AN EXAMINATION OF ERROR PATTERNS ASSOCIATED WITH MIDDLE SCHOOL STUDENTS’ SOLUTION PATHWAYS WHEN SOLVING FRACTION COMPUTATION INVOLVING ADDITION
Open Access
- Author:
- Hwang, Jiwon
- Graduate Program:
- Special Education
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 08, 2016
- Committee Members:
- Paul J Riccomini, Dissertation Advisor/Co-Advisor
Paul J Riccomini, Committee Chair/Co-Chair
Charles A Hughes, Committee Member
Mary Catherine Scheeler, Committee Member
Gwendolyn Monica Lloyd, Outside Member - Keywords:
- fractions
error analysis
mathematics
learning disabilities
solution pathway - Abstract:
- Developing an understanding of fractions is critical as a significant predictor for future mathematical proficiency and an important area of emphasis in the learning progression of advanced domains such as algebra. Despite its importance, students face significant challenges in learning fractions because of their unique properties and students’ difficulty in reorganizing the number system from whole numbers to rational numbers. In order to systematically approach remediation of students’ difficulties, a research basis involving specific patterns or characteristics in performance of solving fractions needs to be established. The current study examined the common error patterns committed by middle school students with and without MLD when solving fraction computations involving addition. Based on the logic that errors reflected meaningful misconceptions and that individual difficulties and flexibility of solution pathway should be taken into consideration, errors associated in each solution stage established in a solution algorithm were analyzed. It is especially essential to examine differences between students with and without MLD because the findings can provide a starting point of instruction when teaching students in different achievement groups in inclusive settings. Moreover, the findings of this study can provide an instructional and diagnostic basis to develop practical guidelines for researchers, insights into identifying individual difficulties, and an awareness about what areas of concepts, sub-skills, or techniques teachers should teach and/or re-teach, especially for students with MLD. Careful consideration of errors in particular solution stages along with solution pathway preference can maximize the efficacy of instructions involving fractions. Future research directions, educational implications, and limitations are discussed.