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).

"Since arithmetic is a skill that presents almost insurmountable difficulty for some children there is a need for investigation of the methods and materials of teaching. Assuming that the meaning theory is a desirable way of teaching numbers the writer has endeavored to organize some ideas and objectives for developing quantitative understanding in children at the first and second grade levels. The writer has not attempted an exhaustive study of the problem but has focused her attention on principles that would be of immediate aid during the coming school year"--Introduction. / "August, 1952." / Typescript. / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Arts." / Advisor: Elizabeth Hamlin, Professor Directing Paper. / Includes bibliographical references (leaf 42).

Bidirectional Translation, devised by the author, is a structured approach to the teaching of addition and subtraction which aims to give children greater understanding of arithmetical operations. The approach systematically involves both: the translation of numerical representations into hypothetical, real world contexts; and the extraction of the appropriate numerical operations from hypothetical, real world contexts. It is this emphasis on translation from and to both the numerical representation and realistic contexts which gives rise to the name, Bidirectional Translation. An experimental group of 90 primary one children were taught to add and subtract (within 10) by the method of Bidirectional Translation. Post-test comparison of the experimental subjects' performance with that of a control group showed significantly superior performance on the part of the experimental subjects in terms of the utilizability of addition, the evocability of addition, the utilizability of subtraction and the evocability of subtraction for five different classes of verbal context, namely: Part-Part Whole, Separating, Joining, Equalizing and Comparison contexts. In all instances the probability of the results being chance ones were less than 5% and in most, were less than 1%. In both the experimental and control groups, most children performed better when they were required to utilize concepts than when they were required to evoke concepts. Similarly they performed better when they were required to add than when they were required to subtract. The differences, however, were not always significant. It is suggested that the effectiveness of the methodology of Bidirectional Translation is rooted in a structure which allows the child to make his/her thinking explicit and which allows the teacher to monitor this.

No description available.

The purpose of this study was to determine: (1) the importance first-grade teachers of San Joaquin County place on manipulative devices for the teaching of arithmetic; (2) the manipulative devices first-grade teachers of San Joaquin County have and use; and (3) the uses first-grade teachers of San Joaquin County make of manipulative devices in the teaching of arithmetic.

by Tan Ah Kiang. / Bibliography: leaves 90-96 / Thesis (M.A.Ed.) -- Chinese University of Hong Kong, 1983

This study was concerned with determining the effectiveness of two methods of teaching arithmetic in the first grade. The primary dimension of this problem was to determine and compare the arithmetic achievement of an experimental group using the Cuisenaire program and the achievement of a control group using a conventional program for the purpose of finding which was the more efficient. The secondary dimension of the problem was to determine whether socio-economic status or sex affects the achievement which results from either the conventional or the Cuisenaire method of instruction.

"Wanting to help children to overcome any fears that might be foremost in them, the writer wishes to make a study of principles of teaching arithmetic and apply in the classroom certain of these principles in an effort to help children hurdle their great fear of arithmetic"--Introduction. / "August 1956." / Typescript. / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Arts." / Advisor: Mildred Swearingen, Professor Directing Paper. / Includes bibliographical references (leaves 29-30).

No description available.

The Mathematics Curriculum and Assessment Policy (CAPS) document defines ‘mathematics [as] . . . a human activity’ (DBE, 2011a, p.8). This adoption of a realistic approach to the learning and teaching of mathematics appears to be partial, however, in that at the entry point of the Intermediate Phase, the recommendations of the policy makers are read as prescriptions by practitioners. In particular, the recommendation that ‘as the number range for doing calculations increases up to Grade 6, learners should develop more efficient techniques for calculations, including using columns’ (DBE, 2011b, p.13) is taken as a prescription to push the standard methods as the way to solving (often de-contextualized) problems from the very start of Grade 4, in disregard to the admonition that ‘these techniques should only be introduced and encouraged once learners have an adequate sense of place value and understanding of the properties of numbers and operations’ (DBE, 2011b, p.13). In the background of reports that place South African schools well below international standards with regard to mathematics, with only a third of the learners in grade 3 having attained the minimum standard required of learners at their level in 2011, this report focuses on an exploration into the purported catalytic role that the emergent model of an empty number line can play in shifting learners’ attention from counting (calculation by counting ) towards a focus on the structural properties of number (calculation by structuring). The use of emergent models is meant to support and improve upon learners’ informal solution strategies whilst seeking to reverse what Freudenthal referred to as the “anti-didactical” use of models in a ‘top-down instructional design strategy in which static models are derived from crystallized expert mathematical knowledge’ (Gravemeijer and Stephan, 2002, p.146). With a particular focus on poor performance in numeracy, the Wits Maths Connect-Primary (WMC-P) project was established with the overarching aim of improving the learning and teaching of primary school mathematics. My investigation is located within one Grade 4 class in one of the WMC-P project schools, and in this project, I act as both the teacher of six intervention lessons focused on additive relation problems, as well as researcher of the models and strategies that learners use prior to the intervention lessons, within these lessons, and subsequently. This report presents evidence to illustrate, firstly, that at the entry point of grade 4 level, learners are highly dependent on concrete strategies for solving addition and subtraction problems, and secondly that with proper intervention, learners can make significant shifts towards more abstract calculation. On the one hand, the key finding that the majority of the problems were tackled using tallies in the pre-test confirms what research has observed regarding the tendency for learners to remain highly dependent on concrete strategies at grade 2 (Venkat, 2011) and grade 3 (Ensor et al., 2009). Also, the results indicate a high proportion of incorrect answers resulting from the use of the column model across all questions in the pre-test and the post-test. On the other hand, the imposition of the use of the empty number line in the delayed-post-test points to the fact that improvements can be achieved in relatively short time frames, and importantly, that these improvements can be retained beyond their immediate coverage in class.