Classifying Combinations: Investigating Undergraduate Students’ Responses to Different Categories of Combination Problems

Classifying Combinations: Investigating Undergraduate Students’ Responses to Different... In this paper we report on a survey designed to test whether or not students differentiated between two different types of problems involving combinations - problems in which combinations are used to count unordered sets of distinct objects (a natural, common way to use combinations), and problems in which combinations are used to count ordered sequences of two (or more) indistinguishable objects (a less obvious application of combinations). We hypothesized that novice students may recognize combinations as appropriate for the first type but not for the second type, and our results support this hypothesis. We briefly discuss the mathematics, share the results, and offer implications and directions for future research. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Research in Undergraduate Mathematics Education Springer Journals

Classifying Combinations: Investigating Undergraduate Students’ Responses to Different Categories of Combination Problems

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Publisher
Springer International Publishing
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Education; Mathematics Education; Learning and Instruction
ISSN
2198-9745
eISSN
2198-9753
D.O.I.
10.1007/s40753-018-0073-x
Publisher site
See Article on Publisher Site

Abstract

In this paper we report on a survey designed to test whether or not students differentiated between two different types of problems involving combinations - problems in which combinations are used to count unordered sets of distinct objects (a natural, common way to use combinations), and problems in which combinations are used to count ordered sequences of two (or more) indistinguishable objects (a less obvious application of combinations). We hypothesized that novice students may recognize combinations as appropriate for the first type but not for the second type, and our results support this hypothesis. We briefly discuss the mathematics, share the results, and offer implications and directions for future research.

Journal

International Journal of Research in Undergraduate Mathematics EducationSpringer Journals

Published: Mar 10, 2018

References

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