Interlocuções e saberes docentes em interações on-line: um estudo de caso com professores de Matemática

Autores

  • Marcelo A. Bairral Universidade Federal Rural do Rio de Janeiro
  • Arthur B. Powell Rutgers University

Palavras-chave:

Ambiente virtual. VMT. Interações docentes. Raciocínio matemá- tico. Geometria do táxi

Resumo

Integrando matemática, educação, comunicação, TIC e ciência cognitiva, este artigo é resultado de um projeto de pesquisa em Educação Matemática que, através de estudos empíricos, tem como objetivo analisar situações cognitivas e condições pedagógicas que favoreçam a aprendizagem em ambientes virtuais. O enquadramento teórico da investigação é baseado em estudos sobre aprendizagem matemática que combinam a comunicação e o pensamento, bem como as interações e as interlocuções. Aqui analisamos reflexões on-line entre os professores de Matemática dentro de um ambiente chamado Virtual Math Teams (VMT), colaborando para resolver um problema de geometria do táxi. Ilustramos diferentes tipos de interlocução (informativa, negociativa, avaliativa e interpretativa), bem como domínios de conhecimentos (epistemologia, didática e mediação) identificados com o conhecimento profissional dos professores. Nossos resultados indicam que interlocuções interpretativas e negociativas têm maior potencial para aprimorar o pensamento matemá- tico dos interlocutores. O estudo também destaca que, por meio da identificação e da análise de propriedades de interlocução, os pesquisadores podem obter insights sobre o conhecimento profissional dos professores.

Abstract

Integrating mathematics, education, communication, ICT, and cognitive science, this study is the result of a research program in mathematics education that aims to analyze cognitive situations and pedagogic conditions, through empirical studies, that favor learning in virtual environments. The theoretical framework of the investigation is based on studies of mathematics learning that combine communication and thought as well as interactions and interlocutions. In this article, we analyze interactions among mathematics teachers who interact online within an environment, called Virtual Math Teams (VMT), collaborating to solve a problem in taxicab geometry. We illustrate different types of interlocution (evaluative, informative, interpretative, negotiatory) as well as knowledge domains (epistemology, didactics, and mediation) identified by the teachers’ professional knowledge. Our results indicate that interpretative and negotiatory interlocutions have greater potential to enhance interlocutors’ mathematical thinking. Our study also highlights that by identifying and analyzing interlocution properties, researchers can obtain insights into the teachers’ professional knowledge.

Key words Virtual environment. VMT. Teachers’ interaction. Mathematical reasoning. Taxicab geometry

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Biografia do Autor

Arthur B. Powell, Rutgers University

Dr. Arthur B. Powell has forged international collaborations in mathematics education.  He has established partnerships between mathematics educators at Rutgers University and those in Mozambique, South Africa, Brazil and Haiti; most recently, he and a Rutgers University, Newark, graduate student went to Haiti to establish a professional development project for elementary school teachers called Elevating Learning above Teaching.

Referências

ABERDEIN, A. The Informal Logic of Mathematical Proof. In: HERSH, R. (Org.). 18 Unconventional Essays on the Nature of Mathematics. New York: Springer, 2006. p.56-70.

BAIRRAL, M. A. et al. Análise de interações de estudantes do Ensino Médio em chats. Educação e Cultura Contemporânea, v.4, n.7, p.113-138, 2007.

DAVIS, B. Teaching Mathematics: Toward a Sound Alternative. New York: Garland, 1996.

DÖRFLER, W. Means for Meaning. In: COBB, P. et al. (Ed.). Symbolizing and Communicating in Mathematics Classrooms: Perspectives on Discourse, Tools, and Instructional Design. Mahwah, NJ: Lawrence Erlbaum Associates, 2000. p. 99-131.

GATTEGNO, C. The Science of Education: Part 1: Theoretical Considerations. New York: Educational Solutions, 1987.

INGLIS, M. et al. Modelling Mathematical Argumentation: The Importance of Qualification. Educational Studies in Mathematics, v.66, n.1, p. 3-21, 2007.

LEHRER, R. et al. The Interrelated Development of Inscription and Conceptual Understanding.

In: COBB, P. et al. (Org.). Symbolizing and Communicating in Mathematics Classrooms: Perspectives on Discourse, Tools, and Instructional Design. Mahwah, NJ: Lawrence Erlbaum Associates, 2000. p.325-360.

LESH, R.; LEHRER, R. Iterative Refinement Cycles for Videotape Analyses of Conceptual Change. In: KELLY, A. E.; LESH, R. (Org.). Handbook of Research Data Design in Mathematics and Science Education. Mahwah, NJ: Lawrence Erlbaum, 2000. p. 665-708.

