PROCEEDINGS OF THE 19TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2016
Pittsburgh, Pennsylvania
Classifying combinations: Do students distinguish between different categories of combination problems?
Page: 296
In this paper we report on a survey study to determine whether or not students differentiated between two different categories 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 category but not for the second category, and our results support this hypothesis. We briefly discuss the mathematics, share the results, and offer implications and directions for future research.