bluuebunny/crossref_metadata_2025 huggingface dataset:
“Locus Makes a Plea”
Authors: McLeod D.
Published: January 2021

To the average pupil—or, for that matter, to the brighter one—the topic called Locus in any geometry text is generally distasteful. The reason may be far-reaching. Perhaps the subject is put in there because it has always been an integral part of an approved geometry course. Tradition! How many things are done in thy name! To many Locus is a detached section having no place in the unity of the whole. In some cases, it may be, the treatment of the topic is so superficial that genuine interest is impossible. Again it may well be that its Latin name marks it off as a thing of mystery. Whatever it is, the fact remains that, in many cases, the pupil can “get by” what he regards as a necessary evil only by sheer memorizing of subject matter which to him can have no practical application. And so Locus teaching goes on and on and such has been its history.
Alice in Dozenland
Authors: Pitcher Wilimina E.
Published: January 2021

Numbers and symbols should be small children. Each has a placard telling what he represents suspended from his neck.
What are the Characteristics of the Progressive Mathematics Teacher?
Authors: Dice Elizabeth
Published: January 2021

I shall talk of three general characteristics of the progressive mathematics teacher: first, scholarship; second, individual characteristics; and, third, capacity for growth. The third characteristic, capacity for growth, is my tribute to the word progressive in the topic assigned to me.
A Student-Made Slide Rule
Authors: Bush Wm. E.
Published: January 2021

For various reasons the treatment of the slide rule in high school mathematics is generally a limited and superficial affair. Many teachers do no more than mention it, while others make attempts at elucidation of the theory involved. A few go further than this by having a large classroom demonstration rule upon which both the teacher and the pupils may work while everyone but the operator watches. It is, of course, possible to furnish rules to the students, but it is an expense which may justly be called unnecessary.
Causes for Failure in Senior High School Mathematics and Suggested Remedial Treatment
Authors: Rudman Barnet
Published: January 2021

Pupils fail in algebra and geometry because they do not apply themselves, because they have poor study habits, because they are unable or unwilling to give sustained attention, because they lack special preparation—they fail, in short, as a result of the many negative influences that militate against achievement everywhere in the high school curriculum. So, too, does inadequate teaching take its toll in the exact sciences as it does in the social sciences or foreign languages. That the percentage of failures is generally higher in mathematics than in other high school subjects is probably due not to additional specific causes but rather to the nature of mathematical skills on which the same causes are apt to leave more profound and far-reaching effects.
An Interpretation and Comparison of Three Schools of Thought in the Foundations of Mathematics
Authors: Russell Stabler E.
Published: January 2021

One of the notable features of twentieth century mathematics has been the extensive and critical investigation into the foundations of the subject. At the present time there seem to be three schools of thought in the foundations which are of special prominence and interest. These are the postulational, the logical, and the formalist schools.
The Use of Original Exercises in Geometry
Authors: Sykes Mabel
Published: January 2021

Recent geometry texts contain a very large number of original exercises; so many that the question of how to handle them is often serious. This is especially true for teachers who believe that it is necessary to take everything in the text in use and take it in the order given. Many of these are young teachers or teachers whose major is not mathematics, teachers who for one reason or another do not trust themselves to cut or to rearrange the material in the text, teachers who do not seem to appreciate that they are teaching geometry, not teaching a book.
The 1002nd Arabian Night
Authors: Hedges Biallcllc B.
Published: January 2021

The palace was aglow with the light of many candles. Though Scheherazade II had: finished her 1001st story, she promised many more, so Al-Mamun was a happy man.
The Prediction of Pupil Success in High School Mathematics
Authors: Douglass Harl R.
Published: January 2021

Far more frequent than any other type of investigation relating to secondary school mathematics has been that which concerned itself with the relationship between scholastic success and other factors—intelligence test scores and their derivatives, I.Q. and M.A., and previous school marks being employed most frequently.
Research in Mathematics Education
Authors: Reeve W. D.
Published: January 2021

Since I have been asked to speak on the need of, and opportunity for research in mathematics education, I will confine my remarks to what I think may be done along research lines to solve some of the problems of a modern mathematics curriculum.
Recreational Aspects of Mathematics in the Junior High School
Authors: Meeks Anna R.
Published: January 2021

It was with some surprise and considerable consternation that I received my assignment of the topic, Recreational Aspects of Mathematics in the Junior High School, for I have been, as I suspect most teachers have been, a slave to courses of study, and the recreational side of mathematics has been as sorely neglected as the recreational side of the average teacher's life. Several readings of the topic convinced me that I was not even sure of its meaning; so I made my own interpretation and proceeded to try to discover the answers to my own questionings. That study proved enlightening and interesting; it is my purpose to pass on to you some of the practical suggestions which I found in various sources.
The Human Side of Mathematics
Authors: Potter Mary A.
Published: January 2021

