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This paper presents a conceptual analysis for students’ images of graphs and their extension to graphs of two-variable functions. We use the conceptual analysis, based on quantitative and covariational reasoning,

This paper presents a conceptual analysis for students’ images of graphs and their extension to graphs of two-variable functions. We use the conceptual analysis, based on quantitative and covariational reasoning, to construct a hypothetical learning trajectory (HLT) for how students might generalize their understanding of graphs of one-variable functions to graphs of two-variable functions. To evaluate the viability of this learning trajectory, we use data from two teaching experiments based on tasks intended to support development of the schemes in the HLT.

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Date Created
  • 2014-09-01
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  • Text
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    Identifier
    • Digital object identifier: 10.1007/s10649-014-9548-0
    • Identifier Type
      International standard serial number
      Identifier Value
      0013-1954
    • Identifier Type
      International standard serial number
      Identifier Value
      1573-0816
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    Weber, Eric, & Thompson, Patrick W. (2014). Students' images of two-variable functions and their graphs. EDUCATIONAL STUDIES IN MATHEMATICS, 87(1), 67-85. http://dx.doi.org/10.1007/s10649-014-9548-0

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