research-article

The role of definition in supporting mathematical activity

Authors:

Marta Kobiela,

Rich LehrerAuthors Info & Claims

ICLS '10: Proceedings of the 9th International Conference of the Learning Sciences - Volume 2

Pages 380 - 381

Published: 29 June 2010 Publication History

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Abstract

Definition is a form of mathematical activity that is fundamental to the profession's emphasis on conjecture, theorem and proof, yet is often treated in school as rote memory. We describe an alternative approach in which sixth-graders invented and revised definitions during investigations of space and geometry. Defining led to contest about taken-for-granted intuitions. A mathematical system emerged as relations among defined objects were constructed and extended, first by conjecture and later by theorem and proof.

References

[1]

Abelson, H., & diSessa, A. (1980). Turtle geometry: The computer as a medium for exploring mathematics. Cambridge, MA: MIT Press.

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[2]

Goldenberg, E. P., Cuoco, A. A. & Mark, J. (1998). In R. Lehrer & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 3--44). Mahwah, NJ: Erlbaum.

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[3]

Lehrer, R., Randle, L., & Sancilio, L. (1989). Learning pre-proof geometry with Logo. Cognition and Instruction, 6, 159--184.

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[4]

Senechal, M. (1990). Shape. In L. A. Steen (Ed.), On the shoulders of giants. New approaches to numeracy, (pp. 139--181). Washington, D.C.: National Academy Press.

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[5]

Vinner, S. (1991). The role of definitions in the teaching and learning of mathematics. In Tall, D. (Ed). Advanced Mathematical Thinking. Dordrecht: Kluwer

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Information & Contributors

Information

Published In

ICLS '10: Proceedings of the 9th International Conference of the Learning Sciences - Volume 2

June 2010

629 pages

Conference Chairs:
Susan Goldman
University of Illinois at Chicago
,
James Pellegrino
University of Illinois at Chicago
,
Editors:
Kimberly Gomez
University of Pittsburgh
,
Leilah Lyons
University of Illinois at Chicago
,
Joshua Radinsky
University of Illinois at Chicago

Publisher

International Society of the Learning Sciences

Publication History

Published: 29 June 2010

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