Interleaved practice in multi-dimensional learning tasks: Which dimension should we interleave?

Learning and Instruction

Volumn 23, Issue 1, 2013, Pages 98-114

  Rau, Martina A ^a   Aleven, Vincent ^a   Rummel, Nikol ^b  

^a Carnegie Mellon University ^*  (United States)

^b RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

Classroom evaluation; Contextual interference; Fractions; Multiple representations; Multiple task types

Indexed keywords

EID: 84868640987     PISSN: 09594752     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.learninstruc.2012.07.003     Document Type: Article

References (100)

1. Ainsworth S. DeFT: a conceptual framework for considering learning with multiple representations. Learning and Instruction 2006, 16(3):183-198. 10.1016/j.learninstruc.2006.03.001.
2. Ainsworth S.E., Bibby P.A., Wood D.J. Analysing the costs and benefits of multi-representational learning environments. Learning with multiple representations 1998, Oxford, Pergamon. M.W. van Someren, P. Reimann, H.P.A. Boshuizen, T. de Jong (Eds.).
3. Ainsworth S., Bibby P., Wood D. Examining the effects of different multiple representational systems in learning primary mathematics. Journal of the Learning Sciences 2002, 11(1):25-61. 10.1207/S15327809JLS1101_2.
4. Aleven V., Koedinger K.R. An effective meta-cognitive strategy: learning by doing and explaining with a computer-based Cognitive Tutor. Cognitive Science 2002, 26(2):147-179. 10.1207/s15516709cog2602_1.
5. Aleven V., McLaren B.M., Sewall J., Koedinger K.R. Example-tracing tutors: a new paradigm for intelligent tutoring systems. International Journal of Artificial Intelligence in Education 2009, 19(2):105-154.
6. Anderson J.R. Rules of the mind 1993, Lawrence Erlbaum Associates, Inc, Hillsdale, NJ, England.
7. Anderson J.R. ACT: A simple theory of complex cognition 2002, MIT Press, Cambridge, MA, US.
8. Anderson J.R., Corbett A.T., Koedinger K.R., Pelletier R. Cognitive tutors: lessons learned. Journal of the Learning Sciences 1995, 4(2):167-207. 10.1207/s15327809jls0402_2.
9. Arbuckle J.L., Wothke AMOS 4.0 User's Guide (S. 395-416) 1999, Small Waters Corp, Chicago.
10. Baker R.S.J.d., Corbett A.T., Koedinger K.R. The difficulty factors approach to the design of lessons in intelligent tutor curricula. International Journal of Artificial Intelligence in Education 2007, 17(4):341-369.
11. Bahrick H.P., Bahrick L.E., Bahrick A.S., Bahrick P.E. Maintenance of foreign-language vocabulary and the spacing effect. Psychological Science 1993, 4(5):316-321. 10.1111/j.1467-9280.1993.tb00571.x.
12. Bannert M. Managing cognitive load - recent trends in cognitive load theory. Learning and Instruction 2002, 12(1):139-146. 10.1016/S0959-4752(01)00021-4.
13. Baranes R., Perry M., Stigler J. Activation of real-world knowledge in the solution of word problems. Cognition and Instruction 1989, 6:287-318. 10.1207/s1532690xci0604_1.
14. Battig W.F. Intratask interference as a source of facilitation in transfer and retention. Topics in learning and performance 1972, 131-159. Academic Press, New York. R.F. Thompson, J.F. Vos (Eds.).
15. Bennett J.M. Holt middle school math 2004, Holt Rinehart & Winston.
16. Bodemer D., Faust U. External and mental referencing of multiple representations. Computers in Human Behavior 2006, 22(1):27-42. 10.1016/j.chb.2005.01.005.
17. Bodemer D., Ploetzner R., Feuerlein I., Spada H. The active integration of information during learning with dynamic and interactive visualisations. Learning and Instruction 2004, 14(3):325-341. 10.1016/j.learninstruc.2004.06.006.
18. Butcher K.R. Learning from text with diagrams: promoting mental model development and inference generation. Journal of Educational Psychology 2006, 98(1):182-197. 10.1037/0022-0663.98.1.182.
19. Caldwell J.H. Communicating about fractions with pattern blocks. Teaching Children Mathematics 1995, 1(9):156-161.
