Skip to main content
Log in

Example-based learning: exploring the use of matrices and problem variability

  • Development Article
  • Published:
Educational Technology Research and Development Aims and scope Submit manuscript

Abstract

The purpose of the study was to investigate the efficacy of using faded worked examples presented in matrices with problem structure variability to enhance learners’ ability to recognize the underlying structure of the problems. Specifically, this study compared the effects of matrix-format versus linear-format faded worked examples combined with equivalent problem structure versus contrast problem structure on learning. A total of 113 undergraduate students recruited from campus were randomly assigned to one of the four experimental conditions formed by a 2 × 2 factorial design. The results revealed three significant interactions on accuracy of anticipations, near transfer and medium transfer, suggesting that matrices foster learning when they contain contrast-structure problems but not with equivalent-structure problems.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  • Atkinson, R. K., Derry, S. J., Renkl, A., & Wortham, D. (2000). Learning from examples: Instructional principles from the worked examples research. Review of Educational Research, 70(2), 181–214.

    Article  Google Scholar 

  • Atkinson, R. K., Levin, J. R., Kiewra, K. A., Meyers, T., Kim, S.-I., Atkinson, L. A., et al. (1999). Matrix and mnemonic text-processing adjuncts: Comparing and combining their components. Journal of Educational Psychology, 91(2), 342–357.

    Article  Google Scholar 

  • Atkinson, R. K., Merrill, M. M., & Renkl, A. (2003). Transitioning from studying examples to solving problems: Effects of self-explanation prompts and fading worked-out steps. Journal of Educational Psychology, 95(4), 774–783.

    Article  Google Scholar 

  • Atkinson, R. K., Merrill-Lusk, M. M., and Bietzel, B. (2007). Learning from book-based examples: Exploring the impact of combining fading with prompts and matrices. Paper presented at the biennial meeting of the European Association for Research on Learning and Instruction, Budapest, Hungary.

  • Belland, B. R. (2010). Portraits of middle school students constructing evidence-based arguments during problem-based learning: The impact of computer-based scaffolds. Educational Technology Research and Development, 58(3), 285–309.

    Article  Google Scholar 

  • Belland, B. R. (2014). Scaffolding: Definition, current debates, and future directions. In J. M. Spector, M. D. Merrill, J. Elen, & M. J. Bishop (Eds.), Handbook of research on educational communications and technology (4th ed., pp. 505–518). New York: Springer.

    Chapter  Google Scholar 

  • Bera, S. J., & Robinson, D. H. (2004). Exploring the boundary conditions of the delay hypothesis with adjunct displays. Journal of Educational Psychology, 96, 381–388.

    Article  Google Scholar 

  • Brünken, R., Plass, J. L., & Moreno, R. (2010). Current issues and open questions in cognitive load research. In J. L. Plass, R. Moreno, & R. Brünken (Eds.), Cognitive load theory (pp. 253–272). New York: Cambridge University Press.

    Chapter  Google Scholar 

  • Chase, W. G., & Simon, H. A. (1973). The mind’s eye in chess. In W. G. Chase (Ed.), Visual information processing. New York: Academic Press.

    Google Scholar 

  • Cho, K., & Jonassen, D. H. (2002). The effects of argumentation scaffolds on argumentation and problem solving. Educational Technology Research and Development, 50, 1042–1629.

    Article  Google Scholar 

  • Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: L. Erlbaum Associates.

    Google Scholar 

  • Gerjects, P., Scheiter, K., & Schuh, J. (2008). Information comparisons in example-based hypermedia environments: Supporting learners with processing prompts and an interactive comparison tool. Educational Technology Research and Development, 56, 73–92.

    Article  Google Scholar 

  • Gerjets, P., Scheiter, K., & Catrambone, R. (2004). Designing instructional examples to reduce intrinsic cognitive load: Molar versus modular presentation of solution procedures. Instructional Science, 32(1–2), 33–58.

    Article  Google Scholar 

  • Greeno, J. (1978). Natures of problem-solving abilities. In W. Estes (Ed.), Handbook of learning and cognitive processes (pp. 239–270). Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Gurlitt, J., Dummel, S., Schuster, S., & Nückles, M. (2012). Differently structured advance organizers lead to different initial schemata and learning outcomes. Instructional Science, 40, 351–369.

