Dissertation/Thesis Abstract

Comparing fractions: The impact of three instructional strategies on procedural and conceptual knowledge development
by Dunham, Jodi Michelle, Ph.D., Union Institute and University, 2008, 166; 3326510
Abstract (Summary)

This research investigation was conducted to gauge the impact of selected instructional interventions on children's procedural and conceptual knowledge of comparing fractions. The investigation randomly assigned 111 sixth-grade students to either a control group or one of three instructional intervention treatments: procedural instruction, conceptual instruction, or a combination of procedural and conceptual instruction. Completing parallel versions of pretest and posttest assessments, participants chose the larger of two given fractions and provided an explanation of their reasoning on each problem. Data was then coded for analysis using two approaches: (1) correct or incorrect for each assessment question; and (2) procedural, conceptual, or alternate incorrect method of explanation for each question based on coding guidelines established by Behr, Wachsmuth, Post, and Lesh (1984).

This investigation analyzed data from three distinct perspectives: (1) the effect of instructional intervention on accuracy; (2) the effect of instructional intervention on participant explanations; and (3) and the relationships between individual differences in explanations and performance accuracy. Results indicated no statistical difference in student performance accuracy following the instructional interventions. Significant modifications were discovered in participant explanations from pretest to posttest, suggesting that the manner in which students are taught to compare fractions directly impacts their accompanying explanations on fraction comparison problems. Research evidence also suggested that conceptual understanding serves as a precursor to learning fraction comparison strategies and continues to support students' accuracy following instructional interventions.

These research results hold important implications for mathematics educators at all levels. Firstly, as mathematics educators wish to cultivate both conceptual and procedural understanding of comparing fractions within their students, instructional activities must expose students to both types of strategies over extended periods of time. Secondly, equipping students with a strong conceptual knowledge base supports overall performance; thus, the traditional focus of procedural methods for comparing fractions (Dehaene, 1997; Smith, 2002; Moseley, 2005) at the elementary level should be modified to include conceptual strategies at early grade levels. Finally, these results demonstrated that students' processing of fraction comparison problems can be successfully influenced by targeted instructional intervention and should therefore be focused upon by future educational research in this area.

Indexing (document details)
Advisor: Buehler, Gary
School: Union Institute and University
School Location: United States -- Ohio
Source: DAI-A 69/08, Dissertation Abstracts International
Subjects: Mathematics education, Educational psychology
Keywords: Comparing fractions, Conceptual knowledge, Instructional strategy, Mathematics, Middle school, Procedural knowledge
Publication Number: 3326510
ISBN: 9780549822141
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