An essay on the articulation between problem solving, semiotic representation registers, and the tool-object dialectic
DOI:
https://doi.org/10.5007/1981-1322.2025.e105400Keywords:
Problem-Solving, Semiotic Registers, Tool-ObjectAbstract
Based on previous observations, it can be inferred that the progress of humanity is closely linked to the ability to solve problems and understand the world around it. In this regard, various studies explore problem-solving situations and their characteristics. Among these, the focus is on the Problem-Solving bias and the potential convergence with other perspectives that discuss teaching and learning processes in Mathematics. In this context, this paper aims to outline the aspects related to Problem-Solving, articulated with the Theory of Registers of Semiotic Representation and the Dialectic of Tool-Object. Therefore, the following question is raised: in what aspects can the teaching of a mathematical object be analyzed through Problem-Solving, Registers of Semiotic Representation, and the Dialectic of Tool-Object? To address this, a qualitative bibliographic research was conducted to develop an essay on the possible correlations between the analyzed perspectives.
References
BRASIL. Ministério da Educação. (2012). Base Nacional Comum Curricular. Brasília: MEC, 2018. Recuperado de http://basenacionalcomum.mec.gov.br/
DENARDI, V. B.; BISOGNIN, E. (2020). Resolução de Problemas e Representações Semióticas na Formação Inicial de Professores de Matemática. Revista de Educação Matemática, v. 17, p. e020022-e020022, 2020. Recuperado de http://www.revistasbemsp. com.br/index.php/REMat-SP/article/view/197
DOUADY, R. (1987). Jeux de cadres et dialectique outil-objet. Recherches en didactique des mathématiques, v. 7, n. 2, p. 5-32, 1987. Recuperado de https://cir.nii.ac.jp/cr id/1570572700049163392. Acesso em: 15, out. 2024.
DOUADY, R. (1991). Tool, object, setting, window: elements for analysing and constructing didactical situations in mathematics. In: Mathematical knowledge: Its growth through teaching. Dordrecht: Springer Netherlands, 1991. p. 107-130. Recuperado de https://link.springer.com/chapter/10.1007/978-94-017-2195-0_6
DUVAL, R. (2003). Registros de representações semióticas e funcionamento cognitivo da compreensão em matemática. Aprendizagem em matemática: registros de representação semiótica. Campinas: Papirus, p. 11-33, 2003.
DUVAL, R. (2012). Registros de representação semiótica e funcionamento cognitivo do pensamento. Tradução de Méricles Thadeu Moretti. Revemat. Florianópolis, v. 07, n. 2, p. 266-297, 2012. Recuperado de https://periodicos.ufsc.br/index.php/revemat/article/view/ 27282
KRULIK, S.; RUDNICK, J. A. (1988). Problem Solving: A Handbook for Elementary School Teachers. Allyn & Bacon/Logwood Division, 160 Gould Street, Needham Heights, MA 02194-2310, 1988. Acesso em: 04, set. 2024.
LEIVAS, J. C. P. (2019). Geometria Euclidiana e do Taxi: um problema concreto e os Registros de Representações Semióticas. Revista de Educação Matemática, v. 16, n. 22, p. 252-269, 2019. Recuperado de http://www.revistasbemsp.com.br/index.php/REMat-SP/article/view/221
LAKATOS, E. M.; MARCONI, M. A. (2003). Fundamentos de metodologia científica. 2003. Recuperado de https://ria.ufrn.br/handle/123456789/3097
MENEGHETTI, F. K. (2011). O que é um ensaio-teórico? Revista Administração Contemporânea, Rio de Janeiro, v. 15, n. 2, p. 320-332, abr. 2011. Recuperado de https://www.scielo.br/j/rac/a/4mNCY 5D6rmRDPWXtrQQMyGN/
NOVAK, J. D.; CAÑAS, A. J. (2010). A teoria subjacente aos mapas conceituais e como elaborá-los e usá-los. Práxis educativa, p. 09-29, 2010. Recuperado de http://educa.fcc.org.br/scielo.php?pid=S180943092010000100002&script=sci_abstract&tl ng=en
POLYA, G. (1995). A arte de resolver problemas: um novo aspecto do método matemático. Rio de Janeiro: Interciência, 1995.
POLYA, G. (2004). How to solve it: A new aspect of mathematical method. Princeton university press, 2004.
POSSAMAI, J. P.; SILVA, V. C. (2020). Comunicação Matemática na Resolução de Problemas. Revista de Educação Matemática, v. 17, p. e020026-e020026, 2020. Recuperado de http://www.revistasbemsp.com.br/index.php/REMatSP/article/view/201
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