bluuebunny/crossref_metadata_2025 huggingface dataset:
Report of the Committee on Elementary-School Mathematics, of the Association of Mathematics Teachers of the Middle States and Maryland
Authors: Germann George B. , Hart Howard F. , Long Agnes , Minnick John H. , Scoboria C. P. , Webb Harrison E.
Published: January 2021

Your Committee on Elementary-School Mathematics is again under the painful necessity of dashing to earth any hopes and expectations which may have arisen from the announcement in the program looking forward to a final report.
The New York State Regents Syllabus in Intermediate Algebra
Authors: Decker F. F.
Published: January 2021

When your president declined my suggestion to furnish a substitute for this occasion he stated that he desired a college teacher to introduce the topic, a fact which I may seem to overlook, for I believe that in general the best course in secondary school algebra for the student who does not go to college is the best course for the one that does. I am in a position to view the product of the high school course, or perhaps I should say the better product, and I might give my conclusions as to the parts of the work that need stressing. I shall try.
War Problems in Mathematics
Authors: Breckenridge William E.
Published: January 2021

In the preparation of this paper the author was assisted by Murray K. Aronson, Mary Baxter, R. P. Bliss, Morris Cohen, Mary Fowler, Earnest Greenwood, Marie L. Guinée, Lena M. Keeler, H. F. MacNeish, L. S. Odell, Anna M. Ohlssen, A. Lila Pratt, Jeannette Romaine, Earl S. Russell, Frank C. Touton, Earnest Townsend, Agnes L. Waring, students in Teachers College.
Greek Philosophers on the Disciplinary Value of Mathematics
Authors: Cajori Florian
Published: January 2021

Two independent methods have been used for the determination of the disciplinary value of mathematics: (1) the method of laboratory measurement, which, though ambitiously pursued, has not yet yielded altogether consistent results;1 (2) the historical method which recounts the experiences and opinions of the great teachers and philosophers of past ages. It is the latter method that we wish to consider in this paper, particularly in reference to Greek testimony.
Remarks on the Report of the National Committee on Mathematical Requirements on College Entrance Requirements
Authors: Hedrick E. R.
Published: January 2021

The report of the National Committee on College Entrance Requirements will seem at first to violate some of the traditions that we have held dear. It is my purpose to discuss briefly these changes and to try to evaluate the effects on collegiate mathematics.
The Aims of Mathematical Education
Authors: Minnick J. H. , _ _
Published: January 2021

Education is a complex process involving a variety of experiences gained through both school and out-of-school activities. Each subject of the curriculum should make its definite contribution to this experience, but we must be sure that the result is a unit. An investigation of conditions in most of our high schools will show that a child is under the instruction of perhaps four or five teachers, all of whom are working independently of each other. Very seldom docs one teacher know what the others are trying to do. In order to avoid such conditions and to insure a unified education for each individual, it is necessary that the aim of each subject shall be determined in the light of the general definition of education. Only by this means can the subject matter of each course be so selected and presented that there is neither useless overlapping on the one hand nor the omission of important elements on the other hand. Hence, in discussing the aim of mathematical education, we shonld consider the general meaning of education and then determine what contribution mathematics can make most effectively. For this purpose we shall accept Ruediger’s definition, namely, “… to educate a person means to adjust him to those elements of his environment that are of concern in modern life, and to develop, organize, and train his powers so that he may make efficient and proper use of them.”1 This definition consists of two parts. One of these is concerned with the adjustment of the individual to his environment; this is the objective side. The other is concerned with the development of the powers of the individual; this is the subjective side of education. However, one’s powers are developed only by contact with and adjustment to his environment, and he is adjusted to his environment only through his powers and abilities. Thus, a child’s power to think correctly is developed most effectively when he is brought face to face with a real situation the solution of which is vital to his welfare; but he can successfully master the situation only by the use of his reasoning power or such other abilities as may be involved. Hence, the two parts of this definition are not independent and we need not consider them separately; when one is satisfied in the most effective way the other will be. At present we shall confine our attention to the objective phase of education.
Teaching Pupils How to Study Mathematics
Authors: Davis Alfred
Published: January 2021