If we scrutinize mathematics carefully looking for its human side, we shall observe that in its teaching we find the human element displayed from several different angles. Teachers are, or at least they should be, human beings; pupils are younger human beings; mathematics is a priceless heritage of knowledge developed by the human mind to meet the requirements of human needs. Hence, the teaching of mathematics is the imparting of this heritage of human knowledge to human beings by human beings.
The Art of Teaching A New Department
Authors: Brown Edith Imogene
Published: January 2021

For Several years the first few weeks of my course in Solid Geometry were very discouraging both to the class and to the teacher. It became evident that a different approach to the subject was necessary. After much thought and research I worked out a method which has proved very satisfactory with my classes.
The 17th Annual Meeting of the National Council of Teachers of Mathematics
Authors: Schreiber Edwin W.
Published: January 2021

The Seventeenth Annual Meeting ofthe National Council of Teachers of Mathematics was held in St. Louis, Missouri, December 31, 1935 to January 1, 1936. This is the first annual meeting the National Council has held with the A.A.A.S. One hundred eighty-four registered for the meetings though the total attendance was well in excess of two hundred. A joint session with Section A of the A.A.A.S., the American Mathematical Society, and the Mathematical Association of America, was held on Tuesday morning, December 31, with approximately 250 in attendance. Professor Kenncth P. Williams of I ndiana University presented a temporary report of the Joint Commission on the Place of Mathematics in the Secondary School. “The Main Purposes and Objectives in Teaching High School Mathematics” was discussed by William Betz of Rochester, New York, representing the National Council, and W. W. Hart, representing the Mathematical Association of America. On Tuesday afternoon the National Council presented a Symposium on the Teaching of Geomcetry. Professor W. H. Roever of Washington University, St. Louis, discussed in a very thorough manner the 11Purpose, Nature, and use of Pictures in the Teaching of Solid Geometry.” John T. Rule, the Taylor School, Clayton, Missouri, presented an interesting paper on “Stereoscopy as an Aid to the Teaching of Solid Geometry.” The session closed with a stimulating discussion by Rolland R. Smith, Classical High School, Springfield, Mass., on “Developing the Meaning of Demonstration in Geometry.” The Tuesday evening session was opened by an address of welcome by the Rev. Father Robert S. Johnston, President of St. Louis University. The response was made by Miss Edith Woolsey of Minneapolis, Minnesota. Professor Edwin W. Schreiber, State Teachers College, Macomb, Illinois, presented an illustrated lecture on “The History of the Development of the Metric System.” Miss Ruth Lane, University High School, Iowa City, Iowa, presented an illuminating paper on “Mathematical Recreations, an Aid or a Relief?” On Wednesday morning, J anuary 1, the Annual Business session of the National Council was held. At this session Professor H. E. Slaught of the University of Chicago was honored in being elected Honorary President of the National Council. Secretary Schreiber as Chairman of the Ballot Committee announced the results of the annual election: President—Miss Martha Hildebrandt, Proviso Township High School, Maywood, Illinois; second Vice President-Miss Mary Kelly, Wichita, Kansas; three new members of the Board of Directors—E. R. Breslich, Chicago, Illinois, Leonard D. Haertter, Clayton, Missouri, and Virgil S. Mallory, Montclair, New Jersey. The morning session closed with two interesting papers: “Functiona! Thinking and Teaching in Secondary School Mathematics” by Professor H. C. Christofferson, Miami University, Oxford, Ohio; and “The Crisis in Mathematics—at Rome and Abroad— by Professor William D. Reeve, Teachers
Mathematical Analysis in the Social Sciences
Authors: Rosander A. C.
Published: January 2021

In the following paragraphs we wish to give illustrations of elementary mathematical analysis applied to social data, the purpose being to show how these facts may be made more meaningful in terms of simple mathematical patterns.
News Notes
Authors: Woolsey Edith
Published: January 2021

The second summer meeting of the National Council of Teachers of Mathematics was held at Portland, Oregon, June 27, 28, and 29. The meetings were held at Reed College where dormitory and dining room accommodations were also available. The local committee had difficulty in getting publicity and a hotel for the convention because the Council is not affiliated with the N.E.A. They were delighted when Dr. F. L. Griffin invited them to meet at Reed College. This college is situated in a beautiful section of Portland. The campus is extensive, with green lawns, holly bushes and hedges, gigantic Douglas firs, and many other natural beauties. The buildings are of Tudor style, inspired by the architecture of Oxford University. The meals served in the College Commons were delicious. A more perfect place for a convention could not be found.
Probability
Authors: Bennett Albert A.
Published: January 2021

