bluuebunny/crossref_metadata_2025 huggingface dataset:
A Study of Prognosis in High School Algebra
Authors: Orleans Joseph B. , Orleans Jacob S.
Published: January 2021

During the past two decades high school registration has increased many fold. The growth has been so rapid that in New York City, for example, the authorities have not been able to supply buildings fast enough to meet the new demands. Chief among the causes of this change is the Compulsory Education Law which complete many boys and girls to remain in school a year or two at least after their graduation from the elementary school. High school education has become the vogue and the high schools have therefore been forced to accept a large number of pupils who are not fitted for the various courses which are offered. The extent to which this condition holds is indicated by the number of failures each term. Commercial and vocational courses of various kinds have been introduced to take care of pupils whose needs are not met by the traditional subjects. The syllabi of the traditional subjects have been modified and simplified to meet the varying abilities and needs of the pupils. The effect of this tendency is seen in such courses as general science, general language and general mathematics.
A Study of Procedures used in the Determination of Objectives in the Teaching of Mathematics
Authors: Georges J. S.
Published: January 2021

The question of the general and specific functions of mathematics in secondary education has been a source of much discussion and dispute for many years. The curriculum studies which have been concerned chiefly with attempts to determine educational objectives have used such methods as analysis of pupil activities, analysis of social needs, opinions of competent persons and authorities in the field, and analysis of existing objectives found in educational investigations, courses of study, and textbooks. The outcome of the specific influence of these studies has been the formulation of a great number of courses of studies with lists of general course-objectives and specific unit objectives. While it is true that in many cases the teachers of mathematics, who should be the most vitally interested in the determination and evaluation of the objectives relating to their subjects have been consulted in the matter, nevertheless, in general the solution of the problem has been left to the “experts” and more “qualified” persons; the teachers have accepted the lists of objectives presented in the courses of study and have tried to attain them the best way they could. It is felt that as a point of pedagogical interest it is worth while to note the r eactions of teachers of mathematics toward the proposed lists of objectivesand the proceddures followed in their determination. This study reports the evaluation by a group of teachers of secondary school mathematics of the merits of certain procedures used in the determination of mathematical objectives.
Editor's Note
Authors: Reeve W. D.
Published: January 2021

The mathematics teacher is the only magazine in the United States devoted entirely to the interests of elementary and secondary teachers of mathematics. Moreover, the subscription price of $2.00, which includes membership in the National Council of Teachers of Mathematics, is the smallest fee known for belonging to any national organization in this country.
Adjusting Algebra to Ability Levels Through the Time Element
Authors: Cline Jessie M.
Published: January 2021

I have been asked to tell you what we are doing in the Bloomington High School to adjust algebra to the different ability levels of our pupils; what problems we have encountered in making such adjustment; and what results we have accomplished.
The Place of Mathematics in Junior High School Education
Authors: Rowlands Agnes
Published: January 2021

Before discussing the place of junior high school mathematics in education, it will be well to decide what criteria to use in determining whether or not a subject or a method has educational value.
The Mathematics Club of the Pontiac High School
Authors: Steward Margaret
Published: January 2021

The purpose of the Mathematics Club of the Pontiac High School is to develop an appreciation of mathematics, a greater interest in it, and a broader understanding of the subject than can be secured in the regular classwork.
Proposed Syllabus in Plane and Solid Geometry
Authors: Evans George W.
Published: January 2021

The following list of propositions, 104 in number, have for plane and solid geometry the same total content as the list of 181 that constitutes the College Entrance Examination Board's definition of those two subjects. It is based upon measurement, and uses systematic approximation as a means of dealing with irrationals. Algebra and trigonometry are used wherever they contribute to clearness and brevity.
Consumer's Uses of Arithmetic
Authors: Shuster C.N.
Published: January 2021

Dr. A. O. Bowden's dissertation, “;Consumer's Uses of Arithmetic,” has received so much publicity that a review and evaluation in The Mathematics Teacher seems not only fitting and proper but quite necessary.
To Postulate or not to Postulate
Authors: Jackson Nelson A.
Published: January 2021

How many of the first principles and theorems of the traditional course in Plane Geometry shall be postulated? On one side are those who say that we should scrap all of the demonstrative work and coofine our attention to intuitive geometry and to practical applications.
New Books
Authors: Zant Jas H. , Smith David Eugene
Published: January 2021

Training in High School Mathematics Essential for Success m Certain College Subjects (With Especial Reference to Physics). By Allan Ray Congdon. Teachers College Contributions to Education No. 403. Bureau of Publications, Teachers College, Columbia University, New York. 1930, pp. 110, $1.75.
The Skills Involved in Problem Solving in Elementary School Arithmetic
Authors: West Guy A.
Published: January 2021