Of all the considerations connected with the study of mathematics, and indeed with the study of any subject, the most important is the mastery of the art of study itself. No topic has been so generally overlooked and neglected heretofore. This neglect is the source of many of our difficulties in teaching, and of many of the criticisms that have been heaped upon the various studies. A supervisor of the high schools of one of our states recently made a general outline for the reorganization of the courses in mathematics for the state. The matter of teaching pupils how to study had been entirely overlooked. His attention was called to the matter, and, realizing its importance, he made it a part of the program. After all, this is the chief thing to be gained from our schools. The pupil must leam the “how.” The “what” is not of so great importance. The “what” frequently changes. The “how” is relatively constant. In other words, the pupil should learn how to attack a problem with economy of time and effort, and with the greatest efficiency. The information he gains in the process is incidental, and illustrative of what he ought to expect as a result of his efforts after he has been trained. It is this sort of training that gives the educated man a measure of his powers, and ability to use these powers in the most effective manner in the various problems which he meets in his daily living. If education fails in this it fails utterly; indeed, it is then not education at all, it is a farce, and the school is a failure. Yet this is the point at which the schools do fail most lamentably. No subject in the high school curriculum is equal to mathematics in its opportunit ies for teaching the art of study. Geometry is especially valuable for this purpose.
The Future of Secondary Instruction in Geometry
Authors: Webb Harrison E.
Published: January 2021

If the future of secondary instruction in geometry is to be judged in the light of the past, two thousand years may elapse without any material change. Horace boasted of a monument more enduring than bronze. Euclid’s Elements has stood like a granite monolith against the intellectual erosion of centuries. This book has seen the decline of great civilizations, the rise and fall of empires, and the birth of great religions. It has passed unscathed through countless successions of languages and dialects. Such is its perfection of detail that all attempts at improvement during its two milleniums of existence have led only to a return to its original form and substance.
The Slide Rule as a Subject of Regular Class Instruction in Mathematics
Authors: Breckenridge William E.
Published: January 2021

In the past year regular class instruction in the use of the slide rule has increased rapidly. During the war it was found that the slide rule was a very efficient calculating instrument on account of its rapidity of operation and the ease with which it could be carried in the pocket. Hence, it became indispensable in the artillery and in other branches of the service where computation was required. The supply of rules ordered for the use of the U. S. Government was so great that one manufacturiug firm was 20,000 rules behind its orders. It was also found that the rule was a very interesting and convenient subject of study for soldiers in hospitals. This study was promoted by the publication under Government supervision of a monograph on the slide rule called Unit Course No. 1 in Mathematics, the purpose of which was to teach the use of the slide rule by very simple exercises with a minimmn of theory. After the close of the war, colleges that had taught the rule for military purposes continued its use in classes of trigonometry. This practice was followed by secondary schools as rapidly as teachers came to understand the use of the rule. Today in many colleges aud secondary schools the slide rule is regularly taught in connection with the work in trigonometry. This gives the student an excellent application of the theory of logarithms and equips him with the power to solve instantly nearly all problems in mechanics, physics, and chemistry, with a great saving of time.
Combined Mathematics
Authors: Webber W. Paul
Published: January 2021

The writer has found a good many teachers of high school mathematics who are not clear as to the nature and significance of combined mathematics, or as some term it, fused mathematics. He has further found that a considerable number of these teachers are honestly, though not always very actively, seeking light on the subject. In localities where the adoption of such courses in high schools is imminent, the question is one of considerable interest. In talking with teachers there has been found a wide divergence of opinion as to what constitutes a combined course in mathematics. Even the text books do not appear to convey a uniform opinion on this point. In what follows, the writer, in giving his views, may inadvertently appear to take sides.
The Nature of Algebraic Abilities
Authors: Thorndike Edward L.
Published: January 2021

One of the most revered features of algebra is training in organizing a set of facts given in a problem described in words, into an equation or set of equations such that solving will produce the desired answer.
Experimental Geometry
Authors: Harper G. A.
Published: January 2021

Before beginning a discussion of the actual topic assigned for this paper, let us consider for a short time what are the requirements that determine whether or not a subject should have a place in the school curriculum. It does seem that we have emphasized two things entirely too much. These are, the ease of handling the subject on the part of pupil and teacher and the practical value of the subject. These two should be considered of course, but there are other considerations of more importance.
Calculus for Schools
Authors: Tyler W. H.
Published: January 2021

The title of this paper may have various psychological reactions on the reader, according to his mental attitude and experience. To some it will perhaps seem as reasonable as teaching Greek in the kindergarten. A generation ago, when some of us were young, calculus was an ultimate goal of college mathematics, to be attained only after prolonged and painful servitude in the regions of college algebra and conic sections. The idea of teaching it even to college freshmen would have seemed heterodox, if indeed anybody had been so radical as to propose it. When finally reached it appealed only to the algebraically minded with its marvelous intricacies of partial fractions and reduction formulas. Excursions into geometry relieved the perplexities of some, to be sure, but the fact that calculus should be anything but an end in itself was more or less effectually disguised.
Discussion
Authors: Werremeyer D. W. , Hart Howard F.
Published: January 2021

