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The Effectiveness of simple enumeration as a strategy for discovery Leask, Isabel Campbell

Abstract

Problem: This study is related to the controversy surrounding the relative merits of teaching by discovery and expository methods. Specifically, it investigated the effectiveness of treatment with simple enumeration as a strategy for discovery compared to treatment using an expository method. It was hypothesized that the two treatments would yield the same mathematical achievement, but the simple enumeration treatment would yield more mathematical and non-mathematical transfer effect than the expository treatment. Procedure: The subjects comprised six classes in Mathematics 12. They had been randomly assigned to classes at the beginning of the school year and three classes were assigned to each treatment group. All classes were taught a unit on arithmetic and geometric progressions by the experimenter. Equivalence of the groups was established in terms of the covariates I. Q. and previous term mark. The measuring instruments consisted of the Lorge-Thorndike Intelligence Test, Form 1, Level H of the 1964 Multi-Level Edition; a mathematical content test; and a mathematical transfer test. In addition, the Nonverbal Battery of Form 1 of the Lorge-Thorndike Test was used as a pretest to measure the ability of students to generalize and discover principles from examples. Form 2 was used as a posttest measure to determine whether any improvement in ability to generalize had occurred as a result of the experience with the unit on progressions. The generalized t-test was used to compare means of achievement on all tests. All results were analysed at the University of British Columbia Computing Centre. Conclusions: On the basis of results on the tests, the following conclusions were reached: 1. Treatment with simple enumeration yielded the same level of mathematical achievement as treatment with an expository method. 2. Treatment with simple enumeration yielded significantly greater effect on a mathematical transfer test than treatment with an expository method. An examination of I. Q. levels showed that the superiority in performance was largely located at the medium I. Q. level. 3. Treatment with simple enumeration was no more effective than treatment with an expository method when the criterion measured general transfer. Both groups showed significant improvement in ability to generalize after studying the unit on arithmetic and geometric progressions. The improvement was mainly located at the medium and low I. Q. levels and was independent of teaching method. The implication of this study is that if concern is centred on acquisition of facts, simple enumeration is no more effective than an expository teaching method. However, if there is concern for pupil participation and for training students to advance independently to related but more difficult material, then discovery-orientated lessons are advantageous.

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