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Using Pictures as Cultural Means in Finding Similarities between Solutions to Algebraic Tasks 927
PhD in Psychology, Senior Researcher, Laboratory for cognitive research, Department of Psychology, National Research University 'Higher School of Economics', Moscow, Russia
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.
- 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.).
- Brushlinskii A.V. Sub”ekt: myshlenie, uchenie, voo- brazhenie [Subject:
thinking, learning, imagination]. Moscow: «Institut prakticheskoi psikhologii»,
1996. 392 p.
- 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.).
- 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.).
- Vygotskii L.S. Myshlenie i rech’ [Thinking and Speech]. Moscow: Publ.
Labirint, 2012. 352 p.
- 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.
- 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.).
- 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.).
- Krutetskii V.A. Psikhologiya matematicheskikh spo- sobnostei shkol’nikov
[Psychology of mathematical abilities of students]. Moscow: Publ.
Prosveshchenie, 1968. 431 p.
- 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.)
- Bernardo A.B. Analogical problem construction and transfer in mathematical
problem solving. Educational Psychol- ogy, 2001, no. 2, pp.
- Beveridge M., Parkins E. Visual representation in analogical problem
solving. Memory & Cognition, 1987, no. 3, pp. 230—237.
- 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.
- 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.
- DeLoache J.S. Symbolic functioning in very young children: Understanding of
pictures and models. Child Devel- opment, 1991, no. 5, pp. 736—752.
- Gallistel C.R. Mental representations, psychology of. Encylopedia of the
Behavioral and Social Sciences. New York: Publ. Elsevier, 2001, pp.
- Gick M.L., Holyoak K.J. Analogical problem solving.
- Cognitive Psychology, 1980, no. 3, pp. 306–355.
- Holyoak K.J., Koh K. Surface and structural similar- ity in analogical
transfer. Memory & Cognition, 1987, no. 4, pp. 332–340.
- 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.
- Novick L.R. Transferring symbolic representations across nonisomorphic
problems. Journal of Experimental Psychology: Learning, Memory and
Cognition, 1994, no. 1, pp. 1296–1321.
- Ohlsson S. Learning from performance errors. Psychological Review,
1996, no. 2, pp. 241–262.
- 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.
- Rehder B. Detecting unsolvable algebra word problems. Journal of
Educational Psychology, 1999, no. 4, pp. 669–683.
- 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.
- 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.