bluuebunny/crossref_metadata_2025 huggingface dataset:
The Future Geometry
Authors: Rudman Barnet
Published: January 2021

Perhaps no educational doctrine has crystallized more definitely from the intense research of the current century than the theory that there is little or no automatic transfer of ability from one field of mental activity to another. Nothing, indeed, was more instrumental in causing the very foundation to quake and convulse under the old philosophy of education. We may not like the finality with which the new doctrine is urged upon us, we can certainly point to many defects in the case against automatic transfer, but the fight is still on, and the last shot is yet to be fired.
An Argument for a Correlated Course in Science and Algebra
Authors: Rich L. Ashley
Published: January 2021

The first-year course in algebra can be the most interesting subject in the curriculum. It would be if it were not devitalized by some of these logical minded college professors who write our texts. Any student sufficiently endowed with mental equipment to enable him to do successfully sixth grade arithmetic would encounter no difficulty in mastering most of the material in the first year algebra if it were properly presented. Yet the percentage failure of algebra students exceeds that for all other subjects in most high schools, and in addition to this it is the exceptional student who at the end of the course in June can demonstrate any true mathematical power. By mathematical power I mean ability to apply mathematical methods to new situations, possession of confidence in one's results, etc. By the following September nearly all the skills in manipulation and most of the problem work have apparently been forgotten.
Problem Analysis in High School Physics
Authors: A. Zeller Karl
Published: January 2021

One wonders if problem analysis is a lost art, whether teachers perceive its value, recognize its necessity in the development of logical reasoning.
Junior High School Mathematics
Authors: L. Mossman Edith
Published: January 2021

What is a real junior high school? What is it inherent in adolescent boys and girls, that has led psychologists and progressive teachers whether st dents of formal psychology or not, to urge the change from the 8-4 plan to a 6-3-3, 6-4-2, or 6-4-4? What are the desires, habits, and necessities of the earliest teens that should greatly influence both content and method in all junior high school subjects?
Preliminary Report of the Committee on Individual Differences
Authors: Schorling Raleigh
Published: January 2021

The National Council of Teachers of Mathematics, at the Washington meeting, authorized the organization of a Committee on Individual Differences which was instructed to investigate the matters of ability grouping, differentiated curriculums, and the like. To avoid a useless and expensive duplication of effort, it seemed desirable that this assignment be assumed by an existing committee operating under the direction of the North Central Association of Colleges and Secondary Schools known as the Committee on Unit Courses in Mathematics for Students of Low Ability. It seemed that it would be much better from every angle to have the National Council and the North Central Association cooperate in this difficult but crucial investigation.
The Jabberwocky Was a Lark or The Mathematician Takes a Holiday
Authors: Jablonower Joseph
Published: January 2021

When Humpty Dumpty turns his perch on the wall into a lecturer's platform and proceeds to popularize the highly technical “Jabberwocky,” he initiates his auditor into only those most obvious of the mathematician's tricks that are exemplified in the poem. He resorts to some of the same dodges on his own account. The present writing is offered as a comment on both the “Jabberwocky” and its commentator- a sort of square root of a negative number. (Eddington, Aldous Huxley, and Bernard Shaw have been setting the fashion of invoking that concept whenever an impossible trick is to be turned.)*
Brook Taylor
Authors: Sanford Vera
Published: January 2021

Brook Taylor took an important part in the development of the calculus, but he crowded his chief activity into the period from 1708 to 1719 when he seems to have ceased working in mathematics and devoted himself to writing. He studied at St. John's College, Cambridge; became a fellow of the Royal Society in 1712; and took Newton's part in the Newton-Leibniz controversy. He engaged in a number of challenges with the Bernoullis and was one of the few Englishmen who were able to hold their own against them. He invented the calculus of finite differences, and wrote on the motion of projectiles and the vibration of strings. His Linear Perspective (London, 1715) and his Principles of Linear Perspective (London, 1719) introduced the subject of vanishing points but much of the work had been anticipated by others.
Analysis Is Not Enough
Authors: Fabricius Alma M.
Published: January 2021

Ever since the explosion of the theory that the faculty of thinking could be developed and strengthened by exercise in thinking regardless of the nature of the subject matter involved, geometry as a universally required subject in the high schools of America has been on the defensive. And, when we consider the large number of failures in the subject, in the light of the educational theory that a child learns only through the encouragement of success, it becomes seriously doubtful whether geometry should be retained as a compulsory subject in the high school.
The Old and the New Mathematics Education
Authors: Collins Joseph V.
Published: January 2021

Much has been written in recent years about McGuffey's Readers, but little or nothing of Ray's Series of arithmetics and algebras. In their day the Ray books had a large sale and were regarded as of as much importance as McGuffey's. The old arithmetic course differed from that of today in two exceedingly important respects. First, the old books employed a rather thoroughgoing inductive and deductive procedure in presenting topics. Second, nearly thrice as much time was devoted to arithmetic in the elementary course as now. The question is, which course is the wiser?
Development of Mathematics in Secondary Schools of the United States
Authors: Wren F. L. , McDonough H. B.
Published: January 2021

