## Date of Award

6-1-1989

## Document Type

Dissertation - NSU Access Only

## Degree Name

Doctor of Education

## Department

Center for the Advancement of Education

## Abstract

Since 1972, the number of students deficient in basic mathematical skills entering Savannah State College has increased significantly. To alleviate these deficiencies, two courses are offered in the mathematics component of the Developmental Studies Program at the college. Despite past efforts of teachers to maximize student learning outcomes in the developmental mathematics component at Savannah State College, the failure rate in mathematics courses continued to rise. No comprehensive program of developmental mathematics existed at the institution prior to this research. This major applied research project addressed this deficiency through the development of a comprehensive program of mathematics for the developmental students at Savannah State College. The newly designed comprehensive program of mathematics includes a criterion-referenced curriculum for each course, a syllabus of mastery teaching strategies for the combined courses, and a set of three criterion-referenced final examinations for each course. The curriculum and the syllabus of mastery teaching strategies were validated by expert opinion. The final examinations were validated by expert opinion, by estimating the concurrent validity of final examination scores for Basic Mathematics II with scores of the Descriptive Test of Algebraic Skills (DAS), and by computing the reliability coefficient of each basic mathematics course. To estimate the concurrent validity of the final examination of Basic Mathematics II with the DTAS, a population of one hundred final examination scores and the corresponding DTAS scores for the fall quarter of 1988 were selected. From the population, a random sample of eighty final examination scores and their companion DTAS scores were chosen using a table of random numbers. A Pearson correlation coefficient, at the α = .05 level of significance and with seventy-eight degrees of freedom, was calculated for the two sets of scores to test the null hypothesis that there is no positive correlation between scores of the final examination and scores of the DTAS. The reliability coefficients were computed for the final examinations of each basic mathematics course by the split-half method. Two populations of one hundred scores each were selected to compute the coefficients. From each population, a random sample of eighty scores were chosen using a table of random numbers. A Pearson product-moment correlation coefficient, at the α = .05 level of significance and with seventy-eight degrees of freedom, was computed for the scores of the two halves of each final examination to test the null hypothesis that there is no positive correlation between the scores of the first half and the scores of the second half of each final examination. Also, a comparison of the performance of three groups of students in the developmental mathematics component at Savannah State College was made. Course averages were selected for three groups of students. Course averages for groups I and Il were for students from the fall quarters of 1986 and 1987; these students had been exposed to traditional teaching tools. Course averages for Group III were students from the fall quarter of 1988; these students had utilized, the preliminary comprehensive mathematics program. A population of one hundred scores was selected for each of the three groups. From each population of one hundred scores, eighty scores were chosen, using a table of random numbers. A one-way analysis of variance (ANOVA) at the α = .05 level of significance and with (2,237) degrees of freedom was calculated for the three sets of final course average scores to test the null hypothesis that there is no significant difference between the three sample means. Also, at least significant difference (LSD) test was applied to the three sample means. The major conclusions of this research were the following: (1) the class of Basic Mathematics II who were taught with the newly designed comprehensive program outperformed the two classes who were taught by more traditional teaching methods; (2) the similarities in high course averages for all students, even though they differed widely on cognitive and affective characteristics, lent support to Bloon's hypothesis (1976), that students tend to become more alike in learning ability, learning rates, and motivation when given adequate time and opportunity: and (3) the results of the preliminary comprehensive program of developmental mathematics supported Gagne's hypothesis (1979), that learning problem-solving skills requires the mastery of prerequisite skills and that additional study of the prerequisite skills will be more effective in preparing students for success in problem-solving than additional practice on the problem-solving skills themselves. Other pertinent implications were drawn from the study about validity, the course guides, the teaching style, basic skills improvement, and final course averages. The major recommendations to the head of the Developmental Studies Program, that seemed appropriate for the results of this research, were the following: (1) one additional mathematics teacher should be employed for the mathematics component to support the implementation of the comprehensive program; (2) periodic review, assessment, and modifications of each component of the comprehensive program should be required; (3) seven additional Apple II-e minicomputers should be purchased for the mathematics laboratory. Also, the ancillary software to accompany each mini-computer should include the instructor's computerized test generator, the computer tutor, and the student disk; (4) research should be conducted to investigate the interrelationship of achievement in the developmental algebra course and other cognitive and affective factors, such as motivation, test anxiety, and attitude towards mathematics and (5) research should be done to compare the achievement of two groups of students in a college algebra course, one group who entered through the comprehensive program and one group who entered through the regular college admissions process.