Accurate Diagnosis Depends upon adequate analysis. This is true of that part of arithmetic which deals with problem solving as well as of the fundamentals of the subject.
Building Tests in Junior High School Mathematics
Authors: Stokes C. N.
Published: January 2021

The Fundamental Problem in teaching junior high school mathematics resolves itself into a matter of effecting real learning. The pupil must have mastery of the minimum essentials. He must have those skills and understandings which are deemed the necessary equipment of every normal individual who must make the necessary adaptations to the environmental conditions of the well-ordered life. He must have the ability which stands the test of normal and habitual use under practical conditions in the everyday life situations. Training in junior high school mathematics must add materially to his stock of abilities which are needed in making adjustments to the demands of society.
New Books
Authors: Swenson, Joan A.
Published: January 2021

The Sextant, How to use it. By Carl N. Shuster, Head of the Mathematics Department, State Teachers College and Normal School, Trenton, N.J., and Instructor in Instrument work, Teachers College, Columbia University, and Aaron Bakst of Teachers College, Columbiz. University, New York.
Number Contents of Front Page of Newspapers
Authors: Sueltz Ben
Published: January 2021

This report is based upon an analysis of the number content of newspapers published in central and southern New York state. A total of thirty-five copies of fourteen different publications were examined for the numbers that appeared in figures. These thirty-five copies were distributed among the publications so that two or three different copies of each publication were used. In no case were more than five copies of a single publication used. In general there was no forethought of the type of news that would be found in the papers and analysis showed that no event of an extraordinary nature which would be full of figures was chronicled in these papers. The papers were selected by name and date before they were published so that it is very evident that it was impossible to select them because of their contents. These newspapers were published in cities ranging in size from 15,000 to 300,000 population. Chart B shows the list of newspapers used and their frequency of use as well as the approximate population of the city represented.
Charles Lutwidge Dodgson (Lewis Carroll)
Authors: Eugene Smith David
Published: January 2021

“… that peculiar love of nonsense so characteristic of the English genius. It springs only from genius as seen in the Shakespearean Fools, Lear's Book of Nonsense, Lewis Carroll's Alice in Wonderland, and the other two inspired works of that rather prim and starchy don, who vainly tried to infuse elementary mathematics into Christ Church undergraduates.” — Henry Wood Nevinson, Rough Islanders, George Routledge and Sons, Ltd., London, 1931, pp. 227.
Trignometry in the High School
Authors: Bailey H. W.
Published: January 2021

Introduction.—The University of Illinois has had for many years a two hour course in trigonometry, known to several thousand present and former students as Mathematics 4; the prerequisites are one unit of algebra and one unit of plane geometry. In the fall of 1924 there was introduced a two hour course in advanced trigonometry, called Mathematics 5. The prerequisites for this course are one and one-half units of algebra, one unit of plane geometry, one-half unit of solid geometry, and one-half unit of trigonometry or Mathematics 4. The experience of the department with this latter course forms the basis of my remarks.
What Do We Owe to the Brighter Pupil?
Authors: Shoesmith Beulah I.
Published: January 2021

It is the ideal of democracy that we should afford each pupil an opportunity to grow intellectually up to the limit of his ability. In striving to attain this ideal, educators have placed great emphasis upon the problem of the poorer pupil. Scientific studies of such pupils have been made; subject matter has been diluted to fit their abilities, and pedagogic skill has been judged by its success in saving these pupils from the ranks of failures. Probably there is much to be said for this attention to the slow learner and doubtless it has been one of the successes of modern education that these pupils have been studied and educated up to their abilities, for in raising the level of the lowest we may have raised the level of the whole mass. If, however, we have exaggerated the importance of training the poorer pupil and have placed undue emphasis upon our duty to him to the consequent neglect of the more able pupil, our loss may have been greater than our gain, for we may have substituted for the two extremes in accomplishment the one dead level of mediocrity.
News Notes
Authors: Clark William , Cam Rhodes Rawlinson
Published: January 2021

Following is the program of the fall meeting of the Connecticut Valley Section of the Association of Teachers of Mathematics in New England, Bulkeley High School, Hartford, Connecticut, October 22, 1932.
The Slide Rule in the Junior College
Authors: Gorsline W. W.
Published: January 2021