20. Carraher T., Carraher D., Schliemann A. Written and oral mathematics. Journal for Research in Mathematics Education 1987, 18(2):83-97. 10.2307/749244.
21. Cepeda N.J., Pashler H., Vul E., Wixted J.T., Rohrer D. Distributed practice in verbal recall tasks: a review and quantitative synthesis. Psychological Bulletin 2006, 132(3):354-380. 10.1037/0033-2909.132.3.354.
22. Charalambous C.Y., Pitta-Pantazi D. Drawing on a theoretical model to study students' understandings of fractions. Educational Studies in Mathematics 2007, 64(3):293-316. 10.1007/s10649-006-9036-2.
23. Clark R.E., Feldon D.F., Van Merrienboer J.J.G., Yates K.A., Early S. Cognitive task analysis. Handbook of research on educational communications and technology 2008, 577-594. Lawrence Erlbaum Associates, Mahwah, NJ. J.M. Spector, M.D. Merrill, J.J.G. Van Merriënboer, M.P. Driscoll (Eds.).
24. Cohen J. Statistical power analysis for the behavioral sciences 1988, Lawrence Erlbaum Associates, Hillsdale, NJ. 2 ed.
25. Common Core State Standards Initiative Common core state standards (Mathematics standards) 2010, Retrieved 07.04.11 from. http://www.corestandards.org/the-standards/mathematics.
26. Corbett A.T., Koedinger K., Hadley W.S. Cognitive tutors: from the research classroom to all classrooms. Technology enhanced learning: Opportunities for change 2001, 235-263. Lawrence Erlbaum Associates Publishers, Mahwah, NJ, US. P.S. Goodman (Ed.).
27. Cramer K., Behr M., Post R., Lesh R. Rational number project: Fraction lessons for the middle grades: Level 1 1997, Kendall/Hunt Publishing, Dubuque, IA.
28. Cramer K., Behr M., Post R., Lesh R. Rational number project: Fraction lessons for the middle grades: Level 2 1997, Kendall/Hunt Publishing, Dubuque, IA.
29. Cramer K.A., Post T.R., delMas R.C. Initial fraction learning by fourth- and fifth-grade students: a comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum. Journal for Research in Mathematics Education 2002, 33(2):111-144. 10.2307/749646.
30. Cramer K., Wyberg T., Leavitt S. Rational number project 2009, Fraction Operations & Initial Decimal Ideas.
31. De Croock M.B.M., Van Merrienboer J.J.G., Paas F. High versus low contextual interference in simulation-based training of troubleshooting skills: effects on transfer performance and invested mental effort. Computers in Human Behavior 1998, 14(2):249-267. 10.1016/S0747-5632(98)00005-3.
32. De Jong T., Ainsworth S.E., Dobson M., Van der Meij J., Levonen J., Reimann P., et al. Acquiring knowledge in science and mathematics: the use of multiple representations in technology-based learning environments. Learning with multiple representations 1998, (Oxford). M.W. Van Someren, W. Reimers, H.P.A. Boshuizen, T. de Jong (Eds.).
33. Eliam B., Poyas Y. Learning with multiple representations: extending multimedia learning beyond the lab. Learning and Instruction 2008, 18(4):368-378. 10.1016/j.learninstruc.2007.07.003.
34. Fitzgerald F., Lappan P., Fey J.T. Connected mathematics (number and operations grade 6, bits and pieces I, understanding rational numbers) 2004, Pearson Prentice Hall.
35. French K.E., Rink J.E., Werner P.H. Effects of contextual interference on retention of three volleyball skills. Perceptual and Motor Skills 1990, 71:179-186.
36. Goldman S.R. Learning in complex domains: when and why do multiple representations help?. Learning and Instruction 2003, 13(2):239-244. 10.1016/S0959-4752(02)00023-3.
37. Hake S. Saxon math 5/6 2004, Saxon Pub.
38. Hebert E.P., Landin D., Solmon M.A. Practice schedule effects on the performance and learning of low- and high-skilled students: an applied study. Research Quarterly for Exercise and Sport 1996, 67(1):52-58.