Prior to the latter part of the nineteenth century the energies of those interested in public education had been primarily directed toward the completion of the educational ladder. Elementary, secondary, and higher education had been placed under public control and to a large extent was financed by public taxation. In 1893 the Committee of Ten reported to the National Educational Association in favor of enriching the course of study in grades below the high school through the introduction of various subjects such as algebra, geometry, foreign languages, and natural sciences but their recommendations made no provisions for adapting these subjects to the abilities and needs of the children of the lower grades. During the early stages this movement for reorganization centered around the approximate equal division of time devoted to elementary and secondary education. The idea of dividing the six-year secondary school into junior and senior departments did not become a prominent one until the latter part of the first decade of the twentieth century.
Some Mathematical Shortcomings of College Freshmen
Authors: Campbell Alan D.
Published: January 2021

When I was teaching mathematics at Northwestern University I had to correct and hand back the homework of my students. I soon wearied of making the same correction on the paper of each student and sometimes over and over again on the papers of the same student. Besides, the students often just threw away their returned homework without looking it over.
Abstracts oF Recent Articles on Mathematical Topics in Other Periodicals
Authors: Lazar Nathan
Published: January 2021

A very readable and interesting account of the development of the decimal system. Its disadvantages are enumerated and the unquestionable superiority of the doudecimal system pointed out. The author fervently advocates the introduction of the duodecimal system, but he is not blind to the obstacles to be met and the adjustments that will have to be made in case of its adoption. “The present generation would have a most awkward time, chiefly in unlearning the old multiplication tables; but children for all future generations would find mathematics made vastly easier by the present sacrifice.”
How Shall We View Elementary Education as Regards
Authors: Bagley William C.
Published: January 2021

In the consideration of the three topics listed for discussion I shall give practically all of the time at my disposal to the second topic, Subject-matter, because at the present time the chief problems of educational theory and practice seem to be centered here. My own remarks concerning the present status of discipline and of psychology will consequently be very brief. I shall deal first with these and for the sake of brevity I shall take the very great liberty of being somewhat dogmatic.
Adrien-Marie Legendre
Authors: Sanford Vera
Published: January 2021

Although Legendre was born in the south of France, he spent the greater part of his life in Paris. He attended the Collège Mazarin in that city and, in 1775, he was made professor of mathematics at the Ecole Militaire where Laplace was also teaching. Legendre kept this position until 1780 when he resigned the position to give more time to his researches. In 1782 he won a prize offered by the Berlin Academy with an essay on the path of a projectile. In 1787 he was a member of a commission which connected the Royal Observatory in Greenwich with the Paris Observatory geodetically. Legendre later was a member of the commission which made up the metric system. In 1795, he was made professor at the Ecole Normale. Unlike Laplace, Legendre had little recognition. Laplace was always unfriendly to him and at length Legendre lost his pension as a member of the Academie and he died in poverty.
Abstracts of Recent Articles on Mathematical Topics in Other Periodicals
Authors: Lazar Nathan
Published: January 2021

The second and final installment of a paper, the first part of which was published in the April 1934 issue of the magazine then known as The Mathematics News Letter.
Official Notice
Authors: Schremer Edwin W.
Published: January 2021

As secretary of the National Council of Teachers of Mathematics, I officially announce the annual election of certain officers of the National Council, said election to take place at St. Louis, Mo. on Wednesday, January 1, 1936. Article Ill Section 7, of the by-laws states: “At least two months before the date of the annual meeting, all members shall be given the opportunity through announcement in the official journal to suggest by mail for the guidance of the directors a candidate for each elective office for the ensuing year. At least one month before the annual meeting the secretary of the board of directors shall send to each member an official ballot giving the names of two candidates for each office to be filled. These candidates shall be selected by a nominating committee of the board of which the secretary shall be chairman. The election shall be by mail or in person and shall close on the date of the annual meeting.”
Economies Found in a Half Century's Teaching of Mathematics
Authors: Collins Jos. V.
Published: January 2021

Only a small fraction of those who teach hand down in written form the results of their experience. Other teachers affect future instruction only through the relatively small number of their students who afterwards become teachers. In this way there is a distinct loss to education and society itself. It occurred to me that my experience might have value, especially for young teachers, even though they may have read many books on mathematical instruction. But I know as well as anybody that many of the younger generation could give me hints for better teaching.
The Status of Mathematics in India and Arabia during the “Dark Ages” of Europe
Authors: Kokomoor F. W.
Published: January 2021

