Sobre processos de aprendizagem da matemática e suas funções epistemológica, conceitual e cognitiva
Tipo de documento
Autores
Lista de autores
Márcia-M.-F., Pinto y Scheiner, Thorsten
Resumen
A pesquisa atual sobre aprendizagem da Matemática reconhece que os indivíduos atribuem significado a objetos de seu pensamento. No entanto, alguns processos dinâmicos e interativos envolvidos na atribuição de significado não estão suficientemente especificados. Aqui, o foco é direcionado a três desses processos: contextualizar, complementarizar e complexificar. Os objetivos do artigo são estender as perspectivas existentes sobre tais processos e destacar aspectos epistemológico, conceitual e cognitivo que são significativos para a aprendizagem da Matemática. Para tal, uma agenda de pesquisa é elaborada colocando em diálogo diferentes perspectivas teóricas e posições. Argumentamos que os três processos – contextualizar, complementarizar e complexificar –, juntos, constituem um modelo interpretativo para a aprendizagem da Matemática de uma perspectiva da atribuição de significados.
Fecha
2022
Tipo de fecha
Estado publicación
Términos clave
Aprendizaje | Cognición | Conceptual-teórico | Epistemología
Enfoque
Nivel educativo
Idioma
Revisado por pares
Formato del archivo
Volumen
36
Número
72
Rango páginas (artículo)
495-514
ISSN
19804415
Referencias
ARZARELLO, F.; BAZZINI, L.; CHIAPPINI, G. A model for analysing algebraic processes of thinking. In: SUTHERLAND, R.; ROJANO, T.; BELL, A.; LINS, R. (ed.). Perspectives on school algebra. Dordrecht: Kluwer, 2001. p. 61-81. ASSUDE, T.; BOERO, P.; HERBST, P.; LERMAN, S.; RADFORD, L. The notions and roles of theory in mathematics education research. In: INTERNATIONAL CONGRESS ON MATHEMATICAL EDUCATION, 11., 2008, Monterrey. Proceedings […] Monterrey: ICMI, 2008. p. 338-356. BIKNER-AHSBAHS, A.; PREDIGER, S. Networking of theories: an approach for exploiting the diversity of theoretical approaches. In: SRIRAMAN, B.; ENGLISH, L. (ed.). Theories of mathematics education: Seeking new frontiers. New York: Springer, 2010. p. 183-506. BIKNER-AHSBAHS, A.; PREDIGER, S. (ed.) Networking of theories as a research practice in mathematics education. New York: Springer, 2014. CAMPBELL, J. I. (ed.). Handbook of mathematical cognition. New York: Psychology Press, 2005. COBB, P. Putting philosophy to work. In: LESTER, F. (ed.). Second handbook of research on mathematics teaching and learning. Greenwich: Information Age Publishing, 2007. p. 3-38. D’AMORE, B. Objetos, significados, representaciones semióticas y sentido. Revista Latinoamericana de Investigación en Matemática Educativa, Del. Gustavo A. Madero, v. 9, n. 1, p. 177-196, 2006. diSESSA, A.; LEVIN, M.; BROWN, N. (ed.). Knowledge and interaction: A synthetic agenda for the learning sciences. New York: Routledge, 2016. DUVAL, R. Signe et objet (I): Trois grandes étapes dans la problématique des rapports entre représentations et objet. Annales de Didactique et de Sciences Cognitives, Strasbourg, v. 6, n. 1, p. 139- 163, 1998a. DUVAL, R. Signe et objet (II): Questions relatives à l’analyse de la connaissance. Annales de Didactique et de Sciences Cognitives, Strasbourg, v. 6, n. 1, p. 165-196, 1998b. DUVAL, R. A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, Dordrecht, v. 61, n. 1-2, p. 103-131, 2006. FAUCONNIER, G.; TURNER, M. The way we think: Conceptual blending and the mind’s hidden complexities. New York: Basic Books, 2002. FONT, V.; GODINO, J. D.; GALLARDO, J. The emergence of objects from mathematical practices. Educational Studies in Mathematics, Dordrecht, v. 82, n. 1, p. 97-124, 2013. FREGE, G. Über Begriff und Gegenstand. Vierteljahresschrift für wissenschaftliche Philosophie, Norderstedt: Hansebooks GmbH, v. 16, p. 192-205, 1892a. FREGE, G. Über Sinn und Bedeutung. Zeitschrift für Philosophie und philosophische Kritik, Leipzig v. 100, p. 25-50, 1892b. FREGE, G. Der Gedanke: Eine logische Untersuchung. Beiträge zur Philosophie des deutschen Idealismus, Berlin: Junker&Dunnhaupt, v. 2, p. 58-77, 1918/1919. KILPATRICK, J.; HOYLES, C.; SKOVSMOSE, O.; VALERO, P. (ed.). Meaning in mathematics education. New York: Springer, 2005. KOESTLER, A. The act of creation. London: Hutchinson, 1964. LERMAN, S. Cultural, discursive psychology: a sociocultural approach to studying the teaching and learning of mathematics. Educational Studies in Mathematics, Dordrecht, v. 46, n. 1-3, p. 87-113, 2001. LINS, R. Por que discutir teoria do conhecimento é relevante para a Educação Matemática. In: BICUDO, M. A. V. (ed.). Pesquisa em Educação Matemática: concepções & perspectivas. São Paulo: Editora UNESP, 1999. p. 75-94. OTTE, M. Mathematical epistemology from a Peircean semiotic point of view. Educational Studies in Mathematics, Dordrecht, v. 