Research in Science Education

, Volume 49, Issue 2, pp 499–520 | Cite as

The Use of Learning Study in Designing Examples for Teaching Physics

  • Jian-Peng GuoEmail author
  • Ling-Yan Yang
  • Yi Ding


Researchers have consistently demonstrated that studying multiple examples is more effective than studying one example because comparing multiple examples can promote schema construction and facilitate discernment of critical aspects. Teachers, however, are usually absent from those self-led text-based studies. In this experimental study, a learning study approach based on variation theory was adopted to examine the effectiveness of teachers’ different ways of designing multiple examples in helping students learn a physics principle. Three hundred and fifty-one tenth-grade students learned to distinguish action-reaction from equilibrium (a) by comparing examples that varied critical aspects first separately and then simultaneously, or (b) by comparing examples that separately varied critical aspects only. Results showed that students with average academic attainment benefited more from comparing examples in the first condition. Students with higher academic attainment learned equally within both conditions. This finding supports the advantage of simultaneous variation. The characteristics of students and instructional support should be taken into account when considering the effectiveness of patterns of variation.


Comparison Multiple examples Learning study Variation theory Physics learning 



This research was based on the project “Creating Effective Teaching Context in Different Subject Areas” supported by the China Fundamental Research Funds for the Central Universities (2013221021).