Political and economic world historians have found it convenient to divide the time from the fall of Rome to the discovery of America into two periods, and to designate the first of these by the term “Dark Ages.” One work accounts for this name by “the inrush into Europe of the ba rbarians and the almost total eclipse of the light of classical culture.” The period covers, roughly, the time from 500 to 1000 A.D. Part of these “barbarians” came down from the north and the rest attacked from the south, the latter bound together politically and religiously by the great, although probably totally illiterate, leader Mohammeed into a vast dominion that at one time or another covered all of eastern Asia, northern Africa, Spain, France in part, and the European islands of the Mediterranean Sea. It was during this period that Europe was dark, learning at low ebb, and the development of mathematics almost negligible. The world as a whole was not dark, and as applied to general history the expression “Dark Ages” is a gross misnomer. Throughout the entire period there was considerable intellectual (including mathematical) activity among the Hindus and, beginning about 750, there developed many centers of Muslim civilization which rose to the very peak of mathematical productivity.
News Notes
Authors: Lavengood L. W.
Published: January 2021

The Tulsa (Oklahoma) Mathematics Council now has a charter from the National Council, dated December 14, 1935. It carries the signature of the national secretary, Edwin W. Schreiber, and the corporate seal of the organization. We have it framed. It was formally presented to our president, Miss Kate Cannon, by our secretary, Miss Narcissa Bond, at the regular quarterly meeting in Central High School, April 16, 1936. We feel that this formal evidence of national recognition marks the successful completion of our efforts toward local unity.
The Mathematics of the Sundial
Authors: Wood LaVergne , Lewis Frances Mack
Published: January 2021

Miss Vevia Blair,1 for many years Head of the Department of Mathematics in the Horace Mann High School for Girls, did outstanding work experimenting with new material in senior high school mathematics. She brought her unusual imagination and originality to bear on the problems of unifying the different branches of elementary mathematics, coordinating mathematics with other subjects, using the arts to make mathematics and its history vivid and satisfying, and presenting the material of elementary mathematics as a means to some immediate accomplishment. She believed that the cultural obon the Sundial, she envisioned as an outlet for the knowledge gained in the study of demonstrative plane geometry, and as a means of fulfilling the objectives which she felt to be so important.
Formal Discipline
Authors: Metzler W. H.
Published: January 2021

I think the student of history would find few, if any, exceptions to the rule that what vitally touches everyday life and has existed for long years has considerable truth underlying it. New things will come in and give new light and show up old things in their true light, but they are not likely to entirely upset beliefs of long standing.
A Shortened form of Synthetic Division and Some of its Applications
Authors: Smith Eugene R.
Published: January 2021

The ordinary form of synthetic division is probably familiar to most if not to all teachers of mathematics. I think the best arrangement for division by a binomial divisor is as follows:
Sex Differences in Secondary School Mathematics
Authors: Douglass Harl R.
Published: January 2021

In connection with a committee report for the American Educational Research Association the author had occasion to search for and abstract the investigations reporting data relative to the respective achievements of boys and girls in high school mathematics. More studies were located than are reported here. Some of them were of doubtful reliability and a few were not available.
The Art of Teaching A New Department
Authors: Wilson Ruth
Published: January 2021

Realtzing that many people, even school administrator, regard mathematics beyond arithmetic as a subject with neither cultural nor practical value, we of the mathematic department of Thomas Jefferson High School decided to make the topic of our second annual exhibit: “The Practical Application of Mathematics in Various Occupations and Industries.” We knew that mere statements of facts would receive little attention—there must be something to attract the eye, and we felt that the statements would be more convincing if they came from buiness men. Our first problem, thefore, was to devise a pleasing scheme for getting the attention of the public in order to sell the idea that all high school mathematics is practical and to stimulate appreciation of the fact that nearly all “big business” uses higher mathematics. Our next problem was to secure the cooperation of various business concerns.
News Notes
Authors: D. K. Howell
Published: January 2021

The eighteenth annual meeting of The National Council of Teachers of Mathematics which was held at the Palmer House in Chicago on February 19 and 20 was by far the biggest meeting that the Council has ever held. There were over one thousand people present at the meeting and the Chicago mathematics teachers showed their loyalty by running their own attendance up to 650.
News Notes
Authors: Georges J. S.
Published: January 2021

The last meeting of the Bay Section of the California Mathematics Teachers’ Association was held on Thursday, October 14, 1937, at the University High School in Oakland. The program was as follows:
A Course in Applied Mathematics for Teachers of Secondary Mathematics
Authors: Richtmeyer Cleon C.
Published: January 2021

It has long been the feeling of the writer that the present curricula for teachers of secondary mathematics tend more to theory than to applications, and that a need exists for a course in which the many applications of mathematics could be considered. This feeling increased in intensity due to the following trends in teaching of secondary mathematics: (1) A shift in emphasis from disciplinary values to appreciation and application; and (2) The reorganization of secondary mathematics to include a general course for all students. These trends both imply a teacher with a broad background of knowledge of the application of mathematics.
What Shall We DO with Our Unfit?
Authors: Seidlin Joseph
Published: January 2021

