Date of Award

8-2018

Document Type

Dissertation

Degree Name

Doctor of Education (EdD)

College/School

College of Science and Mathematics

Department/Program

Mathematical Sciences

Thesis Sponsor/Dissertation Chair/Project Chair

Erin Krupa

Committee Member

Eileen Fernandez

Committee Member

Steven Greenstein

Abstract

This study describes the way 14 pre-service teachers engaged in discourse about integers. The discourse being examined is framed by Sfard’s view of a discourse as being composed of the four elements word use, visual mediators, routines, and narratives (Sfard, 2008). These elements combine to form a means for people to exchange and preserve ideas and coordinate actions within a society. Each of the participants in this study engaged in a seven question, semi-structured interview (Merriam, 2009), which included prompts for the enactment of computations modeled with colored chips and the number line, in addition to written and spoken representations. Using the constant comparison approach to coding (Corbin & Strauss, 1990) of the transcriptions of their spoken words and use of visual mediators, I identified tendencies in the participants’ responses. The first tendency is the procedural manner, unsupported conceptually, with which they approach the expressions presented and questions posed. Secondly, these PSTs tended to base their discourse about integers on narratives which were only partially consistent with common discourse practices. A third tendency is the greater level of success these participants exhibited in the use of the number line as a modeling tool than they had when employing colored chips. This success with the number line was founded on the use of a standard algorithm, which calls for changing the expression into an equivalent form. This change of the expression reverts to the logical structures of whole numbers, rather than the more abstract conceptions required by a discourse about integers as purely mathematical objects.

My findings suggest the need for appreciation of the changes which will be imparted on mathematical discourse when integers are introduced, when course activities with whole numbers, fractions, and decimals are discussed and modeled in mathematics content courses for elementary teachers. It further suggests the need for greater support through provided examples and professional development for the chip and number line models for teachers who are required to teach about integers after participating in an elementary teacher preparation program.

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