61, n. 1-2, p. 11-38, 2006. OTTE, M. F. Evolution, learning, and semiotics from a Peircean point of view. Educational Studies in Mathematics, Dordrecht, v. 77, n. 2-3, p. 313-329, 2011. OTTE, M. F.; BARROS, L. G. X. About complementarity. Jornal Internacional de Estudos em Educação Matemática, Londrina, v. 10, n. 1, p. 2-7, 2017. PIAGET, J. Studies in reflecting abstraction: Recherches sur l’ abstraction réfléchissante. Tradução de R. Campbell. Philadelphia: Psychology Press, 2001. (Trabalho original publicado em 1977). PINTO, M. M. F. Students’ understanding of real analysis. PhD thesis, The Warwick University. Coventry: University of Warwick, 1998. PINTO, M. M. F. Making sense of students’ sense making of mathematics. In: GÓMEZ, D. M. (ed.). In: PME REGIONAL CONFERENCE: SOUTH AMERICA, 1., Rancágua, Chile. 2018. Proceedings […]. Rancagua: PME, 2018. p. 31-45. PINTO, M. M. F.; SCHEINER, T. Visualização e ensino de análise matemática. Educação Matemática Pesquisa, São Paulo, v. 17, n. 3, p. 637-654, 2015. PINTO, M. M. F.; SCHEINER, T. Making sense of students’ sense making through the lens of the structural abstraction framework. In: CONFERENCE OF THE INTERNATIONAL NETWORK FOR DIDACTIC RESEARCH IN UNIVERITY MATHEMATICS, 1., Montpelier, France. 2016. Proceedings […]. Montpellier: INDRUM, 2016. p. 472-483. RADFORD, L. The seen, the spoken and the written: a semiotic approach to the problem of objectification of mathematical knowledge. For the Learning of Mathematics, New Westminster, v. 22, n. 2, p. 14-23, 2002. RADFORD, L. Three key concepts of the theory of objectification: knowledge, knowing, and learning. Journal of Research in Mathematics Education, Reston, v. 2, n. 1, p. 7-44, 2013. RADFORD, L.; SCHUBRING, G.; SEEGER, F. Signifying and meaning-making in mathematical thinking, teaching, and learning. Educational Studies in Mathematics, Dordrecht, v. 77, n. 2-3, p. 149-156, 2011. SCHEINER, T. New light on old horizon: Constructing mathematical concepts, underlying abstraction processes, and sense making strategies. Educational Studies in Mathematics, Dordrecht, v. 91, n. 2, p. 165-183, 2016. SCHEINER, T. Conception to concept or concept to conception? From being to becoming. In: CONFERENCE OF THE INTERNATIONAL GROUP FOR THE PSYCHOLOGY OF MATHEMATICS EDUCATION, 41., Singapore, 2017. Proceedings […]. Singapore: PME. 2017, v. 4. p. 145-152. SCHEINER, T. If we want to get ahead, we should transcend dualisms and foster paradigm pluralism. In: KAISER, G.; PRESMEG, N. (ed.). Compendium for early career researchers in mathematics education. Cham: Springer, 2019. p. 511-532. SCHEINER, T. Dealing with opposing theoretical perspectives: Knowledge in structures or knowledge in pieces? Educational Studies of Mathematics, Dordrecht, v. 104, n. 1, p. 127-145, 2020. SCHEINER, T.; PINTO, M. M. F. Images of abstraction in mathematics education: contradictions, controversies, and convergences. In: CONFERENCE OF THE INTERNATIONAL GROUP FOR THE PSYCHOLOGY OF MATHEMATICS EDUCATION, 40., Szeged, Hungary, 2016. Proceedings […]. Szeged: PME, 2016, v. 4. p. 155-162. SCHEINER, T.; PINTO, M. M. F. Theoretical advances in mathematical cognition. In: PME REGIONAL CONFERENCE: SOUTH AMERICA, 1., Rancagua, Chile, 2018. Proceedings […]. Rancagua: PME, 2018, p. 97-104. SCHEINER, T.; PINTO, M. M. F. Emerging perspectives in mathematical cognition: contextualizing, complementizing, and complexifying. Educational Studies in Mathematics, Dordrecht, v. 101, n. 3, p. 357-372, 2019. SCHOENFELD, A. H. Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In: GROUWS, D. (ed.). Handbook of research on mathematics teaching and learning. Reston: NCTM, 1992. p. 334-370. SCHUBRING, G. Conceptions for relating the evolution of mathematical concepts to mathematics learning: epistemology, history, and semiotics interacting. Educational Studies in Mathematics, Dordrecht, v. 77, n. 1, p. 79-104, 2011. SFARD, A. Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge: Cambridge University Press, 2008. SIERPINSKA, A.; KILPATRICK, J. (ed.). Mathematics education as a research domain: A search for identity. Dordrecht: Kluwer, 1998. SKOVSMOSE, O. Interpretações de significado em educação matemática. Bolema, Rio Claro, v. 32, n. 62, p. 764-780, dez. 2018. TALL, D. O. How humans learn to think mathematically: Exploring the three worlds of mathematics. Cambridge: Cambridge University Press, 2013. VAN OERS, B. From context to contextualizing. Learning and Instruction, Amsterdam: Elsevier Science, v. 8, n. 6, p. 473-488, 1998. VYGOTSKY, L. S. The genesis of higher mental functions. In: RIEBER, R. W. (ed.). The collected works of L. S. Vygotsky: The history of the development of higher mental functions. New York: Springer, 1997, p. 97-120. v. 4.