The subject of probability reminds one of that Australian curiosity enjoying the orotund and circus-stirring name of “ornithorhyncus Paradoxus or duck-billed Platypus”—is it fish or fowl or beast?” Like the sacred cod of Boston this strange animal lives in the water; like the royal swans of his Britannic majesty, it has a flat bill, web-feet, and lays white shell-encased eggs; like the tiger of Kipling's Jungle Tales it has soft fur and suckles its young. And beside all this the male has spurs like a rooster. In a somewhat analogous way, probability, like the quadratic equation, or the removal of parentheses, is a subject in textbooks on algebra. Along with partial differential equations it is one of the advanced topics in mathematical physics. In connection with statistics it comes under education, economics, psychology, biology, or mathematics. It is studied in the theory of manufacturing practice, and in describing the operation of genetic inheritance. It proves absorbing to the dissolute gambler, while the philosopher treats it as an abstruse item of theoretical logic. It is invoked in casual comments about the weather, explained in treatises on practical surveying, and constitutes one of the first principles in the rational discussion of old age pensions, and of business cyles. Is it not strange that to explain how heat causes water to boil, one may well consider first the effect of tossing coins? Where else in algebra is any such economic prudence as that of life insurance brought home to the student, and where else is he asked to contemplate games of dice, gambling at Monte Carlo, and luck in drawing cards for poker?
The Art of Teaching A New Department
Authors: Amig Margaret
Published: January 2021

I have found a very slight departure from the usual arrangement of a proposition in plane geometry, very effective in helping pupils to surmount a common difficulty and to avoid a common error. Most beginners find it hard to see why formal proofs of geometric facts are necessary and some are openly rebellious at the idea of giving tedious demonstrations of the truth of very obvious conclusions. Furthermore many pupils approach formal geometry with a background of intuitive geometry and facts retained from that study are likely to increase the pupil's reluctance to substitute reasoning for inspection. The accepted a rrangement of a proposition—first theorem, then figure, then proof—adds, it seems to me, to his confusion. Why, he asks, should one write at the top of the page or recite that the base angles of an isosceles triangle are equal and then proceed to prove that it is true?
The New Syllabus in Arithmetic for New York State
Authors: Shaver Charles A.
Published: January 2021

Your president has assigned me the topic “The New Syllabus in Arithmetic for New York State.”
Arithmetic and Emotional Difficulties in Some University Students
Authors: Rogers Charles F.
Published: January 2021

The American Chemical Society has recently published a report* in which the general conditions of the high-school teaching of science, chemistry in particular, is examined. The report considers high-school teaching of science in terms of the professional and academic preparation of the teachers.
The Failure in Required Mathematics at Hunter College
Authors: Guggenbuhl Laura
Published: January 2021

Doring the Spring of 1934, plans for the revision of the curriculum at Hunter College were initiated. Questionnaires, asking for expressions of opinion concerning a “hypothetical curriculum” were distributed among members of the staff. There was a great deal of discussion with repeated references to the student who “simply could not do mathematics.” It was surprising to see how many members of the staff believed that there was a person, of normal intelligence, who had satisfactorily completed necessary prerequisite course, a person with normal background and training, willing to spend the required amount of time and thought in study and preparation, who could master every obstacle except mathematics. Some of the statements which were made seemed like a challenge to some of the members of the staff in the Mathematics Department. But when confronted with the questions,—“Why is the percentage of failures so high in mathematics” and “What picture does the failure in mathematics present,”—what could one answer? One could always say that Miss A failed because of lack of diligence; or that Miss B failed because she was inadequately prepared for the course; but one did not have sufficient data to venture from the particular to the general. Thus the following investigation concerning the failure in prescribed mathematics was undertaken.
The Art of Teaching A New Department
Authors: Larson Clara
Published: January 2021

The formula d = rt when applied to living conditions teems with romance and adventure. This formula can be related to the pupils' experience. It can open the door to a wealth of information, and can bring into the classroom some of that feeling of the magic of travel today. The pupils are already familiar with the idea if not with the actual formula. A few days spent on transportation at the beginning of the study of equations and formulas can motivate the entire unit.
A General Educator Looks at Arithmetic Readiness
Authors: Woody Clifford
Published: January 2021

The term “readiness” is one of the latest additions to the family of educational concepts. The term usually refers to readiness for the mastery of things to be learned in the primary grades, although at the present time the concept is beginning to be used in connection with the learning of almost any topic to be taught in the various grades. Many articles have been published on reading readiness and several tests labelled “reading readiness tests” have been developed within the last decade. More recently, attention is being centered on arithmetic readiness.
Editorials
Authors:   W.D.R.
Published: January 2021

Due to the recent death of Miss Mabel Winspear, the secretary for The Mathematics Teacher, it is possible that notices of expirations of subscriptions will be sent to members of the Council who have already paid their dues of $2.00. Other mistakes of this kind will probably be made until we get our records entirely clear. For these and other reasons we have sent the October number of the magazine to all those whose subscriptions expired in May but who, according to our records, have not renewed their subscription. However, we are not sending the November number to those who have not, renewed by November first of this year. The failure of many of our members whose subscriptions expire in May to send in their renewals promptly causes us a great deal of unnecessary labor and expense. We will a ppreciate it greatly if members will remember this and will renew their subscriptions when they receive their first notice.
Random Notes on Geometry Teaching
Authors: Barber Harry C.
Published: January 2021