The mortality in ninth year mathematics is relatively large in the average high school. Some of the reasons for this state of affairs are (1) the course of study is too traditional; (2) the work is not made cumulative with respect to the work that has been done in the seventh and eighth grades; (3) many pupils have not learned how “to study” mathematics before they reach the ninth grade; (4) many pupils have been promoted to the ninth year because they are either unable or unwilling to do the work in the eighth year satisfactorily.
The Origin of Mathematics—A First Lesson in Secondary Mathematics
Authors: Betz William
Published: January 2021

The nineteenth century was characterized by an unparalleled activity in the realm of science. When Darwin and his followers succeeded in popularizing the doctrine of evolution. an amazing impetus was given to research in almost every field of human thought and endeavor. It soon became natural to go back to first principles, to study the growth and development of all existing things, to look for causes, motives, connections, controlling forces. New sciences sprang up over night. Innumerable questions were addressed to nature by carefully arranged experiments. The bulk of scientific knowledge increased immensely. And, as if by magic, even the past gave up many of its long concealed secrets. The geologic record of the rocks became legible. It revealed upheavals extending through aeons of time. The incredibly slow unfolding of life on this globe became established by countless fossilized remains.
Errors in Computations and the Rounded Number
Authors: Rice Harris
Published: January 2021

I believe it is now quite generally felt among teachers of mathematics that it is their duty to give the boy and girl such mathematical instruction as may he of use to them in their daily life after leaving the high school. This feeling has given rise to some of the modern ideas as to what should be taught the boy and girl who does not go beyond the high school. Therefore they say properly that such students should be given a little trigonometry, a little differential calculus, a little integral calculus, not very much of these topics, hut just enough to give the student an idea of what these subjects are and for what they are used. Such modern ideas seem to the writer very desirable. Mathematics has too long been held up as a very mysterious subject, something which the boys and girls of the high school have been very apt to dread—and if mention should be made of such a terrible subject as calculus, they would give up in despair.
Non-Euclidean Geometry
Authors: Bussey W. H.
Published: January 2021

About 2200 years ago there was published in Greek one of the most remarkable books of all times, Euclid's “Elements of Geometry”. It contains a systematic exposition of the leading propositions of elementary geometry and the elementary theory of numbers. It was at once adopted by the Greeks as the standard text book on pure mathematics. The parts that relate to elementary geometry were the standard text book for centuries and are still in use in England to-day. The English school boy does not say “Geometry”, he says “Euclid”. On the Continent of Europe “Euclid” was superseded by Legendre's “Elements of Geometry”, the first edition of which was published in 1794. A translation into English by a man named Davies was widely used in this country. (It was used at Columbia University as late as 1905). But that has been superseded by more modern American texts of which there is now a large number.
Teaching the Algebraic Language to Junior High School Pupils
Authors: Overman James Robert
Published: January 2021

Progressive teachers of high school mathematics are today interested in two types of questions. First there are those questions having to do with the selection of material and with its organization into courses. In the second place, there are questions dealing with methods of presentation in text books and methods of teaching, the answer to which must he based upon an analysis of the subject matter to be taught and upon a study of the psychology of the mental processes involved. The paper read by Dr. Breslich here tonight is typical of the first type, the recent articles by Dr. Thorndike in The Mathematics Teacher are typical of the second. As the other paper on this evening's program dealt with the selection and organization of material, I thought it would be better for me to consider a question of the second type.
Mechanics
Authors: Mirick Gordon R.
Published: January 2021

If any one of us should enter a machine shop we would find a good many cases of rotation about a fixed axes. As we look around us we see revolving wheels, cylinders, shafts, etc.
News and Notes
Authors: Puett Juanita
Published: January 2021

The annual meeing of the Inland Empire Council of Teachers of Mathematics, which was held at Spokane April 4th and 5th, was voted by all who attended it the most successful and interesting session ever held. Since its reorganization three years ago under the present name and plan of organization it has been rapidly expanding in interest and numbers over the field it attempts to cover, the four northwest states of Oregon, Washington, Idaho, and Montana.
The Origin of Our Numerals
Authors: Sherman Charles Pomeroy
Published: January 2021

Suggested, probably, by the present-day inquiry into the origin of things, it occurred to me to look up the origin of our so-called Arabic numerals; and I found, to my great surprise, from the authorities I was able to consult, that it is much disputed and is actually unknown.
The Teaching of Logarithms
Authors: Christofferson H. C.
Published: January 2021

Since the subject of logarithms is recommended by the National Committee to be taught in High Schools, many teachers will be required to teach it who have not had a great deal of experience either in the use or teaching of that very interesting and time saving instrument of mathematics.
From the Shelves of Dr. David Eugene Smith's Unique Mathematical Historical Library
Authors: Refior Sophia R.
Published: January 2021

