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ZDM

, Volume 49, Issue 4, pp 491–496 | Cite as

Applying cognitive psychology based instructional design principles in mathematics teaching and learning: introduction

  • Lieven Verschaffel
  • W. Van Dooren
  • J. Star
Survey Paper
First Online:

Abstract

This special issue comprises contributions that address the breadth of current lines of recent research from cognitive psychology that appear promising for positively impacting students’ learning of mathematics. More specifically, we included contributions (a) that refer to cognitive psychology based principles and techniques, such as explanatory questioning, worked examples, metacognitive training, exemplification, refutational texts, multiple external representations, which are considered as well-established principles or techniques for instructional design in general, and (b) that explore, illustrate and critically discuss the available research evidence for their relevance and efficacy in the specific curricular domain of mathematics teaching and learning. The special issue ends with an interview with Paul Kirchner about the relationships between cognitive psychology, instructional design and mathematics education.

Keywords

Instructional design Cognitive science Domain-general theories Domain-specific theories Conceptual change Cognitive load Metacognition Embodied cognition 
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References

  1. Baten, E., Praet, M., & Desoete, A. (2017). The relevance and efficacy of metacognition for instructional design in the domain of mathematics. ZDM Mathematics Education. doi: 10.1007/s11858-017-0851-y (this issue).Google Scholar
  2. Booth, J. L., McGinn, K. M., Barbrieri, C., Begolli, K. N., Chang, B., Miller-Cotto, D., Young, L. K., & Davenport, J. L. (2017). Evidence for cognitive science principles that impact learning in mathematics. In D. C. Geary, D. B. Berch, R. J. Ochsendorf & K. M. Koepke (Eds.), Acquisition of complex arithmetic skills and higher-order mathematics concepts Vol 3 (pp. 297–325). London: Academic Press (this issue).Google Scholar
  3. Dackermann, T., Moeller, K., Fischer, U., Cress, U., & Nuerk, H.-C. (2017). Applying embodied cognition—from useful interventions and their theoretical underpinnings to practical applications. ZDM Mathematics Education. doi: 10.1007/s11858-017-0850-z (this issue).Google Scholar
  4. De Bock, D., Deprez, J., Van Dooren, W., Roelens, M., & Verschaffel, L. (2011). Abstract or concrete examples in learning mathematics? A replication and elaboration of Kaminski, Sloutsky, and Heckler’s study. Journal for Research in Mathematics Education, 42, 109–126.Google Scholar
  5. De Corte, E., Greer, B., & Verschaffel, L. (1996). Learning and teaching mathematics. In D. Berliner & R. Calfee (Eds.), Handbook of educational psychology (pp. 491–549). New York: Macmillan.Google Scholar
  6. Dunlosky, J., Rawson, K. A., Marsh, E. J., Nathan, M. J., & Willingham, D. T. (2013). What works, what doesn’t. Scientific American Mind, 24(4), 46–53.CrossRefGoogle Scholar
  7. Durkin, K., Rittle-Johnson, B., & Star, J. (2017). Using comparison of multiple strategies in the mathematics classroom: Lessons learned and next steps. ZDM Mathematics Education. doi: 10.1007/s11858-017-0853-9 (this issue).Google Scholar
  8. Duval, R. (2002). The cognitive analysis of problems of comprehension in the learning of mathematics. Mediterranean Journal for Research in Mathematics Education, 1, 1–16.Google Scholar
  9. Fischbein, E. (1990). Introduction. In P. Nesher & J. Kilpatrick (Eds.), Mathematics and cognition: A research synthesis by the International Group for the Psychology of Mathematics Education (pp. 1–13). Cambridge: Cambridge University Press.Google Scholar
  10. Freudenthal, H. (1991). Revisiting mathematics education: The China lectures. Dordrecht: Kluwer.Google Scholar
  11. Graesser, A. C., Halpern, D. F., & Hakel, M. (2008). 25 principles of learning. Washington, DC: Task Force on Lifelong Learning at Work and at Home. https://louisville.edu/ideastoaction/-/files/featured/halpern/25-principles.pdf.
  12. Jones, M. G. (2009a). Transfer, abstraction, and context. Journal for Research in Mathematics Education, 40, 80–89.Google Scholar
