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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. / Education, Faculty of / Curriculum and Pedagogy (EDCP), Department of / Graduate

Many people seem to agree that arithmetic is hard. Because of this difficulty, there has been a movement to postphone the beginning to arithmetic teaching from first grade to second or third grade. This movement presents an opposing view in relation to other subject matter areas. The actual teaching of other subjects is moving into the lower grades rather than out of the lower grades as teachers realize more and more the importance of these subjects in relation to younger children. Each first grade teacher should realize the resonsibility involved in developing the number readiness that will affect the child's future understanding of the various extensions of the initial concept of number. / Typescript. / "August, 1958." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: Sarah Lou Hammond, Professor Directing Paper. / Includes bibliographical references (leaf 39).

Arithmetic probably causes more unhappiness among elementary school children than any other subject. Teachers, doubtless, experience a feeling of failure in this area of their work more than in any other undertaking. Many children and some teachers would be delighted to eliminate arithmetic from the program of the elementary school. In our technological society which requires a high degree of competence in mathematics, this step is not the solution to the problem. To one taking into consideration the usefulness of arithmetic in the lives of young children, it is evident that children must be given an opportunity to succeed in this endeavor; that it should be related to the everyday experiences of children; and that it should be taught meaningfully. / Typescript. / "August, 1956." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: Marian Black, Professor Directing Paper. / Includes bibliographical references (leaves 35-37).

The major purpose of this paper is to show how a class of seventh grade pupils may be led to understand that arithmetic is not merely a book of rules, drills, and meaningless problems to be memorized in order to pass to the next grade, but a means of interpreting the world about them and a means of understanding how arithmetic functions in their everyday lives. / Typescript. / "August, 1952." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: Robert C. Moon, Professor Directing Paper. / Includes bibliographical references (leaf 32).