PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2012
Portland, Oregon
Students’ Ways of Thinking about Enumerative Combinatorics Solution Sets: The Odometer Category
Page: 2-59
This presentation aims to address students’ ways of thinking about the set of elements being counted in enumerative combinatorics problems. Fourteen undergraduates with no formal experience with combinatorics participated in individual task-based interviews in spring 2011. Open coding was used to identify students’ ways of thinking about the set of elements being counted, called the solution set. One category of ways of thinking which emerged from the data analysis involves holding an item constant and cycling through possible items for the remaining spots in order to generate all elements of the solution set. This category is known as Odometer thinking and two ways of thinking from this category, Standard Odometer and Wacky Odometer, are presented here. The conjectured Generalized Odometer way of thinking, which involves holding an array of items constant, is introduced as an extension of Wacky Odometer thinking. Its potential to coordinate set- and process-oriented thinking is discussed.