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Expectation versus Variation: Students' Decision Making in a Sampling Environment


Watson, JM and Kelly, BA, Expectation versus Variation: Students' Decision Making in a Sampling Environment, Canadian Journal of Science, Mathematics and Technology Education, 6, (2) pp. 145-166. ISSN 1492-6156 (2006) [Refereed Article]

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Copyright 2006 Canadian Journal of Science, Mathematics and Education

DOI: doi:10.1080/14926150609556693


A task adapted from one used by Tversky and Kahneman (1971) was used in an interview or questionnaire context with 122 students from Grade 3 to Grade 13. Two questions assessed student understanding of the relationship of a sample to a population and of the expected value of the arithmetic mean, with and without information on a single value from the sample. Combining responses to the two questions, increasingly complex hierarchical sequences were identified in the observed responses in relation to the expected value of the means, an expectation variable, and in relation to the degree that ideas about variation were used to support judgements, a variation variable. Using data from another task performed by 68 of the students, responses were associated with the observed development of understanding of sampling more generally, a basic sampling variable. Overall, the associations of levels of response among the variables was not strong, suggesting more explicit discussion of sampling issues is required in classrooms. © 2006 Taylor and Francis Group, LLC.

Item Details

Item Type:Refereed Article
Research Division:Education
Research Group:Curriculum and pedagogy
Research Field:Mathematics and numeracy curriculum and pedagogy
Objective Division:Education and Training
Objective Group:Other education and training
Objective Field:Other education and training not elsewhere classified
UTAS Author:Watson, JM (Professor Jane Watson)
UTAS Author:Kelly, BA (Mr Ben Kelly)
ID Code:40881
Year Published:2006
Deposited By:Education
Deposited On:2006-08-01
Last Modified:2012-11-06
Downloads:8 View Download Statistics

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