All is not well with the status of mathematics in our schools. Teachers of mathematics more than ever before are under fire on a great many fronts. In particular let me mention a few of our more or less worthy opponents: boards of education, the pure and simple educationist, the left-wingers of the progressive school, the administrative officers of our local school systems, the state and large city superintendents or commissioners of education, the “man in the street,” the university professors of mathematics. The criticisms levelled at the teaching of mathematics are in the main familiar to all of us. I shall mention a few of the more specific charges against us partly in review and partly as a basis for my talk.
Ratio as Multiplier
Authors: Evans George W.
Published: January 2021

Of course a ratio can be defined either as a quotient or as a multiplier. At a recent meeting of this Association I heard a distinguished scholar say that the notation y ∞ x should be regarded as obsolete and replaced by the equation y = mx. It is the equivalent of the orthodox statement “y is proportional to x,” and you notice the ratio is the constant multiplier m.
The Importance of Certain Concepts and Laws of Logic for the Study and Teaching of Geometry
Authors: Lazar Nathan
Published: January 2021

Althouguh the definition of the term inverse (opposite) will be given more fully later in this chapter, it is desirable to present a few examples now so as to clarify the meaning of the term.
The Relation of Reading Comprehension and Efficient Methods of Study to Skill in Solving Algebraic Problems
Authors: Stright Isaac L.
Published: January 2021

This is the report of an investigation to determine the effect specific training in reading and efficient methods of study has upon a ninth grade student's reading ability and his skill in solving algebraic problems. The purpose of this investigagation was to answer the following questions: Is there a definite relationship between a student's skill in solving algebraic problems and his ability to read with comprehension? Will pressure upon a student and guidance which forces him to be conscious of his reading mechanics have any effect on his reading comprehension? Will it carry over in to his ability to solve algebraic problems? Is it important to stress functional terminology in the teaching of algebra?
Mathematics in Mechanical Engineering
Authors: Karelitz George B.
Published: January 2021

The use of Mathematics in Mechanical Engineering is essentially the same as in all other kinds of engineering—electrical, chemical, eivil. However, being a mechanical engineer, the author will use his illustrative examples from this field.
The Art of Teaching: An Attempt to Develop Number Sense
Authors: Nelson A. C.
Published: January 2021

The above incident occurred in a Seventh Grade arithmetic class; while this may be considered an extreme case, yet it is astounding how little number sense has been developed in pupils after seven or eight years of work in mathematics.
The Mathematical Foundations of Architecture
Authors: Craver Mary E.
Published: January 2021

The architecture of the ancient Greeks and the cathedrals of the mediaeval builders have always been looked upon with astonishment and wonder. How were such marvels of beauty designed? What knowledge, which we lack today, was able to produce such unequalled perfection? In architectural schools these ancient works serve as source material in studying the principles of design. The first exercises for a beginning student in design are studies of the ancient “orders,” reproductions of parts of ancient buildings, and original problems adapting the Greek style. Of course students notice that certain proportions between parts produce pleasing results and they try by copying and reproducing the ancient examples to acquire a “feel” for such proportions. No teacher of design, however, ever suggests to a student the possibility that the Greeks had a formula for it. The student's method is a hit and miss, trial and error method-the method of experimentation. But the architecture of the ancients is too consistently beautiful to be the result of such haphazard method of arriving at a finished design. This is the thought of many serious students who are challenged by the consistent perfection in Greek architecture. Regardless of who the architect was, regardless of the number of buildings, we know today the same perfection exists. It almost seems as if this perfection is a divine revelation and the architect merely an agent for translating it into a physical existence. The same is true for the cathedrals in the Middle Ages. We have ample evidence from ancient writer and architects that design was the application of mathematical relationships developed into a science of building. Vitruvius, about 20 B.c., in his work, De Architectura, writes that the Greeks had fundamental measures which seem necessary in all buildings. These are taken from parts of the human body which was considered by them to be divinely proportioned. The height of the head is 1/8 of the height of the body. The foot is 1/6 of the same height, etc. The exact relation, however, between these measures and the modulus as used in their architecture is not known.
The Contribution of Mathematics to General Education
Authors: Hedrick E. R.
Published: January 2021

While I shall speak on the contribution to general education of mathematics, I have no intention of defending or glorifying all of the practices of past or present mathematical instruction. I myself have criticized sharply some of the traditional methods and some of the traditional subject- matter of mathematical courses in all grades of mathematical instruction, and I have pointed out the fallacies which lurk in claims for general improvement in logical power or in ability to think which have been made by some enthusiastic teachers of mathematics. More particularly, I have insisted that the teaching of mathematics for so-called mental discipline is not supported by sound psychological investigation. Indeed, I have pointed out that transfer of training even within the boundaries of mathematics itself is limited in its scope.
The Art of Teaching: A Helpful Technique in Teaching Solid Geometry
Authors: Bernardo James V.
Published: January 2021

