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A Consideration of Alternative Sample Spaces Used in Coin-Toss Problems.
Amy Renelle1, Stephanie Budgett1, Rhys Jones2
1Department of Statistics, University of Auckland, Auckland, New Zealand.
Canadian Journal of Science, Mathematics and Technology Education = Revue Canadienne De L'Enseignement Des Sciences, Des Mathematiques Et De La Technologie
|April 16, 2024
Summary
Understanding coin-toss probability is complex. Different interpretations of sample spaces can make one sequence appear more likely than another, highlighting the need to explore participants' reasoning in probability questions.
Area of Science:
- Cognitive Science
- Mathematics Education
Background:
- Coin-toss probability questions are common in educational research.
- Previous studies show varied student and teacher interpretations of these problems.
Purpose of the Study:
- To analyze coin-toss comparison questions from recent studies.
- To investigate how different sample spaces affect probability perceptions.
- To understand participant reasoning in probability tasks.
Main Methods:
- Examined coin-toss questions from undergraduate and high school teacher studies.
- Explored three alternative sample spaces to critique sequence likelihood.
- Connected findings to existing literature on probability misconceptions.
Main Results:
- Different sample spaces can indeed lead to one coin-toss sequence being perceived as more likely.
- Participant interpretations of sample spaces significantly influence their probability judgments.
- Evidence suggests participants may implicitly use non-standard sample spaces.
Conclusions:
- The choice of sample space is critical in probability problems.
- Educators should probe deeper into students' and teachers' reasoning processes.
- Further research is needed to understand the cognitive underpinnings of probability interpretation.
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