The Program of this meeting was composed of three papers on the following subjects: The Slide Rule in the Junior High School, The Slide Rule in the Senior High School, and The Slide Rule in the Junior College. The first paper advocated that the slide rule should be studied in the seventh, eighth and ninth grades. No explanation of the foundation principles of logarithms was mentioned, and only the simplest operations of multiplication, division, proportion, squares and square roots were explained. If the student starts to study an instrument when he is young, even though he doesn't understand all the reasons, he will be ready for the further study of the foundation principles upon which the slide rule is based when be gets to the senior high school and junior college. When the pupil begins the study of logarithms in the third year of high school then he will be ready to understand fully all the reasons for any procedure with the slide rule.
Second Report of the Committee on Geometry
Authors: Beatley Ralph
Published: January 2021

The first report of this committee appeared in The Mathematics Teacher for November, 1932.
News Notes
Authors: Harmon Elizabeth
Published: January 2021

The mathematics Section of The Central Association of Science and Mathematics Teachers held its annual meeting at the Congress Hotel in Chlcago on Friday December 1, 1933, with Mr. Maurice L. Hartung of the University High School of Madison, Wisconsin presiding. The following program was given: Appointment of Nominating Committee; “Achievement Testing in Secondary Mathematics,” H. T. Lundholm, The Blake School, Minneapolis, Minnesota; “Dimensionality,” Prof. E. P. Lane, University of Chlcago; “Geometry's Tribute to Tradition,” Dr. Elizabeth B. Cowley, Pittsburgh, Pennsylvania; General Discussion; Election of Officers.
Accuracy in Addition
Authors: Nygaard P. H.
Published: January 2021

Much of the mathematics taught in the grades and in high school is being attacked on account of its presumed lack of value. Addition is one of the few parts of mathematics that is not being seriously criticized in this respect. Hence it is highly important that addition should be taught in such a way as not to jeopardize its usefulness.
A Study of Prognosis of Probable Success in Algebra and in Geometry
Authors: Orleans Joseph B.
Published: January 2021

The everpresence of the problem of individual differences in school work and the importance of its solution in the training of the children entrusted to our care is again evidenced by statements that have appeared recently in the press.
The 15th Annual Meeting of the National Council of Teachers of Mathematics, Cleveland, Ohio, February 23-24, 1934
Authors: Schreiber Edwin W.
Published: January 2021

Present: William Betz, Mary A. Potter, Ralph Heatley, Edwin W. Schreiber, Vera Sanford, Mary S. Sabin, C. Louis Thiele, John P. Everett, Elsie Parker Johnson, Raleigh Schorling, Harry C. Barber, J. O. Hassler, W. S. Schlauch.
The Mayan Calendar
Authors: Kinsella John , Bradley A. Day
Published: January 2021

Professor Judd of the University of Chicago in the April 1929 “Mathematics Teacher” while urging teachers of mathematics to keep in mind the informational values as well as the computational uses of mathematics made the following interesting statement: “Number is a general system. It was invented by the race as a useful system by means of which anyone who is in command of the number series can arrange all kinds of miscellaneous experiences and thus greatly facilitate intelligent thought about particular items.” It seems to be a general theorem that races in their evolution toward a higher degree of civilization have almost inevitably developed a number system for the expression of order and precision.
Mathematical Training for Economic Thinking and Social Mindedness
Authors: Schaaf William L.
Published: January 2021

We of today are living in a time of rapid technological advancement and of equally rapid social and economic change. In a democracy such as ours, desirable social reconstruction can come about only if people in general achieve an intelligent comprehension of the complex activities in which perforce they play a part. Hence the training of youth for effective economic thinking becomes an imperative obligation of education. The social-economic processes undergoing evolutionary changes before our very eyes may be regarded from two significant standpoints—their humanistic bearings, and their technical aspects. The technicalities of economic activities and social institutions are both qualitative and quantitative; the qualitative features are largely related to modern physical science, while the quantitative aspects involve statistical and mathematical methods.
There is Fusion in the Air
Authors: Freilich Aaron
Published: January 2021

Despite the great strides education has made through modern experimentation, many laymen and even teachers not only refrain from supporting further experiments, but actually frown upon the conclusions deduced from them. Frankly, too much censure should not be heaped upon such dissenters, for have they ever seen the original report of an experiment to admit failure? Are not all experiments successes, that is, at least until after the results are written up and published? There is no doubt but that the ends of education would be served better if experimenters would not color their reports merely for college credit, publication fame, or personal gain.
The Place of Mathematics in the Curriculum of the Progressive School
Authors: Atherton Charles Russell
Published: January 2021

Two questions confront the curriculum committee of any progressive institution when the course of study in any particular subject matter field is under consideration. First:—What is the claim of the particular subject upon a place in the program? Second:—How can the administrative difficulties involved in the offering of courses in the subject be overcome?
Predicting Achievement in Plane Geometry
Authors: Richardson H. D.
Published: January 2021

