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UBC Theses and Dissertations

An analysis of two approaches to teaching used by grade 8 mathematics teachers Tam, Rosita Tseng


The purpose of the study was to perform an analysis of two approaches to teaching used by Grade 8 mathematics teachers in British Columbia. A comparison was made in the orientation to concrete and abstract approaches. The major question addressed in the study was: Were teacher practices in accordance with the theory of instruction proposed by several authors, in which it is recommended that concepts be presented using manipulative materials, pictures, or diagrams, and then through abstract presentations with symbols? To address this question, an analysis was made of the data collected from approximately 100 mathematics teachers who took part in the Second International Mathematics Study (SIMS) during the 1980-81 school year. The instruments used to collect the data were a set of five topic-specific questionnaires on classroom processes. The items in these questionnaires related to many aspects of classroom practice. This study was concerned with those items that were constructed to collect information on methods used in presenting certain concepts and skills in the Grade 8 mathematics curriculum. Since the nature of the data was not known prior to analysis, the study was designed to explore the nature of the data so that valid comparisons could be made on the concrete-abstract variable. Several data processing procedures were used. These procedures included the categorization of items by a panel of experts; the scoring of items; the preliminary analysis to investigate the justifiability of aggregation of item scores; and the calculation of concrete, abstract, and difference scores for all the teachers. Exploratory data analysis techniques were then used to compare the teachers' choice between concrete and abstract approaches. The results of the analysis seemed to indicate that teachers were abstractly-oriented in teaching most of the skills and concepts included in the study. In their teaching of three new concepts and skills in the Grade 8 curriculum, mathematics teachers were concretely-oriented in their teaching of one concept only. This finding led to the conclusion that teacher practices were not in accordance with the theory of instruction which states that new concepts and skills in mathematics should be initially taught using concretely-oriented approaches.

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