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UBC Theses and Dissertations
An investigation of the effects of convergent/divergent teaching methods on the mathematical problem-solving abilities of grade ten students Koe, Carryl Diane
It was the purpose of this study to investigate the effects of convergent/divergent teaching methods on student performance on two mathematical problem solving tasks (routine/non-routine problems). A concurrent purpose was to investigate the interaction between the convergent/ divergent teaching methods and the thinking style (either convergent or divergent) of the learner. Four grade ten classes were randomly selected from the eleven academic mathematics classes in the secondary school involved in the study. Due to subject absenteeism a total of sixty-six subjects were used for the analyses. Each subject was given the Watson-Glaser Test of Critical Thinking (Form YM) and the Torrance test of Thinking Creatively With Words (Booklet A) to determine their level on the independent measures of convergent and divergent thinking, respectively. Each subject was taught by one teacher using one method for approximately two hours. The content of these lessons involved the Fibonacci Sequence and Pascal's Triangle. At the end of treatment, each subject received a test on the dependent measures Croutine/non-routine problems). Trained observers were used to ensure consistency of teaching method. Analysis of covariance using the regression model was performed with convergent/divergent thinking styles as the covariates. There was no significant difference between convergent teaching methods and divergent teaching methods (p ≤ 0.05). Convergent thinkers scored significantly higher than did divergent thinkers on both dependent measures. However, as convergent thinking is far more highly correlated with intelligence than is divergent thinking, this result may have been confounded by intelligence. Therefore, in further studies in this area, the variance in problem solving due to intelligence should be partialled out. Only one of eight interaction effects was significant (p ≤ 0.05). This suggested that non-divergent thinkers did better with convergent (as opposed to divergent) teaching methods and that non-convergent thinkers did better with divergent (as opposed to convergent) teaching methods. The lack of other significant interactions indicated that intelligence may have been a confounding effect in this study.
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