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  5.     <title>UTas ePrints - Developing student's understandings and representations of statistical covariation</title>
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  13.     <meta content="Moritz, Jonathan" name="eprints.creators_name" />
  14. <meta content="thesis" name="eprints.type" />
  15. <meta content="2007-07-26" name="eprints.datestamp" />
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  18. <meta content="Developing student's understandings and representations of statistical covariation" name="eprints.title" />
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  24. <meta content="statistical covariation, education, graph production and graph interpretation, speculative data generation, statistical literacy" name="eprints.keywords" />
  25. <meta content="Statistical covariation refers to the correspondence of variation of two
  26. statistical measures that vary along numerical scales. Reasoning about covariation
  27. commonly involves translation processes among three representations: (1) numerical
  28. data, (2) graphical representations, and (3) verbal statements such as &quot;taller people
  29. tend to be heavier&quot;. Two well-known translations are graph production and graph
  30. interpretation. Less well known is the process of speculative data generation,
  31. involving translating a verbal statement into a possible graph or other data
  32. representation. This study explored school students' reasoning involving these three
  33. translation skills through various tasks in surveys and interviews. Evidence is
  34. presented concerning methods to assess these skills, and concerning how students as
  35. young as third-grade can engage covariation tasks involving familiar contexts.
  36. Interviews involved prompting for cognitive conflict using responses from other
  37. students, and provided evidence of limited engagement of ideas that were slightly
  38. more sophisticated than their own responses.
  39. Responses for each of the three translation skills were described within
  40. assessment frameworks involving four levels - Nonstatistical, Single Statistical
  41. Aspect, Inadequate Covariation, and Appropriate Covariation - distinguished by the
  42. structure of combining correspondence and variation. Distinguishing features of the
  43. levels suggested stages of development that may inform instruction. For
  44. development from prior beliefs to data-based judgements, tasks involving
  45. counterintuitive covariation were designed to prompt students to engage data. For
  46. development from single variables to bivariate data, time was observed as a natural
  47. covariate, implicit in statements such as &quot;it's getting hotter&quot;, with a connotation of
  48. order that supported pattern recognition of passing time being associated with corresponding change in a measured variable. For development from single cases to
  49. global trends, many students represented correspondence in a single pair of values, at
  50. the expense of representing variation. Tasks involving discrete data with few cases,
  51. and the use of case labels in responses, were observed to support the view of two
  52. data values each linked to the same corresponding case label. This consolidated view
  53. of correspondence supported consideration of additional bivariate cases involving
  54. variation. Students tended to articulate covariation using the language of comparison
  55. and change.
  56. Findings were related to issues in the historical development of coordinate
  57. graphing, to findings from educational research in statistics, algebra, science and
  58. psychology, and to recommendations within curriculum documents. Student
  59. representations of statistical covariation were observed to provide a window into
  60. statistical reasoning, and are advocated as a valuable basis for classroom discussions
  61. to help develop statistical literacy." name="eprints.abstract" />
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  70. <meta content="Moritz, Jonathan (2006) Developing student's understandings and representations of statistical covariation. PhD thesis, University of Tasmania." name="eprints.citation" />
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  79. <meta content="Statistical covariation refers to the correspondence of variation of two
  80. statistical measures that vary along numerical scales. Reasoning about covariation
  81. commonly involves translation processes among three representations: (1) numerical
  82. data, (2) graphical representations, and (3) verbal statements such as &quot;taller people
  83. tend to be heavier&quot;. Two well-known translations are graph production and graph
  84. interpretation. Less well known is the process of speculative data generation,
  85. involving translating a verbal statement into a possible graph or other data
  86. representation. This study explored school students' reasoning involving these three
  87. translation skills through various tasks in surveys and interviews. Evidence is
  88. presented concerning methods to assess these skills, and concerning how students as
  89. young as third-grade can engage covariation tasks involving familiar contexts.
  90. Interviews involved prompting for cognitive conflict using responses from other
  91. students, and provided evidence of limited engagement of ideas that were slightly
  92. more sophisticated than their own responses.