The first thing to do in the study of demonstrative geometry is to understand what demonstration is and why we demonstrate. If this is not done at the outset, the pupil becomes involved in misconceptions, doubts, and troublesome questions. “Why do we need to prove what we can see?” “What is the good of proving that?”
Everyman's Visit to the Land of the Mathematicians
Authors: Paterson Edith Bruce
Published: January 2021

This sketch of the history of mathematics is intended for a junior high school audience, although it would not be too simple for a senior high school audience.
The New Arithmetic Course in the Chicago Elementary Schools
Authors: Johnson William H.
Published: January 2021

Arithmetic in the early days of American education was a subject relegated to the tradesmen and industrialists, but not considered worthy of the attention of those destined for higher learning. And so for about a century, the schools, in particular those which prepared for college, laid no stress upon the subject. But conditions changed in America. Farmers were no longer the only ones to be considered. Tradesmen and industrial workers were becoming a substantial part of the population; and so arithmetic came into its own. Books on the subject were in the nature of guidebooks in arithmetical computations and solutions covering, as far as possible, all the needs of business. To these a business man could refer to find help in solving any problem with which he was confronted.
A Letter from the New President of the National Council of Teachers of Mathematics
Authors: Christofferson H. C.
Published: January 2021

The presidency of the National Council of Teachers of Mathematics is an honor and a responsibility of no mean significance. I greatly appreciate the honor of being president of an organization which for nearly twenty years has fought valiantly and successfully for the improvementof mathematics teaching.
Can We Adapt Arithmetic Instruction to the Needs of All the Children?
Authors: Cayce Morrison J.
Published: January 2021

A committee was assembled to determine the procedures that should guide them in preparing a State arithmetic syllabus for use in elementary schools. Early in their deliberations, some one asked whether it were possible for a State committee to prepare a syllabus that would actually help teachers to adapt arithmetic instruction to the needs of individual pupils. This question stimulated a healthy and not altogether comfortable discussion. It was apparent that all assembled were thinking primarily in terms of their grade placement of subject matter. For most, the only conception of adaptation to the individual differences among ch1ldren was acceptance of the inevitable conclusion that some would learn more and some less from any exposure to which the entire group might be subjected.
Editorials
Authors:   W. D. R.
Published: January 2021

There are many people who feel that mathematics is a dark and mysterious subject devoid of all interest. To others it seems, at best, a rather drab affair, while to a rather significant number mathematics. makes a decided appeal. Be that as it may, there is no reason why teachers of mathematics in the elementary and secondary schools, to say nothing of the colleges, should not do something to make their classrooms a little more appealing. If mathematics itself is dry to some pupils, the situation may be improved by having an interesting looking classroom and an inspiring teacher. Not all teachers are equally inspiring in all that they do, but they can, at least, make their classrooms more attractive than the majority are today. Many of these classrooms not only have no proper mathematical equipment such as rulers, protractors, squared boards for graphic work, and the like, but they have no pictures of any kind to relieve the monotony of the formality of the algebra or geometry which the pupils have to study.
News Notes
Authors: Thompson Lydia D. , Moles Florence M.
Published: January 2021

“Instructional Procedures-for the-Slow-and Bright Pupil” was the theme of the morning meeting of the all day sessions of the Illinois Association of the National Council of Teachers of Mathematics at the annual meeting this fall. The following aspects of the problem were discussed in ten and twenty minute talks:
The Challenge of the Slow Pupil
Authors: Eisner Harry
Published: January 2021

The immense growth of the secondary school population throughout the country during the past twenty years is a fact of universal knowledge. In New York City, senior high school registration has increased from about 60,000 in 1917 to 250,000 in 1937. This tremendous increase is composed largely of pupils from the lower brackets of intelligence who find themselves completely submerged by the traditional mathematics and are failing in vast numbers. Probably no problem in the field of the teaching of secondary school mathematics is more pressing for early relief or solution than the problem of providing an appropriate education for the so-called slow pupils.
In Other Periodicals
Authors: Lazar Nathan
Published: January 2021

This is the first of a series of reports to be presented by the Test and Measurements Committee of the recently organized Association of Teachers of Mathematics of New York City.
Ancient Mathematics and the Development of Primitive Culture
Authors: Cordrey William A.
Published: January 2021

The historian has been unable to ascertain whether the number sense was a part of the original endowment of the genus homo or not. It is known, however, that this innate or acquired ability possessed by man in the early periods of his development permitted him to recognize that a change had been made in a small group of objects when one had been deleted or added.
Air Navigation and Secondary School Mathematics
Authors: Kinsella John , Bradley A. Day
Published: January 2021

