Students need opportunities to construct definitions in mathematics. We describe a sorting activity that can help students construct and refine definitions through discussion and argumentation. We include examples from our own work of planning and implementing this sorting activity to support constructing a definition of linear function.

Supplementary Materials

Supplemental Materials (PDF 658 KB)

Supplemental Materials (PDF 125 KB)

Footnotes

This activity can help middle and high school students construct and refine a definition of linear function through discussion and argumentation.

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Baldinger, Erin E., Sarah KateSelling, and RajeevVirmani. 2016. “Supporting Novice Teachers to Lead Discussions That Reach a Mathematical Point: Defining and Clarifying Mathematical Ideas.” )| false

Cooney, Thomas J., SybillaBeckmann, and Gwendolyn M.Lloyd. 2010. Developing Essential Understanding of Functions for Teaching Mathematics in Grades 9–12. Edited byPatricia S.Wilson. Essential Understanding series. Reston, VA: National Council of Teachers of Mathematics.

Cooney, Thomas J., SybillaBeckmann, and Gwendolyn M.Lloyd. 2010. )| false

Kobiela, Marta, and RichardLehrer. 2015. “The Codevelopment of Mathematical Concepts and the Practice of Defining.” Journal for Research in Mathematics Education46, no. 4 (July): 423–54. doi:10.5951/jresematheduc.46.4.0423.

Smith, Margaret Schwan, and Mary KayStein. 2011. 5 Practices for Orchestrating Productive Mathematical Discussions. Reston, VA: National Council of Teachers of Mathematics.

Smith, Margaret Schwan, and Mary KayStein. 2011. )| false

Vinner, Shlomo. 1991. “The Role of Definitions in the Teaching and Learning of Mathematics.” In Advanced Mathematical Thinking, edited byDavidTall, pp. 65–81. Dordrecht: Kluwer Academic Press.

Vinner, Shlomo. 1991. “The Role of Definitions in the Teaching and Learning of Mathematics.” In )| false