It has been my experience; as it has been undoubtedly that of many who teach solid geometry, to find that the three-dimensional concepts are not easily conceived by the average student. He does not comprehend fully the meaning of the drawings of “solid” figures in one plane. To develop an aptitude for drawing and for interpreting figures is the real job for the teacher who is attempting to expound the propositions of the sixth, seventh, and eighth “Books” of Euclid.
The Twenty-First Annual Meeting of the National Council of Teachers of Mathematics at St. Louis, Missouri, February 22-23, 1940
Authors: Schreiber Edwin W.
Published: January 2021

Some 400 people were in attendance at this meeting at the Hotel Chase and 361 registered.
Alligation Alternate for the Algebra Course
Authors: Katra A. E.
Published: January 2021

The ways of the traditional mathematics texts do indeed pass understanding. Factoring is still retained in practically all the current Algebra books even though this phase of work is obsolete and almost without any practical or stimulating value for the students, while alligation which was found in most mathematics publications about fifty years ago is today forgotten in spite of the fact that this Science of Mixtures or Method of Comparisons as it is sometimes called has much application in business, chemistry, pharmacy, metallurgy, and all other fields where metals, merchandise, moneys and solutions are mixed.
Training Teachers of High School Arithmetic
Authors: Foust Judson W.
Published: January 2021

One is confronted with the necessity of choosing in a very limited way when attempting to discuss in a few minutes the training of teachers of high school arithmetic and keep in mind as a background theme the student who is not going to college. May we then assume the necessity of a broad liberal education, sound scholarship, professional training and a period of supervised teaching. This leaves us the time to bring into sharp relief a few points whose emphasis seems most likely to produce worthwhile improvement in this area of teacher training. In doing so it may be necessary in giving direction to our teacher training program to discuss somewhat in detail the aims and methods and points of view to be employed in arithmetic itself.
The Art of Teaching: Introduction of “One” Negative Number
Authors: Ransom William R.
Published: January 2021

One who has read the article “Introduction of negative numbers,” in the October (1940) issue of THE MATHEMATICS TEACHER, with its elaboration of types of order, transfinite numbers, ordinal augends, cardinal auctors, and the “5+3” may be interested to consider an alternative introduction to algebra, in which the beginner is asked to introduce only one negative number, − 1.
A Functional Revision of Plane Geometry
Authors: Nygaard P. H.
Published: January 2021

MANY HIGH SCHOOL teachers of plane geometry introduce their subject by proudly stating that it is over 2000 years old. They announce in awe inspiring phrases that Euclid wrote his plane geometry textbook before the time of Christ, and that the present course is much as he left it. They insist that revision has been unnecessary because mathematical truths never change.
Models in Solid Geometry
Authors: Hartley Miles C.
Published: January 2021

The development of the pupil's ability to visualize spatial relationships has for a long time been recognized as one of the problems confronting the teacher of Solid Geometry. In 1923, the National Committee on Mathematics Requirements wrote: “The aim of the work in Solid Geometry should be to exercise further the spatial imagination of the student and to give him both a knowledge of the fundamental relationships and the power to work with tbem.”1 In 1940, the Joint Commission of the Mathematical Association of America and the National Council of Teachers of Mathematics reported: “Much attention should be given to the visualization of spatial figmes and relations, to the representation of three dimensional figures on paper.…”2
Why Teach Mathematics?
Authors: Kinney Lucien B.
Published: January 2021

A favorite argument in educational circles, in times not long passed, concerned the relative importance of subject-matter, as compared to methods, in the preparation of the teacher. Stated positively, the subject for debate might be stated in the cliché, “If you know your subject you can teach it.” Today we recognize that both are necessary, and neither is useful without the other. Yet even together they are not sufficient without a third component-an appreciation of the purposes of education here and now.
Geometry for All Laymen
Authors: Fawcett Harold
Published: January 2021

During the summer it is my privilege to guide the thinking of twenty-two young people as together we explore the inviting opportunities offered in the study of demonstrative geometry. On meeting these boys and girls for the first time about two weeks ago I discussed with them the nature of their previous experiences in mathematics. I listened while some who were more talkative than others told of their work during the preceding years and in their reports I saw reflections of what might be recognized as arithmetic and informal geometry. Through encouragement and an occasional leading question I learned that all of them had had various degrees of experience with a course in elementary algebra. One girl did insist that she had never had such a course but when assured by the other members of her class that she had taken it with them she replied “Oh! I remember now and you are right. I was in there.” I learned that four of the twenty-two students really enjoyed their algebra while six thought that the course had been of some value to them although they were unable to say just what these values were.
What Can the Teacher of Mathematics Do About Vocational Guidance?
Authors: Welch Harriet A.
Published: January 2021

