An approach to the design of mathematical task sequences: Conceptual learning as abstraction

Martin A. Simon

Resumen


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

Este artículo describe una aproximación emergente al diseño de secuencias de tareas y la teoría que la sustenta. La aproximación pretende promover conceptos matemáticos concretos como resultado de una abstracción reflexiva. Es central en esta aproximación la identificación de actividades disponibles para los estudiantes con las que puedan abstraer las ideas pretendidas. La aproximación difiere de aquellas en las que el aprendizaje para resolver problemas es el aprendizaje que se pretende. El artículo ilustra la aproximación a través de datos de un experimento de enseñanza sobre la división de fracciones.

Handle: http://hdl.handle.net/10481/41628

WOS-ESCI


Palabras clave


Abstracción reflexiva; Ingeniería didáctica; Tareas matemáticas; Teoría de aprendizaje

Citas


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.


Texto completo: PDF (English)

Refbacks





La descarga de archivos se rige por la licencia Creative Commons Reconocimiento-No comercial-Sin obras derivadas

ISSN: 1887-3987