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Cultural-Historical Psychology

Publisher: Moscow State University of Psychology and Education

ISSN (printed version): 1816-5435

ISSN (online): 2224-8935


License: CC BY-NC 4.0

Started in 2005

Published quarterly

Free of fees
Open Access Journal

Affiliated ISCAR


Using Pictures as Cultural Means in Finding Similarities between Solutions to Algebraic Tasks 939

Kotov A.A.
PhD in Psychology, Senior Researcher, Laboratory for cognitive research, Department of Psychology, National Research University 'Higher School of Economics', Moscow, Russia

Kotova T.N.
PhD in Psychology, Senior Research Fellow, Russian Presidential Academy of National Economy and Public Administration under the President of the Russian Federation, Moscow, Russia

Solving textual algebraic tasks requires finding important mathematical variables in the text and turning them into equations. Many students, following their teacher’s advice or at their own initiative, use pictures as a means of better understanding the mathematical structure of the task. In this study we explored which features of pictures were the most essential to the students in finding the appropriate solution based on their experience. We created a set of pictures that differed in parameters of analogy and completeness of relationships between elements. The subjects were asked to evaluate the usefulness of the solution to the initial task (represented by the picture) for solving the target task. As it was revealed, in their evaluations the subjects were more likely to focus on the completeness of the depicted relationships rather than on the analogy of the picture. This tendency was also more evident in experienced subjects as compared to inexpe- rienced ones. The outcomes of our study are interpreted in terms of the development of cultural means in the transition from everyday concepts to scientific concepts in the process of learning.

Keywords: algebraic tasks, solution, representation, symbolization, cultural means

Column: Empirical Research


For Reference

  1. Akhutina T.V., Obukhova L.F., Obukhova O.B. Trudnosti usvoeniia nachal’nogo kursa matematiki v forme kvaziissledovatel’skoi deiatel’nosti [The difficulties of the initial de- velopment of the mathematics in the form of quasi–research activi- ties]. Psikhologicheskaya nauka i obrazovanie [Psychological Science and Education], 2001, no. 1. pp. 65—78. (In Russ., abstr. In Engl.).
  2. Brushlinskii A.V. Sub”ekt: myshlenie, uchenie, voo- brazhenie [Subject: thinking, learning, imagination]. Moscow: «Institut prakticheskoi psikhologii», 1996. 392 p.
  3. Valueva E., Lapteva E. Ispol’zovanie podskazok pri reshenii zadach: modal’naia spetsifichnost’ ili universal’naia sposobnost’ [Using a Cue in Problem Solving: Modal Specific- ity or Universal Ability?]. Rossiiskii zhurnal kognitivnoi nauki [The Russian Journal of Cognitive Science], 2015, no. 2 (2—3), pp. 53—65. (In Russ., abstr. In Engl.).
  4. Veraksa A.N., Iakupova V.A., Martynenko M.N. Sim- volizatsiia v strukture sposobnostei detei doshkol’nogo i shkol’nogo vozrasta [Symbolization in the Structure of Abili- ties in Children of Preschool and School Age]. Kul’turno- istoricheskaia psikhologiia [Cultural-Historical Psychology], 2015, no. 2, pp. 48—56. (In Russ., abstr. In Engl.).
  5. Vygotskii L.S. Myshlenie i rech’ [Thinking and Speech]. Moscow: Publ. Labirint, 2012. 352 p.
  6. Vygotskii L.S. Problema obucheniia i umstvennogo razvitiia v shkol’nom vozraste. Psikhologicheskaia nauka i ob- razovanie [Psychological Science and Education], 1996, no. 4, pp. 5—18.
  7. Gal’perin P.Ia. O formirovanii umstvennykh deistvii i poniatii. Kul’turno-istoricheskaia psikhologiia [Cultural-Histor- ical Psychology], 2010, no. 3, pp. 111—114. (In Russ.).
  8. Davydov V.V., Markova A.K. Kontseptsiia uchebnoi deiatel’nosti shkol’nikov [The concept of educational activity of schoolers]. Voprosy psikhologii [Questions of Psychology], 1981, no. 6, pp. 13—26. (In Russ.).
  9. Krutetskii V.A. Psikhologiya matematicheskikh spo- sobnostei shkol’nikov [Psychology of mathematical abilities of students]. Moscow: Publ. Prosveshchenie, 1968. 431 p.
  10. Spiridonov V.F. Psikhologicheskie mekhanizmy resh- eniya tekstovykh zadach po matematike [Psychological mech- anisms of solving word problems in mathematics]. Vestnik RGGU [RSUH Bulletin], 2006, no. 1, pp. 156—173. (In Russ.)
  11. Bernardo A.B. Analogical problem construction and transfer in mathematical problem solving. Educational Psychol- ogy, 2001, no. 2, pp. 137—150.
  12. Beveridge M., Parkins E. Visual representation in analogical problem solving. Memory & Cognition, 1987, no. 3, pp. 230—237.
  13. Catrambone R., Holyoak K.J. Overcoming contextual limitations on problem-solving transfer. Journal of Experimen- tal Psychology: Learning, Memory and Cognition, 1989, no. 6, pp. 1147.
  14. Charles A.W., Kintsch W. Enhancing Students’ Com- prehension of the Conceptual Structure of Algebra Word Prob- lems. Journal of Educational Psychology, 1992, no. 4, pp. 419— 428.
  15. DeLoache J.S. Symbolic functioning in very young children: Understanding of pictures and models. Child Devel- opment, 1991, no. 5, pp. 736—752.
  16. Gallistel C.R. Mental representations, psychology of. Encylopedia of the Behavioral and Social Sciences. New York: Publ. Elsevier, 2001, pp. 9691–9695.
  17. Gick M.L., Holyoak K.J. Analogical problem solving.
  18. Cognitive Psychology, 1980, no. 3, pp. 306–355.
  19. Holyoak K.J., Koh K. Surface and structural similar- ity in analogical transfer. Memory & Cognition, 1987, no. 4, pp. 332–340.
  20. Kintsch W., Weaver C.A. Enhancing students’ compre- hension of the conceptual structure of algebra word problems. Journal of Educational Psychology, 1992, no. 3, pp. 419–428.
  21. Novick L.R. Transferring symbolic representations across nonisomorphic problems. Journal of Experimental Psychology: Learning, Memory and Cognition, 1994,  no.  1, pp. 1296–1321.
  22. Ohlsson S. Learning from performance errors. Psychological Review, 1996, no. 2, pp. 241–262.
  23. Reed D.K., Dempster A., Ettinger M. Usefulness of analogous solutions for solving algebra word problems. Journal of Experimental Psychology: Learning, Memory and Cognition, 1985, no. 5, pp. 106–125.
  24. Rehder B. Detecting unsolvable algebra word problems. Journal of Educational Psychology, 1999, no. 4, pp. 669–683.
  25. Seifert C.M., McKoon G., Abelson R.P., Ratcliff R. Memory connections between thematically similar episodes. Journal of Experimental Psychology: Learning, Memory and Cognition, 1986, no. 2, pp. 220–231.
  26. Waltz J.A., Lau A., Grewal S.K., Holyoak K.J. The role of working memory in analogical mapping. Memory & Cogni- tion, 2000, no. 7, pp. 1205–1212.

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