Teaching With Concrete and Abstract Visual Representations: Effects on Students' Problem Solving, Problem Representations, and Learning Perceptions

Journal of Educational Psychology

Volumn 103, Issue 1, 2011, Pages 32-47

  Moreno, Roxana ^a   Ozogul, Gamze ^b   Reisslein, Martin ^b  

^a UNIVERSITY OF NEW MEXICO   (United States)

^b Arizona State University   (United States)

Author keywords

Abstract visual representation; Concrete visual representation; Problem solving

Indexed keywords

EID: 79951787229     PISSN: 00220663     EISSN: None     Source Type: Journal    
DOI: 10.1037/a0021995     Document Type: Article

References (80)

1. Alexander C.K., Sadiku M. Fundamentals of electric circuits 2004, McGraw-Hill, New York, NY. 2nd ed.
2. Anderson J.R. Problem solving and learning. American Psychologist 1993, 48:35-44. doi: 10.1037/0003-066X.48.1.35.
3. Atkinson R.K., Derry S.J., Renkl A., Wortham D.W. Learning from examples: Instructional principles from the worked examples research. Review of Educational Research 2000, 70:181-214.
4. Bassok M., Holyoak K.J. Interdomain transfer between isomorphic topics in algebra and physics. Journal of Experimental Psychology: Learning, Memory, and Cognition 1989, 15:153-166. doi: 10.1037/0278-7393.15.1.153.
5. Bétrancourt M., Tversky B. Effect of computer animation on users' performance: A review. Le Travail Humain 2000, 63:311-329.
6. Bransford J.D., Brown A.L., Cocking R.R. How people learn: Brain, mind, experience, and school 2000, National Academies Press, Washington, DC.
7. Bransford J.D., Schwartz D.L. Rethinking transfer: A simple proposal with multiple implications. Review of research in education 1999, 24:61-100. American Educational Research Association, Washington, DC. A. Iran-Nejad, P.D. Pearson (Eds.).
8. Bransford J.D., Stein B.S. The IDEAL problem solver 1984, Freeman, New York, NY.
9. Brenner M.E., Mayer R.E., Moseley B., Brar T., Durán R., Reed B.S., Webb D. Learning by understanding: The role of multiple representations in learning algebra. American Educational Research Journal 1997, 34:663-689.
10. Bruning R.H., Schraw G.J., Norby M., Ronning R. Cognitive psychology and instruction 2004, Prentice-Hall, Upper Saddle River, NJ. 4th ed.
11. Butcher R.K. Learning from text with diagrams: Promoting mental model development and inference generation. Journal of Educational Psychology 2006, 98:182-197. doi: 10.1037/0022-0663.98.1.182.
12. Cheng P.C.H. Electrifying diagrams for learning: Principles for complex representational systems. Cognitive Science 2002, 26:685-736. doi: 10.1207/s15516709cog2606_1.
13. Chi M.T.H., Feltovich P.J., Glaser R. Categorization and representation of physics problems by experts and novices. Cognitive Science 1981, 5:121-152. doi: 10.1207/s15516709cog0502_2.
14. Clements D.H., McMillen S. Rethinking " concrete" manipulatives. Teaching Children Mathematics 1996, 2:270-279.
15. Colin P., Chauvet F., Viennot L. Reading images in optics: Students' difficulties and teachers' views. International Journal of Science Education 2002, 24:313-332. doi: 10.1080/09500690110078923.
16. Collins A., Brown J.S., Newman S.E. Cognitive apprenticeship: Teaching the craft of reading, writing and mathematics. Knowing, learning and instruction: Essays in honor of Robert Glaser 1989, 453-494. Erlbaum, Hillsdale, NJ. L.B. Resnick (Ed.).
17. Collins A., Ferguson W. Epistemic forms and epistemic games: Structures and strategies to guide inquiry. Educational Psychologist 1993, 28:25-42. doi: 10.1207/s15326985ep2801_3.
18. Day R.S. Alternative representations. The psychology of learning and motivation 1988, 22:261-305. Academic Press, San Diego, CA. G.H. Bower (Ed.).
