Course In Arithmetic Research Articles

The Pythagorean Theorem in the Fifth Grade

In the fall of 1957, a fifth-grade teacher introduced a small group of pupils in his class to the rule concerning squares on the sides of right triangles-the familiar Pythagorean theorem. By no fair estimate could the teacher's background qualify him as an expert or a specialist in mathematics. Although he had studied algebra, plane and solid geometry, and trigonometry in high school and had taken one course in general mathematics required for the degree of Bachelor of Arts in college, he had taken no special course in arithmetic. Like many elementary-school teachers, he had had to relearn the decimal system when the meaning emphasis was introduced ten or fifteen years ago. However, after attending a panel discussion in which a group of mathematicians considered the sad state of the teaching of mathematics in elementary and junior high schools, he decided to seek more content to enrich

Divisibility and Prime Numbers

Being an elementary discussion of some of the useful and interesting properties of numbers which are not often considered in elementary and secondary arithmetic courses.

The Organization of Instruction in Arithmetic and Basic Mathematics in Selected Secondary Schools

During the school-year of 1951-52, the Southern Section of the California Mathematics Council sponsored a research project concerned with the offerings in arithmetic and other non-traditional mathematics courses at the high school level.1 The purpose of the project was two-fold: (1) to discover current practices which might be adapted for use in improving non-traditional mathematics courses at the secondary level and (2) to find bases for making recommendations for the reorganization of the high school mathematics program. The nature of the study, therefore, was that of “action research” such as was recently proposed by the Commission on Life Adjustment Education.

Influence of Research on Instruction in Arithmetic

Research on instruction in arithmetic has influenced and continues to influence teaching procedures and the content of arithmetic at various grade levels. The influence of research operates through individual teachers and supervisors who keep informed about investigations in arithmetic. It operates, also, through arithmetic courses of study and textbooks which translate research findings on arithmetic content and procedures into suggestions for classroom activities and methods. It is recognized that widespread adoption of research findings in arithmetic instruction is a slow and gradual process, but the evidence is clear that research alters current practices. Since the early days of systematic research on arithmetic in social usage, as reported by Wilson and others (15),* content of the curriculum has progressively changed. The influence of selected research studies on instruction in arithmetic is summarized in this paper.

Picturing Fractions

My class in Methods of Teaching Arithmetic at Child Education Foundation, New York City, is composed of students in the third year of their teachertraining course. The students have had no teaching experience except a little student teaching. Their arithmetic course is a three-strand course. One strand deals with studying and evaluating current theory and practice in the teaching of arithmetic.

Arithmetic for the Twelfth Year

I will not go into detail concerning the teaching of a twelfth year arithmetic class, because you teachers know far more about that than I, but I will give you the development of the class in Ridgewood and its possibilities. What we are doing in Ridgewood is not new. Many schools throughout the country are giving the same work but under various titles. There are some who feel that our spade work in this branch of mathematics will be interesting to you. I believe the course fills a definite need in our school and community. The fact that the joint commission in 1940 suggested a social-economic arithmetic course for grade twelve or that the Commission for Postwar Plans in 1944 urged the high schools to include new and better courses for a large fraction of the school population, whose mathematical needs are not met in the traditional sequential courses, might be necessary to justify such a course in the eyes of some educators or college admittance officers, but not to me, nor to most of you. Even in a community such as Ridgewood, where 75% of the high school students plan to enter college, to contend that the sequential courses are the only ones of value and other courses may not be included in the curriculum is either due to pure stupidity or laziness. We either can't see beyond a few college requirements or knowing something else should be done for the students, we pass over the opportunity because of the work involved.

The New Arithmetic Course in the Chicago Elementary Schools

Arithmetic in the early days of American education was a subject relegated to the tradesmen and industrialists, but not considered worthy of the attention of those destined for higher learning. And so for about a century, the schools, in particular those which prepared for college, laid no stress upon the subject. But conditions changed in America. Farmers were no longer the only ones to be considered. Tradesmen and industrial workers were becoming a substantial part of the population; and so arithmetic came into its own. Books on the subject were in the nature of guidebooks in arithmetical computations and solutions covering, as far as possible, all the needs of business. To these a business man could refer to find help in solving any problem with which he was confronted.

