A study of the effects of mathematics manipulative materials in college developmental mathematics classes

Mary Nell Bullock

Abstract

This study was designed to determine if mathematics achievement and attitudes of college students would be improved by experiencing a college-level mathematics course requiring students to revisit foundations of mathematics first using concrete manipulative materials, then employing reflections and pictorial representations of mathematics ideas, and finally making a secure connection from materials and pictures to abstract mathematical symbols. Additionally, the interaction of the demographic variables of gender and students' classification with the treatment were investigated. The sample for this study ($N=59$) was composed of students from three sections of developmental mathematics in a four-year, private, denominational university. All students in developmental mathematics were taught using the same textbook and following the same syllabus. The students in the experimental group worked with mathematics manipulative materials related to the course objective in large and small groups and individually. The control group consisted of traditional lecture procedures involving lecture, group work, board work, and individual work. All students were required to attend a one-hour lab each week. The hypotheses were tested by a three-way analysis of variance. The subscales of Confidence in Learning Mathematics and Mathematics Anxiety of the Fennema-Sherman Attitudes Scales and Mathematics Achievement Scores on a course test revealed no significant differences between experimental and control group scores. Additionally, a t test was run on the pretest and posttest data to determine if taking the developmental mathematics course makes a difference in the students' mathematics achievement, and attitudes toward mathematics. The t-test analysis on the pretest and posttest data revealed a significant difference in the students' mathematics achievement scores, mathematics anxiety levels, and confidence in learning mathematics. Developmental courses, then, do make a positive contribution to the students' cognitive knowledge of mathematics as well as their more positive attitudes towards mathematics. How to maximize these effects is still open to questions.