Date of Award

7-3-2007

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Middle-Secondary Education and Instructional Technology

First Advisor

Dr. Christine Thomas - Chair

Second Advisor

Deborah Najee-Ullah

Third Advisor

Barbara Kawulich

Fourth Advisor

Clara Nosegbe-Okoka

Fifth Advisor

Pier Junor-Clarke

Abstract

A relatively large number of 8th-grade public middle school students in the United States, particularly in urban communities, are not performing at acceptable levels in mathematics. One concept that poses significant difficulty for these students and negatively affects their overall mathematics achievement is fractions. Many researchers have attributed these difficulties primarily to traditional fraction instruction that emphasizes procedural rather than conceptual knowledge. Therefore this study was designed to investigate how students use their computational and conceptual knowledge and fraction representations to solve fraction-related performance-based mathematical tasks. Social constructivism was used as the theoretical framework in examining conceptual knowledge related to learning fractions. This qualitative study was implemented in an urban middle school in the southeast. It involved an initial sample of 37, 8th-grade, African American pre-algebra students who completed a fraction interest questionnaire and two fraction pretests. During the implementation period, 34 students in the researcher’s pre-algebra class completed three performance-based tasks, three reflection logs, and participated in an interview after completing each task. Of the 34 students who completed all tasks, three were purposefully selected as the informants for the study. In addition, observations, field notes, and artifacts (student work) were utilized to facilitate triangulation of the data. The findings of the study indicated the informants could compute fractions with an average of 85% of mastery but could conceptualize fractions only to a small extent. This validated prior findings and led to the conclusion that student deficiency with fractions results primarily from their level of conceptual knowledge. In the investigation of the ways in which 8th-grade students use fraction representations, this study found the informants used representations to develop a visual map of their mathematical thinking and reasoning and to check the accuracy of their computations. Therefore, this study suggests, when students’ mathematical learning experiences relative to fractions have not emphasized the use of representations to develop conceptual knowledge, they may not be comfortable with the accuracy of the solutions demonstrated in their fractions models.

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