LO, J.-J.; GADDIS, K. Problem Centered Learning for Prospective Elementary School Teachers: Focusing on Mathematical Tasks. In: REYNOLDS, A. (Org.). Problem-Centered Learning in Mathematics: Reaching All Students. Saarbrücken, Germany: Lambert Academic, 2010. p.123-136.

MARTIN, L. C. Growing Mathematical Understanding: Teaching and Learning as Listening and Sharing. In: SPEISER, R. et al. (Org.). Proceedings of the Twenty-Third Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Snowbird, Utah). Columbus, OH: ERIC, 2001. p.245-253.

MARTIN, L. et al. Collective Mathematical Understanding as Improvisation. Mathematical Thinking and Learning, v.8, n.2, p.149-183, 2006.

POWELL, A. B. Socially Emergent Cognition: Particular Outcome of Student-to-Student Discursive Interaction During Mathematical Problem Solving. Horizontes, v. 24, n. 1, p. 33-42, 2006.

POWELL, A. B. “So Let’s Prove It!”: Emergent and Elaborated Mathematical Ideas and Reasoning in the Discourse and Inscriptions of Learners Engaged in a Combinatorial Task. Tese (Doutorado) — Department of Learning and Teaching, Rutgers, The State University of New Jersey, New Brunswick, 2003.

POWELL, A. B.; LAI, F. F. Inscription, Mathematical Ideas, and Reasoning in Vmt. In: STAHL, G. (Org.). Studying Virtual Math Teams. New York: Springer, 2009. p. 237-259.

RASMUSSEN, C.; STEPHAN, M. A Methodology for Documenting Collective Activity. In: KELLY, A. E. et al. (Org.). Handbook of Design Research Methods in Education: Innovations in Science, Technology, Engineering, and Mathematics Learning and Teaching. New York: Routledge, 2008.

SALLES, A. T.; BAIRRAL, M. A. Identificando e analisando heurísticas em interações no VMT-Chat. In: BAIRRAL, M. A. (Org.). Pesquisa, ensino e inovação com tecnologias em educação matemática: de calculadoras a ambientes virtuais. Rio de Janeiro: Edur, 2012a. p. 117-139. (Série InovaComTic, v. 4).

SALLES, A. T.; BAIRRAL, M. A. Interações docentes e aprendizagem matemática em um ambiente virtual. Investigações em Ensino de Ciências (IENCI), v.17, n.2, p. 453- 466, 2012b.

SFARD, A. Symbolizing Mathematical Reality into Being — or How Mathematical Discourse and Mathematical Objects Create Each Other. In: COBB, P. et al. (Org.). Symbolizing and Communicating in Mathematics Classrooms: Perspectives on Discourse, Tools, and Instructional Design. Mahwah, NJ: Lawrence Erlbaum Associates, 2000. p.37-98.

SFARD, A. Thinking as Communicating: Human Development, the Growth of Discourses, and Mathematizing. Cambridge: Cambridge, 2008.

SPEISER, B. et al. Preservice Teachers Undertake Division in Base Five: How Inscriptions Support Thinking and Communication. In: NEWBORN, D. S. et al. (Org.). Proceedings of the Twenty-Fourth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Athens, Georgia). Columbus, OH: ERIC, 2002. p.1153-1162.

SPEISER, B. et al. Representing Motion: An Experiment in Learning. The Journal of Mathematical Behavior, v.22, n.1, p.1-35, 2003.

STAHL, G. Mathematical Discourse as Group Cognition. In: STAHL, G. (Org.). Studying Virtual Math Teams. New York: Springer, 2009. p. 31-40 STEPHAN, M.; RASMUSSEN, C. Classroom Mathematical Practices in Differential Equations. Journal of Mathematical Behavior, v.21, p. 459-490, 2002.

STRUIK, D. J. A Concise History of Mathematics. New York: Dover, 1967.

TOULMIN, S. The Uses of Arguments. Cambridge: Cambridge, 1969.

WALTON, D. N. Dialog Theory for Critical Argumentation. Philadelphia: John Benjamins, 2007.

WALTON, D. N. The New Dialectic. Buffalo, NY: University of Toronto, 1992.

WEBER, K. et al. Learning Opportunities from Group Discussions: Warrants Become the Objects of Debate. Educational Studies in Mathematics, v.68, n.3, p. 247-261, 2008.

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Publicado

2016-01-06

Como Citar

BAIRRAL, M. A.; POWELL, A. B. Interlocuções e saberes docentes em interações on-line: um estudo de caso com professores de Matemática. Pro-Posições, Campinas, SP, v. 24, n. 1, p. 61–77, 2016. Disponível em: https://periodicos.sbu.unicamp.br/ojs/index.php/proposic/article/view/8642661. Acesso em: 31 jan. 2023.

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