The students in the seminary in the History of Mathematics under Dr. David Eugene Smith have been privileged at various times to visit the unique private library of their instructor and to use such manuscripts as were necessary in their field of research. The inspiration derived from examining these priceless objects has stimulated one of the pupils to write the following account. This theme is restricted to the selected portion of the library which the class viewed and which is only a small part of the entire collection.
Unified Mathematics in Secondary Schools
Authors: Jones Gertrude
Published: January 2021

The reform movement in mathematics which had its beginning in England, France and Germany has been felt in this country for more than twenty years, and the end is not yet. In 1901 Professor J. Perry delivered his now famous address on the teaching of mathematics before a congress of mathematicians in Glasgow. Professor Perry was then in charge of certain apprenticeship schools in London. He felt that the mathematics which the students in these schools had studied did not function in their later work. Consequently there must be something wrong with the aim, content, and method of the traditional instruction in mathematics. The movement in this country was first started among college men by Professor E. H. Moore of the University of Chicago. In 1903 in order to spread the doctrine among classroom teachers, associations of mathematics teachers were formed in various sections of the United States and mathematical magazines were established.
The International Mathematical Congress
Authors: Mirick G. R.
Published: January 2021

The seventh International Mathematical Congress was held in Toronto, August 11th to 16th, 1924. These meetings are held every four years for the purpose of interchange of ideas along mathematical lines. The first was held in 1896 at Zurich, Switzerland, second in 1900 at Paris, France; the third in 1904 at Heidelberg, Germany; the fourth in 1908 at Rome, Italy; the fifth in 1912 at Cambridge, England; the sixth in 1920 at Strasbourg, France.
Drawing for Teachers of Solid Geometry
Authors: Bradshaw John W.
Published: January 2021

The College Entrance Examination Board in its Document No. 108, containing a definition of the requirements in geometry adopted by the board on April 21, 1923, has included an appendix on drawing which opens with the following paragraphs:

“An important aid to the visualization of space figures is the ability to draw these figures on paper. The pupil should be trained to make neat free-hand drawings, inserting whatever construction lines are needed and supplementing the representation of the space figure by independent drawings of plane sections, whenever such contribute to clearness. Ruler and compasses may often be used with advantage, but no technical knowledge of descriptive geometry or the niceties of mechanical drawing forms any part of the requirement. The use of ruler and compasses in the examination is permitted and to a moderate degree, desirable but it is not prescribed.
A Study of the Factors of Success in First Year Algebra
Authors: Schreiber Edwin W.
Published: January 2021

It will be the function of this chapter to reveal the results of the relationships of the various abilities examined in Chapter II as measured by co-efficients of correlation, both of the zero and the first order (partial correlation). It will also deal in a limited degree with regression lines and equations.
The Carus Mathematical Monographs
Authors: Slaught H. E.
Published: January 2021

A book is just off the press which promises to be the beginning of a far-reaching epoch in American mathematical literature and to have a vital interest for teachers of mathematics in the secondary schools and in the junior colleges. It has long been felt that if the various mathematical subjects could be set forth in a somewhat expository form in a manner comprehensible to those who have only a moderate acquaintance with elementary mathematics, say through a year's introductory course in the calculus, and if such expositions could be made attractive and accessible at moderate cost, then many more would be glad to extend their mathematical knowledge and to keep in touch with the developments in these fields.
Ten Reasons Why Pupils Fail in Mathematics
Authors: Osburn W. J.
Published: January 2021

Why does William stare at you in helpless confusion when you ask him a question? Why is Mary failing in mathematics? Why are mathematics classes so often beset with hopeless groups of tail enders? These are burning questions for teacher, parent and pupil. In days gone by puzzled physicians when pressed for a reason as to why their patients did not recover hit upon the happy idea of saying that the patient was possessed of some evil spirit and backed their assertions by all kinds of resorts to conjuring and necromancy. Today puzzled teachers when pressed for a reason why their pupils do not learn are using the same strategy. They tell us that their pupils are possessed with a spirit of carelessness, indifference, laziness or lack of perseverance. Long before the final chapter is written concerning the teaching of mathematics these reasons wil doubtess prove to be as great subterfuges as were those of the ancient medicine men.
Announcement: An Investigation in the Teaching of the Skills of Ninth Grade Algebra.
Authors: Sohorling Raleigh , Lindell Selma A.
Published: January 2021

Purpose—The purpose of this study is to measure the effect of applying certain principles from the psychology of drill. In recent years considerable gain has been achieved from our knowledge of habit formation. It is now possible to formulate over twenty principles that are generally accepted in psychology but which are not applied in our school texts in algebra.
Some Higher Aspects of Secondary School Mathematics
Authors: Bandman Chester G.
Published: January 2021