It is generally conceded by mathematics teachers and school administrators that all students who now attend the secondary school should not be required to study plane geometry. This position rests upon the belief that many of the students who now come to high school possess neither the ability necessary to succeed in the subject nor the capacity to profit greatly from its content. The experience of numerous students who have pursued the subject only to fail at the end serves to substantiate the contention of teachers that many do not possess the requisite ability. The increasing number of such unfortunate experiences has led to a search for means that might be used in identifying those students most likely to find the subject least fitted to their needs and abilities.
Abstracts of Recent Articles on Mathematical Topics in Other Periodicals
Authors: Lazar Nathan
Published: January 2021

I. Chistakoff, I. Notes on progressions. Matematika i fisika v srednei shkole. (Mathematics and Physics in the secondary schools.) Quarterly Publication of the Commissariat of Education and Public Instruction of U.S.S.R. 1: 15-17. 1934 no. 1.
Abstracts of Recent Articles on Mathematical Topics in Other Periodicals
Authors: Lazar Nathan
Published: January 2021

A description of a method of teaching algebra by means of a “mastery chart.” The writer determined at first what skills were essential for the first term of algebra and then proceeded to make a chart with the names of all the pupils in the class, providing as many columns alongside each name as there were skills to be mastered.
Teaching for Transfer
Authors: Fawcett Harold P.
Published: January 2021

Out of the confusion of viewpoints relative to the transfer of training there seems to be one general agreement which is clear and well defined: transfer is not automatic. If as teachers of mathematics, we believe that there are values in our subject which are able to change the behavior of a pupil in such a way as to make him a more useful citizen and better equipped to solve the problems of life, we have no right to expect that this desirable result may be accomplished by simply hoping that it will follow inevitably from any kind of teaching.
What Research Reveals on Proper Drill Content of Elementary Arithmetic
Authors: Wilson G. M.
Published: January 2021

Drill may be profitably regarded as a key word in the topic assigned me for discussion.
Some Little Known Applications of Mathematics
Authors: Hotelling Harold
Published: January 2021

I am very much flattered by Professor Reeve's kind words, and by the invitation to speak to you tonight. I must disclaim one honor that Professor Reeve heaps upon me. I am not a professor of mathematics. I happen to be in the Economics Department at Columbia University. That is also relevant to what I have to say. I have taught mathematics at other places, and I am teaching mathematics now in the forms of mathematical statistics and mathematical economics.
News Notes
Authors: Edith Woolsey
Published: January 2021

At Teachers College, Columbia University, from July 7th to August 14th, in addition to the major course on the teaching and supervision of mathematics and one on the teaching of algebra given by Professor Reeve, the following courses will be offered. By Miss Sutherland: Teaching arithmetic in primary grades, teaching arithmetic in intermediate grades, and professionalized subject matter in junior high school mathematics. By Professor Shuster: Modern business arithmetic and field work in mathematics. By Dr. Sanford: Teaching algebra in junior high schools, and the history of mathematics. By Mr. Smith: Teaching geometry in secondary schools and a demonstration class in plane geometry. By Dr. Swenson: Professionalized subject matter in senior high school mathematics, and a demonstration class in eleventh year mathematics. By Dr. Wolff, visiting professor from Germany: Teaching mathematics in the secondary schools of Germany and the correlation of secondary school mathematics with science and art.
Mathematics on the Offense
Authors: Moulton E. J.
Published: January 2021

On a number of occasions in the last year or two I have heard someone remark that “Mathematics is on the defensive.” Whatever significance there may be to this remark, it is certainly a fact that in a truer sense “Mathematics is on the offensive.” As a result of a consideration of the matter, I have decided to make Rome remarks this evening concerning the present vitality and the significance of mathematics.
Observations on the Study and Teaching oF Mathematics
Authors: Browne E. T.
Published: January 2021

I have chosen for the subject of my discussion this evening the rather broad topic “The Study and the Teaching of Mathematics.” Doubtless some of you will think that either of these subjects is too broad to be covered in one evening's discussion, and that I should at least confine myself to one of them. But the two things are so closely intertwined that I do not wish to separate them. The study and teachmg of mathematics go hand in hand. Most of us who study mathematics do so under the direction and guidance of some more experienced person who has been along that way himself and who is, or should be, fully acquainted, not only with the pitfalls and the difficult spots in the path, but with the beautiful scenery on all sides which we can enjoy provided only it be pointed out to us. It is true that there are notable exceptions to this rule, the best known of which is perhaps that of Blaise Pascal. But not many of us are Pascals. In our study of mathematics the difficulties in our path would be so great and we would be so busily engaged in getting over them that we would scarcely have the time, even if we had the ability, to see the beauties that lie all around us. Hence we need a guide. For that reason I have had the temerity to include both the study and teaching of mathematics in the title of this discusion tonight.
Gestalt Psychology and Mathematical Insight
Authors: Hartmann George W.
Published: January 2021

