Scientific Program > Topic 6 > Session 6A >
Presentation 6A5. Aspects of Students' Understandings of Variation

Mike Shaughnessy (USA)
Matthew Ciancetta (USA)


Presentation Abstract

A repeated samples task and a probability task were presented to mathematics students in both written and interview format in order to study students' thinking and reasoning in contexts where repetitions of experiments lead to variation in the results of the trials. Over 300 middle level and secondary level students (predominantly ages 12 - 16) were given a survey to explore their thinking. Students predicted outcomes from a series of repetitions of a the sampling activity and of the probability task. They were then asked to explain their reasoning, why they thought the results would occur as they predicted. Student responses to the written survey led to the development of an interview script for each of the two tasks in order to more explicitly address some of the issues that were surfacing in the written task. Audio taped interviews were conducted with 24 secondary school mathematics students. Results indicated that a variety of types of thinking arise among students who are given such tasks to tap their conceptions of variation, including either too narrow or two wide an expectation for the range of results. In addition to these types of thinking, this presentation will share evidence of students' beliefs about how they feel repeated experiments "should" come out, about their confidence, or lack of confidence, in predicting the results of sampling experiments, and about the apparent connection between students' conceptions of sample space, and their ability to predict the results of repeated trials of a probability experiment.


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