Technique for Evaluating Arithmetic Courses of Study

While much has been written concerning curriculum evaluation and the preparation of criteria for course-of-study revision, the dis cussions have been confined to a limited point of view, presenting only one type or method for setting up criteria. No one individual or committee has attacked the problem from its many possible angles. The writer surveyed the problem of course-of-study evaluation in arithmetic in a comprehensive manner, in order to set up a definite body of criteria and to formulate a specific procedure based on objective material. Statement of the Problem. The purposes of this problem were (i) to develop a tech nique for evaluating courses of study and syllabi in arithmetic, and (2) to apply this technique to a critical study and evaluation of the New York City Course of Study and Syllabus in Arithmetic of 1929, for Grades I to VI. General Procedure. The general nature of the first portion of this problem was to col late a body of criteria for evaluating courses of study in arithmetic from an examination of informed opinion, judgments, and sugges tions of educational and arithmetic experts, educational investigations, research studies, and statistical and experimental data. The technique thus derived was applied in the second portion of the problem to a critical study of the New York City Course of Study and Syllabus in Arithmetic of 1929, for Grades I to VI. The sources of the material used comprised 623 articles culled from a number of period icals published since 1900, as well as from many books in the field of education, curricu lum construction, and the teaching of arith metic. From this mass, 174 items were sum marized and critically evaluated. For the complete bibliography, the reader is referred to the author's dissertation for the doctorate.1 The Evidence. The evidence for the con clusions was set forth in ten chapters and thirteen tables,1 a brief summary of which follows:

The Old and the New Mathematics Education

Much has been written in recent years about McGuffey's Readers, but little or nothing of Ray's Series of arithmetics and algebras. In their day the Ray books had a large sale and were regarded as of as much importance as McGuffey's. The old arithmetic course differed from that of today in two exceedingly important respects. First, the old books employed a rather thoroughgoing inductive and deductive procedure in presenting topics. Second, nearly thrice as much time was devoted to arithmetic in the elementary course as now. The question is, which course is the wiser?

A First and Second Course in Arithmetic; Examples only. By W G. Borchardt. With Answers. Pp. viii, 282, lviii. 3s. 6d. 1932. (Rivingtons)

A First and Second Course in Arithmetic; Examples only. By W G. Borchardt. With Answers. Pp. viii, 282, lviii. 3s. 6d. 1932. (Rivingtons)

A First Course in Arithmetic. By W. G. Borchardt. Pp. viii, 202, xxxvi. With answers, 2s. 6d. 1931. (Rivingtons) - A Junior Arithmetic. By R. C. Fawdry. Pp. vii, 178, xl. Without answers, 2s. With answers, 2s. 6d. 1931. (Bell)

A First Course in Arithmetic. By W. G. Borchardt. Pp. viii, 202, xxxvi. With answers, 2s. 6d. 1931. (Rivingtons) - A Junior Arithmetic. By R. C. Fawdry. Pp. vii, 178, xl. Without answers, 2s. With answers, 2s. 6d. 1931. (Bell)

Arithmetic of Citizenship

In putting forward a plea for the inclusion of “Arithmetic of Citizenship” in the regular arithmetic course in secondary schools, there are two points which I want to make clear : (i) the purpose of such a course, and (ii) suggestions as to how it may be carried out in practice.

Commercial Mathematics in a Small High School

Most references on this subject express the view that arithmetic is the only mathematical study necessary for the pupil preparing to enter the business world, and such is the practice at the present time. Mathematics for the commercial student is confined to a one-year course in commercial arithmetic. However from personal experience as a statistician, I have reached the conclusion that something is radically wrong. Either commercial students are not receiving enough mathematical training; the subject matter taught is not of value to them after leaving school; or the material is not taught, so that they acquire the ability to use it or rather apply it to the new conditions which they must meet. I am inclined to believe that the fault does not lie in any one of the above conditions, but in all of them. There should be a radical revision of both our curricula and teaching methods, and a realization of the need for more thorough mathematical preparation for the commercial student.

