Title

A Comparison of the Procedural Error Patterns, Scores, and Other Variables, of Selected Groups of University and Eight-Grade Students In Mississippi On a Test Involving Arithmetic Operations On Fractions

Date of Award

1989

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Curriculum, Instruction, and Special Education

First Advisor

Bobby D. Moore

Advisor Department

Curriculum, Instruction, and Special Education

Abstract

The purpose of this study was to examine and compare the procedural error patterns and performances of two groups of elementary education majors at the University of Southern Mississippi, and a group of eighth-grade public school students on a test of arithmetic problems involving fractions. One group of university students consisted of all those students who took the Mathematics Placement Test administered by the Department of Curriculum and Instruction during the spring of 1988. These students had recently declared their intent to be elementary education majors and were about to start the required sequence of math courses. The second group consisted of elementary education majors who had recently completed CIE 301, the last math/math-methods course required of elementary education majors at USM. All subjects were administered in a 16-item test on arithmetic operations on fractions in which they showed their calculations. Eleven hypotheses, eight of them global hypotheses, were tested at a significance level of.05. Three hypotheses were accepted, five were partially accepted, and three were rejected. The mean scores of the eighth-grade subjects on the fractions test, and on subscores of the test as grouped by operation, were equivalent to those of the students who had recently completed CIE 301. The university students who were just starting the math sequence performed significantly lower than the other two groups both on the total test, and on its subsections (except for addition, which showed no significant difference with the CIE 301 subjects). The rank order of difficulty of the problems was different for each group. For the eighth graders, there were positive correlations between their seventh- and eighth-grade math averages and their scores on the Stanford Achievement Test (quantitative section), but they were not significant. The college subjects about to start the math sequence showed significant positive correlations between their scores on the fractions test, and the number of math courses taken, but not with the placement test, GPA, or ACT scores. The subjects who had completed CIE 301 showed positive correlations between their scores on the fractions test and their GPA, ACT scores, and number of math courses taken, but the correlations were not significant. Problems involving division were the most difficult for all three groups.