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UBC Theses and Dissertations

Two different instructional procedures for a multiplication algorithm and their transfer effects to a higher-order algorithm Hope, John Alfred

Abstract

This was a study to determine the effects of two instructional procedures for a multiplication algorithm on the ability of elementary school children to extend this algorithm to the solving of computational tasks involving the use of a higher-order algorithm. Each of two groups was given preliminary instruction in solving multiplication problems via the application of the distributive law. After this readiness phase was completed, students were randomly assigned to either a Tl or T2 treatment group. The Tl subjects were taught a rote-type standard multiplication algorithm for determining the solution of 2 x 1 and 3 x 1 products. No explicit instruction was given to indicate the relationships between the two learning tasks, viz. the acquisition of the distributive law and the standard multiplication algorithm. Unlike the Tl instructional sequence, the T2 instructional sequence was designed to promote the learning of the relationships between the series of learning tasks. That is, the T2 subjects were taught a standard multiplication algorithm that required the explicit use of the distributive law and other acquired algebraic skills. It was hypothesised that this continual integration of learning tasks would enable the T2 subjects to exhibit superiority over the Tl subjects in extending their standard multiplication algorithm to computational tasks requiring the use of an untaught higher-order algorithm. A total of 238 subjects and 8 teachers were used in all phases of the experiment. A mixed model of analysis of variance was used to validate the performance hypothesis. It was found that the Tl subjects were significantly better than the T2 subjects in the performance of the standard multiplication algorithm. An analysis of covariance was performed to determine the validity of the transfer hypothesis. A subject's score on the performance test was used as a covariate in order to equate the disparate computational abilities of the Tl and T2 subjects. Although the mean score of the T2 subjects was higher than that of the Tl subjects on the transfer test, this difference was not statistically significant.

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