Skip to main content
SpringerLink
Log in

Emerging Representation Technologies for Problem Solving

  • Chapter
  • First Online:
Handbook of Research on Educational Communications and Technology

Abstract

When learners solve problems they often create an external representation to organize the information given in the problem statement, to translate this problem description into underlying domain terms, and to complete this with knowledge they already have. This representation is subsequently used to solve the problem. For creating such a representation learners have many formats available: text, diagrams, formulas, and the like. The choice for a specific representation format partly determines the solution strategy that is triggered. Today, technology supported representations have become available that extend the possibilities for learners. Technology can be used to present different but connected representations, to adapt the representation to the problem solving phase and to add aspects such as dynamics, reified objects, three dimensional (3D) representations, and haptic experiences. These new representational formats open new affordances but also create new challenges for learning. In this chapter the different affordances that representational formats offer are explored with an emphasis on modern technology supported representations.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 229.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  • Ainsworth, S., & Loizou, A. T. (2003). The effects of self-explaining when learning with text or diagrams. Cognitive Science, 27, 669–681. doi:10.1207/s15516709cog2704_5.

    Article  Google Scholar 

  • Aleven, V., Roll, I., McLaren, B. M., & Koedinger, K. R. (2010). Automated, unobtrusive, action-by-action assessment of self-regulation during learning with an intelligent tutoring system. Educational Psychologist, 45, 224–233. doi:10.1080/00461520.2010.517740.

    Article  Google Scholar 

  • Battle, G. M., Allen, F. H., & Ferrence, G. M. (2010). Teaching three-dimensional structural chemistry using crystal structure databases. 2. Teaching units that utilize an interactive web-accessible subset of the Cambridge structural database. Journal of Chemical Education, 87, 813–818. doi:10.1021/ed100257t.

    Article  Google Scholar 

  • Birchfield, D., & Megowan-Romanowicz, C. (2009). Earth science learning in SMALLab: A design experiment for mixed reality. International Journal of Computer-Supported Collaborative Learning, 4, 403–421. doi:10.1007/s11412-009-9074-8.

    Article  Google Scholar 

  • Braune, R., & Foshay, W. R. (1983). Towards a practical model of cognitive information-processing task-analysis and schema acquisition for complex problem-solving situations. Instructional Science, 12, 121–145. doi:10.1007/BF00122453.

    Article  Google Scholar 

  • Cheng, P. C. H. (2002). Electrifying diagrams for learning: Principles for complex representational systems. Cognitive Science, 26, 685–736. doi:10.1016/s0364-0213(02)00086-1.

    Article  Google Scholar 

  • Chi, M. T. H., Bassok, M., Lewis, M. W., Reimann, P., & Glaser, R. (1989). Self explanations: How students study and use examples in learning to solve problems. Cognitive Science, 13, 145–183. doi:10.1207/s15516709cog1302_1.

    Article  Google Scholar 

  • Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. Cognitive Science, 5, 121–152. doi:10.1207/s15516709cog0502_2.

    Article  Google Scholar 

  • Cook, M., Wiebe, E. N., & Carter, G. (2008). The influence of prior knowledge on viewing and interpreting graphics with macroscopic and molecular representations. Science Education, 92, 848–867. doi:10.1002/sce.20262.

    Article  Google Scholar 

  • Cox, R. (1999). Representation construction, externalised cognition and individual differences. Learning and Instruction, 9, 343–363. doi:10.1016/s0959-4752(98)00051-6.

    Article  Google Scholar 

  • de Jong, T. (2005). Problem solving methodologies. In K. Kempf-Leonard (Ed.), Encyclopedia of social measurement (pp. 171–177). San Diego, CA: Academic.

    Chapter  Google Scholar 

  • de Jong, T., & Ferguson-Hessler, M. G. M. (1991). Knowledge of problem situations in physics: A comparison of good and poor novice problem solvers. Learning and Instruction, 1, 289–302. doi:10.1016/0959-4752(91)90010-6.

    Article  Google Scholar 

  • de Jong, T., & Ferguson-Hessler, M. G. M. (1996). Types and qualities of knowledge. Educational Psychologist, 31, 105–113. doi:10.1207/s15326985ep3102_2.

    Article  Google Scholar 

  • de Jong, T., & van der Meij, J. (2012). Learning with multiple representations. In N. Seel (Ed.), Encyclopaedia of the sciences of learning (Vol. 12, pp. 2026–2029). Berlin: Springer.