  13. Jones, M. G. (2009b). Examining surface features in context. Journal for Research in Mathematics Education, 40, 94–96.Google Scholar
  14. Kaminski, J. A., Sloutsky, V. M., & Heckler, A. F. (2008). The advantage of abstract examples in learning math. Science, 320, 454–455.CrossRefGoogle Scholar
  15. Koedinger, K. R., Booth, J. I., & Klahr, D. (2013). Instructional complexity and the science to constrain it. Science, 342, 935–937.CrossRefGoogle Scholar
  16. Kullberg, A., Runesson Kempe, U., & Marton, F. (2017). Teaching mathematics in lower secondary school in accordance with the variation theory of learning, appropriated by teachers. doi: 10.1007/s11858-017-0858-4 (this issue).
  17. Lehtinen, E., Hannula-Sormunen, M., McMullen, J., & Gruber, H. (2017). Cultivating mathematical skills: from drill and practice to deliberate practice. ZDM Mathematics Education. doi: 10.1007/s11858-017-0856-6 (this issue).Google Scholar
  18. Lem, S., Onghena, P., Verschaffel, L., & Van Dooren, W. (2017). Using refutational text in mathematics education. ZDM Mathematics Education. doi: 10.1007/s11858-017-0843-y (this issue).Google Scholar
  19. Pashler, H., Bain, P. M., Bottge, B. A., Graesser, A., Koedinger, K., McDaniel, M., & Metcalfe, J. (2007). Organizing instruction and study to improve student learning. IES Practice Guide. NCER 2007–2004. Washington, DC:National Center for Education Research.Google Scholar
  20. Podolefsky, N. S., & Finkelstein, N. D. (2009). Counterexamples and concerns regarding the use of abstract examples in learning math[Letter]. Retrieved August 29, 2009, from http://www.sciencemag.org/cgi/eletters/320/5875/454#11970.
  21. Rau, M., & Matthews, P. G. (2017) How to make ‘more’ better? Principles for effective use of multiple representations to enhance students’ learning about fractions. ZDM Mathematics Education. doi: 10.1007/s11858-017-0846-8 (this issue).Google Scholar
  22. Renkl, A. (2017) Interconnecting conceptual and procedural knowledge in mathematics: The worked-examples principle. ZDM Mathematics Education. doi: 10.1007/s11858-017-0859-3 (this issue).Google Scholar
  23. Rittle-Johnson, B., & Loehr, A. M., Durkin, K. (2017) Promoting self-explanation to improve mathematics learning: A meta-analysis and instructional design principles. ZDM Mathematics Education. doi: 10.1007/s11858-017-0834-z (this issue).Google Scholar
  24. Roediger, H. L. III, & Pyc, M. A. (2012). Inexpensive techniques to improve education: Applying cognitive psychology to enhance educational practice. Journal of Applied Research in Memory and Cognition, 1(4), 242–248.CrossRefGoogle Scholar
  25. Schneider, M., & Stern, E. (2010). The cognitive perspective on learning: Ten cornerstone findings. In Organisation for Economic Co-Operation and Development (OECD) (Ed.), The nature of learning: Using research to inspire practice (pp. 69–90). Paris: OECD.CrossRefGoogle Scholar
  26. Star, J. R., & Verschaffel, L. (2017). Providing support for student sense making: Recommendations from cognitive science for the teaching of mathematics. In J. Cai (Ed.), Compendium for research in mathematics education. Reston, VA: National Council of Teachers of Mathematics (in press).Google Scholar
  27. Vamvakoussi, X. (2017) Using bridging analogies to facilitate conceptual change in mathematics learning. ZDM Mathematics Education. doi: 10.1007/s11858-017-0857-5 (this issue).Google Scholar
  28. Verschaffel, L., & Greer, B. (2013). Domain-specific strategies and models: Mathematics education. In J. M. Spector, M. D. Merrill, J. Elen & M. J. Bishop (Eds.), Handbook of research on educational communications and technology (fourth edition) (pp. 553–563). New York: Springer Academic.Google Scholar
  29. Walkington, C. (2017) Designing learning personalized to students’ interests: Balancing rich experiences with mathematical goals. ZDM Mathematics Education. doi: 10.1007/s11858-017-0842-z (this issue).Google Scholar
  30. Wittmann, E. Ch. (1995). Mathematics education as a design science. Educational Studies in Mathematics, 29, 355–374.CrossRefGoogle Scholar

Copyright information

© FIZ Karlsruhe 2017

Authors and Affiliations

  1. 1.Center for Instructional Psychology and Technology, Van den Heuvel InstituutKU LeuvenLeuvenBelgium
  2. 2.Harvard School of EducationCambridgeUSA

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