Abstract:
The aim of this project is to evaluate to what extent it is possible to improve the mastery of the meaning and functionality of algebraical manipulation of standard seven pupils, who were taught algebraical manipulation in the traditional way. The empirical investigation involved a group of 25 standard seven pupils from a suburban high school under the Cape Education Department. The investigation included a pre-test, 10 instruction sessions, a post test and a postponed post test. During the first phase of the intervention an attempt was made to establish the pupils' understanding of letter symbols as variables. After that the pupils were made aware of the existence of equivalent expressions. The meaning and functionality of equivalent expressions were stressed throughout the intervention. The success of the intervention was evaluated by means of a post test and a delayed post test which was similar to the pre-test. The post test was written immediately after the intervention and the delayed post test 7 weeks later. An analysis of the answers to the pre-test indicates clearly that a vast majority of the pupils do not fully master the meaning and functionality of algebraical manipulation at present, although they have a clear understanding of the meaning of algebraical expressions and demonstrate skill in algebraical manipulation. It seems that pupils manipulate expressions and letter symbols mechanically without really understanding what they are doing, or what the use or applicability of algebraical manipulation can be. The investigation indicated that it is indeed possible to increase the pupil's mastery of the meaning and functionality of algebraical manipulation dramatically within only ten periods of 35 minutes each. The same measure of success was however not obtained with all the pupils. An assumption can be made that a greater measure of success will be obtained if this approach is followed from the start of the teaching of algebra.
