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ERIC Number: ED489640
Record Type: Non-Journal
Publication Date: 2004-Jul
Pages: 8
Abstractor: Author
Types of Student Reasoning on Sampling Tasks
Shaughnessy, J. Michael; Ciancetta, Matt; Canada, Dan
International Group for the Psychology of Mathematics Education, 28th, Bergen, Norway, July 14-18, 2004
As part of a research project on students' understanding of variability in statistics, 272 students, (84 middle school and 188 secondary school, grades 6-12) were surveyed on a series of tasks involving repeated sampling. Students' reasoning on the tasks predominantly fell into three types: additive, proportional, or distributional, depending on whether their explanations were driven by frequencies, by relative frequencies, or by both expected proportions and spreads. A high percentage of students' predominant form of reasoning was additive on these tasks. When secondary students were presented with a second series of sampling tasks involving a larger mixture and a larger sample size, they were more likely to predict extreme values than for the smaller mixture and sample size. In order for students to develop their intuition for what to expect in dichotomous sampling experiments, teachers and curriculum developers need to draw explicit attention to the power of proportional reasoning in sampling tasks. Likewise, in order for students to develop their sense of expected variation in a sampling experiment, they need a lot of experience in predicting outcomes, and then comparing their predictions to actual data. (Contains 6 tables.) [For complete proceedings, see ED489597.]
International Group for the Psychology of Mathematics Education, 35 Aandwind Street, Kirstenhof, Cape Town, 7945, South Africa. Web site:
Publication Type: Reports - Evaluative; Speeches/Meeting Papers
Education Level: Middle Schools; Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A