    Article  Google Scholar 

  • Hart, S. G., & Staveland, L. E. (1988). Development of NASA-TLX (Task Load Index): Results of experimental and theoretical research. In P. A. Hancock & N. Meshkati (Eds.), Human mental workload (pp. 139–183). Amsterdam: North-Holland.

    Chapter  Google Scholar 

  • Jairam, D., & Kiewra, K. A. (2010). Helping students soar to success on computers: An investigation of the SOAR study method for computer-based learning. Journal of Educational Psychology, 102, 601–614.

    Article  Google Scholar 

  • Jairam, D., Kiewra, K. A., Kauffman, D. F., & Zhao, R. (2012). How to study a matrix. Contemporary Educational Psychology, 37, 128–135.

    Article  Google Scholar 

  • Jonassen, D. H. (1997). Instructional design models for well-structured and ill-structured problem-solving learning outcomes. Educational Technology Research and Development, 45, 65–94.

    Article  Google Scholar 

  • Kalyuga, S., Chandler, P., Tuovinen, J., & Sweller, J. (2001). When problem solving is superior to studying worked examples. Journal of Educational Psychology, 93(3), 579–588.

    Article  Google Scholar 

  • Kauffman, D. F., & Kiewra, K. A. (2010). What makes a matrix so effective? An empirical test of the relative benefits of signaling, extraction, and localization. Instructional Science, 38, 679–705.

    Article  Google Scholar 

  • Kim, M., & Hannafin, M. J. (2011). Scaffolding problem solving in technology-enhanced learning environments (TELEs): Bridging research and theory with practice. Computers and Education, 56, 255–282.

    Google Scholar 

  • Langan-Fox, J., Waycott, J. L., & Albert, K. (2000). Linear and graphic advance organizers: Properties and processing. International Journal of Cognitive Ergonomics, 4(1), 19–34.

    Article  Google Scholar 

  • Lin, L., & Atkinson, R. K. (2013). Enhancing learning from different visualizations by self-explanations prompts. Journal of Educational Computing Research, 49(1), 83–110.

    Article  Google Scholar 

  • National Assessment of Educational Progress (2003). Retrieved from http://nces.ed.gov/nationsreportcard/mathematics/abilities.asp.

  • National Mathematics Advisory Panel (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education. Retrieved January 13, 2015, from http://www.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf.

  • Paas, F. G. W. C. (1992). Training strategies for attaining transfer of problem-solving skill in statistics: A cognitive-load approach. Journal of Educational Psychology, 84(4), 429–434.

    Article  Google Scholar 

  • Paas, F., Renkl, A., & Sweller, J. (2003). Cognitive load theory and instructional design: Recent developments. Educational Psychologist, 38(1), 1–4.

    Article  Google Scholar 

  • Quilici, J. L., & Mayer, R. E. (1996). Role of examples in how students learn to categorize statistics word problems. Journal of Educational Psychology, 88(1), 144–161.

    Article  Google Scholar 

  • Quilici, J. L., & Mayer, R. E. (2002). Teaching students to recognize structural similarities between statistics word problems. Applied Cognitive Psychology, 16(3), 325–342.

    Article  Google Scholar 

  • Reisslein, J., Reisslein, M., & Seeling, P. (2006). Comparing static fading with adaptive fading to independent problem solving: The impact on the achievement and attitudes of high school students learning electrical circuit analysis. Journal of Engineering Education, 95, 217–226.

    Article  Google Scholar 

  • Renkl, A., & Atkinson, R. K. (2003). Structuring the transition from example study to problem solving in cognitive skill acquisition: A cognitive load perspective. Educational Psychologist, 38(1), 15–22.

    Article  Google Scholar 

  • Renkl, A., Atkinson, R. K., & Große, C. S. (2004). How fading worked solution steps works—A cognitive load perspective. Instructional Science, 32, 59–82.

    Article  Google Scholar 

  • Renkl, A., Atkinson, R. K., Maier, U. H., & Staley, R. (2002). From example study to problem solving: Smooth transitions help learning. The Journal of Experimental Education, 70(4), 293–315.

    Article  Google Scholar 

  • Robinson, D. H., Katayama, A. D., DuBois, N. F., & Devaney, T. (1998). Interactive effects of graphic organizers and delayed review of concept application. Journal of Experimental. Education, 67(1), 17–31.

