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.
|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|
Copyright in each Dissertation and Thesis is retained by the author. All Rights Reserved
The supplemental file or files you are about to download were provided to ProQuest by the author as part of a
dissertation or thesis. The supplemental files are provided "AS IS" without warranty. ProQuest is not responsible for the
content, format or impact on the supplemental file(s) on our system. in some cases, the file type may be unknown or
may be a .exe file. We recommend caution as you open such files.
Copyright of the original materials contained in the supplemental file is retained by the author and your access to the
supplemental files is subject to the ProQuest Terms and Conditions of use.
Depending on the size of the file(s) you are downloading, the system may take some time to download them. Please be