39. Helsdingen A., van Gog T., Van Merrienboer J.J.G. The effects of practice schedule and critical thinking prompts on learning and transfer of a complex judgement task. Journal of Educational Psychology 2011, 103(2):383-398. 10.1037/a0022370.
40. Immink M.A., Wright D.L. Contextual interference: a response planning account. The Quarterly Journal of Experimental Psychology A: Human Experimental Psychology 1998, 51(4):735-754. 10.1080/027249898391369.
41. Jones L.I., French K.E. Effects of contextual interference on acquisition and retention of three volleyball skills. Perceptual and Motor Skills 2007, 105:883-890.
42. Kilpatrick J., Swafford J., Findell B. Adding it up: Helping children learn mathematics 2001, National Academy Press, Washington, DC.
43. Kline R.B. Principles and practice of structural equation modeling 1998, Guilford Press, New York.
44. Koedinger K.R. Toward evidence for instructional design principles: examples from Cognitive Tutor Math 6. Proceedings of twenty-fourth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education 2002, Vol. 1:21-49. ERIC Clearinghouse for Science, Mathematics, and Environmental Education, Columbus, OH.
45. Koedinger K.R., Aleven V. Exploring the assistance dilemma in experiments with Cognitive Tutors. Educational Psychology Review 2007, 19(3):239-264. 10.1007/s10648-007-9049-0.
46. Koedinger K.R., Baker R.S.J.d, Cunningham K., Skogsholm A., Leber B., Stamper J. A data repository for the EDM community: the PSLC DataShop. Handbook of educational data mining 2010, 10-12. CRC Press, Boca Raton, FL. C. Romero, S. Ventura, M. Pechenizkiy, R. Baker (Eds.).
47. Koedinger K.R., Corbett A. Cognitive tutors: Technology bringing learning sciences to the classroom 2006, Cambridge University Press, New York, NY, US.
48. Koedinger, K. R., Corbett, A. T., & Perfetti, C. The knowledge-learning-instruction (KLI) framework: bridging the science-practice chasm to enhance robust student learning. Cognitive Science, in press.
49. Koedinger K., Nathan M. The real story behind story problems: effects of representations on quantitative reasoning. Journal of the Learning Sciences 2004, 13(2):129-164. 10.1207/s15327809jls1302_1.
50. Kozma R. The material features of multiple representations and their cognitive and social affordances for science understanding. Learning and Instruction 2003, 13(2):205-226. 10.1016/S0959-4752(02)00021-X.
51. Lamon S. Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers 2005, Lawrence Erlbaum Assoc Inc, US. 2 ed.
52. Lappan G., Fey J.T., Fitzgerald W.M. Bits & pieces: Understanding rational numbers (Connected math series: Number) 1998, Dale Seymour Publications.
53. Lee T.D., Magill R.A. The locus of contextual interference in motor-skill acquisition. Journal of Experimental Psychology: Learning, Memory, and Cognition 1983, 9:730-746. 10.1037//0278-7393.9.4.730.
54. Lee T.D., Magill R.A. Can forgetting facilitate skill acquisition?. Differing perspectives in motor learning, memory, and control 1985, 3-22. Elsevier, Amsterdam, the Netherlands. D. Goodman, R.B. Wilberg, I.M. Franks (Eds.).
55. Lee T.D., Simon D.A. Contextual interference. Skill acquisition in sport: Research, theory and practice 2004, 29-44. Routledge, London, United Kingdom. A.M. Williams, N.J. Hodges (Eds.).
56. Lewis D., Barron A. Animated demonstrations: evidence of improved performance efficiency and the worked example effect. Human Centered Design, Lecture Notes in Computer Science 2009, 5619:247-255. 10.1007/978-3-642-02806-9_29.
57. Lewalter D. Cognitive strategies for learning from static and dynamic visuals. Learning and Instruction 2003, 13(2):177-189. 10.1016/S0959-4752(02)00019-1.
58. Li Y.H., Wright D.L. An assessment of the attention demands during random- and blocked-practice schedules. Quarterly Journal of Experimental Psychology Section A-Human Experimental Psychology 2000, 53(2):591-606. 10.1080/027249800390628.