The World's Fair of 1939 has the distinction of being the first of its kind to be heralded around the world by men from the air. The flight of Howard Hughes and his men will long be remembered by millions of Americans who followed his progress hour by hour around the globe. The speed of the trip startled the whole nation. The constant radio contact between the plane and the rest of the world was especially remarkable. The flight followed a prearranged schedule with such precision that the distance traveled was only twenty miles greater than the planned mileage.
Modern Curriculum Problems in the Teaching of Mathematics in Secondary Schools
Authors: Reeve W. D.
Published: January 2021

The United States has more children above fourteen years of age in school than all the other countries of the world. In many communities, we have sixty per cent and in a few cases as high as ninety per cent of the ten million pupils of eligible age in school. High school enrollment has grown five times as fast as the population in general. According to Douglass,
Meaningful Symbols as a Better Preparation For Junior and Senior High School Mathematics
Authors: Duncan Myrtle
Published: January 2021

In the tentative report entitled “Mathematics in General Education,” The Commission on the Secondary School Curriculum of the Progressive Education Association emphasizes the importance of teaching symbolism in secondary mathematics and states that it seldom receives enough attention before the student reaches the high school level.
The Use of Calculating Machines in Teaching Arithmetic
Authors: Schlauch W. S.
Published: January 2021

Calculating machines were invented, and are used in business, industry and finance as well as in research and statistics to accomplish the following objectives:
Functional Thinking in Geometry
Authors: Pickett Hale
Published: January 2021

Geometry has been questioned as a high school subject by the general educator. However, this criticism has not been due so much to the subject as to the manner of teaching.
Three Major Difficulties in the Learning of Demonstrative Geometry
Authors: Smith Rolland R.
Published: January 2021

During the interval between the analysis of the results in Part I, and the beginning of the experiment for Part II of this study, methods of dealing with the three fundamental difficulties were devised and tried out on several successive classes. Elements of the methods which were awkward or inefficient were dropped and replaced by others. Finally, a complete course of study based on the new methods was written.
Reminiscences
Authors: Hutchins Robent M.
Published: January 2021

Four years ago I had the honor of addressing my fellow Yale men on the Higher Learning in America. Since the lectures had of course a very narrow sale, the effect they would otherwise have produced did not follow. Instead, all the movements they were designed to arrest, all the attitudes they were calculated to change, went rushing onward, in the case of the movements, or became more firmly entrenched, in the case of the attitudes.
Improving the Teaching of High School Mathematics
Authors: Dice Elizabeth Sue
Published: January 2021

The Texas Section is to be commended for beginning a long-time study of improving the teaching of mathematics in Texas. The teachers of the secondary schools welcome the opportunity to work with the college group. The teachers of the elementary schools are just as interested. The problem of improving the teaching— and the studying—of all subjects is one which should challenge the interest of parents and of teachers from the nursery schools through the graduate schools.
Professional Preparation of Teachers of Algebra
Authors: Congdon A. R.
Published: January 2021

Since just two of us have been assigned to the task of discussing the training of teachers of algebra, I presume I am justified in assuming that any phase of this training which has not been covered by Profesor Hassler is a legitimate topic for me to discuss. Thus, you see, I am avoiding the necessity of defining professional training.
Mathematical Skills of College Freshmen in Topics Prerequisite to Trigonometry
Authors: Wolfe Jack
Published: January 2021

The lack of retention of subject matter is an indisputable phenomenon which must be recognized in any program of education which is to be not merely consistent within itself and “logically” sound but also applicable in the world in which we live. The assumption that the students had at one time actually mastered the prerequisite topics and have retained their skills may lead to a well knit system of education on paper, but the failure of this assumption in practice may well be a chief factor contributing to some of our educational ills, especially those of student-failure and its consequent problems.
Where the Importance of Mathematics Need Not Be Taught
Authors: Jones Edna M.
Published: January 2021

The imperative need for relating mathematics to other subjects without devoting courses merely to the practical, social and business aspects of the subject has been significantly stressed in the national reports of both the Joint Commission on the Place of Mathematics in Secondary Education and the Progressive Education Association on mathematics in General Education. In most place our subject matter is on trial for its places in the secondary school curriculum. But there are exceptions.
The Twenty-Second Annual Meeting of the National Council of Teachers of Mathematics Atlantic City, New Jersey
Authors: Schreiber Edwin W.
Published: January 2021

The 22nd Annual Meeting of the National Council of Teachers of Mathematics was held in Atlantic City, New Jersey, February 21-22, 1941, at the Hotel Chelsea. Approximately 350 were in attendance at this meeting and 320 registered.
The Improvement of Mathematics Teaching in the Secondary School
Authors: Gray Hob , Votaw David
Published: January 2021

