3
    • 4
  • Melody Wiseheart
    • 3
    • 4
  1. 1.Center for Integrative Research on Cognition, Learning, and Education (CIRCLE)Washington University in St. LouisSt. LouisUSA
  2. 2.Department of PsychologyUniversity of MannheimMannheimGermany
  3. 3.Department of PsychologyYork UniversityTorontoCanada
  4. 4.LaMarsh Centre for Child and Youth ResearchYork UniversityTorontoCanada

Personalised recommendations