The Effects of a Problem Solving Model as an Alternative in the General Mathematics Curriculum
Date of Award:
Doctor of Education (EdD)
School of Teacher Education and Leadership
Department name when degree awarded
Ross R. Allen
Ross R. Allen
The purpose of this study was to evaluate an approved problem solving module as a model for use in the general mathematics curriculum, and assess its effectiveness in bringing about literacy in and a better attitude toward mathematics. Included in the module were topics on fundamental operations, fractions, decimals and percents, and problem solving. Specifically, the module focused on concerns of the National Assessment of Educational Progress (NAEF), that is the inability of students and young adults to use numbers skillfully enough to meet the demands of a modern society.
The sample used in this study consisted of eight intact classes- -four control and four experimental groups. The groups were composed of students enrolled in ninth grade general mathematics from Logan City School District, Cache County School District, and Box Elder County School District. The three districts are comprised of urban, semi-rural, and rural developments in northern Utah. The total of 210 students included 131 males and 79 females. There were 117 students in the experimental groups and 93 students in the control groups.
The diagrammatic problem solving module (composed of 20 lessons) was distributed among the teachers of the experimental groups for their perusal of content, lesson plans, and approach. When the teachers finished previewing the module, sessions were scheduled to accommodate each of their questions and concerns, and to cement the philosophy of the unit. Also, sessions were held with the control group teachers to delineate the kinds of experiences that would enhance equitable comparisons.
To facilitate the use of the Solomon Four-Group Design, a least squares analysis of variance (ANOVA) technique with unequal numbers of subjects per treatment was used to analyze the null hypotheses at the .05 level of significance. The ANOVA was used for both the Algebra Readiness Test and the Mathematics Attitude Scale.
On the basis of the findings of the five null hypotheses that were replicated in five different fashions, in regard to treatment effects, the following conclusions seem warranted.
1. There was a significantly more favorable attitude toward mathematics among students who were taught using the diagrammatic method.
2. There was a significantly more favorable performance among students on fundamental operations who were taught using the diagrammatic method.
3. There was a significantly more favorable performance among students on fractions who were taught using the diagrammatic method.
4. There was no difference in the performance among students on decimals and percents who were taught using the diagrammatic method and students who were taught using the traditional method.
5. There was a significantly favorable difference in the performance of students on problem solving who were taught using the diagrammatic method.
6. Sex differences were highly significant on one of the five replications, favoring the females. Inasmuch as the number of males far exceeded the number of females, a conclusion was not reached on sex differences.
7. Students who took both pretests and posttests, using the attitude scale, scored significantly higher than those who took only the posttest. Therefore it was concluded that pretesting served to raise scores on the attitude scale.
8. Students who took both pretests and posttests, using the readiness battery, did not perform significantly better than students who only took the posttest. Therefore, it was concluded that pretesting did not serve to enhance scores on the readiness battery.
Edwards, Leo Jr., "The Effects of a Problem Solving Model as an Alternative in the General Mathematics Curriculum" (1976). All Graduate Theses and Dissertations. 8729.
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