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Constructing sample space with combinatorial reasoning: a mixed methods study

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
William A. McGalliard III (Creator)
Institution
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/
Advisor
Sarah Berenson

Abstract: Recent curricular developments suggest that students at all levels need to be statistically literate and able to efficiently and accurately make probabilistic decisions. Furthermore, statistical literacy is a requirement to being a well-informed citizen of society. Research also recognizes that the ability to reason probabilistically is supported and enabled by other forms of mathematical reasoning and concepts. One of these supporting concepts is sample space, the enumeration of all outcomes of a probability experiment. As a concept, sample space supports the construction of probability distributions, which in turn enables statistical inference, a form of probabilistic reasoning. This mixed methods study investigated how undergraduate pre-service elementary teachers construct and generalize their understanding about sample space. One hundred fifty students participated in a series of three tasks designed to investigate the ways in which they enumerate sample space and the associations between their enumeration strategies and their generalization rules. A subset of eight participants engaged in follow- up interviews designed to explore their understandings of sample space enumeration and generalization. Findings from the study suggest that there was growth across tasks in the sophistication of the enumeration strategies used and that participants attempted to find explicit and formalized generalizations. However, in spite of this growth in the sophistication of enumeration, there was little association between the enumeration strategies participants used and the generalizations that they constructed. Students compartmentalized their understanding of generalization rules, often looking for a numeric formula that had little do to with their enumerated solutions.

Additional Information

Publication
Dissertation
Language: English
Date: 2012
Keywords
Combinatorics, Distributional understanding, Mathematics Education, Probabilistic Reasoning, Sample Space
Subjects
Mathematics $x Study and teaching (Higher) $z North Carolina
Statistics $x Study and teaching (Higher) $z North Carolina
Mathematics teachers $x Training of $z North Carolina