What can teachers of mathematics do about vocational guidance? First of all, whether intentionally or not, every teacher of mathematics plays an important part in vocational guidance, for today, with young men throughout the country taking examinations to enter some branch of the army or navy their success is in a very large measure determined by their ability to pass the test in mathematics. Some of them due, in part at least, to thorough training pass easily, while far too many have difficulty or utterly fail. It is therefore quite probable that teachers who saw to it that their pupils actually learned arithmetic and algebra did the finest possible work in vocational guidance although they may never have heard of the term. At any rate, at the present time, the first duty of teachers of mathematics is to make certain that students really know fundamentals. Unless this is first done, talk of vocational guidance in mathematics is worse than useless.
Pre-Induction Courses in Mathematics
Authors: Studebaker John W.
Published: January 2021

The United States Office of Education has received urgent and repeated requests from individuals and organizations throughout the country to give the secondary schools detailed suggestions for the teaching of mathematics for pre-induction purposes. In December 1942, the Office in cooperation with the President of The National Council of Teachers of Mathematics appointed a committee to make a survey of the mathematical needs of the armed forces and upon this basis to make a report concerning what the schools can do for the emergency. The committee consisted of Virgil S. Mallory, Professor of Mathematics, New Jersey State Teachers College at Montclair; William D. Reeve, Professor of Mathematics, Teachers College, Columbia University; Giles M. Ruch, Chief, Research and Statistical Service, U. S. Office of Education; Raleigh Schorling, Professor of Education, University of Michigan; and Rolland It. Smith, Specialist in Mathematics for the Public Schools of Springfield, Massachusetts, and President of the National Council of Teachers of Mathematics. Dr. Smith served as chairman of the Committee.
Guidance for Girls in Mathematics
Authors: Burr Harriette
Published: January 2021

The challenge has been given to womankind: A WOMAN TRAINED TO DO THE WORK OF EVERY MAN NEEDED ON THE BATTLEFRONT. Herein is one of the greatest contributions of teachers to the manpower problem in this war effort: to see that each girl, as well as her family, hears this challenge; and to so guide a girl in her program of studies that she is becoming a specialist in some one field of work in order that she will be competent to assume her duties in the war effort.
Readiness in Mathematics
Authors: Richter Charles O.
Published: January 2021

The title of my talk this morning has a very ambitious sound, and I would prefer that it read “One Man's Approach to the Problem of Readiness for Mathematics in the Junior High School.” The title on the program suggests that I have something new and startling to present and therefore if you came for that reason you will be greatly disappointed. There is very little new, in my opinion, in any branch of our educational system but frequently truths are rediscovered and interpreted differently by different people. Witness the rediscovery that there is great value in having children read orally. The practice used to be to have approximately 90% of all reading in the sixth grade silent reading. Hence my effort this morning will be concerned exclusively with one man's application of his understanding of child growth and development as it is applied to arithmetic.
Ungraded Classes for Superior Pupils
Authors: Coe Burr D.
Published: January 2021

Elementary algebra, plane geometry, intermediate algebra, plane and spherical trigonometry, solid geometry, and advanced algebra are all being studied in the same room at the same time. Sounds something like a one-room country school, doesn't it? This is being done by a group of mentally superior pupils in two ungraded classes (taught by the writer) at Monroe High School.
The Art of Teaching: Errors in Ninth Grade Algebra
Authors: Snider Everett
Published: January 2021

The purpose of this study was to attempt to determine (1) the classes of errors most likely to occur in ninth grade algebra and (2) whether or not it is better to follow the rules as presented in most texts for algebraic addition and subtraction or to omit the rules entirely.
Mastery of Mathematics Adapted to Needs and Abilities: A Reply to the Previous Article by Professor Kempner
Authors: Douglass Harl R.
Published: January 2021

While naturally I am pleased with the good things Professor Kempner says about me and our book, and while I certainly have no quarrel with the desire to have students come into college classes in mathematics better prepared than they do, I believe that some parts of Professor Kempner's assumptions and reasoning should be challenged and I should like to object strenuously to any criticism of the Doug-lass-Kinney book, Senior Mathematics, for failing to serve a purpose for which it was definitely not intended.
A New Approach to College Mathematics
Authors: Doyle William C.
Published: January 2021

Arithmetic is the foundation of all mathematics. It took a world war to prove that fact. As a result, elementary and secondary schools are revising their mathematics programs to fit the new discovery. Meanwhile the unhappy college teacher has still to worry about the many freshmen who had their training in fundamentals in the days when computational skills were held in contempt.
Some More Thoughts on Placing the Decimal Point in Quotients
Authors: Engen H. Van
Published: January 2021

