Honors College Thesis


Undergraduate Generalization of Lists and Tables to Solve Introductory Combinatorial Problems Public Deposited

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  • In this study I viewed video and corresponding transcripts of two students solving introductory combinatorial problems. Using an adapted version of Harel’s (2008) concepts of Result Pattern Generalization and Process Pattern Generalization, I analyzed the work done by the two students. Both students primarily worked through the problem How many ways are there to distribute 3 identical hats to 5 friends? Student 4 generated tally style lists that marked friends who did have hats and left blank spaces for friends who did not receive hats. This visual structure allowed Student 4 to make generalizations about symmetry and support those generalizations contextually. Meanwhile, Student 11 made lists of sets of numbers, where numbers included in the set represented friends who received hats. This numerical structure caused Student 11 to focus more intently on the order they presented the outcomes on their list. Student 11 also was not as conscious of the students who did not receive hats, so their generalizations of symmetry were less contextualized. Overall, this observational study showed the generalizations students make in combinatorial problems is at least partially tied to the visual structure of the lists they use to count outcomes.
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