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Developing student's understandings and representations of statistical covariation


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Moritz, J 2006 , 'Developing student's understandings and representations of statistical covariation', PhD thesis, University of Tasmania.

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Statistical covariation refers to the correspondence of variation of two
statistical measures that vary along numerical scales. Reasoning about covariation
commonly involves translation processes among three representations: (1) numerical
data, (2) graphical representations, and (3) verbal statements such as "taller people
tend to be heavier". Two well-known translations are graph production and graph
interpretation. Less well known is the process of speculative data generation,
involving translating a verbal statement into a possible graph or other data
representation. This study explored school students' reasoning involving these three
translation skills through various tasks in surveys and interviews. Evidence is
presented concerning methods to assess these skills, and concerning how students as
young as third-grade can engage covariation tasks involving familiar contexts.
Interviews involved prompting for cognitive conflict using responses from other
students, and provided evidence of limited engagement of ideas that were slightly
more sophisticated than their own responses.
Responses for each of the three translation skills were described within
assessment frameworks involving four levels - Nonstatistical, Single Statistical
Aspect, Inadequate Covariation, and Appropriate Covariation - distinguished by the
structure of combining correspondence and variation. Distinguishing features of the
levels suggested stages of development that may inform instruction. For
development from prior beliefs to data-based judgements, tasks involving
counterintuitive covariation were designed to prompt students to engage data. For
development from single variables to bivariate data, time was observed as a natural
covariate, implicit in statements such as "it's getting hotter", with a connotation of
order that supported pattern recognition of passing time being associated with corresponding change in a measured variable. For development from single cases to
global trends, many students represented correspondence in a single pair of values, at
the expense of representing variation. Tasks involving discrete data with few cases,
and the use of case labels in responses, were observed to support the view of two
data values each linked to the same corresponding case label. This consolidated view
of correspondence supported consideration of additional bivariate cases involving
variation. Students tended to articulate covariation using the language of comparison
and change.
Findings were related to issues in the historical development of coordinate
graphing, to findings from educational research in statistics, algebra, science and
psychology, and to recommendations within curriculum documents. Student
representations of statistical covariation were observed to provide a window into
statistical reasoning, and are advocated as a valuable basis for classroom discussions
to help develop statistical literacy.

Item Type: Thesis - PhD
Authors/Creators:Moritz, J
Keywords: statistical covariation, education, graph production and graph interpretation, speculative data generation, statistical literacy
Journal or Publication Title: xx
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