    Google Scholar 

  • diSessa, A. A. (1993). Toward an epistemology of physics. Cognition and Instruction, 10, 105–225. doi:10.1207/s1532690xci1002&3_2.

    Article  Google Scholar 

  • Duffield, J. (1991). Designing computer software for problem-solving instruction. Educational Technology Research and Development, 39, 50–62. doi:10.1007/bf02298106.

    Article  Google Scholar 

  • Frederiksen, C. H., Kehoe, E. J., & Wood, R. (2011). Effects of instructional aids on the acquisition of dynamic decision-making skills. Learning and Instruction, 21, 601–613. doi:10.1016/j.learninstruc.2011.01.002.

    Article  Google Scholar 

  • Gamo, S., Sander, E., & Richard, J. (2010). Transfer of strategy use by semantic recoding in arithmetic problem solving. Learning and Instruction, 20, 400–410. doi:10.1016/j.learninstruc.2009.04.001.

    Article  Google Scholar 

  • Goldstone, R. L., & Landy, D. (2010). Learning mathematics by learning how to look at, and act on, notation. Paper presented at the Conference of the American Education Research Association, Denver, Colorado.

    Google Scholar 

  • Goldstone, R. L., & Son, J. Y. (2005). The transfer of scientific principles using concrete and idealized simulations. The Journal of the Learning Sciences, 14, 69–110. doi:10.1207/s15327809jls1401_4.

    Article  Google Scholar 

  • Gräsel, C., Fischer, F., & Mandl, H. (2000). The use of additional information in problem-oriented learning environments. Learning Environments Research, 3, 287–305. doi:10.1023/a:1011421732004.

    Article  Google Scholar 

  • Jonassen, D. (2010). Learning to solve problems: A handbook for designing problem-solving learning environments. New York, NY: Routledge.

    Google Scholar 

  • Koedinger, K. R., Alibali, M. W., & Nathan, M. J. (2008). Trade-offs between grounded and abstract representations: Evidence from algebra problem solving. Cognitive Science, 32, 366–397. doi:10.1080/03640210701863933.

    Article  Google Scholar 

  • Koedinger, K. R., & Nathan, M. J. (2004). The real story behind story problems: Effects of representations on quantitative reasoning. The Journal of the Learning Sciences, 13, 129–164. doi:10.1207/s15327809jls1302_1.

    Article  Google Scholar 

  • Kohl, P. B., & Finkelstein, N. D. (2005). Representational format, student choice, and problem solving in physics. In J. Marx, P. Heron, & S. Frankin (Eds.), 2004 physics education research conference (Vol. 790, pp. 121–124). Melville, NY: American Institute of Physics.

    Google Scholar 

  • Kohl, P. B., Rosengrant, D., & Finkelstein, N. D. (2007). Strongly and weakly directed approaches to teaching multiple representation use in physics. Physical Review Special Topics - Physics Education Research, 3, 010108. doi:10.1103/PhysRevSTPER.3.010108.

    Article  Google Scholar 

  • Kollöffel, B. (2012). Exploring the relation between visualizer-verbalizer cognitive styles and performance with visual or verbal learning material. Computers in Education, 58. doi:10.1016/j.compedu.2011.09.016.

    Google Scholar 

  • Kolloffel, B., Eysink, T. H. S., de Jong, T., & Wilhelm, P. (2009). The effects of representational format on learning combinatorics from an interactive computer-simulation. Instructional Science, 37, 503–517. doi:10.1007/s11251-008-9056-7.

    Article  Google Scholar 

  • Kozma, R., & Russell, J. (2005). Multimedia learning of chemistry. In R. E. Mayer (Ed.), Cambridge handbook of multimedia learning (pp. 409–428). New York, NY: Cambridge University Press.

    Chapter  Google Scholar 

  • Landy, D. (2010). Toward a physics of equations. In R. Goebel, J. Siekmann, & W. Wahlster (Eds.), Diagrammatic representation and inference (pp. 160–166). Berlin: Springer Verlag.

    Chapter  Google Scholar 

  • Larkin, J. H. (1983). The role of problem representations in physics. In D. Gentner & A. L. Stevens (Eds.), Mental models (pp. 75–98). Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Larkin, J. H., McDermott, J., Simon, D. P., & Simon, H. A. (1980). Expert and novice performance in solving physics problems. Science, 208, 1335–1342.