This paper is presented as an expression of belief and hope that some of the newer formulations in psychological theory will bring about a democratization of mathematical competence somewhat akin to the astonishing elevations of performance often obtained in the field of reading. The symbolism and thought processes involved in using conventional language are not essentially different from those employed in the more universal terminology and operations of mathematics. If reading ability is now better and more widespread among Americans than at any previous time in our history, there is no reason why a better comprehension of numbers, figures, and conceptual relations should not make quantitative inferences as common as simple words and sentences. Although it is probably true that algebra and geometry as ordinarily taught are unable to become more influential because of the present intellectual and motivational limitations of the average learner, I should like to maintain the position that by taking more adequate advantage of the princip1es of mental development, our teachers could make the special modes of thought of the mathematician a part of the daily routine of our citizenry. The deserved success of the Bell and Hogben volumes reveals what some of these possibilities are.
Random Notes on Geometry Teaching
Authors: Barber Harry C.
Published: January 2021

A great philosopher1 has said that we should teach school subjects so as to yield ideas that illumine great areas of human experience.
Teaching Geometry for the Purpose of Developing Ability to Do Logical Thinking
Authors: Ulmer Gilbert
Published: January 2021

The development of ability to do logical thinking has long been counted one of the important objectives in the teaching of demonstrative geometry. In the past it was generally believed that the student acquired from the logic of geometry a mode of thought which he would use in solving many problems of life. Little or no direct attention, however, was given to the mode of thought itself, nor was any consideration given to the manner in which this mode of thought would be expected to function in various types of situations that are non-geometric. We have now come to believe that if transfer of this kind is desired, definite provisions must be made to teach for it. The teacher must definitely hold this outcome clearly in view and so arrange the teaching program that thjs outcome may be realized. It is possible that our whole teaching procedure needs to be reorganized.
News Notes
Authors: Schreiber Edwin W.
Published: January 2021

The third summer meeting of the National Council was held in the city of Detroit at tho time of the Annual summer meeting of the N.E.A. The Local Committee with Miss Hildegarde Beck as Chairman, had made splendid arrangements before hand for taking care of the three-day session. On Monday, June 28 the following program was presented. The first session on 1uithmetic was as follows:
The Dandelin Spheres
Authors: Boyer Lee Emerson
Published: January 2021

Within recent years at least four references to the Dandelin spheres have appeared in American mathematical literature.1
Geometry a Way of Thinking
Authors: Christofferson H. C.
Published: January 2021

A student of geometry who gets the most out of his work will learn two types of things. First he will learn many facts and principles about form and space. These will enable him to solve numerous problems. Second, he will learn how statements are proved and the nature of sound proof. He will never again be content with statements which merely seem to be true; he will demand proof and will require the proof to be correct, clear, and precise. Because of the simple and concrete nature of the ideas with which geometry deals, the nature of rigorous proof is illustrated with relative ease.
Some Problems in Evaluation
Authors: Hartung Maurice L.
Published: January 2021

The mere mention of the word “test” to a group of boys and girls often stimulates a chorus of groans and sighs, and rare indeed is the teacher who is enthusiastic about the task of preparing and marking examinations. It is not unlikely that many of you have recently expressed a fervent wish that you would never again have to struggle through the rites of a departing school year. But testing—or to use a broader term, evaluation of student progress—is a very important part of instructional activity. In a few weeks you will return to your schools and once again face the problems associated with arriving at judgments concerning the educational status of your pupils. It seems to me that the present occasion, before you become subject to the stress and strain of classroom teaching, may be an unusually appropriate time to think about some of these problems. Since at this time we are not faced with the task of planning specific tests for immediate use, we can concentrate upon certain general problems encountered in any careful evaluation of pupil progress.
The Art of Teaching
Authors: Alexander Edyth Clarke
Published: January 2021

An important concept of mathematics which relatively has been overlooked in the mathematics courses of study in our American schools is the concept of approximation.
Editorials
Authors:   W.D.R.
Published: January 2021

Dr. H. C. Christofferson of Miami University at Oxford, Ohio has taken up his duties as President of the National Council of Teachers of Mathematics. His experience as presiding officer at several past meetings of the Council will not only be helpful to him in his new role but it has given Council members a chance to find out what a good presiding office he would make.
Preparation for Teaching Secondary-School Mathematics
Authors: Hagen Henry H. , Samuelson Norman L.
Published: January 2021

