Following the template: transfer of modeling skills to new problems



The importance of the ability of mathematical modeling as a method of application of mathematics in different contexts is emphasized in numerous studies. It is unknown, however, what happens to the skill of modeling formed on typical tasks in solving problems with atypical context. In the sample 106 first-year students, we experimentally verified how transfer occurs of modeling stages from a typical problem on an atypical, but structurally similar one. The results of the study of modeling skills transfer show that with close and distant transfer the success of different stages of modeling is different. With the close transfer, the formal template reproduction takes place, without the alignment with the text of a new problem, which hinders further interpretation. With the distant transfer, modeling skills are replaced with an ordinary way of addressing problems, a simple selection. Thus, modeling skills as a multi-stage process transforms differently in close and distant transfer.

General Information

Keywords: transfer, mathematical modeling, verbally formulated task, atypical context

Journal rubric: Psychology of Thinking

Article type: scientific article


For citation: Tyumeneva Y.A., Goncharova M.V. Following the template: transfer of modeling skills to new problems. Eksperimental'naâ psihologiâ = Experimental Psychology (Russia), 2016. Vol. 9, no. 1, pp. 69–81. DOI: 10.17759/exppsy.2016090106. (In Russ., аbstr. in Engl.)


  1. Salmina N.G. Znak i simvol v obuchenii [Sign and symbol in learning]. Moscow, Izd-vo Moskovskogo universiteta, 1988,216 p. (in Russ.).
  2. Tyumeneva Ju. A. Istochniki oshibok pri vypolnenii obydennyh matetmtaicheskih zadanij [Sources for errors when real-life mathematic problems are solving], Voprosy psihologii [Questions of psychology], 2015. no. 2. pp. 21-31 (in Russ.; abstract in English).
  3. Fridman L. M. Nagljadnost’ i modelirovanie v obuchenii [Visual aids and modeling in learning], Moscow, Znanie, 1984. T. 80. 69 p. (in Russ.).
  4. Barnett S. М., Ceci S. J. When and where do we apply what we learn?: A taxonomy for far transfer. Psy­chological Bulletin, 2002, vol. 128, no 4, pp. 612-637. doi:10.1037/0033-2909.128.4.612
  5. Berends I. E., van Lieshout E. C. D. M. The effect of illustrations in arithmetic problem-solving: Effects of increased cognitive load. Learning and Instruction, 2009, vol. 19, no. 4, pp. 345-353. doi:10.1016/j.leam- instruc.2008.06.012
  6. Blessing S. B., Ross В. H. Content effects in problem categorization and problem solving. Journal of Ex­perimental Psychology: Learning, Memory, and Cognition, 1996, vol. 22, no. 3, pp. 792. doi: 10.1037/00332909.128.4.612
  7. Blum, W., Ferri R. B. Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 2009, vol. 1, no. 1, pp. 45-58. Retrieved from php/modelling/article/view/1620
  8. Day S. B., Goldstone R. L. The Import of Knowledge Export: Connecting Findings and Theories of Trans­fer of Learning. Educational Psychologist, 2012, vol. 47, no. 3, pp. 153-176. doi:10.1080/00461520.2012.69 6438
  9. Dewolf Т., Dooren W. van., Hermens F., Verschaffel L. Do students attend to representational illustra­tions of non-standard mathematical word problems, and, if so, how helpful are they? Instructional Science, 2015, vol. 43, no. 1, pp. 147-171. doi:10.1007/sl 1251-014-9332-7
  10. Frejd R Modes of modelling assessment — a literature review. Educational Studies in Mathematics, 2013, vol. 84, no. 3, pp. 413-438. doi:10.1007/sl0649-013-9491-5
  11. Gick M. L., Holyoak K. J. Analogical problem solving. Cognitive Psychology, 1980, no. 12, pp. 306-355.
  12. Gick M. L., Holyoak K.J. Schema induction and analogical transfer. Cognitive Psychology, 1983, vol. 15, no. 1, pp. 1-38. doi: 10.1016/0010-0285(83)90002-6
  13. Hickendorff M. The Effects of Presenting Multidigit Mathematics Problems in a Realistic Context on Sixth Graders’ Problem Solving. Cognition and Instruction, 2013, vol. 31, no. 3, pp. 314-344.
  14. Markman A. B. Structural alignment, similarity, and the internal structure of category representations. Ox­ford University Press, 2001, p. 109.
  15. Martin S. A., Bassok M. Effects of semantic cues on mathematical modeling: Evidence from word- problem solving and equation construction tasks. Memory cognition, 2005, vol. 33, no. 3, pp. 471-478. doi:10.3758/BF03193064
  16. Mayer R. Frequency norms and structural analysis of algebra story problems into families, categories, and templates. Instructional Science, 1981, no. 10, pp. 135-175. doi:10.1007/BF00132515
  17. Rapp М., Bassok, М., DeWolf, М., Holyoak, K. J. Modeling discrete and continuous entities with frac­tions and decimals./омпга/ of Experimental Psychology: Applied, 2015, vol. 21, no. 1, pp. 47-56.
  18. Van Dooren W., De Bock D., Vleugels K., Verschaffel L. Just Answering ... or Thinking? Contrasting Pupils’ Solutions and Classifications of Missing-Value Word Problems. Mathematical Thinking and Lear­ning, 2010, vol. 12, no. 1, pp. 20-35.

Information About the Authors

Yu. A. Tyumeneva, PhD in Psychology, Senior Research Associate of Institute of Education, National Research University Higher School of Economics, Russia, e-mail:

M. V. Goncharova, Master student, Institute of Education, National Research University Higher School of Economics, e-mail:



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