It is a significant and compelling fact that an inordinate percentage of high school pupils regard the subject of mathematics as drudgery and that the percentage of failures is usually larger in mathematics than in almost any high school study. There is undoubtedly a close correlation between the two statements.
Meeting the Attacks on Algebra
Authors: Quigley Mary J.
Published: January 2021

No subject in the high school curriculum, according to some educators, has yielded such unsatisfactory results as Algebra. It has been the subject of most severe criticisms on all sides, and has been held responsible for a great deal of freshman mortality. A leading educator of Massachusetts, in one of his public speeches, has expressed the desire that less time should be devoted to the study of algebra in the high school. An influential body of educators has even gone so far as to ask some of our Massachusetts colleges to reduce their entrance requirements in algebra. We not only find educators loudly declaiming algebra; but this spirit of criticism has carried still farther. We know that many school children hate algebra because their parents hated it, or because other pupils have told them how uninteresting and difficult it is. Parents dread the time when their children must study algebra. In a magazine article of recent date, a father was discussing the education of his daughter. In the course of the, discussion he said that his daughter did not go to college because of her intense dislike of algebra.
Why is It?
Authors: Stroup P.
Published: January 2021

I have just looked through copies of 10 current high school geometries and in not one of them can I find a direct and explicit proof of the fact that if the square on one side of a triangle equals the sum of the squares on the other 2 sides, it is a right triangle. In some books it is proved indirectly by proving its converse and its opposite, but no attention is called to the fact. Some authors use the fact in problems without having proved it or mentioned it and these same authors seem worried in their opening chapters if the converse of any little proposition is assumed to be true without giving the proof of it.
Checking Up the Prophets
Authors: Evans George W.
Published: January 2021

The Yearbook of the National Council of Teachers of Mathematics, published last February, contains much of permanent importance, and in particular two papers by men of foremost authority and influence. One is by Professor E. H. Moore, his presidential address to the American Mathematical Society in 1902, a plan for progress and a hopeful forecast at the beginning of the new century; the other a cheerful summary of progress since that time and some indication of present tendencies by David Eugene Smith.
You Know What I Mean
Authors: Morley Raymond K.
Published: January 2021

The proper way to begin a story is “Once upon a time,” so I shall start mine that way.
A Pleasant Approach to Demonstrative Geometry
Authors: Sadley E. V.
Published: January 2021

The introduction of experimental geometry into our junior high school courses and the willingness to call any study of form in the lower grades by the high sounding name of “intuitive geometry” have done much to pave the way for the more formal treatment of the subject in the senior high schools.
Mathematics for Service
Authors: Nardroff Ernest R. Von
Published: January 2021

For a long time mathematics has enjoyed the position of first place in the elementary schools, and in the high schools the time devoted to the subject is nearly as great as that for any other subject. Almost daily for ten years, reaching from the first primary grade up to the conclusion of the second year in the high school, a pupil is required to bend his best energies toward the mastery of mathematics. What are the results? It is needless to state that the average graduate going into business or into any of the learned professions, except engineering, fails to put his mathematics to any use whatsoever. Beyond the requirements of keeping one’s accounts and calculating interest and taxes, the ordinary citizen has no need of formal mathematics. The result is that practically everything in this subject learned in the high school is promptly forgotten.
Mathematics in the Ethical Culture High School
Authors: Walsh C. B.
Published: January 2021

In giving a report of the mathematics in the Ethical Culture H igh School I do so with the fear that we of the school may seem to profess or at least to consider that we have discovered or attained the ideal. Let me preface the paper by saying that we are keenly conscious that there are defects both in the conception and in the execution of our course. Whatever I may say that sounds otherwise please pardon on the ground of enthusiasm. The purpose I hold in mind in giving this paper is an exchange of testimony—a practice which, to my way of thinking, is very helpful in all professions. Hence, I shall feel gratified if my paper simply provokes fu rther discussion of the nature indicated. This exchange of testimony I consider a very encouraging sign of our generation. For example of what I mean look at the lists of problems found effective by various teachers now being published in School Science and Mathematics.
A Mathematics Club
Authors: Hatton Mary Caroline
Published: January 2021

In November, 1923, the mathematics department of Leonia High School, Leonia, N. J., realizing the wealth of material in mathematics that cannot he touched in the classsroom because of lack of time, organized a club to supplement its classroom work. Any student of Grades X, XI, or XII who is enrolled in a mathematics class is eligible for membership in the club, but the constitution which the students have drawn up, states that no officer may be chosen from the lowest class, and the honor of presidency may be bestowed only upon a Senior. The meetings are held semi-monthly, at the close of the last recitation period of the day. The projects and programs of the club are carefully worked out by committees of students under faculty supervision. These activities are planned to meet the definite aims of the organization.
The Arithmetical Productiveness of Utilitarian, Social and Scientific Ideals; Viewed Historically
Authors: Myers G. W.
Published: January 2021