    Article  Google Scholar 

  • Larkin, J. H., & Simon, H. A. (1987). Why a diagram is (sometimes) worth ten thousand words. Cognitive Science, 11, 65–99. doi:10.1016/S0364-0213(87)80026-5.

    Article  Google Scholar 

  • Lee, V. R. (2010). How different variants of orbit diagrams influence student explanations of the seasons. Science Education, 94, 985–1007. doi:10.1002/sce.20403.

    Article  Google Scholar 

  • Liu, C., & Shen, M. H. (2011). The influence of different representations on solving concentration problems at elementary school. Journal of Science Education and Technology, 20, 621–629. doi:10.1007/s10956-011-9293-4.

    Article  Google Scholar 

  • Meltzer, D. E. (2005). Relation between students’ problem-solving performance and representational format. American Journal of Physics, 73, 463–478. doi:10.1119/1.1862636.

    Article  Google Scholar 

  • Minogue, J., & Jones, G. (2009). Measuring the impact of haptic feedback using the solo taxonomy. International Journal of Science Education, 31, 1359–1378. doi:10.1080/09500690801992862.

    Article  Google Scholar 

  • Moreno, R., Ozogul, G., & Reisslein, M. (2011). Teaching with concrete and abstract visual representations: Effects on students’ problem solving, problem representations, and learning perceptions. Journal of Educational Psychology, 103, 32–47. doi:10.1037/a0021995.

    Article  Google Scholar 

  • Nathan, M. J., Kintsch, W., & Young, E. (1992). A theory of algebra-word-problem comprehension and its implications for the design of learning environments. Cognition and Instruction, 9, 329. doi:10.1207/s1532690xci0904_2.

    Article  Google Scholar 

  • Noss, R., Hoyles, C., Mavrikis, M., Geraniou, E., Gutierrez-Santos, S., & Pearce, D. (2009). Broadening the sense of ‘dynamic’: A microworld to support students’ mathematical generalisation. ZDM, 41, 493–503. doi:10.1007/s11858-009-0182-8.

    Article  Google Scholar 

  • Olympiou, G., Zacharias, Z., & de Jong, T. (2013). Making the invisible visible: Enhancing students’ conceptual understanding by introducing representations of abstract objects in a simulation. Instructional Science, 41, 575–596. doi: 10.1007/s11251-012-9245-2.

  • Pol, H., Harskamp, E. G., Suhre, C., & Goedhart, M. (2008). The effect of hints and model answers in a student-controlled problem-solving program for secondary physics education. Journal of Science Education and Technology, 17, 410–425. doi:10.1007/s10956-008-9110-x.

    Article  Google Scholar 

  • Robertson, S. I. (2001). Problem solving. Philadelphia, PA: Taylor & Francis.

    Book  Google Scholar 

  • Roschelle, J., Kaput, J., & Stroup, W. (2000). Simcalc: Accelerating students’ engagement with the mathematics of change. In M. J. Jacobson & R. B. Kozma (Eds.), Innovations in science and mathematics education: Advanced designs for technologies of learning (pp. 47–75). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Rosengrant, D., Van Heuvelen, A., & Etkina, E. (2009). Do students use and understand free-body diagrams? Physical Review Special Topics - Physics Education Research, 5, 010108. doi:10.1103/PhysRevSTPER.5.010108.

    Article  Google Scholar 

  • Savelsbergh, E., de Jong, T., & Ferguson-Hessler, M. G. M. (2002). Situational knowledge in physics: The case of electrodynamics. Journal of Research in Science Teaching, 39, 928–952.

    Article  Google Scholar 

  • Savelsbergh, E., de Jong, T., & Ferguson-Hessler, M. G. M. (2011). Choosing the right solution approach: The crucial role of situational knowledge in electricity and magnetism. Physical Review Special Topics - Physics Education Research, 7(010103), 12. doi:10.1103/PhysRevSTPER.7.010103.

    Google Scholar 

  • Scaife, M., & Rogers, Y. (1996). External cognition: How do graphical representations work? International Journal of Human Computer Studies, 45, 185–213. doi:10.1006/ijhc.1996.0048.

    Article  Google Scholar 

  • Scheiter, K., Gerjets, P., & Catrambone, R. (2006). Making the abstract concrete: Visualizing mathematical solution procedures. Computers in Human Behavior, 22, 9–25. doi:10.1016/j.chb.2005.01.009.