A teacher of trigonometry was once asked in class why it was necessary to be so painstakingly accurate in working the problems given in his assignments. To illustrate the need for accuracy he related the story of two engineers who had just completed the building of a bridge and were going out the next morning to see how it looked when completed. On arriving at the spot they found the bridge a tangled, twisted mass far down in the river bottom. One of them turned to the other and said despairingly, “See there, Bill, we got that decimal point wrong.”
Factoring Has a Meaning
Authors: Murtaugh Thomas H.
Published: January 2021

All Mathematics teachers on the secondary level have at some time or other experienced difficulty in making abstract but necessary mathematical principles purposeful and vital to students. The average high school student often asks, “What's the use of learning such meaningless operations as (a2 − b2) = (a + b) (a − b)?” The student who gives expression to this thought is not “de facto” the “ne'er-do- well.” He is the student who has factored “c squares minus d squares” until he has felt like “the difference of two squares.” He joins other students who, ordinarily docile, have risen in sheer consternation and now demand to know the use, the purpose, the function—the part such rules as a2−b2 = (a + b)(a − b) play in their lives.
The “Art of Nombryng”
Authors: Sleight E. R.
Published: January 2021

The art of Nombryng is a translation into 15th Century English of de Arte Numerandi, which is attributed to John of Holywood,1 better known by the name of Sacrobosco.
Distribution of Content in Twenty-three Ninth-grade Mathematics Textbooks for Non-academic Pupils
Authors: Novinger Faith F.
Published: January 2021

To what extent do textbook writers agree on the content to be included in the ninth-grade mathematics textbooks for the non-academic pupil? What are the tendencies with respect to emphasis on subject matter in these books? To answer these questions the writer analyzed the distribution of content according to subject matter in twenty-three ninth-grade mathematics textbooks, published from 1934 to 1940, which are designated as suitable for the non-academic group. Four of the texts studied are business arithmetics. The remainder of the books deal with “social mathematics,” which means “practical applications” of mathematics. Three of the textbooks represent the third volume in a series of three books. The rest are “terminal” texts, since no others have been written.
Education in the War Economy
Authors: Venable B. W.
Published: January 2021

From the point of view of the army, the training in the schools and colleges falls into two general classifications. First, military training. Second, training of a military nature which may be of value to the military service.
Mathematical Education in War-Time
Authors: Mallory Virgil S. , Fehr Howard F.
Published: January 2021

For a number of years past, conventional academic subjects have been subjected to critical analysis both by general educators, and by subject matter specialists.
What the Schools Should Do to Further Defense
Authors: Bond E. A.
Published: January 2021

My topic for this morning's program was submitted before the seventh of December. Yet the theme is far more important now that it was before that date. At the outset, I want to say that the schools should carry on as far as possible as they have been doing but with a stronger drive. Our work should be augmented and our efforts should be pointed more nearly towards our preparedness problems. Our national need is great. Indeed, America faces a number of supreme needs to meet which will take the combined powers of all of our people. Of these needs I shall speak of some which I consider to be paramount. In doing so, I purpose to show the ways that our schools can contribute towards supplying them.
The Art of Teaching: Teacher-Pupil Planning in Junior High School Mathematics
Authors: Ullsvik Bjarne R.
Published: January 2021

The goal of all school activities, irrespective of the individual pupil or his level of maturity, should be directed toward the perpetuation and fostering of a democracy. The present international situation should place a premium on the democratic way of life, and our schools should rededicate their energies in developing pupils whose characteristics are conducive to a democratic way of life.
The Next Step Forward
Authors: Wren F. Lynwood
Published: January 2021

The Great adventure which we call Life is a strange mixture of many peculiar ingredients. There is a great deal of comedy and much of tragedy in store for all of us. One of the greatest tragedies that can take place in the life of any individual is the betrayal of friends or loved ones. Overcome by such a tragedy, the bachelor philosopher Marcus Ordeyne was in a very hypochondriacal state of mind when, on the evening of November 12th, he turned to his diary to make the entry for the day.
The Teaching of Approximate Computation
Authors: West Roscoe L. , Shuster Carl N.
Published: January 2021

Approximate computation is needed in a large proportion of the problems of life since these problems contain approximate data secured from measurements or taken from various t ables. The table on the properties of saturated steam in the Handbook of Physics and Chemistry1 contains 3591 approximate factors, and there are hundreds of similar tables in the various handbooks. In solving problems containing approximate data, the laws of approximate computation should always be followed.
The Effect of the War on College Women and Mathematics
Authors: Bower Julia Wells
Published: January 2021

It is my privilege to consider with you the effect of the war on women and mathematics, particularly in the women's colleges.
Mathematics for Electricity and Radio
Authors: Cooke Lieutenant Nelson M.
Published: January 2021