In the February issue of The Mathematics Teacher, Claude H. Brown has stated a very good argument for properly placing the decimal point in a quotient by the subtraction method.1 Since this article presented arguments for the subtraction method, it might be well to state some arguments for the caret method as well as try to show that advocates of the caret method cannot necessarily be charged with mechanistic teaching.
Number Concepts of Small Children
Authors: Mott Sina M.
Published: January 2021

In order to study the development of number concepts an investigation was made of those concepts held by two groups of children attending the Laboratory School of Southern Illinois Normal University. The first group were studied during the year of 1944-1945 and the second in the summer of 1945. The children were interviewed separately that the remarks of one might not influence the response of another. The teacher sat opposite each child at a small table on which had been placed a working sheet, fifteen small colored cubes, a toy truck containing 28 cubes, a pencil and a paper.
The Fallacy of Social Arithmetic
Authors: Wheat Harry G.
Published: January 2021

It is axiomatic that when a theory concerning education sounds too good the teacher should be suspicious of it. For a decade the theory of social arithmetic has been sounding too good,—much too good. It embodies an esaily understood method of instructing pupils in arithmetic. It suggests an already familiar content. It supplies meaning much as a gift to be accepted instead of an achievement to be striven for. In short, social arithmetic is a ready-made answer to the problems that confront the teacher. He does not need to turn to the back of the book. Indeed, he is supplied the answers before he meets the problems. It is about time for the teacher to become suspicious. It is about time for him to inquire what social arithmetic is and how it got that way.
On Square Root by Division
Authors: Chittenden E. W.
Published: January 2021

In a recent article1 Mr. William S. Tobey has written regarding the advantages of teaching root extraction by a method which he calls “Approximation and Division.” I wish to suggest some improvements in the method he proposes and to discuss several related educational questions. Let us begin by considering the proposed modifications.
Mathematical Probabilities in Games of Chance The Game of Sevens
Authors: Dagobert E. Bonavent
Published: January 2021

In a letter to Pascal from a courtier, friend of Mme. de Maintenon and gambler, we read the following: “Remember that I am discovering things which you would have never seen for yourself, things so rare that the wisest ancients completely ignored them and at which the greatest modern mathematicians have been surprised.” The writer was Antoine Gombault, Chevalier de Méré (1610-1684). The “things so rare” were the gambling chances in a dice game. The things the wisest ancients completely ignored were the problems presented by random events, and the things at which the greatest modern mathematicians have been surprised were the heretofore unexplored realms of chance, of mathematical probabilities, which the keen intellects of Pascal, Fermat, De Moivre, Bernoulli, Lagrange and Laplace organized into an important science, the science of Modern Statistics.
Some Proposals Regarding the Preparation for Teaching High School Mathematics
Authors: Breslich E. R.
Published: January 2021

Those teachers of mathematics whose teaching experiences extend over a period of forty years, or more, can recall how easy it was in the early years of the new century to qualify as a teacher of high school mathematics. A college graduate with a bacherlor's degree, with a sequence in college mathematics, and with a minor in one related subject, such as physics, chemistry, or astronomy, was rated as “well prepared.” If he obtained the recommendation of the department he had no difficulty in securing a position in a good high school. If he continued his studies while in service and acquired a master's degree he was looked upon as unusually well prepared.
The Case of Decimals Versus Common Fractions
Authors: Johnson J. T.
Published: January 2021

We are living in an atomic age where space and time have been reduced and shortened. Simplified practice and speed is the order of the day. We have learned through excursions into the field of chemistry how to make new products in plastics. We have discovered new medicines and new vitamins. We are planning new kinds of houses and have learned new methods of preparing foods. We have added new and safer methods of transportation. We can span our continent in less than 12 hours. We can reach any spot on the globe in 60 hours or less. We have sent rockets 60 miles into the stratosphere and we have even hit the moon 240,000 miles away.
Demonstrative Algebra
Authors: Stabler E. R.
Published: January 2021

High School or college algebra, in comparison with high school geometry, is commonly recognized as a loosely organized subject. In algebra, the usual emphasis is on generalization of the concepts and rules of arithmetic, and on the use of a more powerful symbolism to solve numerical problems, but not on the systematic, logical development of the subject from a set of postulates and undefined terms. Standard terminology distinguishes between informal geometry of the junior high school and demonstrative geometry of the senior high school, but in the field of algebra we generally have only such designations as elementary, intermediate, advanced, or college algebra. These various courses certainly differ in the complexity of topics considered, and in the later courses somewhat more attention is probably paid to such fundamental postulates as commutative and associative laws, and more proofs of specific thorems may be given. But it can hardly be said that under usual conditions the logical structure of the subject, as a whole, is significantly much more advanced in the later than in the earlier courses. Somehow, we do not hear of courses entitled “demonstrative algebra.”
Mathematics in the Skilled Trades
Authors: Carlton Carl J.
Published: January 2021