59. Mack N.K. Confounding whole-number and fraction concepts when building on informal knowledge. Journal for Research in Mathematics Education 1995, 26(5):422-441. 10.2307/749431.
60. Meiran N. Reconfiguration of processing mode prior to task performance. Journal of Experimental Psychology-Learning Memory and Cognition 1996, 22(6):1423-1442. 10.1037//0278-7393.22.6.1423.
61. Meiran N., Chorev Z., Sapir A. Component processes in task switching. Cognitive Psychology 2000, 41(3):211-253. 10.1006/cogp.2000.0736.
62. Moss J., Case R. Developing children's understanding of the rational numbers: a new model and an experimental curriculum. Journal for Research in Mathematics Education 1999, 30(2):122-147. 10.2307/749607.
63. Moyer P., Bolyard J., Spikell M.A. What are virtual manipulatives?. Teaching Children Mathematics 2002, 8:372-377.
64. National Council of Teachers of Mathematics Principles and standards for school mathematics 2000, National Council of Teachers of Mathematics, Reston, VA.
65. National Council of Teachers of Mathematics Curriculum focal points for prekindergarten through grade 8 mathematics: A quest for coherence 2006, (Reston, VA).
66. National Mathematics Advisory Board Panel Foundations for success: Report of the National mathematics Advisory Board Panel 2008, U.S. Government Printing Office.
67. National Research Council Scientific research in education 2002, National Academy Press, Washington, DC.
68. National Science Teachers Association Standards for science teacher preparation 2009, Revised (2003), National Science Teachers Association, Retrieved 14.11.11, from. http://www.nsta.org/preservice.
69. Nelson D.W. Effects of practice sequence variations on the transfer of complex cognitive skills practiced in computer-based instruction 2006, Florida State University.
70. Ollis S., Button C., Fairweather M. The influence of professional expertise and task complexity upon the potency of the contextual interference effect. Acta Psychologica 2005, 118(3):229-244. 10.1016/j.actpsy.2004.08.003.
71. Paas F.G.W.C., van Merrienboer J.J.G. The efficiency of instructional conditions: an approach to combine mental-effort and performance measures. Human Factors 1993, 35(4):737-743.
72. Paas F., Van Gog T. Optimising worked example instruction: different ways to increase germane cognitive load. Learning and Instruction 2006, 16(2):87-91. 10.1016/j.learninstruc.2006.02.004.
73. Pashler H., Rohrer D., Cepeda N.J., Carpenter S.K.P. Enhancing learning and retarding forgetting: choices and consequences. Psychonometric Bulletin & Review 2007, 14(2):187-193. 10.3758/BF03194050.
74. Rasch T., Schnotz W. Interactive and non-interactive pictures in multimedia learning environments: effects on learning outcomes and learning efficiency. Learning and Instruction 2009, 19(5):411-422. 10.1016/j.learninstruc.2009.02.008.
75. Rau M.A., Aleven V., Rummel N. Intelligent tutoring systems with multiple representations and self-explanation prompts support learning of fractions. 14th International conference on artificial intelligence in education 2009, 441-448. IOS Press, Amsterdam. V. Dimitrova, R. Mizoguchi, B. du Boulay (Eds.).
76. Raudenbush S.W., Bryk A.S. Hierarchical linear models: Applications and data analysis methods 2002, Sage Publications, Newbury Park, CA. 2nd ed.
77. Reimer K., Moyer P.S. Third-graders learn about fractions using virtual manipulatives: a classroom study. Journal of Computers in Mathematics and Science Teaching 2005, 24(1):5-25.
78. Ritter S., Anderson J.R., Koedinger K.R., Corbett A.T. Cognitive Tutor: applied research in mathematics education. Psychonomic Bulletin & Review 2007, 14(2):249-255. 10.3758/BF03194060.
79. Ritter S., Kulikowich J., Lei P.-W., McGuire C.L., Morgan P. What evidence matters? A randomized field trial of cognitive tutor algebra I. Supporting Learning Flow Through Integrative Technologies 2007, 126:13-20.