When I was invited to appear before this Society, I accepted with pleasure, but more or less on the spur of the moment. Later, upon giving the matter more serious consideration, I realized that I had taken on more of an assignment than was apparent at first glance. The reasons for this are simple; here I am appearing before a distinguished group of mathematicians and educators and I profess to be neither a professional mathematician nor an educator in the sense that the name implies. Furthermore, a schedule of sixteen hours per day allows little time to prepare a polished paper. Therefore, this morning I do not propose to expound any new mathematical theories or burden you with my ideas of the proper methods to be used in educating your students. The latter is your job and I feel that, in general, it is being accomplished in a splendid manner.
Influence of the War on the Teaching of Secondary Mathematics
Authors: Breslich E. R.
Published: January 2021

Adequate preparations for post-war conditions are being made before the war ends. For months statesmen and governments have been at work, searching for ways and means of securing a peace that will be lasting. Industries are making preparations for converting plants from war to peacetime production. Investors are weighing the possibilities for future safe and profitable investments for their funds. Questions of unemployment, transportation, business, housing, food and supplies are being studied. There is hardly a field in which problems are not waiting for solution.
The Latent Proportional Parts Table in Ordinary Interpolation
Authors: Cheney Wm. Fitch
Published: January 2021

Ordinary interpolation is probably used more widely than any other process in arithmetic, save only the fundamental ones of addition, subtraction, multiplication and division. The object of this paper is to point out the presence, in every logarithm table, of a hidden subsidiary table of proportional parts. This may be called the Latent Table of Proportional Parts. Its use is recommended with all logarithm tables not equipped with auxiliary tables of Proportional Parts, as it saves time without producing unusual errors.
Relational Thinking as a Criterion for Success in College Mathematics
Authors: Mayor J. R.
Published: January 2021

The recent emphasis on evaluation is reaching college teachers and is beginning to have its effect on college teaching. Although the college or university curriculum allows considerable specialization, particularly in the last two years, an important objective of any college mathematics course could be to teach relational thinking.
The Art of Teaching: Adjusting Low Scores
Authors: Grossman G. W.
Published: January 2021

It is a common experience of teachers to find after marking the test papers of a class, that all the marks are very low. Sometimes it is evident that the fault lies in the fact that the teacher has made the test too difficult, or in some other factor which can not be justly attributed to the poor work of the students. When the teacher realizes this she desires to adjust these marks to equivalent scores which she feels are just, and which she can use in combination with other marks in making up a final grade for the student.
Applications of Quadratic Equations
Authors: Cordrey William A.
Published: January 2021

The advent of quadratic equations antedates the dawn of the Christian era by about two millennia. The study of conics, however, did not get under way until the fourth century prior to the birth of Christ. The first writer on this subject, Menaechmus, used the parabola and hyperbola in duplicating the cube. Several years later Euclid wrote a treatise on conic sections. This work was continued by Apollonius, whose investigations added much to the existing knowdedge of the subject.
A Mathematics Work Room for the Senior High School
Authors: Smith Jessie Roselle
Published: January 2021

In the field of mathematics, the advent of the war has not yet created many major changes. The most noticeable one is that more pupils are now enrolled in the mathematics courses than formerly. That the pupils are learning the subject better than in pre-war days is also quite apparent. I am not quite so certain that we are teaching it better. The war is the cause of the great increase in the enrollments, and the pupil's motive for studying mathematics is the most powerful in existence, that of retaining his life, and the life of freedom. If we do not recognize the strength of this force acting in our favor there is danger of our becoming apathetic. It behooves us to add vitality and meaning to the abstract theory that we teach. Unless we improve the quality of our work, and arouse the interest of the pupils in this field, we are going to experience a terrific jolt when the motive furnished by the war is gone.
Can We Teach Numbers for Meaning?
Authors: Whiteaker George H.
Published: January 2021

Methods of instruction growing directly from interpretations of the psychology of learning have produced such limited success in the teaching of number that any further proposal to discuss theoretical backgrounds of learning imposes considerable strain on the patience of the practical teacher. Yet such topics must be investigated. A better program for the presentation of number must be found, and if past experience is a criterion, the work must be done with the cooperation of classroom teachers.
The Art of Teaching: How to Teach the Work Problem
Authors: Lueck William R.
Published: January 2021

In the writer's classes in beginning algebra there have been many pupils who experienced difficulty with the so-called “work problem.” Because of this fact he busied himself with the task of devising a more satisfactory technique of presenting such problems when first taught. In these times of record machine production, improvement in the presentation of problems involving work assumes added significance. The technique given in this discussion has given good to excellent results in the writer's classes anil is presented here for the reader's approval or modification.
Aerial Navigation as Applied Mathematics
Authors: Blank Laura
Published: January 2021