The shortage of skilled workers in the United States is tending to become a serious bottleneck in the production of consumer's goods and more seriously a handicap in tooling for defense production. A glance through the Help Wanted columns of every newspaper in a manufacturing area makes this apparent to everyone. It might be thought that this is a transitory situation which will ease when the most urgent tooling has been completed for the swelling arms program. A little research into the reasons for the current shortage of skilled men will quickly dispel this belief.
Watch your figures
Authors: Sexton Maude
Published: January 2021

Displaying an attractive bulletin board is a good way to attract attention and stimulate interest.
An algebra program for the bright ninth grader
Authors: Latino Joseph J.
Published: January 2021

What to do about the bright student in the mathematics classes is always a perplexing question. Here are some suggestions for your consideration.
The national status of mathematics contests
Authors: Lloyd Daniel B.
Published: January 2021

Ways to stimulate interest in mathematics are being sought by all. While mathematical contests and examinations are not universally looked upon with favor, their use is increasing.
Mathematics in the Junior High School: Sequoia Junior High School Math Team
Authors: Hofeditz Paul H.
Published: January 2021

The Sequoia Junior High School Math Team is now in its third year. It was originally organized as a demonstration group consisting of hand-picked students of outstanding mathematical ability. They were to develop skills in rapid calculation and learn a number of dramatic short-cut “tricks” with which to impress and amaze other students and lay groups.
School and college mathematics
Authors: Duren William L.
Published: January 2021

A mathematician's thoughts on how to revise the high-school mathematics courses so as to minimize the “break” in the mathematics program at the beginning of the thirteenth year.
Proximity of prerequisite learning and success in trigonometry in college
Authors: Wolfe J. M.
Published: January 2021

Educational nomenclature would call this “action research.” This is action research at its best.
The Work of an English Mathematical Student
Authors: Bateman H.
Published: January 2021

A few weeks ago Professor Babb invited me to give you a short address on some topic connected with the study of mathematics at English schools and universities. In thinking over the subject I have naturally tried to recall the various impressions I received during my school and college days, leaving out, of course, the marks of the cane. For a little while it has seemed just as if time had been put back ten years or so, that I was again looking at things from the point of view of the student and comparing experiences and opinions with my college friends.
What Mathematical Subjects Should be Included in the Curriculum of the Secondary School? From the Point of View of the Technical School
Authors: Hathaway Arthur S.
Published: January 2021

After careful consideration of this question, it has appeared to me that any changes in the present curriculum of secondary schools in mathematical subjects should be not in the subjects taught, but in the object and character of the instruction. What the technical student most needs is a working knowledge of arithmetic, algebra, and geometry. He should be able to make ordinary arithmetical computations with accuracy, perform ordinary algebraic operations without making those numerous blunders which result from a confused perception of their arithmetical foundation, and have a store of geometrical facts and principles fixed in his mind by having logically worked many original exercises.
Max Stirner y la política de la insurrección
Authors: D'Angelo Valerio
Published: January 2021

En este artículo se quiere trazar una teoría política de la insurrección en el pensamiento de Max Stirner, en tanto alternativa ética y política a la revolución. Se mostrará cómo, según el pensador alemán, la revolución es en última instancia una estrategia fallida de emancipación en tanto en cuanto no libera al individuo de las formas de subjetividad que lo mantienen dependiente del poder. Más en general, se enseñará como el orden liberal post-revolucionario, detrás del lenguaje secular de los derechos, las libertades y la igualdad, engendra técnicas más sutiles de gobernabilidad del individuo. La insurrección, en cambio, puede ser vista como un rechazo de las identidades y de los roles que disciplinan al individuo. Al respecto, se prestará una atención especial al concepto stirneriano de Eigenheit (propiedad de sí), como estrategia ética de auto-determinación y liberación de las formas rígidas de la subjetividad. En última instancia, se querrá mostrar cómo todo el proyecto político de la insurrección stirneriana se basa en un anarquismo ontológico que rechaza la lógica teleocrática del racionalismo moderno y pone en entredicho la misma noción de realización.

The aim of this article to outline a political theory of insurrection in Max Stirner’s thought as an ethical and political alternative to revolution. I will show that revolution is ultimately a failed strategy of emancipation as it does not free the individual from the forms of subjectivity that keep her dependent on power. Insurrection, on the other hand, can be seen as a rejection of the identities and roles that discipline the individual. In this regard, special attention will be paid to the Stirnerian concept of Eigenheit as an ethical strategy of self-determination and liberation from rigid forms of subjectivity. Ultimately, I will show how the whole political project of the Stirnerian insurrection is based on an ontological anarchism that rejects the teleocratic logic of modern rationalism and calls into question the very notion of realization.