Over five hundred principals and teachers of mathematics in one hundred secondary schools in twenty states agree that the successful teacher of mathematics is usually one whose training and experiences have been extensive, one who is not merely a specialist in the field of mathematics, as the child—not the subjectmatter—is the first consideration here, as in all fields. The basis for this statement results from a recent investigation made by the Commission on Unit Courses and Currirula of the North Central Association of Colleges and Secondary Schools, a preliminary report of which has been previously published.* The generalization was drawn from responses to questionnaires submitted by this group of educators.
The Expediency of Compromise in Mathematical Curricula and Instruction
Authors: Maddox A. C.
Published: January 2021

Intelligent men and women who have diligently and consistently pursued the study of mathematics and who have seriously considered the contributions of mathcmatics to civilization and the value of proper mathematical study to individuals find it very difficult to believe that there is real justification or educational wisdom in the current trend toward the removal of prescribed mathematics from high school and college curricula. The consciousness that mathematics is a “universal and permanent element in education” naturally causes the devotees of mathematics to deplore any movement that would give to mathematics a relatively minor place in a system of general education. The writer of this brief paper shares in a growing sense of uneasiness caused by the real or apparent lack of appreciation of mathematics that is being revealed by many educational officials in whom rests the final responsibility of determining what the various school curricula shall be. It is precisely this common uneasiness among those who place a high evaluation upon mathematical study that should lead them to make a united effort to bring about a more effective understanding between themselves as advocates of mathematical education and the school administrators as the official promoters of general education. It seems possible that such an effort would result in agreements that would produce significant benefits to individual students and to society. Let us consider briefly a few of the simpler general facts that ought to be accepted, both by school administrators and by teachers of mathematics, as basic in the serious business of advancing the highest interests of education. If such agreement as to basic facts necessitates significant concessions on the part of teachers of mathematics or of school administrators, such concessions should be forthcoming at appropriate times and places.
Repeating Decimals
Authors: Nygaard P. H.
Published: January 2021

When a fraction is converted into a decimal by long division, it often happens that the quotient contains a continuously repeating series of figures. Thus, …, which has two figures in its repeating group. It should be noted that many repeating decimals do not start repeating immediately,—that is, the first figures after the decimal point may not be a part of the recurring series. On the other hand, a fraction may give an exact decimal value. For instance, . These two possibilities are not exceptions; it is a well established mathematical law that all division problems in which the dividend and the divisor are integers will eventually give, as the quotient, either an exact decimal or a repeating decimal. The converse law is also true,—namely, for every exact decimal or repeating decimal it is possible to find a fraction, with integral terms, to which the decimal is equal.
Some Debatable Facts and Some Suggestions
Authors: Hart William L.
Published: January 2021

1. Introduction. On several occasions I have read discussions of the curriculum in secondary mathematics which have commenced with arguments, pro or con, about existing college entrance requirements.1 More appropriately, I believe, associated collegiate problems should be proposed for solution only after the secondary program is formulated and justified. In particular, in a discussion of secondary mathematics, this viewpoint leads me to label as irrelevant, or misplaced, any preliminary conclusion about college entrance requirements such as follows:2
Applying Geometric Methods of Thinking to Life Situations
Authors: Hall Elizabeth Loetzer
Published: January 2021

It is the purpose of this paper to deal with actual class room experiences in applying geometric methods of thinking to life situations and so I shall merely state briefly some of the considerations upon which our attempts have been based. I think we agree that geometry is the simplest and most convenient introduction to postulational thinking that has been devised, and that it offers the one procedure that promises valid conclusions on the basis of clearly formulated assumptions. There are those, however, who claim that the traditional place of mathematics in the curriculum is due to the “exploded doctrine of mental discipline” and that accordingly the alleged educational values of mathematics are largely a myth. Such opinions are obsolete in the light of the results obtained from the careful research work in the transfer of training of men like Lashley and Orata. The fact of transfer (of training) from one activity to related activities seems established. But the equally important consideration that in order to obtain this transfer we must teach for it, has not yet received due emphasis.
The Art of Teaching: A Device for Teaching the Concept of the Trigonometric Functions
Authors: Blank Laura
Published: January 2021

Pupils begin the study of trigonometry, however brief, intensive, or extensive the course, and, whatever the grade in which it is taught, with the definitions of the six trigonometric ratios or functions. Much emphasis is put on these functions. Immediate applications to practical problems are made of the simpler ratios, such as sin 30°, tan 45°, cos 60°, and cot 135°. Shortly, the pupil is introduced to a table of “natural” functions, as we designate them to distinguish them from logarithmic trigonometric functions. The pupil learns to read the tables. He learns to apply them to problems that are not too difficult. It becomes an interesting game to use them. However, in his eagerness to make them serve him in solving problems of many sorts, whether he is a ninth-, tenth-, eleventh-, or twelfth-grade high school pupil, he loses the realization that he is using a ratio in decimal form. Somehow, to him, ratios are common fractions, and common fractions, ratios, but not so decimal fractions. The denominator of the decimal fraction is not apparent to him. Nor is it to us teachers until we make ourselves deliberately conscious of it. In truth, it is for this very reason that we use a decimal fraction, when we prefer it to a common fraction. It is due to this very fact that decimal fractions were invented.
The Efficiency of Certain Shapes in Nature and Technology
Authors: Hickey May
Published: January 2021

