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Reasoning About Variation

In: The Challenge of Developing Statistical Literacy, Reasoning and Thinking

Author

Listed:
  • Chris Reading

    (University of New England)

  • J. Michael Shaughnessy

    (Portland State University)

Abstract

Summary Basically two main aspects of variation have come to light in these descriptions. One aspect is how spread out the numbers are. Students give responses that suggest that some indication of variation is being considered when they are dealing with extreme values using the range. The other aspect is what is happening with the numbers contained within that range. Responses considering the behavior of the middle values may give specific information about the numbers; or they may just give attributes that are necessary for the numbers, such as wanting them to be different. When these two aspects of variation description are brought together, deviations begin to become an issue; and when these deviations are anchored to a specific value, usually a center of some description, it will eventually become the focus of the student’s description of a distribution. These hierarchies were developed to code how responses may demonstrate reasoning about variation. Coding of student responses, according to a spread scale, was reported in Shaughnessy et al. (1999). These hierarchies are describing reasoning in relation to variation, from two perspectives: how students describe the variation and how they attribute cause to variation.

Suggested Citation

  • Chris Reading & J. Michael Shaughnessy, 2004. "Reasoning About Variation," Springer Books, in: Dani Ben-Zvi & Joan Garfield (ed.), The Challenge of Developing Statistical Literacy, Reasoning and Thinking, chapter 0, pages 201-226, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4020-2278-4_9
    DOI: 10.1007/1-4020-2278-6_9
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