The history of arithmetic, as such, really begins with the devices and technics that were created, collated and employed by the Phœnicians. The demands of their commercial transactions between Sidon, Tyre, Carthage, and other Mediterranean cities were extensive and made considerable demands for numbers. The affairs of this ancient sea-faring and commercial people called for account-keeping, record-making, money-exchanging and for figuring balances. This demanded a number symbolism and a system of weights and measures. Out of these needs developed the beginnings of an arithmetic. The Phoenicians had no body of calculatory rules nor any laws applicable to number relations. They were in fact not conscious of more than a loose collection of procedures to be acquired and transmitted through a trade apprenticeship. They had not even given any distinctive name to their body of empirical rules. They felt no other than a utilitarian need and required only a conventional number symbolism and a crude abacus. We are told that the Tyrians regularly supplied the weights and measures used in Babylon. The utilitarian ideal here produced only the most meager beginnings of calculatory procedure. It was not strongly creative.
Looking Backward
Authors: McCullough H. L.
Published: January 2021

I read “Fads and Plane Geometry,” by Mr. Merrell, in the January issue of your magazine with a feeling of admiration. Then I read it again and the glaring inconsistencies began to take form.
Esthetics and Mathematics
Authors: Smith David Eugene
Published: January 2021

In considering mathematics in relation to the beautiful, the range of possibility is so vast that a brief article like this can hardly be expected even to list the salient points of contact. The field might properly include all that we designate as the fine arts or, to use the more expressive phrase of the French, the beaux arts. Painting, for example, might be considered with reference to the works of that great genius in science, in mathematics, and in art—Leonardo da Vinci. Sculpture might equally well be included because of the mathematical principles employed by that majestic user of ponderous masses, Michelangelo. Architecture might have place with reference to the works of that Oxford professor of mathematics, Sir Christopher Wren, who rebuilt ecclesiastical London; engraving, with reference to that gifted artist of Niirnberg, Albrecht Diirer, who published the first modern work on curves; music, with reference to the fact that it always ranked as a branch of mathematics until the sixteenth century; decoration, with reference to the geometric designs found in all ages and reaching their highest degree of perfection in the works of the Moslems; and literature, with reference to the mathematics of poetry, and the poetry of mathematics. Indeed, we might properly include the beauties of nature, where mathematics plays a part of which we are usually quite unconscious.
Mathematics and Sunshine
Authors: Slaught H. E.
Published: January 2021

If the average man in the street were asked to name the benefits derived from sunshine, he would probably say “light and warmth” and there he would stop. But, if we analyze the matter a little more deeply, we will soon realize that sunshine is the one great source of all forms of life and activity on I his old planet of ours. To mention only a few particulars, wood, peat, coke, soft coal, anthracite, kerosene, fuel oil, gas, gasoline, are one and all forms of canoed sunshine in varying degrees of transformation. Hence I cannot stoke my furnace, turn on my oil-burner, step on the gasoline jn my automobile, cook my meals by wood, gas, oil or coal, light my house with kerosene or gas, without drawing upon the sunshine which was stored up for me in the form of carbon long ages ago in the deep recesses of the earth. All the industries of the world, great and small, all transportation by rail, water or air, are made possible only through the products of sunshine. Even the wind which drives my sailboat is only the rushing currents of sun-heated air.
Mathematics One Hundred Years Ago
Authors: Meserve Harrison G.
Published: January 2021

Although tbe books I have had access to have been of varying ages, none of them have been exactly one hundred years old. So, strictly speaking, my subject should be “Mathematics about One Hundred Years Ago”. The earliest book I have was given to me a few years ago by some friends who found it in the attic of an old house they bought in New Hampshire, and was published in 1797. Other books I have been looking through vary in date of publication from 1822 to 1869.
Geometric Aids for Elementary Algebra
Authors: Wanemacher Alberta S.
Published: January 2021

When Doctor John R. Clark's small son in a beginning class in demonstrative geometry was asked by his father where he had learned a certain geometric principle, he replied with a tone of disgust.
Informational Mathematics Versus Computational Mathematics
Authors: Judd Charles H.
Published: January 2021

