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.
International Journal of Research in Undergraduate Mathematics Education – Springer Journals
Published: Mar 10, 2018
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