19. DeLoache J.S. Dual representation and young children's use of scale models. Child Development 2000, 71:329-338. doi: 10.1111/1467-8624.00148.
20. DeLoache J.S., Marzolf D.P. When a picture is not worth a thousand words: Young children's understanding of pictures and models. Cognitive Development 1992, 7:317-329. doi: 10.1016/0885-2014(92)90019-N.
21. DiFonzo N., Hantula D.A., Bordia P. Microworlds for experimental research: Having your (control and collections) cake and realism too. Behavioral Research Methods, Instruments, and Computers 1998, 30:278-286.
22. Donovan M.S., Bransford J.D. How students learn: History, mathematics, and science in the classroom 2005, National Academies Press, Washington, DC.
23. Dwyer F.M. The effectiveness of visual illustrations used to complement programmed instruction. Journal of Psychology 1968, 70:157-162.
24. Dwyer F.M. The effect of varying the amount of realistic detail in visual illustrations designed to complement programmed instruction. Programmed Learning 1969, 6:147-153.
25. Edens K., Potter E. The relationship of drawing and mathematical problem solving: Draw for Math tasks. Studies in Art Education 2007, 48:282-298.
26. Edens K., Potter E. How students " unpack" the structure of a word problem: Graphic representations and problem solving. School Science and Mathematics 2008, 108:184-196. doi: 10.1111/j.1949-8594.2008.tb17827.x.
27. Elia I., Gagatsis A., Demetriou A. The effects of different modes of representation on the solution of one-step additive problems. Learning and Instruction 2007, 17:658-672. doi: 10.1016/j.learninstruc.2007.09.011.
28. Ericsson K.A., Smith J. Toward a general theory of expertise 1991, Cambridge University Press, Cambridge, MA.
29. Gianutsos R. Driving advisement with the elemental driving simulator (EDS): When less suffices. Behavioral Research Methods, Instruments, and Computers 1994, 26:183-186.
30. Gick M.L. Problem-solving strategies. Educational Psychologist 1986, 21:99-120. doi: 10.1207/s15326985ep2101&2_6.
31. Glasgow J.I., Narayanan H., Chandrasekaran C. Diagrammatic reasoning 1995, AAAI/MIT Press, Cambridge, MA.
32. Goldstone R.L., Sakamoto Y. The transfer of abstract principles governing complex adaptive systems. Cognitive Psychology 2003, 46:414-466. doi: 10.1016/S0010-0285(02)00519-4.
33. Goldstone R.L., Son J.Y. The transfer of scientific principles using concrete and idealized simulations. Journal of the Learning Sciences 2005, 14:69-110. doi: 10.1207/s15327809jls1401_4.
34. Grady S.M. Virtual reality: Computers mimic the physical world 1998, Facts on File, New York, NY.
35. Hayes J.R. The complete problem solver 1988, Erlbaum, Mahwah, NJ. 2nd ed.
36. Hegarty M., Carpenter P.A., Just M.A. Diagrams in the comprehension of scientific texts. Handbook of reading research 1991, 2:641-668. Longman, New York, NY. R. Barr, M. Kamil, P.B. Mosenthal, P.D. Pearson (Eds.).
37. Hegarty M., Kozhevnikov M. Types of visual-spatial representations and mathematical problem solving. Journal of Educational Psychology 1999, 91:684-689. doi: 10.1037/0022-0663.91.4.684.
38. Heim M. Virtual realism 2000, Oxford University Press, New York, NY.
39. Irwin D., Nelms M.R. Basic engineering circuit analysis 2005, Wiley, New York, NY. 8th ed.
40. Joseph J.H., Dwyer F.M. Effects of prior knowledge, presentation mode, and visual realism on student achievement. Journal of Experimental Education 1984, 52:110-121.
41. Kirshner D. The visual syntax of algebra. Journal for Research in Mathematics Education 1989, 20:274-287. doi: 10.2307/749516.
42. Knorr-Cetina K.D., Amann K. Image dissection in natural scientific inquiry. Science, Technology, and Human Values 1990, 15:259-283. doi: 10.1177/016224399001500301.
