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ERIC Number: ED551588
Record Type: Non-Journal
Publication Date: 2012
Pages: 296
Abstractor: As Provided
Reference Count: N/A
ISBN: 978-1-2677-9767-4
Equivalent Fraction Learning Trajectories for Students with Mathematical Learning Difficulties When Using Manipulatives
Westenskow, Arla
ProQuest LLC, Ph.D. Dissertation, Utah State University
This study identified variations in the learning trajectories of Tier II students when learning equivalent fraction concepts using physical and virtual manipulatives. The study compared three interventions: physical manipulatives, virtual manipulatives, and a combination of physical and virtual manipulatives. The research used a sequential explanatory mixed-method approach to collect and analyze data and used two types of learning trajectories to compare and synthesize the results. For this study, 43 Tier II fifth-grade students participated in 10 sessions of equivalent fraction intervention. Pre- to postdata analysis indicated significant gains for all three interventions. Cohen d effect size scores were used to compare the effect of the three types of manipulatives-at the total, cluster, and questions levels of the assessments. Daily assessment data were used to develop trajectories comparing mastery and achievement changes over the duration of the intervention. Data were also synthesized into an iceberg learning trajectory containing five clusters and three subcluster concepts of equivalent fraction understanding and variations among interventions were identified. The syntheses favored the use of physical manipulatives for instruction in two clusters, the use of virtual manipulatives for one cluster, and the use of combined manipulatives for two clusters. The qualitative analysis identified variations in students' resolution of misconceptions and variations in their use of strategies and representations. Variations favored virtual manipulatives for the development of symbolic only representations and physical manipulatives for the development of set model representations. Results also suggested that there is a link between the simultaneous linking of the virtual manipulatives and the development of multiplicative thinking as seen in the tendency of the students using virtual manipulative intervention to have higher gains on questions asking students to develop groups of three or more equivalent fractions. These results demonstrated that the instructional affordances of physical and virtual manipulatives are specific to different equivalent fraction subconcepts and that an understanding of the variations is needed to determine when and how each manipulative should be used in the sequence of instruction. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page:]
ProQuest LLC. 789 East Eisenhower Parkway, P.O. Box 1346, Ann Arbor, MI 48106. Tel: 800-521-0600; Web site:
Publication Type: Dissertations/Theses - Doctoral Dissertations
Education Level: Grade 5; Intermediate Grades; Middle Schools; Elementary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A