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ERIC Number: ED516732
Record Type: Non-Journal
Publication Date: 2010
Pages: 158
Abstractor: As Provided
Reference Count: N/A
ISBN: ISBN-978-1-1240-5642-5
Investigating Mathematics Students' Use of Multiple Representations when Solving Linear Equations with One Unknown
Beyranevand, Matthew L.
ProQuest LLC, Ed.D. Dissertation, University of Massachusetts Lowell
Although it is difficult to find any current literature that does not encourage use of multiple representations in mathematics classrooms, there has been very limited research that compared such practice to student achievement level on standardized tests. This study examined the associations between students' achievement levels and their (a) ability to recognize the same linear relationship represented in different ways, (b) ability to solve linear equations with one unknown presented multiple ways, and (c) preference towards particular representations. To answer the associations, an instrument consisted of a survey and problem sets and student interviews were used to collect data. Four hundred and four three (N = 443) seventh and eighth grade students from a culturally diverse urban setting in Massachusetts completed the survey that included Liken scale questions on their attitudes towards different representations and were asked to solve problems presented in three different modalities, verbal, pictorial and symbolic. In addition, based on their responses to the instrument nine students were selected and interviewed. The data were analyzed with multiple regression/correlation and chi-square tests of independence that compared student responses to survey questions and problems to their standardized test score. This researcher found that those students who were able to (a) identify the same linear relationship with one unknown problem represented in different ways and (b) solve linear equations with one unknown presented multiple ways were significantly morel likely to be high-achieving on the Massachusetts' standardized test. This conclusion is consistent with multiple other studies that have indicated the benefits of the practices that requires and encourages students to use of multiple representations in mathematics classes (Moseley, 2005; Swafford & Langrall, 2000; Lowrie, 2001; Niemi, 1996; Cifarelli, 1993). This study also found that the low-achieving students had a significant perceived preference for using pictorial representations, while high-achieving students had a significant perceived preference for using symbolic representations. Although there are benefits for students to be able to use all types of representations, this significant preference based on achievement level can be a valuable tool for educators attempting to help their students understand the mathematical concepts. The results of this study might be of a great value to educators, professional development leaders, and curriculum developers. It is suggested that future mathematics curricula ensure that mathematical concepts are illustrated in different representational modes. Those curricula that believe in the importance of students' being able to represent ideas in many different modes appears to yield higher standardized test scores. [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 7; Grade 8; Junior High Schools; Middle Schools
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers - Location: Massachusetts