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    <title>UTas ePrints - Statistical variation in a chance setting: a two-year study</title>
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    <meta content="Watson, Jane M." name="eprints.creators_name" />
<meta content="Kelly, Ben A." name="eprints.creators_name" />
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<meta content="A series of 13 survey questions based on a 50-50 spinner is used to explore
school students’ understanding of statistical variation in a chance setting. Five questions
set the context by assessing the understanding of theoretical expectation and representation
of repeated trials in a stacked dot (line) plot. Four questions provide opportunity to display
appreciation of variation from point expectation and four questions address variation from
distributional expectation. Three hundred and seventy-five students in Grades 3–9 answered
some or all of these questions. These students then took part in a unit of study on chance and
data emphasizing variation. Of these students, 334 answered a post-test including the same
items and a further subset of 199 students completed a longitudinal survey of the same items
two years later. Analysis of the initial data showed a progression of understanding across
the years of schooling, plateauing at Grade 7, improvement for all grades after instruction,
and generally sustained and continuing improved performance after two years. Educational
issues are considered." name="eprints.abstract" />
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Introducing Data Analysis in the Schools: Who Should Teach It? International Statistical
Institute, Voorburg, The Netherlands, pp. 219–239.
Kelly, B.A. and Watson, J.M.: 2002, ‘Variation in a chance sampling setting: The
lollies task’, in B. Barton, K.C. Irwin, M. Pfannkuch and M.O.J. Thomas (eds.),
Mathematics Education in the South Pacific: Proceedings of the 25th Annual
Conference of the Mathematics Research Group of Australasia, Auckland, NZ, Vol. 2,
MERGA,Sydney, pp. 366–373.
Konold, C. and Higgins, T.L.: 2002, ‘Working with Data: Highlights Related to Research’,
in S.J. Russell, D. Schifter and V. Bastable (eds.), Developing Mathematical Ideas:
Collecting, Representing, and Analyzing Data, Dale Seymour Publications, Parsippany,
NJ, pp. 165–201.
Lee, C. (ed.): 2003, Reasoning About Variability: Proceedings of the Third International
Research Forum on Statistical Reasoning, Thinking, and Literacy [CD-ROM], Central
Michigan University, Mt. Pleasant, MI.
Moore, D.S.: 1990. ‘Uncertainty’, in L.A. Steen (ed.), On the Shoulders of Giants: New
Approaches to Numeracy, National Academy Press, Washington, D.C., pp. 95–137.
National Council of Teachers of Mathematics: 2000, Principles and Standards for School
Mathematics, Author, Reston, VA.
Reading, C. and Shaughnessy, M.: 2000, ‘Student perceptions of variation in a sampling
situation’, in T. Nakahara and M. Koyama (eds.), Proceedings of the 24th Conference of
the International Group for the Psychology of Mathematics Education, Vol. 4,Hiroshima
University, Hiroshima, pp. 89–96.
Shaughnessy, J.M.: 1997, ‘Missed opportunities in research on the teaching and learning of
data and chance’, in F. Biddulph and K. Carr (eds.), People in Mathematics Education:
Proceeding of the 20th Annual Conference for the Mathematics Education Research
Group of Australasia, MERGA, Rotorua, NZ, pp. 6–12.
Shaughnessy, J.M.: 2003, ‘Research on students’ understandings of probability’, in J.
Kilpatrick, W. Martin and B. Schifter (eds.), A Research Companion to Principles
and Standards for School Mathematics, National Council of Teachers of Mathematics,
Reston, VA, pp. 216–226.
Shaughnessy, J.M., Canada, D. and Ciancetta, M.: 2003, ‘Middle school students’ thinking
about variability in repeated trials: A cross-task comparison’, in N.A. Pateman,
B.J. Dougherty and J.T. Zilliox (eds.), Proceedings of the 27th Conference of the
International Group for the Psychology of Mathematics Education Held Jointly with
the 25th Conference of PME-NA, Vol. 4, Center for Research and Development Group,
University of Hawaii, Honolulu, HI, pp. 159–165.
Shaughnessy, J.M.,Watson, J., Moritz, J. and Reading, C.: 1999, April, ‘School mathematics
students’ acknowledgment of statistical variation’, in C. Maher (Chair), There’s More
to Life Than Centers, Presession Research Symposium Conducted at the 77th Annual
National Council of Teachers of Mathematics Conference, San Francisco, CA.
Torok, R.: 2000, ‘Putting the variation into chance and data’, Australian Mathematics
Teacher 56(2), 25–31.
Torok, R. and Watson, J.: 2000, ‘Development of the concept of statistical variation: An
exploratory study’, Mathematics Education Research Journal 12, 147–169.
Watson, J.M. and Kelly, B.A.: 2002a, ‘Can Grade 3 students learn about variation?’,
in B. Phillips (ed.), Proceedings of the Sixth International Conference on Teaching
Statistics: Developing a Statistically Literate Society, Cape Town, South Africa,
International Statistical Institute, Voorburg, The Netherlands.
Watson, J.M. and Kelly, B.A.: 2002b, ‘Grade 5 students’ appreciation of variation’, in A.
Cockburn and E. Nardi (eds.), Proceedings of the 26th Conference of the International
Group for the Psychology of Mathematics Education, Vol. 4, University of East Anglia,
Norwich, UK, pp. 385–392.
