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An experimental study to determine the effectiveness of two types of geometric exercises in improving critical thinking. Sankey, Gerald Robert

Abstract

Demonstrative geometry as a subject in secondary schools has been justified by many educational leaders on the basis that the critical thinking ability acquired in this subject would transfer to situations outside of mathematics. However, many of the research studies in this area indicate that very little of this critical thinking ability acquired in the usual course in demonstrative geometry transfers to life situations. The usual course in demonstrative geometry employs a text which includes as a very important type of exercise, problems in which the pupil is supplied with data either given or assumed and told precisely what conclusions he must derive from these data. That is, the pupil knows the conclusion before he attempts to solve the problem. This particular method of presentation is thought by some educational leaders to deprive the student of a very important learning process, namely, that of discovery. This study is an attempt to determine what the effect on critical thinking ability would be, if the students were not told precisely what conclusion they must derive, but were exposed to exercises in which there were many alternative conclusions of which some may or may not be valid with respect to the given or assumed data. That is, the onus for determining which alternative (if any) was valid, was the responsibility of the student. Two groups consisting of thirty pupils each at the grade ten level on the University Entrance Program were equated on the basis of the control variables of intelligence as determined by the "Otis Quick-Scoring Mental Ability Tests" and critical thinking as measured by the "Watson-Glaser Critical Thinking Appraisal" test Form A. The control group followed the usual course in geometry in which the students were supplied with exercises in which they were told precisely what conclusions they must derive. The experimental group, however, were exposed to exercises in which it was the responsibility of the pupil to determine which (if any) of the many possible conclusions supplied could be proven valid in terms of the data given. This experiment was conducted for two months, after which Form B of the "Watson-Glaser Critical Thinking Appraisal" test was given. As the groups were equated at the beginning of the study by the control variables, differences in means between the control and experimental group on this test were investigated for significance by means of "t" tests. Each of the paired groups was sub-divided into three sub-groups of ten each and classified as "superior", "average", and "inferior" on the basis of scores on the control variables. The analysis of the data from this study indicates that students of "superior", "average", and "inferior" ability who were exposed to the experimental type of exercise did not show larger gains in critical thinking than those who followed exercises outlined in a traditional text.

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