Graduate Thesis Or Dissertation
 

Listing as a Potential Connection between Sets of Outcomes and Counting Processes

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/kw52jc138

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  • Counting problems are rich in opportunities for students to make meaningful mathematical connections and develop non-algorithmic thinking; their accessible nature and applications to computer science make counting problems a valuable part of mathematics curricula. However, students struggle in various ways with counting, and while previous studies have indicated that listing may be a useful way to address student difficulties, little work has been done toward understanding exactly how students may connect lists of outcomes to their solutions to counting problems. To begin to address this, I conducted twenty task-based interviews with undergraduate students to probe the ways in which students conceptualize the relationship between sets of outcomes and counting processes. In this thesis, I describe the ways that students listed outcomes using an elaboration of English's (1991) solution strategies, and I frame my findings about their understanding using Lockwood's (2013) model of students' combinatorial reasoning. I discover that students reason about the relationship between lists of outcomes and counting processes with varying levels of sophistication, and I suggest that teachers could help students by making connections between sets of outcomes and counting processes more explicit.
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