Publication Date

1991

Document Type

Dissertation/Thesis

First Advisor

Behr, Merlyn J.

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Mathematical Sciences

LCSH

Algebra--Study and teaching (Secondary); Educational tests and measurements; Variables (Mathematics)--Study and teaching (Secondary)

Abstract

Algebra was created as an abstraction of arithmetic. The transition between arithmetic and Algebra is facilitated by the introduction of the concept of variable. Research suggests that students have a definite lack of understanding numerical variables which may account for difficulties with Algebra. The purpose of this study was to examine students’ understanding of numerical variables and the relationship between their level of variable understanding and performance in an algebraic context. In order to investigate the relationship between students’ level of variable understanding and their performance in an algebraic context, 248 students were randomly selected to take two tests. The two evaluation instruments were the Chelsea Diagnostic Mathematics Test for Algebra, developed by the Social Science Research Council during 1974 to 1979, and the Algebra Performance Test. The purpose of the Chelsea Diagnostic Mathematics Test was to determine students’ level of variable understanding. The purpose of the Algebra Performance Test was to evaluate students’ performance on specific algebraic tasks which involve variables in the contexts of expressions, equations, tables, functions and graphs. The percentage of students operating at each level of variable understanding was determined and students’ responses on the Algebra Performance Test were classified as low, medium or high. A Chi-Square analysis was conducted to determine the relationship between the students’ level of variable understanding and their performance on the Algebra Performance Test. Another Chi-Square analysis was conducted to determine the relationship between seven mathematics class levels and levels of variable understanding. Classification of incorrect responses was made to determine misconceptions. The significant results of this study include that students’ level of variable understanding is highly related to their achievement on the Algebra Performance Test. The majority of students who scored low on the Algebra Performance Test were operating at a low level of variable understanding and the majority of students who scored high on the Algebra Performance Test were operating at a higher level of variable understanding. The majority of students in this study were operating at a level of variable understanding where they could use letters as specific unknowns. There existed no significant relationship between students’ level of variable understanding and their mathematics class.

Comments

Includes bibliographical references (pages [136]-137)

Extent

v, 143 pages

Language

eng

Publisher

Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type

Text

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