  1. Albro, E., Uttal, D., De Loache, J., Kaminski, J. A., Sloutsky, V. M., Heckler, A. F., et al. (2007). Fostering transfer of knowledge in education settings. In D. S. McNamara & G. Trafton (Eds.), Proceedings of the 29th meeting of the Cognitive Science Society (pp. 21–22). Austin: Cognitive Science Society.Google Scholar
  2. Anderson, J. R. (1993). Rules of the mind. Hillsdale: Erlbaum.Google Scholar
  3. Catrambone, R. (1995). Aiding subgoal learning: effects on transfer. Journal of Educational Psychology, 87, 5–17.CrossRefGoogle Scholar
  4. Catrambone, R. (1996). Generalizing solution procedures learned from examples. Journal of Experimental Psychology: Learning, Memory, & Cognition, 22(4), 1020–1031.Google Scholar
  5. Catrambone, R., & Holyoak, K. J. (1989). Overcoming contextual limitations on problem-solving transfer. Journal of Experimental Psychology: Learning, Memory, & Cognition, 15(6), 1147–1156.Google Scholar
  6. Clarke, T., Ayres, P., & Sweller, J. (2005). The impact of sequencing and prior knowledge on learning mathematics through spreadsheet applications. Educational Technology Research and Development, 53(3), 15–24.CrossRefGoogle Scholar
  7. Cooper, G., & Sweller, J. (1987). Effects of schema acquisition and rule automation on mathematical problem-solving transfer. Journal of Educational Psychology, 79, 347–362.CrossRefGoogle Scholar
  8. Gentner, D. (2005). The development of relational category knowledge. In D. H. Rakison & L. Gershkoff-Stowe (Eds.), Building object categories in developmental time (pp. 245–275). Mahwah: Erlbaum.Google Scholar
  9. Gentner, D., & Namy, L. L. (1999). Comparison in the development of categories. Cognitive Development, 14(4), 487–513.CrossRefGoogle Scholar
  10. Gentner, D., Loewenstein, J., & Hung, B. (2007). Comparison facilitates children’s learning of names for parts. Journal of Cognition and Development, 8(3), 285–307.CrossRefGoogle Scholar
  11. Guo, J. P., & Pang, M. F. (2011). Learning a mathematical concept from comparing examples: the importance of variation and prior knowledge. European Journal of Psychology of Education, 26, 495–525.CrossRefGoogle Scholar
  12. Guo, J. P., Pang, M. F., Yang, L. Y., & Ding, Y. (2012). Learning from comparing multiple examples: on the dilemma of “similar” or “different”. Educational Psychology Review, 24, 251–269.CrossRefGoogle Scholar
  13. Guo, J. P., Yang, L. Y., & Ding, Y. (2014). Effects of example variability and prior knowledge in how students learn to solve equations. European Journal of Psychology of Education, 29, 21–42.CrossRefGoogle Scholar
  14. Hammer, R., Bar-Hillel, A., Hertz, T., Weinshall, D., & Hochstein, S. (2008). Comparison processes in category learning: from theory to behavior. Brain Research, 1225, 102–118.CrossRefGoogle Scholar
  15. Ingerman, Å., Berge, M., & Booth, S. (2009). Physics group work in a phenomenographic perspective-learning dynamics as the experience of variation and relevance. European Journal of Engineering Education, 34(4), 349–358.CrossRefGoogle Scholar
  16. Kalyuga, S. (2006). Rapid assessment of learners’ proficiency: a cognitive load approach. Educational Psychology, 26(6), 735–749.CrossRefGoogle Scholar
  17. Kalyuga, S., & Sweller, J. (2004). Measuring knowledge to optimize cognitive load factors during instruction. Journal of Educational Psychology, 96(3), 558–568.CrossRefGoogle Scholar
  18. Ki, W. W. (2007). The enigma of Cantonese tones: how intonation language speakers can be assisted to discern them. (Unpublished doctoral dissertation). University of Hong Kong.Google Scholar
  19. Linder, C., Fraser, D., & Pang, M. F. (2006). Using a variation approach to enhance physics learning in a college classroom. The Physics Teacher, 44, 589–592.CrossRefGoogle Scholar
  20. Lo, M. L., Chik, P., & Pang, M. F. (2006). Patterns of variation in teaching the colour of light to primary 3 students. Instructional Science, 34, 1–19.CrossRefGoogle Scholar
  21. Ma, L. (1999). Knowing and teaching elementary mathematics. Mahwah: Erlbaum.Google Scholar
  22. Marton, F. (1999, August). Variatio est mater Studiorum. Opening address delivered to the 8th European Association for Research on learning and instruction biennial conference, Goteborg, Sweden.Google Scholar
  23. Marton, F., & Booth, S. (1997). Learning and awareness. Mahwah: Erlbaum.Google Scholar
  24. Marton, F., & Morris, P. (2002). What matters? Discovering critical conditions of classroom learning. Kompendiet, Goteborg, Sweden: Acta Universitatis Gothoburgensis.Google Scholar
  25. Marton, F., & Pang, M. F. (2006). On some necessary conditions of learning. Journal of the Learning Sciences, 15(2), 193–220.CrossRefGoogle Scholar
  26. Marton, F., & Tsui, A. B. M. (2004). Classroom discourse and the space of learning. Mahwah: Erlbaum.Google Scholar
  27. Namy, L. L., & Clepper, L. E. (2010). The differing roles of comparison and contrast in children’s categorization. Journal of Experimental Child Psychology, 107, 291–305.CrossRefGoogle Scholar
  28. Pang, M. F. (2002). Making learning possible: the use of variation in the teaching of school economics. (Unpublished doctoral dissertation). University of Hong Kong.Google Scholar
  29. Pang, M. F., & Marton, F. (2003). Beyond lesson study: comparing two ways of facilitating the grasp of some economic concepts. Instructional Science, 31(3), 175–194.CrossRefGoogle Scholar
  30. Pang, M. F., & Marton, F. (2005). Learning theory as teaching resource: enhancing students’ understanding of economic concepts. Instructional Science, 33(2), 159–191.CrossRefGoogle Scholar
  31. Pang, M. F., & Marton, F. (2013). Interaction between the learners’ initial grasp of the object of learning and the learning resource afforded. Instructional Science, 41(6), 1065–1082.CrossRefGoogle Scholar
  32. Prosser, M., & Millar, R. (1989). The “how” and “what” of learning physics. European Journal of Psychology of Education, 4(4), 513–528.CrossRefGoogle Scholar
  33. Quilici, J. L., & Mayer, R. E. (1996). Role of examples in how students learn to categorize statistics word problems. Journal of Educational Psychology, 88, 144–161.CrossRefGoogle Scholar
  34. Renkl, R. (2014). Toward an instructional oriented theory of example-based learning. Cognitive Science, 38(1), 1–37.CrossRefGoogle Scholar
  35. Renkl, A., Stark, R., Gruber, H., & Mandl, H. (1998). Learning from worked-out examples: the effects of example variability and elicited self-explanations. Contemporary Educational Psychology, 23, 90–108.CrossRefGoogle Scholar
  36. Richland, L. E., & McDonough, I. M. (2010). Learning by analogy: discriminating between potential analogs. Contemporary Educational Psychology, 35, 28–43.CrossRefGoogle Scholar
  37. Rittle-Johnson, B., & Star, J. R. (2007). Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations. Journal of Educational Psychology, 99(3), 561–574.CrossRefGoogle Scholar
  38. Rittle-Johnson, B., & Star, J. R. (2009). Compared with what? The effects of different comparisons on conceptual knowledge and procedural flexibility for equation solving. Journal of Educational Psychology, 101(3), 529–544.CrossRefGoogle Scholar
  39. Rittle-Johnson, B., Star, J. R., & Durkin, K. (2009). The importance of prior knowledge when comparing examples: influences on conceptual and procedural knowledge of equation solving. Journal of Educational Psychology, 101(4), 836–852.CrossRefGoogle Scholar
  40. Schwartz, D. L., & Martin, T. (2004). Inventing to prepare for future learning: the hidden efficiency of encouraging original student production in statistics instruction. Cognition and Instruction, 22(2), 129–184.CrossRefGoogle Scholar
  41. Silver, E. A., Ghousseini, H., Gosen, D., Charalambous, C., & Strawhun, B. (2005). Moving from rhetoric to praxis: issues faced by teachers in having students consider multiple solutions for problems in the mathematics classroom. Journal of Mathematical Behavior, 24, 287–301.CrossRefGoogle Scholar
  42. Staples, M. (2007). Supporting whole-class collaborative inquiry in a secondary mathematics classroom. Cognition and Instruction, 25(2), 161–217.CrossRefGoogle Scholar
  43. Stigler, J. W., & Hiebert, J. (1999). The teaching gap: best ideas from the world’s teachers for improving education in the classroom. New York: The Free Press.Google Scholar
  44. Svensson, L. (1989). The conceptualization of cases of physical motion. European Journal of Psychology of Education, 4(4), 529–545.CrossRefGoogle Scholar
  45. Sweller, J. (2010). Element interactivity and intrinsic, extraneous, and germane cognitive load. Educational Psychology Review, 22, 123–138.CrossRefGoogle Scholar
  46. Sweller, J., & Cooper, G. A. (1985). The use of worked examples as a substitute for problem solving in learning algebra. Cognition and Instruction, 2, 59–89.CrossRefGoogle Scholar
  47. Wittwer, J., & Renkl, A. (2010). How effective are instructional explanations in example-based learning? A meta-analytic review. Educational Psychology Review, 22, 393–409.CrossRefGoogle Scholar
  48. Zhu, X., & Simon, H. A. (1987). Learning mathematics from examples and by doing. Cognition and Instruction, 4, 137–166.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Institute of EducationXiamen UniversityXiamenChina
  2. 2.School of Public AffairsXiamen UniversityXiamenChina
  3. 3.Graduate School of EducationFordham UniversityBronxUSA

Personalised recommendations