  93. Responses for each of the three translation skills were described within
  94. assessment frameworks involving four levels - Nonstatistical, Single Statistical
  95. Aspect, Inadequate Covariation, and Appropriate Covariation - distinguished by the
  96. structure of combining correspondence and variation. Distinguishing features of the
  97. levels suggested stages of development that may inform instruction. For
  98. development from prior beliefs to data-based judgements, tasks involving
  99. counterintuitive covariation were designed to prompt students to engage data. For
  100. development from single variables to bivariate data, time was observed as a natural
  101. covariate, implicit in statements such as &quot;it's getting hotter&quot;, with a connotation of
  102. order that supported pattern recognition of passing time being associated with corresponding change in a measured variable. For development from single cases to
  103. global trends, many students represented correspondence in a single pair of values, at
  104. the expense of representing variation. Tasks involving discrete data with few cases,
  105. and the use of case labels in responses, were observed to support the view of two
  106. data values each linked to the same corresponding case label. This consolidated view
  107. of correspondence supported consideration of additional bivariate cases involving
  108. variation. Students tended to articulate covariation using the language of comparison
  109. and change.
  110. Findings were related to issues in the historical development of coordinate
  111. graphing, to findings from educational research in statistics, algebra, science and
  112. psychology, and to recommendations within curriculum documents. Student
  113. representations of statistical covariation were observed to provide a window into
  114. statistical reasoning, and are advocated as a valuable basis for classroom discussions
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  230.     <h1 class="ep_tm_pagetitle">Developing student's understandings and representations of statistical covariation</h1>
  231.     <p style="margin-bottom: 1em" class="not_ep_block"><span class="person_name">Moritz, Jonathan</span> (2006) <xhtml:em>Developing student's understandings and representations of statistical covariation.</xhtml:em> PhD thesis, University of Tasmania.</p><p style="margin-bottom: 1em" class="not_ep_block"></p><table style="margin-bottom: 1em" class="not_ep_block"><tr><td valign="top" style="text-align:center"><a onmouseover="EPJS_ShowPreview( event, 'doc_preview_1878' );" href="http://eprints.utas.edu.au/1473/1/jm-Front.pdf" onmouseout="EPJS_HidePreview( event, 'doc_preview_1878' );"><img alt="[img]" src="http://eprints.utas.edu.au/style/images/fileicons/application_pdf.png" class="ep_doc_icon" border="0" /></a><div class="ep_preview" id="doc_preview_1878"><table><tr><td><img alt="" src="http://eprints.utas.edu.au/1473/thumbnails/1/preview.png" class="ep_preview_image" border="0" /><div class="ep_preview_title">Preview</div></td></tr></table></div></td><td valign="top"><a href="http://eprints.utas.edu.au/1473/1/jm-Front.pdf"><span class="ep_document_citation">PDF (Front Matter)</span></a> - Requires a PDF viewer<br />88Kb</td></tr><tr><td valign="top" style="text-align:center"><a onmouseover="EPJS_ShowPreview( event, 'doc_preview_1879' );" href="http://eprints.utas.edu.au/1473/2/jm-Whole.pdf" onmouseout="EPJS_HidePreview( event, 'doc_preview_1879' );"><img alt="[img]" src="http://eprints.utas.edu.au/style/images/fileicons/application_pdf.png" class="ep_doc_icon" border="0" /></a><div class="ep_preview" id="doc_preview_1879"><table><tr><td><img alt="" src="http://eprints.utas.edu.au/1473/thumbnails/2/preview.png" class="ep_preview_image" border="0" /><div class="ep_preview_title">Preview</div></td></tr></table></div></td><td valign="top"><a href="http://eprints.utas.edu.au/1473/2/jm-Whole.pdf"><span class="ep_document_citation">PDF (Whole Thesis)</span></a> - Requires a PDF viewer<br />7Mb</td></tr></table><div class="not_ep_block"><h2>Abstract</h2><p style="padding-bottom: 16px; text-align: left; margin: 1em auto 0em auto">Statistical covariation refers to the correspondence of variation of two
  232. statistical measures that vary along numerical scales. Reasoning about covariation
  233. commonly involves translation processes among three representations: (1) numerical
  234. data, (2) graphical representations, and (3) verbal statements such as "taller people
  235. tend to be heavier". Two well-known translations are graph production and graph
  236. interpretation. Less well known is the process of speculative data generation,
  237. involving translating a verbal statement into a possible graph or other data
  238. representation. This study explored school students' reasoning involving these three
  239. translation skills through various tasks in surveys and interviews. Evidence is
  240. presented concerning methods to assess these skills, and concerning how students as
  241. young as third-grade can engage covariation tasks involving familiar contexts.
