Advisor

Sean Larsen

Date of Award

1-1-2011

Document Type

Dissertation

Degree Name

Doctor of Philosophy (Ph.D.) in Mathematics Education

Department

Mathematics and Statistics

Physical Description

1 online resource (ix, 445 p.) : ill. (chiefly col.)

Subjects

Combinatorial analysis -- Study and teaching, Computer science -- Mathematics -- Study and teaching, Counting -- Study and teaching

DOI

10.15760/etd.338

Abstract

Combinatorics is a growing topic in mathematics with widespread applications in a variety of fields. Because of this, it has become increasingly prominent in both K-12 and undergraduate curricula. There is a clear need in mathematics education for studies that address cognitive and pedagogical issues surrounding combinatorics, particularly related to students' conceptions of combinatorial ideas. In this study, I describe my investigation of students' thinking as it relates to counting problems. I interviewed a number of post-secondary students as they solved a variety of combinatorial tasks, and through the analysis of this data I defined and elaborated a construct that I call set-oriented thinking. I describe and categorize ways in which students used set-oriented thinking in their counting, and I put forth a model for relationships between the formulas/expressions, the counting processes, and the sets of outcomes that are involved in students' counting activity.

Description

Portland State University. Dept. of Mathematics and Statistics

Persistent Identifier

http://archives.pdx.edu/ds/psu/7054

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