A study of the cognitive styles of low-achieving algebra students in individualized and expository classes

Statement of the Problem. Mathematics has traditionally been taught using only one method - the lecture/discussion approach. Recently, many studies have been conducted regarding the effectiveness of individualized approaches which are self-paced and child centered. While studies have not proved conclusively that overall achievement was improved, they have shown that some students did perform better under the newer approaches. Therefore, the determination of methods and procedures for the identification and placement of students between instructional methods was the basic problem considered in this study. Nature of the Study. In the determination of the proper placement of students between instructional methods, many factors have been tried with varying degrees of success. This study investigated the areas of a student's cognitive style which might be helpful in making this decision. Cognitive style was defined as the characteristic way an individual derives meaning from the environment. The 101 subjects were selected from Introductory Algebra classes at a medium size high school and were randomly placed in either individualized or expository sections. During the first week of the study, the subject's cognitive style preferences were determined by their answers on J. E. Hill's Cognitive Style Preference Inventory (1970). After twenty-two weeks of instruction, the successful and unsuccessful students in each instructional method were determined by their scores on the Lankton First-Year Algebra Test. Discriminant analysis was used to identify those categories of the Cognitive Style Preference Inventory (CSPI) which accounted for the variation in the groups. Comparisons were made both within the instructional method and between the instructional methods. In a similar manner, students with high and low attitudes were determined by their scores on the Aiken-Dreger Revised Math Attitude Scale. Again, discriminant analysis was used to identify those categories which were significant in accounting for the variation between the groups. All hypotheses were tested at the .05 level. Results. The subjects were found to have different cognitive styles when the successful and unsuccessful individualized groups were compared. Nine different variables on the CSPI accounted for 59% of the variation between the groups. Also significant differences were found when all of the successful students were compared with all of the unsuccessful. Successful students in each instructional method were compared and significant differences found. However, no significant differences were found to exist between successful and unsuccessful expository students. When attitude was the basis for forming the comparison groups, significant results were also obtained. Significant differences were found to exist between the overall high and low attitude groups, the high and low expository groups, and the high expository and the high individualized groups. Conclusions and Recommendations. The results of this study indicated that students do have identifiable cognitive styles which may be used to place students between instructional methods. By using the classification functions developed in this study, schools having more than one instructional method for a course could improve the placement of students between these methods. Since this study indicated that students do have different cognitive styles, schools having only one instructional method cannot address these individual differences as effectively as schools with more than one method. It is recommended that further studies be conducted in order to determine the reliability of the classification functions, their universality in mathematics, and their applicability to other subject areas.Education, College o