Keywords

Preservice Teachers, Prospective Teachers, Whole Number Concepts, Whole Number Operations, Classroom Teaching Experiment

Abstract

A classroom teaching experiment was conducted to document prospective teachers' development of whole number concepts and operations. The purpose of this mixed-methods study was to examine the collective understanding of prospective teachers in an elementary mathematics content course. Design research methodology, specifically a classroom teaching experiment was the methodology selected for this study since it allows learning to be documented in a classroom environment and is iterative in nature. A revised hypothetical learning trajectory and instructional tasks from a previous classroom teaching experiment were used in this study (Andreasen, 2006). Research about children's development of whole number concepts and operations was used in developing instructional learning goals. In addition, research regarding prospective teachers' development supported the instructional modification that all tasks would be presented and expected to be reasoned about in base-8. Both qualitative data and quantitative data were collected. Qualitative data included whole class dialogue that was videotaped and transcribed, as well as student work samples. Quantitative data included items from the Content Knowledge for Teaching Mathematics database that were administered prior to and subsequent to the instructional sequence in base-8 (Hill, Schilling, & Ball, 2005). It should be noted that the items selected from the database were in base-10. The emergent perspective served as the interpretive framework of the collected qualitative data. This perspective reflexively coordinates the social or group perspective simultaneously with psychological or individual perspective. As stated, this study sought to describe the communal mathematics understanding of prospective teachers in an elementary mathematics content course. Toulmin's (1969) model of argumentation and Rasmussen and Stephan's three-phase methodology served to document normative ways of group reasoning called classroom mathematical practices. The following classroom mathematical practices were identified as taken-as-shared by prospective teachers: (a) developing small number relationships using Double 10-Frames, (b) developing two-digit thinking strategies using the open number line, (c) flexibly representing equivalent quantities using pictures or Inventory Forms, and (d) developing addition and subtraction strategies using pictures or an Inventory Form. Quantitative results indicated that prospective teachers were able to apply mathematical understandings grounded in base-8 to whole number concepts in base-10. In the end, counting and calculating in base-8 provides a meaningful context for prospective teachers to reconstruct their knowledge of whole number concepts and operations.

Notes

If this is your thesis or dissertation, and want to learn how to access it or for more information about readership statistics, contact us at STARS@ucf.edu

Graduation Date

2008

Advisor

Dixon, Juli

Degree

Doctor of Philosophy (Ph.D.)

College

College of Education

Department

Teaching and Learning Principles

Degree Program

Education

Format

application/pdf

Identifier

CFE0002398

URL

http://purl.fcla.edu/fcla/etd/CFE0002398

Language

English

Release Date

December 2008

Length of Campus-only Access

None

Access Status

Doctoral Dissertation (Open Access)

Included in

Education Commons

Share

COinS