43. Koedinger K.R., Aleven V. Exploring the assistance dilemma in experiments with cognitive tutors. Educational Psychology Review 2007, 19:239-264. doi: 10.1007/s10648-007-9049-0.
44. Koedinger K.R., Alibali M.W., Nathan M.J. Trade-offs between grounded and abstract representations: Evidence from algebra problems. Cognitive Science 2008, 32:366-397. doi: 10.1080/03640210701863933.
45. Koedinger K.R., Anderson J.R. Illustrating principled design: The early evolution of a cognitive tutor for algebra symbolization. Interactive Learning Environments 1998, 5:161-179. doi: 10.1080/1049482980050111.
46. Koedinger K.R., Nathan M.J. The real story behind story problems: Effects of representations on quantitative reasoning. Journal of the Learning Sciences 2004, 13:129-164. doi: 10.1207/s15327809jls1302_1.
47. Kozma R. The material features of multiple representations and their cognitive and social affordances for science understanding. Learning and Instruction 2003, 13:205-226. doi: 10.1016/S0959-4752(02)00021-X.
48. Kozma R., Chin E., Russell J., Marx N. The roles of representations and tools in the chemistry laboratory and their implications for chemistry learning. Journal of the Learning Sciences 2000, 9:105-143. doi: 10.1207/s15327809jls0902_1.
49. Kozma R., Russell J. Multimedia and understanding: Expert and novice responses to different representations of chemical phenomena. Journal of Research in Science Teaching 1997, 34:949-968. doi: 10.1002/(SICI)1098-2736(199711)34:9<949::AID-TEA7>3.0.CO;2-U.
50. Larkin J.H., Simon H.A. Why a diagram is (sometimes) worth ten thousand words. Cognitive Science 1987, 11:65-100. doi: 10.1111/j.1551-6708.1987.tb00863.x.
51. Lynch M. Laboratory space and the technological complex: An investigation of topical contextures. Ecologies of knowledge: Work and politics in science and technology 1995, 226-256. State University of New York Press, Albany, NY. S.L. Star (Ed.).
52. Lynch M., Woolgar S. Representation in scientific practice 1990, MIT Press, Cambridge, MA.
53. Markman A.B., Gentner D. Structural alignment during similarity comparisons. Cognitive Psychology 1993, 25:431-467. doi: 10.1006/cogp.1993.1011.
54. Mayer R.E., Hegarty M. The process of understanding mathematical problems. The nature of mathematical thinking 1996, 29-53. Erlbaum, Mahwah, NJ. R.J. Sternberg, T. Ben-Zeev (Eds.).
55. Meece J.L. Child and adolescent development for educators 2002, McGraw-Hill, New York, NY. 2nd ed.
56. Miller P. Theories of developmental psychology 2002, Worth, New York, NY. 4th ed.
57. Moreno R., Reisslein M., Delgoda G.M. Toward a fundamental understanding of worked example instruction: Impact of means-ends practice, backward/forward fading, and adaptivity. Proceedings of IEEE/ASEE Frontiers in Education Conference 2006, 5-10. IEEE, Piscataway, NJ. A. Gates, M. Piket-May, E. Eschenbach (Eds.).
58. Moreno R., Reisslein M., Ozogul G. Optimizing worked-example instruction in electrical engineering: The role of fading and feedback during problem-solving practice. Journal of Engineering Education 2009, 98:83-92.
59. Moreno R., Reisslein M., Ozogul G. Pre-college electrical engineering instruction: Do abstract or contextualized representations promote better learning?. Proceedings of IEEE/ASEE Frontiers in Education Conference 2009, 1-6. IEEE, Piscataway, NJ. R.A. Layton, M. Mina, D. Cordes (Eds.).
60. Nathan M.J. Knowledge and situational feedback in a learning environment for algebra story problem solving. Interactive Learning Environments 1998, 5:135-159. doi: 10.1080/1049482980050110.
