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

http://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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  • description.provenance : Approved for entry into archive by Julie Kurtz(julie.kurtz@oregonstate.edu) on 2015-12-21T20:40:06Z (GMT) No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: bb87e2fb4674c76d0d2e9ed07fbb9c86 (MD5) EricksonSarahA2015.pdf: 1189539 bytes, checksum: 65d2e918ddc54c2a7a9777017cee9cfb (MD5)
  • description.provenance : Made available in DSpace on 2015-12-21T23:22:41Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: bb87e2fb4674c76d0d2e9ed07fbb9c86 (MD5) EricksonSarahA2015.pdf: 1189539 bytes, checksum: 65d2e918ddc54c2a7a9777017cee9cfb (MD5) Previous issue date: 2015-12-04
  • description.provenance : Submitted by Sarah Erickson (ericksos@oregonstate.edu) on 2015-12-20T07:14:05Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: bb87e2fb4674c76d0d2e9ed07fbb9c86 (MD5) EricksonSarahA2015.pdf: 1189539 bytes, checksum: 65d2e918ddc54c2a7a9777017cee9cfb (MD5)
  • description.provenance : Approved for entry into archive by Laura Wilson(laura.wilson@oregonstate.edu) on 2015-12-21T23:22:41Z (GMT) No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: bb87e2fb4674c76d0d2e9ed07fbb9c86 (MD5) EricksonSarahA2015.pdf: 1189539 bytes, checksum: 65d2e918ddc54c2a7a9777017cee9cfb (MD5)

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