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Following the template: transfer of modeling skills to new problems 846
PhD in Psychology, Senior Research Associate of Institute of Education, National Research University Higher School of Economics, Russia
Master student, Institute of Education, National Research University Higher School of Economics
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.
- Salmina N.G. Znak i simvol v obuchenii [Sign and symbol in learning].
Moscow, Izd-vo Moskovskogo universiteta, 1988,216 p. (in Russ.).
- 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).
- Fridman L. M. Nagljadnost’ i modelirovanie v obuchenii [Visual aids and
modeling in learning], Moscow, Znanie, 1984. T. 80. 69 p. (in Russ.).
- 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.
- 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-
- 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
- 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
- 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
- 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
- Frejd R Modes of modelling assessment — a literature review. Educational
Studies in Mathematics, 2013, vol. 84, no. 3, pp. 413-438.
- Gick M. L., Holyoak K. J. Analogical problem solving. Cognitive Psychology,
1980, no. 12, pp. 306-355.
- Gick M. L., Holyoak K.J. Schema induction and analogical transfer.
Cognitive Psychology, 1983, vol. 15, no. 1, pp. 1-38. doi:
- 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.
- Markman A. B. Structural alignment, similarity, and the internal structure
of category representations. Oxford University Press, 2001, p. 109.
- 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
- 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
- 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.
- 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.