Open Access Dissertation
Variables (Mathematics); Mathematics--Study and teaching; Algebra--Study and teaching;
Algebra is a difficult subject for a number of high school students. One of the major concepts involved in the learning of algebra is the use of variables. The purpose of this study was to investigate the effect of the use of concrete manipulatives on middle school students' knowledge of the concept of variable and attitudes toward mathematics.
An experimental study was conducted involving 335 students and 13 teachers. Teachers volunteered to be in the treatment or comparison group. Teachers in the treatment group were trained in the use of Hands-On Equations and used the materials in their classrooms for seven weeks. Teachers in the comparison group used the traditional mathematics curriculum during the same seven-week interval. Pre- and post-tests using The Mathematics Self Concept Scale and the Chelsea Diagnostic Mathematics Test were administered in all classrooms to assess students attitudes toward mathematics and their knowledge of the concept of variable. In addition, this study compared the performance of students in Northeast Iowa with students in the United Kingdom who had taken the same assessment of the concept of variable in 1976.
Tests of significance were conducted using the post-test scores on the concept of variable measure and the attitude measure as dependent variables. Independent variables were two approaches to instruction (experimental, comparison) and three grade levels (sixth, seventh, eighth). The pre-test scores from the Chelsea Diagnostic Mathematics Test and The Mathematics Self Concept Scale served as covariates.
The data were analyzed using the Pearson r product moment correlation coefficient, 2 X 3 analyses of covariance, one-way analyses of covariance, and post hoc t tests. Significance was tested at the .05 level. Students' knowledge of the concept of variable improved significantly at the sixth grade level in the group using Hands-On Equations. Students' attitudes in grades six and eight did not change significantly, however, students' attitudes in the experimental group at the seventh grade level declined.
A comparison of this study with a study conducted in 1976, which assessed English children's knowledge of the concept of variable, revealed that sixth and seventh grade students in England were more accurate in their responses than children in Northeast Iowa. At the eighth grade level,the performance level of students in Northeast Iowa was similar to English children of the same age level.
The findings of this study suggest that a program based on the use of concrete manipulatives may be beneficial to students' understanding of the concept of variable. While attitudes of middle school students' toward mathematics are generally positive, their knowledge of the concept of variable is limited.
Year of Submission
Doctor of Education
Department of Curriculum and Instruction
Gregory Stefanich, Co-Advisor
Marlene Strathe, Co-Advisor
1 PDF file (X, 230 pages)
©1993 Maureen E. Busta
Busta, Maureen E., "The relationship between middle school students' knowledge of the concept of variable and the use of concrete manipulatives" (1993). Dissertations and Theses @ UNI. 805.