Abstract
Solving mathematical problems, as well as understanding mathematical concepts, very often involves building and handling representations. Representations are a powerful means for a person to communicate with and reflect on his environment. They can be a tool for dialogue both with oneself and with others.
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References
Boero P., Ferrari, P.L., Ferrero, E. (1989). Division problems for children aged 8 to 10 in a curricular project: meanings and procedures in the transition to a written algorithm, For the Learning of Mathematics 9-3, pp. 17–25.
2 Boero, P. (1991). The crucial role of semantic fields in the development of problemsolving skills in the school environment. In: J.P. Ponte, J.F. Matos, J.M. Matos, and D. Fernandes (eds), Mathematical problem solving and new information technologies. Springer Verlag, NATO ASI Series, Series F, vol. 89, pp. 77–91.
Bottino, R.M., Chiappini G., Ferrari, P.L. (1993). Arithmetic Microworlds in a Hypermedia System for Problem Solving, Proc.Intern. Conf. Techn. in Math. Teaching, TMT93, Birmingham, UK, pp. 157–164.
Bottino, R.M., Chiappini, G. (1993). ARI-LAB: Models,Issues and Strategies in the Design of a Hypermedia Problem Solving System. Proc. Intern. PEG Conf., Edinburgh, UK, vol. 11, pp. 409–420.
Dörfler, W. (1991). Meaning: image schemata and protocols. Proc. PME XV, Assisi, Italy, F. Furinghetti (ed.), pp. 17–39.
Dreyfus, T. (1990) On difficulty with Diagrams: theoretical issues. Proc. PME XIV, Mexico, G. Booker, P. Cobb, T. Mendicuti (eds), pp. 27–34.
Dreyfus, T. (1991). On the states of Visual Reasoning, in Mathematics and Mathematics Education. Proc. PME XV, Assisi, Italy, F. Furinghetti (ed.), pp. 33–48.
Dufour-Janvier B., Bednarz N., Belanger M. (1987). Pedagogical Considerations Concerning the Problem of Representation. In C. Janvier (ed.), Problems of Representation in the teaching and Learning of Mathematics, LEA, pp. 109–122.
Douady, R. (1986). Jeux de cadres et dialectique outil-object. Recherches en Didactique des Mathematiques, Vol. 7, N. 2, pp. 5–31.
Ferrara A., Scali, E. (1991). Alcuni aspetti linguistici della risoluzione dei problemi aritmetici e della rappresenta-zione delle risoluzioni nel primo ciclo. Working Papers of the National Congress “Internuclei Scuola Elementare”.
Fishbein E., Tirosh D., Stavy R., Oster A. (1990). The Autonomy of Mental Models. For the Learning of Mathematics, 101, 23–30.
Lesh R., Post T., Behr, M. (1987). Representations and Translations Among Representations in Mathematics Learning and Problem Solving. In C. Janvier (ed.) Problems of Representation in the Teaching and Learning of Mathematics, Laurence Erlbaum Associates, pp. 33–40.
Scali E., Ferrara, A. (1992). Aspetti cognitivi e didattici della transizione dalla comprensione della situazione problematica alla risoluzione del problema. National Congress “Intergruppi Scuola Elementare”.
Vergnaud G. (1986). Interactions sujet-situations, Comptes Rendus III Ecole D’ETE de Didactique des Mathématiques, Grenoble, IMAG.
Bibliography
Bondesan, M.G., Ferrari, P.L. (1991). The active comparison of strategies in problem solving: An Exploratory Study. Proc. of PME XV, Assisi (Italy), F. Furinghetti (ed.), pp. 168–175.
Kaputt, J.J. (1991). Notations and Representations as a mediators of constructive processes. In: Von Glaserfeld E. (ed.) Radical Constructivism in Mathematics Education, pp. 53–74.
Nesher, P. (1986). Are mathematics understanding and algorithmic performance related? For the Learning of Mathematics, Vol. 6 N. 3, pp. 2–9.
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Dettori, G., Lemut, E. (1995). External Representations in Arithmetic Problem Solving. In: Sutherland, R., Mason, J. (eds) Exploiting Mental Imagery with Computers in Mathematics Education. NATO ASI Series, vol 138. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57771-0_2
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DOI: https://doi.org/10.1007/978-3-642-57771-0_2
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