Watson, J.M. and Kelly, B.A.: 2002c, ‘Variation as part of chance and data in Grades
7 and 9’, in B. Barton, K.C. Irwin, M. Pfannkuch and M.O.J. Thomas (eds.),
Mathematics Education in the South Pacific: Proceedings of the 25th Annual
Conference of the Mathematics Research Group of Australasia, Auckland, NZ, Vol. 2,
MERGA,Sydney, pp. 682–689.
Watson, J.M. and Kelly, B.A.: 2002d, ‘Emerging concepts in chance and data’, Australian
Journal of Early Childhood 27(4), 24–28.
Watson, J.M. and Kelly, B.A.: 2002e, December, School Students’ Understanding of
Stacked Dot (Line) Plots, Refereed Paper Presented at the Australian Association for
Research in Education Conference, Brisbane. Available at: http://www.aare.edu.au/
02pap/index.htm
Wild, C.J. and Pfannkuch, M.: 1999, ‘Statistical thinking in empirical enquiry’,
International Statistical Review 67, 223–265.
Zawojewski, J.S. and Shaughnessy, J.M.: 2000, ‘Data and chance’, in E.A. Silver and
P.A. Kenney (eds.), Results from the Seventh Mathematics Assessment of the National
Assessment of Educational Progress, NCTM, Reston, VA, pp. 235–268." name="eprints.referencetext" />
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school students’ understanding of statistical variation in a chance setting. Five questions
set the context by assessing the understanding of theoretical expectation and representation
of repeated trials in a stacked dot (line) plot. Four questions provide opportunity to display
appreciation of variation from point expectation and four questions address variation from
distributional expectation. Three hundred and seventy-five students in Grades 3–9 answered
some or all of these questions. These students then took part in a unit of study on chance and
data emphasizing variation. Of these students, 334 answered a post-test including the same
items and a further subset of 199 students completed a longitudinal survey of the same items
two years later. Analysis of the initial data showed a progression of understanding across
the years of schooling, plateauing at Grade 7, improvement for all grades after instruction,
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    <h1 class="ep_tm_pagetitle">Statistical variation in a chance setting: a two-year study</h1>
    <p style="margin-bottom: 1em" class="not_ep_block"><span class="person_name">Watson, Jane M.</span> and <span class="person_name">Kelly, Ben A.</span> (2004) <xhtml:em>Statistical variation in a chance setting: a two-year study.</xhtml:em> Educational Studies in Mathematics, 57 (1). pp. 121-144. ISSN 0013-1954</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 href="http://eprints.utas.edu.au/2024/1/WatsonKellyESM2004.pdf"><img alt="[img]" src="http://eprints.utas.edu.au/style/images/fileicons/application_pdf.png" class="ep_doc_icon" border="0" /></a></td><td valign="top"><a href="http://eprints.utas.edu.au/2024/1/WatsonKellyESM2004.pdf"><span class="ep_document_citation">PDF</span></a> - Full text restricted - Requires a PDF viewer<br />161Kb</td><td><form method="get" accept-charset="utf-8" action="http://eprints.utas.edu.au/cgi/request_doc"><input accept-charset="utf-8" value="2547" name="docid" type="hidden" /><div class=""><input value="Request a copy" name="_action_null" class="ep_form_action_button" onclick="return EPJS_button_pushed( '_action_null' )" type="submit" /> </div></form></td></tr></table><p style="margin-bottom: 1em" class="not_ep_block">Official URL: <a href="http://dx.doi.org/10.1023/B:EDUC.0000047053.96987.5f">http://dx.doi.org/10.1023/B:EDUC.0000047053.96987.5f</a></p><div class="not_ep_block"><h2>Abstract</h2><p style="padding-bottom: 16px; text-align: left; margin: 1em auto 0em auto">A series of 13 survey questions based on a 50-50 spinner is used to explore&#13;
school students’ understanding of statistical variation in a chance setting. Five questions&#13;
set the context by assessing the understanding of theoretical expectation and representation&#13;
of repeated trials in a stacked dot (line) plot. Four questions provide opportunity to display&#13;
appreciation of variation from point expectation and four questions address variation from&#13;
distributional expectation. Three hundred and seventy-five students in Grades 3–9 answered&#13;
some or all of these questions. These students then took part in a unit of study on chance and&#13;
data emphasizing variation. Of these students, 334 answered a post-test including the same&#13;
items and a further subset of 199 students completed a longitudinal survey of the same items&#13;
two years later. Analysis of the initial data showed a progression of understanding across&#13;
the years of schooling, plateauing at Grade 7, improvement for all grades after instruction,&#13;
and generally sustained and continuing improved performance after two years. Educational&#13;
issues are considered.</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">Article</td></tr><tr><th valign="top" class="ep_row">Additional Information:</th><td valign="top" class="ep_row">The original publication is available at www.springerlink.com</td></tr><tr><th valign="top" class="ep_row">Keywords:</th><td valign="top" class="ep_row">chance, distribution, instruction, longitudinal data, point estimate,&#13;
probability, spinners, variation</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/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">2024</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">Mrs Anita Cubit</span></span></td></tr><tr><th valign="top" class="ep_row">Deposited On:</th><td valign="top" class="ep_row">04 Oct 2007 13:38</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=2024;">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=2024">item control page</a></p>
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