I am indebted to Professor G.M. Wilson for the title of this paper. In a book entitled What Arithmetic Shall We Teach, which he published through Houghton Mifflin Company in 1926, Professor Wilson says that his findings justify him in recommending a drastic reduction in the amount of computational arithmetic to be taught in elementary schools. He had found in various communities that practical life demands very little training in addition, subtraction, multiplication, and division. It is for the purpose of promoting this idea of, drastic reduction that he wrote his book. The reader is almost persuaded that the book should have been entitled, What Arithmetic Shall We Not Teach.
The Permanent Nature of the Necessity for Mathematics in the Secondary Schools
Authors: Karpinski Louis C.
Published: January 2021

Some years ago I heard a prominent educator, or, at least, professor of education, assert that the day would come when we would in our schools give special courses in the arithmetic for the plumber, the arithmetic for the carpenter, the arithmetic for the housewife, and the like. In some most mysterious way these poor children were to be labeled “plumbers” or “carpenters” or “housewives” and the education given would be fitted to the label. It is the glory of our American schools that the children are not ticketed and labeled, and the ultimate destiny of the great majority lies in the hands of Providence and, mayhap, the teachers.
Mathematics and The Future
Authors: Moore Charles N.
Published: January 2021

In recent educational literature and discussion much has been said of the modernization of education. I take it that this phrase usually means the adjustment of education to what the speakers or writers conceive as the needs of the modern world. But what is the modern world? Most thinking persons will concede that the world of to-day is different in many important respects from the world of five years ago, or even of one year ago. While we are engaged in the process of constructing an educational system that will exactly fit a world as we have visioned it, the world as it is will have changed into something quite different.
What the State Teachers College means to Bemidji Financially
Authors: Rice Marbel Frances
Published: January 2021

Interesting units of work occupying several days or weeks of school time, growing out of the work in IIistory, Geography, Health, Community Life, or English, have not been unusual in the last few years. Entire projects in Arithmetic have been more rare. The children of the seventh and eighth grades of the Junior High School department of the Bemidji State Teachers College completed a six weeks, project that was unique in that arithmetic was the subject that formed the nucleus of the study.
A Layman Looks at Mathematics
Authors: French John R. P.
Published: January 2021

One's philosophy about anything is necessarily based upon one's experiences with thnt particular thing. I can't remember my mathematical experiences in the grammar school-evidentlythey made no profound impression. At the tender age of ten I was consigned to the-Latin School, and I remember my mathematical experiences there with some vividness. They were painful. I was perpetually " conditioned " in arithmetic. I felt myself absolutely and finally and completely incompetent in arithmetic. In rhe language of childhood I " hated " arithmetic-and in any language I certainly dreaded and feared it.
Locorphobia: Its Causes and Cure
Authors: Selleck George H.
Published: January 2021

Of the forty-eight questions on the College Board Mathematics C examinations during the last eight years, five have been locus questions. Thus the examiners have, intentionally or not, rated the study of locus as ten per cent of the study of geometry. At first thought this seems too high a value to set, but a careful consideration of the frequency of the use of loci in the construction of figures and the proof of problems perhaps justifies their valuation. These loci have not been especially hard, but they have obviously caused the candidates more worry than any other questions and have been treated more unsuccessfully.
A Plan for Meetings of Mathematics Teachers in a High School
Authors: McLaughlin H. P.
Published: January 2021

The writer is the head of a mathematics department containing six teachers besides himself in a high school enrolling about 1800 boys each year. The principal finds that his administrative duties keep him from giving as much time to supervision as he would like to give so that he has asked the heads of the different departments to hold meetings of their departments to assist him in improving the instruction iu the school. This paper will be confined to a plan for teachers' meetings of this kind.
A Comparison of the mathematics in the Secondary Schools of Germany and England and the Training of Teachers of Secondary Mathematics in these Countries with the United States
Authors: Zant James H.
Published: January 2021

I. Organization.

1. As parallel units.

2. Extends over the whole system.

3. Essentially the same in all courses.

4. Course of study.
News Notes
Authors: Nygaard P. H.
Published: January 2021

"I was tnught here to learn." perhaps most commonly paid to the These words and those of the Aeademy. What is meant is that parent who says, "You taught my the drive of the place has led the son to work," contain the tribute boy to acquire habits of industry and persistence, to assume responsibility for his own success, and to refuse to be beaten by hard tasks. Realizing that he had to compete in order to get in to tho school and that he had to struggle in order to remain, he readily accepted the hardwork tradition of a school in which “the student bears the laboring oar.”
News Notes
Authors: Stroup P. , Baum Kathryn E.
Published: January 2021

The Mathematics Club of Cleveland, Ohio, has appointed a committee to investigate the feasibility of interscholastic competition in mathematics. Any reports on that subject by anyone who has had experience will be gratefully received.
Using Ration in Problem Solving
Authors: Allison John R.
Published: January 2021

