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Tracing middle school students' understanding of probability: a longitudinal study

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Title
Tracing middle school students' understanding of probability: a longitudinal study
Name (ID = NAME001); (type = personal)
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Shay
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Kathleen B.
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Kathleen B. Shay
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author
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Maher
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Carolyn
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Advisory Committee
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Carolyn A Maher
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chair
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Naus
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Joseph
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Advisory Committee
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Joseph I Naus
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Powell
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Arthur
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Advisory Committee
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Arthur B Powell
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Weber
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Keith
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Advisory Committee
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Keith H Weber
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Sackrowitz
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Harold
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Advisory Committee
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Harold B Sackrowitz
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outside member
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Rutgers University
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degree grantor
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Graduate School - New Brunswick
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school
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Text
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theses
OriginInfo
DateCreated (qualifier = exact)
2008
DateOther (qualifier = exact); (type = degree)
2008-10
Language
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English
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electronic
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application/pdf
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text/xml
Extent
ix, 407 pages
Abstract
This study traces the probabilistic reasoning of five students from an urban middle school who attended an after-school mathematics enrichment program through grades 6, 7, and 8. Case study methodology is used to describe the ways of thinking and development of ideas of these students as they were presented with open-ended tasks intended to engage them in building ideas about chance. The tasks called for the students to investigate dice games to determine whether or not they were fair, and to devise strategies to make the games fair. Students were encouraged to discuss their ideas and justify their conjectures in small groups and with the whole class.
The data for this study come from videotape records of seven after-school sessions and interviews in the Rutgers Informal Mathematics Learning project (IML) during the spring of 2004 and 2005, when the students were in grade 6 and 7. The video data were transcribed and analyzed along with student work according to the model for studying the development of mathematical thinking proposed by Powell, Francisco, and Maher (2003).
Analysis of the data revealed that students exhibited the use of common judgmental heuristics such as representativeness, availability, and the equiprobability bias. At least three of the students combined the representativeness heuristic with the outcome approach to create what I call the hybrid heuristic for chance events. The application of this heuristic to assessing the fairness of games is the belief that if either player is able to win a game, then the game must be fair.
All of the students studied came to reject the idea that dice sums are equally likely. They reached conclusions based on both classical and experimental approaches. Each student produced a sample space or worked with a partner who did. Though small samples were used, all of the students used experimental data to inform or provide support for their conjectures about fairness.
In grade 7, the question of whether permutations of dice outcomes should be counted as different events was raised repeatedly, and, despite persistent challenges and questions by graduate interns, the students did not change their beliefs about this issue.
Note (type = degree)
Ph.D.
Note (type = bibliography)
Includes bibliographical references (p. 402-406).
Subject (ID = SUBJ1); (authority = RUETD)
Topic
Education
Subject (ID = SUBJ2); (authority = ETD-LCSH)
Topic
Probabilities--Study and teaching (Middle school)
Subject (ID = SUBJ3); (authority = ETD-LCSH)
Topic
Mathematics--Study and teaching (Middle school)
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Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
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http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.17569
Identifier
ETD_1181
Location
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NjNbRU
Identifier (type = doi)
doi:10.7282/T3BR8SGM
Genre (authority = ExL-Esploro)
ETD doctoral
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The author owns the copyright to this work.
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Copyright protected
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Open
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Name
Kathleen Shay
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Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
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Non-exclusive ETD license
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Author Agreement License
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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