Existing curricula in the junior high schools show a weakness in failing to provide pupils with adequate experiences in intuitive solid geometry. Those space problems that appear are usually of a static nature where a formula is used to obtain some geometrical property of the figure. The visual and tactual experience with solids and their properties, the manual construction of various figures, and the dynamic purpose of certain shapes are missing. The inclusion of these would infuse vitality and purpose into the curriculum and allow the subject of solid geometry to become effective and functional in the lives of pupils.
Vocabulary Instruction in Mathematics
Authors: Drake Richard M.
Published: January 2021

The attempt to provide more satisfactory study direction in secondary schools started with the administrative problem of securing the most appropriate time and place for study. The outcome was a widespread use of “supervised study” in the classroom procedure. This study activity in the presence of the teachers brought to their attention the need for analyzing those activities in which the pupils engage when they study and the need for the improvement of the pupil in the use of desirable study techniques.
Number Concepts Held by Seven-Year-Olds
Authors: Gunderson Agnes G.
Published: January 2021

After reading Whiteaker's article1 in the January issue, one is challenged to make some attempt to discover what idea or concepts children at different ages or grade levels have regarding number.
Extra-Curricular Mathematical Activities In Secondary Schools
Authors: Leontius schulte M.
Published: January 2021

It has long been the practice of the writer to advocate extra-curricular activities as an important supplementary means for stimulating the interest of pupils in secondary courses in mathematics. It is true that the development and maintenance of interest in mathematics depends primarily on the presentation of the subject by the teacher, but it often becomes necessary to use additional devices for promoting enthusiasm. Extra-curricular activities in mathematics, including those of a recreational character, are invaluable for vitalizing the so-called dead language of mathematics.
Improving Instruction in Arithmetic
Authors: Bond E. A.
Published: January 2021

What peculiar values does a knowledge of number give one who has acquired this knowledge? This is the first problem that confronts one who is giving serious thought to ways of improving instruction in arithmetic. The answer to the question stated above depends on the answer given to a larger and more fundamental question, namely, “In general what kind of product must the school envisage?” When he has solved this problem he is in a position better to ascertain how arithmetic can contribute.
Does Mathematics Belong in General Secondary Education?
Authors: Havigrurst Robert J.
Published: January 2021

There is no use trying to guess how important these two reports will be. Guessing will not affect the answer which will be given five or ten years from now. But it is not guessing to say that these reports are important, because they are written by important groups of people, and they deal with an important problem—namely, does mathematics belong in the general secondary education of the great mass of American boys and girls?
The Performance of the Mathematics Candidates in the 1940 National Teacher Examinations1
Authors: Spaney Emma
Published: January 2021

Probably every superintendent of schools has often wished for some measure of the the ability and knowledge of the applicants who offer themselves for positions on his staff which would be comprehensive, accurate, and comparable from applicant to applicant. In order to help meet this need, the American Council on Education in the spring of 1939 appointed a National Committee on Teacher Examinations and authorized it to supervise and delegate to the Cooperative Test Service the task of preparing a battery of objective tests for the examination of teacher candidates.
Regional Organizations of Mathematics Teachers
Authors: Mayor J. R.
Published: January 2021

If the mathematics teachers will get together in groups to work out common problems, to add to their own and their students' enthusiasm and satisfaction, and to observe and enjoy success of others in a field where the ideals of success and perfection are held high, they will be serving their own interests in many ways. Such groups can contribute much to the improvement of teaching mathematics and the work of such a group will bring the importance of mathematics before the public which is now hearing so much carelessly said about the value of mathematics. The National Council of Teachers of Mathematics is encouraging the organization of regional groups of mathematics teachers, for the field is wide open for regional work in improving the instruction in mathematics and in letting people know of its contribution to their everyday living.
What Professional Knowledge and Experiences Should the Teacher Training Program Provide?
Authors: Mills C. N.
Published: January 2021

The general theme of the various sections of the Council centers around the student who is not going to college after high school graduation. This idea that many students will not go to college might apply to certain highly industrialized communities or to students who are classified as the below average group. I am of the opinion that the non-college student will soon be a condition of the past. A few years ago about 1 out of 20 went to college; latest reports say that the ratio is about 1 to 9; however today it might be around 1 to 5. What is making for all of this change? Many factors have their contributing influences. Today we hear about the junior college, or closely related post-high school plan; the Night School; Correspondence Study; the NYA Movement; and the CCC camp development. Colored by all of these movements we have the students facing the problem of unemployment. Hence there seems to be only one general course for him to continue, and that is he must take up some phase of advanced training.
The Art of Teaching: The Determinant Notation
Authors: Locke L. Leland
Published: January 2021

A leasson on cooosing a pattern and on adhering to that pattern
The Role of the Mathematics Teacher in Our Defense Program
Authors: Atherton C. R.
Published: January 2021

My topic—“The Role of the Mathematics Teacher in Our Defense Program”—is so broad as to be almost all inclusive in its scope. With such a topic one might select almost any phase of mathematical education at random and prepare a pert inent paper. In every aspect of the defense program—financing, preparation, productions and use of defense mechanisms-one finds ample evidence of the importance of mathematical education. How then is the topic to be delimited?
Progress Report of the Subcommittee on Education for Service of the War Preparedness Committee of the American Mathematical Society and the Mathematical Association of America
Authors: Hart Wm. L.
Published: January 2021

1. Introduction. A report of activities and recommendations was recently presented to Professor Marston Morse, Chairman of the War Preparedness Committee, by its Subcommittee on Education for Service. The following extracts differ from the complete report through the omission of certain recommendations which at the moment are not sufficiently matured to be appropriate for publication. All curricular recommendations are included in the following paragraphs.
The Cross-Staff
Authors: Schimpff W. E.
Published: January 2021

The cross-staff and its application to surveying and navigation was used in earliest times. Apparently it was completely forgotten during the middle ages, but at about the time of the discovery of America it was revived, and during the period of great di discoveries that followed the voyages of Columbus, it was the principal navigating instrument of those sailors who have left their wake on the history of the seven seas. There is no mention of the instrument by Christopher Columbus, but there is a vast amount of reference to its use by subsequent discoverers.
How Intuitive Geometry Serves the Community
Authors: Miller A. Brown
Published: January 2021

As a rule, we are at first impressed by the possibility of mathematics serving the community commercially. We think of those situations in which the dollar sign is used. There are the banks, stores, places of entertainment, and so on, where we either pay for services or recreation, or receive money for goods, or services rendered. Before it is possible for many of these activities to exist, other forms of mathematics have been utilized in providing the buildings, streets, bridges sanitation, light, and so forth. Beauty and orderly arrangement are desirable in all of these as well as comfort and convenience.
The Coming Revolution—in Mathematics
Authors: Oakley C. O.
Published: January 2021

Few people, I am sure, would have had any question as to the significance of that arresting dash in the title of this paper even some months ago when the title was sent in. It clearly was not intended to be a subtle way of predicting our own entry into the war. But now that the whole world is in the struggle, it is abundantly evident that that little dash calls attention to the fact that one revolution is in full swing.
School and Community Look at the Content of Consumer Mathematics
Authors: Wittich Walter A.
Published: January 2021

In the Madison Public Schools, we have a situation where curriculum problems and course of study evaluation and revision are carried on as a cooperative effort by teachers, principals, and supervisors. Early during the current year, a committee of junior high school mathematics teachers, heads of mathematics departments, an administrator and a supervisor met to suggest a means by which they could evaluate and make more meaningful to the junior high school pupil who was not going into college preparatory work, the study of arithmetic and mathematics as he would meet it on graduation from high school.
The Foundation Stones of the Number System
Authors: Brinkmann H. W.
Published: January 2021

A famous mathematician has said that the natural numbers 1, 2, 3, ⋯, are a gift to us from the deity. Since the whole of our number system is based upon them, it is fitting that they should be studied in all possible ways and that such investigations should be regarded as fundamental in mathematics. One way to begin such a study is to break the integers down by factoring them, to see what they are made of. When we attempt to do this we find certain integers that cannot be factored (except in a trivial way); these are called prime numbers and the first few of them are clearly 2, 3, 5, 7, ⋯. It is immediately obvious that any other natural number can be expressed as the product of such primes (some of which may be repeated); for example, 60 = 22 · 3 · 5. In addition it is true, though not obvious, that this expression is unique. It therefore seems appropriate to think of these prime numbers as the foundation stones of our number system and we shall devote this paper to some of their properties.
Mathematics Skit
Authors: Gowan John Curtis
Published: January 2021

Time: The present. Scene: The office of Mr. Strumpelbein, third vice president of the Consolidated Construction Corporation, who has just risen to greet an inspector from the U. S. Government.