The Teachers’ Course in Arithmetic in the Normal School: A Plea for Professionalized Subject Matter

What training is necessary to prepare high-school graduates to teach arithmetic and other subjects in the modern elementary school? This question has come to be a very important one in every normal school and particularly in those normal schools which still have a two-year course at the end of which the students accept positions to teach. This question is a difficult one to answer because teachers to-day need a much broader professional training than formerly. One attempt to solve this problem has been to increase the length of the normal-school course from two years to four years, but even in those schools where the four-year course exists comparatively few students remain to complete it, the large majority accepting positions after finishing the two-year or three-year curricula offered in those schools. Hence, how to Prepare students in two or three years to teach effectively in elementary schools is still a vital question in practically all our normal schools.

The Teachers’ Course in Arithmetic in the Normal School

The Teachers’ Course in Arithmetic in the Normal School

Directed Drill in the Comprehension of Verbal Problems in Arithmetic

Teachers of arithmetic are coming to consider that their two most important teaching tasks are that of increasing the skill with which their pupils use the fundamentals, and that of in creasing their knowledge of when to use them. The first deals with the matter of tool acquisition, the question of how. The second deals with the matter of use at the right time, the question of when. Those who set up arithmetic courses of study tend to standardize somewhat the order of emphasis on these skills. In theory, at least, training in number work up through the fourth grade consists largely of drill having as its purpose the development of skill?accuracy and facility?in these fundamen tal processes. From this point on there is a tendency to decrease the emphasis on the tools of number work as such, and to give increased attention to the application of these skills in the prac tical solution of arithmetic problems. Observation of the methods followed by pupils and measure ment of the resulting product both lead to the conclusion that there is a vast difference between the two phases of the teaching of arithmetic. One phase deals with habit formation and the other with the development of technical judgment. The results of measurement show clearly that many children have a knowl edge of the fundamental combinations and can give correctly the answers to such examples as 4

A Course in Arithmetic for Teachers and Teacher-Training Classes. James Robert Overman

Previous articleNext article FreeEducational WritingsA Course in Arithmetic for Teachers and Teacher-Training Classes. James Robert Overman Frederick S. BreedFrederick S. Breed Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by The Elementary School Journal Volume 24, Number 7Mar., 1924 Article DOIhttps://doi.org/10.1086/455575 Views: 4Total views on this site PDF download Crossref reports no articles citing this article.

(1) A Short Course in Commercial Arithmetic and Accounts (2) The Use of Graphs in Commerce and Industry

(i) MR. PALMER'S books on the application of elementary mathematics to commerce and industry are a welcome addition to the literature on the subject. His “Short Course” is a brief account of the most important arithmetical methods and processes required in commerce. Those who know Palmer and Stevenson's “Commercial Arithmetic and Accounts” will expect to find the new volume useful and interesting, and they will not be disappointed. There is a touch of real life about most of the chapters, especially that on “The Home Trade”: one only misses the Public Receiver and the creditors' meeting. But are contracted methods really used in commercial life? (1) A Short Course in Commercial Arithmetic and Accounts. By A. Risdon Palmer. (Mathematical Series for Schools and Colleges.) Pp. x + 171 + xv. (London: G. Bell and Sons, Ltd.) 2s. 6d. (2) The Use of Graphs in Commerce and Industry. By A. Risdon Palmer. (Handbooks of Commerce and Finance.) Pp. ix + 47. (London: G. Bell and Sons, Ltd.) 2s. net.

A Short Course in Commercial Arithmetic and Accounts. By A. Risdon Palmer. Pp. 171+xv. 2s. 6d. 1922. (Bell & Sons.)

A Short Course in Commercial Arithmetic and Accounts. By A. Risdon Palmer. Pp. 171+xv. 2s. 6d. 1922. (Bell & Sons.)

The Practical in Arithmetic

The following article is an attempt to show how a review course in eighth-grade arithmetic may be centered around one large problem. The decided advantages of the plan are: (i) it gives ample opportunity for the practical applications of principles already learned; (2) it is easily carried out and may be easily adapted to any community; (3) it furnishes abundant resources for the individualistic need; (4) it requires no more time than would an ordinary review course in arithmetic; and (5) it secures better results, in that the subject-matter is of real, vital interest to the pupils. The particular problem here discussed is centered around the building and furnishing of a city home. The plan in brief is as follows: