Practice versus graphical representation for maintainance of basic arithmetic competencies : first year primary

Educators such as Edith Biggs in Britain and Vincent Glennon and the Cambridge Conference on School Mathematics in the United States have suggested that the amount of time children spend on direct practice of newly learned skills and understandings can be greatly reduced. The Americans propose an Integration of this practice with the presentation and learning of new topics. The British favour an activity approach, where new learnings are put to immediate use, and the need for acquisition and perfection of mathematical competencies becomes obvious to the children. A few American research studies have substantiated the merits of reduced practice, at the intermediate level. This study explores the place of practice for maintenance of the basic competencies of First Year Primary children in British Columbia at the end of the school year. The competencies chosen for study were 1) Numeration: reading, writing and understanding of base ten numerals ≤99, and 2) Computation: addition and subtraction operations with sums and minuend ≤10. The new material, chosen to be presented as an alternative to direct practice, was Graphical Representation, a unit developed from the Nuffield Project booklet, Pictorial Representation 1. Two schools in the Vancouver area were used, the first with a class of 54 children and the second with 34. Parallel pre-tests and post-tests in the basic competencies were administered. During a three week Intervening interval, the Investigator taught the children, who were divided into groups, by random selection, as follows: In the first school, three groups of 18 children were instructed respectively in Graphical Representation, in review and practice, using familiar materials, and in geometry, involving no use of numbers (control group). In the second school, two groups of 17 children were Instructed in Graphical Representation, and in review and practice, respectively. At the end of the experiment, there was no significant difference in the tested numeration competencies of the two experimental groups in their respective schools. The control group showed a slightly lower achievement. Time did not permit a retention test. In the first school, where computational efficiency was low, the results slightly favoured the review and practice group, over the other groups. In the second school, there was no significant difference between the two groups, regarding progress in computational skills. Within Its limitations, this study demonstrates the possibility of maintaining basic competencies, while introducing new topics, at the first year level.

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