61. Nathan M.J., Kintsch W., Young E. A theory of algebra word problem comprehension and its implications for the design of computer learning environments. Cognition and Instruction 1992, 9:329-389. doi: 10.1207/s1532690xci0904_2.
62. Newell A., Simon H.A. Human problem solving 1972, Prentice-Hall, Englewood Cliffs, NJ.
63. Orsak G.C., Wood S.L., Douglas S.C., Munson D.C., Treichler J.R., Athale R., Yoder M.A. Engineering our digital future 2004, Prentice-Hall, Upper Saddle River, NJ.
64. Perry B., Howard P., Tracey D. Head mathematics teachers' beliefs about the learning and teaching of mathematics. Mathematics Education Journal 1999, 11:39-53.
65. Petre M., Green T.R.G. Learning to read graphics: Some evidence that " seeing" an information display is an acquired skill. Journal of Visual Languages and Computing 1993, 4:55-70. doi: 10.1006/jvlc.1993.1004.
66. Renkl A. The worked-out-example principle in multimedia learning. Cambridge handbook of multimedia learning 2005, 229-245. Cambridge University Press, Cambridge, England. R.E. Mayer (Ed.).
67. Renkl A., Atkinson R.K. Structuring the transition from example study to problem solving in cognitive skills acquisition: A cognitive load perspective. Educational Psychologist 2003, 38:15-22. doi: 10.1207/S15326985EP3801_3.
68. ®: Applied research in mathematics education. Psychonomic Bulletin and Review 2007, 14:249-255.
69. Rittle-Johnson B., Siegler S., Alibali M. Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology 2001, 93:346-362. doi: 10.1037/0022-0663.93.2.346.
70. Roth W., Bowen J.M., McGinn M.K. Differences in graph-related practices between high school biology textbooks and scientific ecology journals. Journal of Research in Science Teaching 1999, 36:977-1019. doi: 10.1002/(SICI)1098-2736(199911)36:9<977::AID-TEA3>3.0.CO;2-V.
71. Schank R.C. Goal-based scenarios: A radical look at education. Journal of the Learning Sciences 1994, 3:429-453. doi: 10.1207/s15327809jls0304_5.
72. Scheiter K., Gerjets P., Huk T., Imhof B., Kammerer Y. The effects of realism in learning with dynamic visualizations. Learning and Instruction 2009, 19:481-494. doi: 10.1016/j.learninstruc.2008.08.001.
73. Sharp J., Adams B. Children's constructions of knowledge for fraction division after solving realistic problems. Journal of Educational Research 2002, 95:333-347. doi: 10.1080/00220670209596608.
74. Simon H.A., Hayes J.R. The understanding process: Problem isomorphs. Cognitive Psychology 1976, 8:165-190. doi: 10.1016/0010-0285(76)90022-0.
75. Sloutsky V.M., Kaminski J.A., Heckler A.F. The advantage of simple symbols for learning and transfer. Psychonomic Bulletin and Review 2005, 12:508-513.
76. Stenning K., Cox R., Oberlander J. Contrasting the cognitive effects of graphical and sentential logic teaching: Reasoning, representation and individual differences. Language and Cognitive Processes 1995, 10:333-354. doi: 10.1080/01690969508407099.
77. Tulving E., Osler S. Effectiveness of retrieval cues in memory for words. Journal of Experimental Psychology 1968, 77:593-601. doi: 10.1037/h0026069.
78. Uttal D.H., Liu L.L., DeLoache J.S. Taking a hard look at concreteness: Do concrete objects help young children learn symbolic relations?. Child psychology: A handbook of contemporary issues 1999, 177-192. Psychology Press, Philadelphia, PA. C.S. Tamis-LeMonda (Ed.).
79. van Garderen D., Montague M. Visual-spatial representation, mathematical problem solving, and students of varying abilities. Learning Disabilities Research and Practice 2003, 18:246-254. doi: 10.1111/1540-5826.00079.
80. Zhang J. The nature of external representations in problem solving. Cognitive Science 1997, 21:179-217. doi: 10.1207/s15516709cog2102_3.