An approach to the design of mathematical task sequences: Conceptual learning as abstraction
DOI:
https://doi.org/10.30827/pna.v10i4.6083Palavras-chave:
Abstracción reflexiva, Ingeniería didáctica, Tareas matemáticas, Teoría de aprendizajeResumo
This paper describes an emerging approach to the design of task sequences and the theory that undergirds it. The approach aims at promoting particular mathematical concepts, understood as the result of reflective abstraction. Central to this approach is the identification of available student activities from which students can abstract the intended ideas. The approach differs from approaches in which learning to solve the problem posed is the intended learning. The paper illustrates the approach through data from a teaching experiment on division of fractions.
Una aproximación al diseño de secuencias de tareas matemáticas: aprendizaje conceptual como abstracción
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Referências
DiSessa, A., & Cobb, P. (2004). Ontological innovation and the role of theory in design experiments. The Journal of the Learning Sciences, 13(1), 77-103.
Gravemeijer, K. P. E. (1994). Developing realistic mathematics education. Utrecht, The Netherlands: CD-ß Press/Freudenthal Institute.
Hershkowitz, R., Schwarz, B., & Dreyfus, T. (2001). Abstraction in context: Epistemic actions. Journal for Research in Mathematics Education, 32(2), 195-222.
Mitchelmore, M. C., & White, P. (2008). Teaching mathematics concepts: Instruction for abstraction. In M. Niss (Ed.), ICME-10 Proceedings [CD]. Denmark: Roskilde University, IMFUFA, Department of Science, Systems and Models.
Piaget, J. (2001). Studies in reflecting abstraction (R. L. Campbell, Ed. & Trans.). Philadelphia, PA: Psychology Press.
Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114-145.
Simon, M. A. (2006). Key developmental understandings in mathematics: A direction for investigating and establishing learning goals. Mathematical Thinking and Learning, 8(4), 359-371.
Simon, M. A. (in press). Explicating mathematical concept and mathematical conception as theoretical constructs for mathematics education research. Educational Studies in Mathematics.
Simon, M. A., Placa, N., & Avitzur, A. (2016). Participatory and anticipatory stages of mathematical concept learning: Further empirical and theoretical development. Journal for Research in Mathematics Education, 47(1), 63-93.
Simon, M. A., Saldanha, L., McClintock, E., Karagoz Akar, G., Watanabe, T., & Ozgur Zembat, I. (2010). A developing approach to studying students' learning through their mathematical activity. Cognition and Instruction, 28(1), 70-112.
von Glasersfeld, E. (1995). A constructivist approach to teaching. In L. Steffe & J. Gale (Eds.), Constructivism in Education (pp. 3-16). Hillsdale, NJ: Lawrence Erlbaum.