    Article  Google Scholar 

  • Robinson, D. H., & Kiewra, K. A. (1995). Visual argument: Graphic organizers are superior to outlines in improving learning from text. Journal of Educational Psychology, 87(3), 455–467.

    Article  Google Scholar 

  • Robinson, D. H., & Schraw, G. (1994). Computational efficiency through visual argument: Do graphic organizers communicate relations in text too effectively? Contemporary Educational Psychology, 19(4), 399–415.

    Article  Google Scholar 

  • Robinson, D. H., & Skinner, C. H. (1996). Why graphic organizers facilitate search processes: Fewer words or computationally efficient indexing? Contemporary Educational Psychology, 21(2), 166–180.

    Article  Google Scholar 

  • Roy, M., & Chi, M. T. H. (2005). The self-explanation principle in multimedia learning. In R. E. Mayer (Ed.), The Cambridge handbook of multimedia learning (pp. 271–286). New York: Cambridge University Press.

    Chapter  Google Scholar 

  • Suzuki, A., Sato, T., & Awazu, S. (2008). Graphic display of linguistic information in English as a foreign language reading. TESOL Quarterly, 42, 591–616.

    Article  Google Scholar 

  • Sweller, J. (1988). Cognitive load during problem solving: Effects on learning. Cognitive Science, 12, 257–285.

    Article  Google Scholar 

  • Sweller, J. (2010). Element interactivity and intrinsic, extraneous, and germane cognitive load. Educational Psychology Review, 22, 123–138.

    Article  Google Scholar 

  • Sweller, J., & Copper, G. (1985). The use of worked examples as a substitute for problem solving in learning algebra. Cognition and Instruction, 2, 59–89.

    Article  Google Scholar 

  • Sweller, J., van Merriënboer, J. J. G., & Paas, F. G. W. C. (1998). Cognitive architecture and instructional design. Educational Psychology Review, 10(3), 251–296.

    Article  Google Scholar 

  • van Gerven, P. W. M., Paas, F. G. W. C., van Merriënboer, J. J. G., & Schmidt, H. G. (2000). Cognitive load theory and the acquisition of complex cognitive skills in the elderly: Towards an integrative framework. Educational Gerontology, 26, 503–521.

    Article  Google Scholar 

  • van Gog, T., Kester, L., & Paas, F. (2012). Effects of worked examples, example-problem, and problem-example pairs on novices’ learning. Contemporary Educational Psychology, 36, 212–218.

    Google Scholar 

  • van Gog, T., Paas, F., & van Merriënboer, J. J. G. (2004). Process-oriented worked examples: Improving transfer performance through enhanced understanding. Instructional Science, 32, 83–98.

    Article  Google Scholar 

  • van Gog, T., & Rummel, N. (2010). Example-based learning: Integrating cognitive and social-cognitive research perspectives. Educational Psychology Review, 22, 155–174.

    Article  Google Scholar 

  • van Loon-Hillen, N., van Gog, T., & Brand-Gruwel, S. (2012). Effects of worked examples in a primary school mathematics curriculum. Interactive Learning Environments, 20, 89–99.

    Article  Google Scholar 

  • van Merriënboer, J. J. G., Kester, L., & Paas, F. (2006). Teaching complex rather than simple tasks: Balancing intrinsic and germane load to enhance transfer of learning. Applied Cognitive Psychology, 20(3), 343–352.

    Article  Google Scholar 

  • van Merriënboer, J. J. G., Schuurman, J. G., de Croock, M. B. M., & Paas, F. G. W. C. (2002). Redirecting learners’ attention during training: Effects on cognitive load, transfer test performance and training efficiency. Learning and Instruction, 12(1), 11–37.

    Article  Google Scholar 

  • Vekiri, I. (2002). What is the value of graphical displays in learning? Educational Psychology Review, 14(3), 261–312.

    Article  Google Scholar 

Download references

Acknowledgments

This research was partially supported by Shanghai Pujiang Program (13PJC031), Shanghai Planning Office of Philosophy and Social Science (2014JJY001), and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, China.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Lijia Lin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hancock-Niemic, M.A., Lin, L., Atkinson, R.K. et al. Example-based learning: exploring the use of matrices and problem variability. Education Tech Research Dev 64, 115–136 (2016). https://doi.org/10.1007/s11423-015-9403-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11423-015-9403-8

Keywords

Navigation