First Advisor

Sean Larsen

Date of Publication

1-1-2011

Document Type

Dissertation

Degree Name

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

Department

Mathematics and Statistics

Language

English

Subjects

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

DOI

10.15760/etd.338

Physical Description

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

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.

Rights

In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).

Comments

Portland State University. Dept. of Mathematics and Statistics

Persistent Identifier

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

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