The word ratio is the name for a simple and extremely useful idea. The traditional discussion of ratio and proportion would not be likely to convince anyone that the idea was either very simple or very useful. The fact that this idea is so often misused is evidence that we must teach our pupils to understand ratios better and use them more advantageously. Ratio and proportion still maintain their conventional co-partnership in most of our arithmetics, usually setting forth an array of problems inherited from some generations past. The introduction of the ratio concept in the elementary grades, however, tends to break up the partnership and show ratio as an important subject.
Geometric Proofs for Trignometric Formulas
Authors: Haas Arthur
Published: January 2021

The following rather interesting method of proving geometrically the trigonometric formulas for the sum and difference of two angles, which involves a very simple construction, seems not to have claimed the attention of text book writers in mathematics. Furthermore, no one to whom I have shown it, seems to recall having seen it anywhere else, so I submit herewith to the readers of Them athematics Teacher.
A Message from the New President of the National Council
Authors: Everett John P.
Published: January 2021

Just One century ago the colleges of America were in process of recognizing and accepting algebra and geometry as appropriate subjects to be studied and presented by candidates for higher education as evidence of their fitness for admission to institutions of higher education. Just a decade ago there was organized the National Council of Teachers of Mathematics. None of us took part in the earlier movement: very few of us were present in Cleveland when the Council held its first meeting in 1920: yet both events very properly engage our interest.
A New Idea for Review Work
Authors: H. Blaisdell Walter
Published: January 2021

If You, As A Teacher of mathematics, lack the time for needed review work in your classes or if your pupils tend to loiter in the corridors or to take more time than is needed to settle themselves for the work of the period, you may be able to find a partial solution of your problems below.
Living Mathematics
Authors: B. Freeman Neda
Published: January 2021

Why Is It that speakers in the field of general education so frequently draw their illustrations of uninspired teaching, of the use of dead subject matter, or of almost any type of undesirable procedure, from the mathematics classroom? Why do many people consider mathematics a necessary evil which must be endured for supposedly practical though rather indefinite ends? Is there any reason why mathematics in itself and of itself may not be as vitally interesting as any other field of study? Is the pupil's past experience so completely devoid of mathematical content as to give no true teaching basis? We hear and read much, in mathematical circles, of methods by which we may vitalize our teaching. But do we succeed in leading our pupils to see the life in mathematics and the mathematics in life?
Conic Sections Formed by Some Elements of a Plane Triangle
Authors: Bakst Aaron
Published: January 2021

A simple application of elementary analytical geometry (within the scope of the twelfth grade of high school, or, at most, in Freshman College Mathematics) in the process of examining the properties of geometrical figures leads to some very interesting results.
Notes on the First Year of Demonstarative Geometry in Secondary Schools
Authors: Beatley Ralph
Published: January 2021

For most pupils in our secondary schools the first year of demonstrative geometry is the only year of demonstrative geometry. A great many schools devote the whole of Grade X to this subject and some return to it in a later year. The course of study in mathematics could probably be arranged so that no school need give more than one academic year, or the equivalent, to this first course in demonstrative geometry. One way of doing this would be to teach the geometry parallel with the algebra in the tenth and eleventh grades, giving the geometry Monday, Tuesday, and Wednesday of each week in Grade X, and twice a week in Grade XI. There would probably be no algebra in the opening weeks of Grade X until the geometry is well started.
The Training of Teachers of Mathematics with Special Reference to the Relation of Mathematics to Modern Thought
Authors: Cairns W. D.
Published: January 2021

The National Council has in its recent programs been considering current problems, topics in the teaching of mathematics, the revision of courses in algebra and in geometry, and various other topics, and has incorporated these in the Council's notable series of Yearbooks. This consideration is wise and timely and it makes the Yearbooks most valuable for the present and prospective teachers of mathematics. I want to develop the thesis that along with all of this inspiring work much remains to be done in the training of teachers in order that we may help them to extend their horizons.
The National Council of Teachers of Mathematics in 1930-31
Authors: Everett John P.
Published: January 2021

There are Some things concerning the National Council that are especially obvious and that a great many people know about, such as the annual meeting and The Mathematics Teacher. There are some other types of the Council's activities that also deserve mention and about which I think you will be glad to hear.
Constructing a Transit as a Project in Geometry
Authors: Engle T. L. , Connelly Max , C. Elston Issac
Published: January 2021

Psychologists may call it by various names, but teachers of mathematics know that most boys pass through a stage of development which might be called the "civil engineering" period. Fortunately for the engineering profession and for the individuals, the majority change to other fields. However, during this period of development, the interest in engineering is real and it may be used to advantage by the high school teachers of mathematics, especially in the geometry courses.