    Article  Google Scholar 

  • Scheiter, K., Gerjets, P., & Schuh, J. (2010). The acquisition of ­problem-solving skills in mathematics: How animations can aid understanding of structural problem features and solution procedures. Instructional Science, 38, 487–502. doi:10.1007/s11251-009-9114-9.

    Article  Google Scholar 

  • Schwartz, D. L. (1995). The emergence of abstract representations in dyad problem solving. The Journal of the Learning Sciences, 4, 321–354. doi:10.1207/s15327809jls0403_3.

    Article  Google Scholar 

  • Sherin, B. L. (2001). How students understand physics equations. Cognition and Instruction, 19, 479–541. doi:10.1207/S1532690XCI1904_3.

    Article  Google Scholar 

  • Stenning, K., & Oberlander, J. (1995). A cognitive theory of graphical and linguistic reasoning: Logic and implementation. Cognitive Science, 19, 97–140. doi:10.1207/s15516709cog1901_3.

    Article  Google Scholar 

  • Sweller, J., Mawer, R. F., & Ward, M. R. (1983). Development of expertise in mathematical problem solving. Journal of Experi­mental Psychology. General, 112, 639–661. doi:10.1037/0096-3445.112.4.639.

    Article  Google Scholar 

  • Tatar, D., Roschelle, J., Knudsen, J., Shechtman, N., Kaput, J., & Hopkins, B. (2008). Scaling up innovative technology-based mathematics. The Journal of the Learning Sciences, 17, 248–286. doi:10.1080/10508400801986090.

    Article  Google Scholar 

  • Thevenot, C. (2010). Arithmetic word problem solving: Evidence for the construction of a mental model. Acta Psychologica, 133, 90–95. doi:10.1016/j.actpsy.2009.10.004.

    Article  Google Scholar 

  • Tolentino, L., Birchfield, D., Megowan-Romanowicz, C., Johnson-Glenberg, M., Kelliher, A., & Martinez, C. (2009). Teaching and learning in the mixed-reality science classroom. Journal of Science Education and Technology, 18, 501–517. doi:10.1007/s10956-009-9166-2.

    Article  Google Scholar 

  • van der Meij, J., & de Jong, T. (2006). Supporting students’ learning with multiple representations in a dynamic simulation-based learning environment. Learning and Instruction, 16, 199–212. doi:10.1016/j.learninstruc.2006.03.007.

    Article  Google Scholar 

  • van der Meij, H., van der Meij, J., & Mulder, Y. G. (2012). Dynamische representaties op het digitale schoolbord [dynamic representations on the digital blackboard]. Enschede: University of Twente.

    Google Scholar 

  • Verschaffel, L., de Corte, E., de Jong, T., & Elen, J. (Eds.). (2010). Use of external representations in reasoning and problem solving. Abingdon, OX: Routledge Press.

    Google Scholar 

  • Wu, H., Krajcik, J. S., & Soloway, E. (2001). Promoting understanding of chemical representations: Students’ use of a visualization tool in the classroom. Journal of Research in Science Teaching, 38, 821–842. doi:10.1002/tea.1033.

    Article  Google Scholar 

  • Zhang, J. (1997). The nature of external representations in problem solving. Cognitive Science, 21, 179–217. doi:10.1016/s0364-0213(99)80022-6.

    Article  Google Scholar 

  • Zhang, J., & Norman, D. A. (1994). Representations in distributed cognitive tasks. Cognitive Science, 18, 87–122. doi:10.1207/s1551670.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Behavioral Science, University of Twente, 217, 7500 AE, Enschede, The Netherlands

    Ton de Jong

Authors
  1. Ton de Jong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ton de Jong .

Editor information

Editors and Affiliations

  1. , Department of Learning Technologies, C, University of North Texas, North Elm 3940, Denton, 76207-7102, Texas, USA

    J. Michael Spector

  2. W. Sunset Blvd. 1812, St. George, 84770, Utah, USA

    M. David Merrill

  3. , Centr. Instructiepsychol.&-technologie, K.U. Leuven, Andreas Vesaliusstraat 2, Leuven, 3000, Belgium

    Jan Elen

  4. Research Drive, Iacocca A109 111, Bethlehem, 18015, Pennsylvania, USA

    M. J. Bishop

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media New York

About this chapter

Cite this chapter

de Jong, T. (2014). Emerging Representation Technologies for Problem Solving. In: Spector, J., Merrill, M., Elen, J., Bishop, M. (eds) Handbook of Research on Educational Communications and Technology. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3185-5_65

Download citation

Publish with us

Policies and ethics

Search

Navigation