Uniform TitleTracing middle school students' understanding of probability: a longitudinal study
NameShay, Kathleen B. (author), Maher, Carolyn (chair), Naus, Joseph (internal member), Powell, Arthur (internal member), Weber, Keith (internal member), Sackrowitz, Harold (outside member), Rutgers University, Graduate School - New Brunswick,
Probabilities--Study and teaching (Middle school),
Mathematics--Study and teaching (Middle school)
DescriptionThis 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.
NoteIncludes bibliographical references (p. 402-406).
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.