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)

Notes

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

Desmos Activity

Mathematics Teacher: Learning and Teaching PK-12
  • Baldinger, Erin E., Sarah Kate Selling, and Rajeev Virmani. 2016. “Supporting Novice Teachers to Lead Discussions That Reach a Mathematical Point: Defining and Clarifying Mathematical Ideas.Mathematics Teacher Educator 5, no. 1 (September): 828. doi:10.5951/mathteaceduc.5.1.0008.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Cooney, Thomas J., Sybilla Beckmann, 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.

    • Search Google Scholar
    • Export Citation
  • Harel, Guershon. 2013. “Intellectual Need.” In Vital Directions for Mathematics Education Research, edited byKeith R. Leatham, 11951. New York: Springer Science+Business Media, LLC. doi:10.1007/978-1-4614-6977-3.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hillen, Amy F., and LuAnn Malik. 2013. “Sorting out Ideas about Function.Mathematics Teacher 106, no. 7 (March): 52633. doi:10.5951/mathteacher.106.7.0526.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kobiela, Marta, and Richard Lehrer. 2015. “The Codevelopment of Mathematical Concepts and the Practice of Defining.Journal for Research in Mathematics Education 46, no. 4 (July): 42354. doi:10.5951/jresematheduc.46.4.0423.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • National Council of Teachers of Mathematics (NCTM). 2014. Principles to Actions: Ensuring Mathematical Success for All. Reston, VA: NCTM.

    • Search Google Scholar
    • Export Citation
  • Raymond, Kate Meredith. 2015/2016. “Making Sense of Representations: Card Sorting.” Mathematics Teacher 109, no. 5 (December/January): 38085. doi:10.5951/mathteacher.109.5.0380.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smith, Margaret Schwan, and Mary Kay Stein. 2011. 5 Practices for Orchestrating Productive Mathematical Discussions. Reston, VA: National Council of Teachers of Mathematics.

    • Search Google Scholar
    • Export Citation
  • Vinner, Shlomo. 1991. “The Role of Definitions in the Teaching and Learning of Mathematics.” In Advanced Mathematical Thinking, edited byDavid Tall, pp. 6581. Dordrecht: Kluwer Academic Press.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 15 15 6
Full Text Views 0 0 0
PDF Downloads 3 3 0
EPUB Downloads 0 0 0