In the fall of 1942 at the urgent request of the federal government, as an incentive to interest in piloting and navigating airplanes, many of the secondary schools of our country set into operation classes in aerial navigation, aerodynamics and meteorology. The navigation courses were in the main, the responsibility of the teachers of mathematics. They have been preparing youth including a few young women now for three years. The motive of these young folk in selecting the course is either the wish to pilot soon or that of understanding a timely subject. Many of the young men of the earlier classes are flying missions now “down under” in the South Pacific.* Some are flying their own planes from England for furloughs and then new assignments. Now the Army Air Corps is closed to admissions, and moreover, many men classified in that branch of the service for months, “on the line,” awaiting anxiously their transfer to preflight have been notified officially that they will not be needed as pilots or navigators or even bombardiers. One wonders what the effect will be on elections to a high school course in navigation. Will it develop that aerial navigation is an emergency subject, incident to the war, in secondary schools, to vanish from the curriculum in a few years, parts of it to be taken over into the courses in so-called pure mathematics? Or will navigation continue as a course optional in high school? At the moment options are holding up well.
Practical Mathematics
Authors: Bowie Harold E.
Published: January 2021

World War II has focused our attention on the practical side of mathematics. Training in this subject has been a necessary part of the programs for turning out fliers, engineers, teachers, doctors, chemists, meteorologists and other workers. The amount of mathematics needed varies with the type of work and the level upon which the individual is eventually to perform. A test chemist may find use for only a little arithmetic and proportion. On the other hand, a research chemist may be handicapped without some graduate courses.
Trigonometry without Angles
Authors: Newson C. V. , Randolph John F.
Published: January 2021

Either by definition or by implication, the great majority of textbooks on trigonometry regard the subject as fundamentally concerned with angles. In fact, the idea is presented with such insistence and emphasis that advanced instruction in science and mathematics is definitely handicapped. Whenever the expert on wave theory writes a collection of trigonometric functions upon the blackboard, he must expect the question, “Where are the angles?” The physicist explaining the use of sine functions in the study of vibratory phenomena invariably discovers that his students are puzzled by his failure to introduce angles somewhere in the discussion. In calculus the trigonometric transformations are a perpetual headache for students who have been disciplined to always think of cos x as meaning the cosine of angle x. Very good scientists have confided to the authors of this article that the graphical representation of y = sin x upon a cartesian axis-system always bothered them because they had difficulty accepting the device of marking x upon a straight axis; such a situation undoubtedly resulted from the false emphasis found in our textbooks on trigonometry.
Pet Peeves of a Mathematics Teacher
Authors: Ahrendt M. H.
Published: January 2021

The dictionary defines “peeve” as a colloquial word meaning “complaint” or “fit of resentment.” The word “pet” means “favorite” or “indulged.” Thus, to use the more mild of these definitions, a “pet peeve” is a “favorite complaint.” Now every person has a right to his favorite complaints, and in a democracy he has the right and sometimes the obligation to express them. The writer does not feel, however, using the stronger of these two definitions, that he has “indulged in fits of resentment” over the problems that he has met as a mathematics teacher. But he does feel that he is entitled to make three complaints, and that perhaps other teachers of mathematics will find common ground with him in some of them.
Mathematics Takes a Holiday
Authors: Haner Wendall W.
Published: January 2021

“If I could spend one whole day at the side of every student, pointing out to him the importance of numbers in everyday living, what a difference it would make in student interest!”
The First Calculus Textbooks
Authors: Boyer Carl B.
Published: January 2021

The year 1946 marks just a quarter of a millennium since the appearance of the Analyse des infiniment petils of L’Hospital.1 This book, the first published text on the calculus, could boast truly that in its day it filled with distinction that ubiquitous lure of textbook writers—the long-felt need. Moreover, its influence and popularity dominated the whole of the eighteenth century, the period during which the new analysis developed until it completely overshadowed other branches of mathematics.
Effective Guidance in Problem Solving
Authors: Karstens Harry
Published: January 2021

The amount of research in the field of problem solving, while not in proportion to the recognized importance of the subject, is still far from meagre. Unfortunately, for several reasons the results in some instances have been contradictory. Then, too, the published writings of prominent workers in the field have included assertions and recommendations that were not, at times, in accord with each other.
Adjusting the Program in Mathematics to the Needs of Pupils
Authors: Hawkins G. E.
Published: January 2021

Providing for individual differences is an ever present problem of teachers, particularly in mathematics. Pupils vary in their ability in past achievement, in interests, and in their needs. The educational literature furnishes numerous solutions. The suggestions include such plans as individualized instruction and progress as illustrated in the Dalton Plan, sectioning into X, Y, and Z groups, dividing a given section of pupils into two or three groups and working with these groups separately during the class period, giving the same basic content and instruction to a class and including optional work for the better pupils, and so on. However, no one method seems to furnish the single best answer.
Senior High School Mathematics Differentiated According to What Needs?
Authors: McAlpine Margaret
Published: January 2021

We have been hearing a great deal lately about mathematics in the senior high school differentiated according to needs. What are these needs of senior high school pupils? How can they he determined?