  242. Interviews involved prompting for cognitive conflict using responses from other
  243. students, and provided evidence of limited engagement of ideas that were slightly
  244. more sophisticated than their own responses.
  245. Responses for each of the three translation skills were described within
  246. assessment frameworks involving four levels - Nonstatistical, Single Statistical
  247. Aspect, Inadequate Covariation, and Appropriate Covariation - distinguished by the
  248. structure of combining correspondence and variation. Distinguishing features of the
  249. levels suggested stages of development that may inform instruction. For
  250. development from prior beliefs to data-based judgements, tasks involving
  251. counterintuitive covariation were designed to prompt students to engage data. For
  252. development from single variables to bivariate data, time was observed as a natural
  253. covariate, implicit in statements such as "it's getting hotter", with a connotation of
  254. order that supported pattern recognition of passing time being associated with corresponding change in a measured variable. For development from single cases to
  255. global trends, many students represented correspondence in a single pair of values, at
  256. the expense of representing variation. Tasks involving discrete data with few cases,
  257. and the use of case labels in responses, were observed to support the view of two
  258. data values each linked to the same corresponding case label. This consolidated view
  259. of correspondence supported consideration of additional bivariate cases involving
  260. variation. Students tended to articulate covariation using the language of comparison
  261. and change.
  262. Findings were related to issues in the historical development of coordinate
  263. graphing, to findings from educational research in statistics, algebra, science and
  264. psychology, and to recommendations within curriculum documents. Student
  265. representations of statistical covariation were observed to provide a window into
  266. statistical reasoning, and are advocated as a valuable basis for classroom discussions
  267. to help develop statistical literacy.</p></div><table style="margin-bottom: 1em" cellpadding="3" class="not_ep_block" border="0"><tr><th valign="top" class="ep_row">Item Type:</th><td valign="top" class="ep_row">Thesis (PhD)</td></tr><tr><th valign="top" class="ep_row">Keywords:</th><td valign="top" class="ep_row">statistical covariation, education, graph production and graph interpretation, speculative data generation, statistical literacy</td></tr><tr><th valign="top" class="ep_row">Subjects:</th><td valign="top" class="ep_row"><a href="http://eprints.utas.edu.au/view/subjects/330109.html">330000 Education &gt; 330100 Education Studies &gt; 330109 Assessment and Evaluation</a><br /><a href="http://eprints.utas.edu.au/view/subjects/330100.html">330000 Education &gt; 330100 Education Studies</a><br /><a href="http://eprints.utas.edu.au/view/subjects/330202.html">330000 Education &gt; 330200 Curriculum Studies &gt; 330202 Curriculum Studies - Mathematics Education</a></td></tr><tr><th valign="top" class="ep_row">ID Code:</th><td valign="top" class="ep_row">1473</td></tr><tr><th valign="top" class="ep_row">Deposited By:</th><td valign="top" class="ep_row"><span class="ep_name_citation"><span class="person_name">Ms Sandy von Allmen</span></span></td></tr><tr><th valign="top" class="ep_row">Deposited On:</th><td valign="top" class="ep_row">26 Jul 2007</td></tr><tr><th valign="top" class="ep_row">Last Modified:</th><td valign="top" class="ep_row">09 Jan 2008 02:30</td></tr><tr><th valign="top" class="ep_row">ePrint Statistics:</th><td valign="top" class="ep_row"><a target="ePrintStats" href="/es/index.php?action=show_detail_eprint;id=1473;">View statistics for this ePrint</a></td></tr></table><p align="right">Repository Staff Only: <a href="http://eprints.utas.edu.au/cgi/users/home?screen=EPrint::View&amp;eprintid=1473">item control page</a></p>
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