80. Rittle-Johnson B., Koedinger K.R. Designing better learning environments: knowledge scaffolding supports mathematical problem solving. Cognition & Instruction 2005, 23:313-349. 10.1207/s1532690xci2303_1.
81. Rogers Y. What is different about interactive graphical representations?. Learning and Instruction 1999, 9:419-425.
82. Rohrer D., Taylor K. The shuffling of mathematics practice problems boosts learning. Instructional Science 2007, 35:481-498. 10.1007/s11251-007-9015-8.
83. Schmidt R.A., Bjork R.A. New conceptualizations of practice: common principles in three paradigms suggest new concepts for training. Psychological Science 1992, 3(4):207-217. 10.1111/j.1467-9280.1992.tb00029.x.
84. Schneider W. Training high-performance skills - fallacies and guidelines. Human Factors 1985, 27(3):285-300.
85. Schnotz W., Bannert M. Construction and interference in learning from multiple representation. Learning and Instruction 2003, 13(2):141-156. 10.1016/S0959-4752(02)00017-8.
86. Seufert T. Supporting coherence formation in learning from multiple representations. Learning and Instruction 2003, 13(2):227-237. 10.1016/S0959-4752(02)00022-1.
87. Shea J.B., Morgan R.L. Contextual interference effects on acquisition, retention and transfer of a motor skill. Journal of Experimental Psychology: Human Learning and Memory 1979, 5:179-187. 10.1037//0278-7393.5.2.179.
88. Simon D.A., Bjork R.A. Metacognition in motor learning. Journal of Experimental Psychology 2001, 27(4):907-912. 10.1037//0278-7393.27.4.907.
89. Suh J., Moyer P.S., Heo J.-J. Examining technology uses in the classroom: developing fraction sense using virtual manipulative concept tutorials. Journal of Interactive Online Learning 2005, 3(4):1-21.
90. Sweller J. Cognitive load as a factor in the structuring of technical material. Journal of Experimental Psychology; General 1990, 119(2):176-192. 10.1037//0096-3445.119.2.176.
91. Taylor K., Rohrer D. The effects of interleaved practice. Applied Cognitive Psychology 2010, 24(6):837-848. 10.1002/acp.1598.
92. Thußbas C. Beeinflussen Cover Stories mathematischer Texaufgaben analogen Transfer in der Mathematik?. Zeitschrift für Experimentelle Psychologie 2001, 48(4):272-289. 10.1026//0949-3946.48.4.272.
93. Van der Meij J., de Jong T. Supporting students' learning with multiple representations in a dynamic simulation-based learning environment. Learning and Instruction 2006, 16(3):199-212. 10.1016/j.learninstruc.2006.03.007.
94. Van Gog T., Paas F. Instructional efficiency: revisiting the original construct in educational research. Educational Psychologist 2008, 43:1-11. 10.1080/00461520701756248.
95. Van Merriënboer J.J.G., Schuurman J.G., de Croock M.B.M., Paas F.G.W.C. Redirecting learners' attention during training: effects on cognitive load, transfer test performance and training efficiency. Learning and Instruction 2002, 12(1):11-37. 10.1016/S0959-4752(01)00020-2.
96. VanLehn K. The behavior of tutoring systems. International Journal of Artificial Intelligence in Education 2006, 16(3):227-265.
97. VanLehn K., Koedinger K., Skogsholm A., Nwaigwe A., Hausmann R.G.M., Weinstein A., et al. What's in a step? Toward general, abstract representations of tutoring system log data. Proceedings of user modeling 2007, C. Conati, K. McCoy (Eds.).
98. Wrisberg G.A., Liu Z. The effect of contextual variety on the practice, retention, and transfer of an applied motor skill. Research Quarterly for Exercise and Sport 1991, 62:406-412.
99. Wulf G., Shea C.H. Principles derived from the study of simple skills do not generalize to complex skill learning. Psychological Bulletin & Review 2002, 9:185-211. 10.3758/BF03196276.
100. Yang D.-C., Reys R.E. One fraction problem, many solution paths. Mathematics Teaching in the Middle School 2001, 7(3):164-166.