bluuebunny/crossref_metadata_2025 huggingface dataset:
William James and Henri Poincaré
Authors: Ingraham M. H.
Published: January 2021

Mr. Chairman, Ladies and Gentlemen: A good many times today I have heard it said that we should emphasize in class those things that would interest the man in the street. I suppose that this is good doctrine. But if it is sound, it seems to me that our most important task is to find the right man in the street. Some years ago I succeeded in doing this to a marked degree here in Worcester. Between my sophomore and junior years in college I spent some time tramping in the White Mountains and on the way took the opportunity to see a little of New England. I had a very pleasant trolley trip starting from Hartford, including Springfield, Amherst, Northampton and ending here in Worcester. I had never been off the train in Worcester before and had only a few hours to stay. I knew nothing of the city except its population and the hours of a few departing trains. What should I see? What should T do? I went to the man in the street, the first policeman that I saw, and told him my plight. To my surprise he directed me to the Art Gallery. It was an unexpected answer but a very good one, for it is truly a gallery of which to be proud.
An Earlier Place for the Calculus in the Curriculum
Authors: Nordgaard Martin
Published: January 2021

The history of the mathematical curriculum is an interesting study. In colonial Harvard and Yale, algebra, geometry, and trigonometry were college disciplines; Latin and Greek were required for entrance; science had little place. At present, algebra and geometry are high school studies; Latin and Greek are often begun in college; the natural and social sciences are taken from high school freshman to college senior classes. A hundred years ago secondary school mathematics meant chiefly arithmetic, including such difficult topics as alligation, continued fractions, and circulating decimals. It was later realized that the student would gain more practical values and experience greater intellectual pleasure by omitting the more difficult portions of arithmetic, and in their place take the simpler parts of algebra and geometry; the new curriculum harmonized better with the student's capacity, adapted itself better to his experience, and formed a better basis for the courses in science that began to make their appearance in the college curriculum.
A Few Class-Room Devices to Stimulate Interest in Mathematics
Authors: Rabourn Sara B. F.
Published: January 2021

In the writer's capacity as supervisor of mathematics in the Fresno High School, many interesting plans and methods in the class-room have been brought to her attention; and it is the purpose of this paper to recount a few of the devices which teachers and writer have used on various occasions to stimulate an interest in mathematics.
Some Suggestions On the Technique of Teaching Plane Geometry
Authors: Cowley E. B.
Published: January 2021

Probably every experienced teacher who reads this article has his own method of teaching plane geometry, which he has been gradually developing for many years. In his own hands his method is something live, keen, and powerful. But if another were to attempt to take that method and use it just as it is, he would find it a dead and uselcsss thing. If anyone wants to make profitable use of the methods of another, he must transform them into harmonious accord with his own personality and the needs of his class. On the other hand, it may be quite worth while for us to hear other teachers discuss their methods; for, although we may have no desire to make any direct use of the plans set forth, a chance phrase may suggest to our minds a new line of attack upon some weak point or some obstinate difficulty in our own methods. It is with this thought in mind that I have written out this account, although I claim no particular merit for my methods.
Lest We Forget
Authors: Lindquist Theodore
Published: January 2021

In those days of project-problems, attempts at fascinating appeals to the pupils of our schools, as well as the rapid transit in the topics taught in our classes, may it not be worth our while to stop, look, and listen to find if we are not in the danger zone of forgetting some of the fine old golden principles that have stood the test of time. There will be no attempt to decry the good new things but to recall some of the good tried things lest these he forgot. Nor is even this idea of recalling good old standards new. The fine old gardens of our grandmothers are coming into their own again with the good old-fashioned “pineys,” phlox, snapdragons, mignonette, and so on.
An Attempt to Improve Computation
Authors: Potter Mary
Published: January 2021

“The bananas are 30c a dozen, 4 for a dime, or 8 for 20c,” the clerk at the little store at the summer resort informed me.
Civic Values in the study of Mathematics
Authors: Adams A.S.
Published: January 2021

At one time or another, we all have the question from parent or student or both as to just what the average student can expect to get out of the study of mathematics. As a brief, and necessarily incomplete, answer to this question, the following paper is offered. My thought has been to present facts and ideas which, while seeming to only touch the vital idealistic views of the subject which would appeal to the educator, will nevertheless mean something to the parent and student.
Understanding and Practice
Authors: Jablonower Joseph
Published: January 2021

We want our pupils to have thorough understanding of the subject which we are teaching. But thoroughness is au ideal of perfection and, like any ideal of perfection, it can be approximated only, approximated closely or crudely, according as we are more or less fortunate in our approach and in our treatment of the subject.
A Chapter on the Æsthetics of the Quadratic
Authors: Shaw J. B.
Published: January 2021

It may not have occurred to the student that mathematics is one of the fine arts, and exhibits the same characters as those we find in poetry, music, painting, and sculpture. The material or medium of mathematics is of a more subtle stuff than that used in the arts mentioned, for it is dealing with purely ideal or non-material objects. But it takes little reflection on the problem to see that we may find in every part of mathematics instances of the qualities that determine a work of art. The object of this chapter is to bring some of these to the notice of the student.
Technique and Devices Conductive to better teaching of Geometry
Authors: Blank Laura
Published: January 2021

The difficulties facing the teacher of plane geometry grow constantly more baffling. Enforced attendance at school until the boy or girl is sixteen, with a group of pupils often unfitted mentally, by environment, or by ambition for a high school education, presents an immediate and ever-looming problem. An insufficient number of trade schools or excessive ambition on the part of generous parents, desirous of seeing their children in the professions rather than in the trades, fills the classes of such a subject as plane geometry. Moreover the subject is generally required for college entrance, and is regarded almost universally as cultural, broadening, and conducive to mental development characterized by clear expression and logical thinking. The position of the teacher of this subject fifteen or twenty years ago when a select few with real ability pursued the subject was not nearly so complex. Now every youth who has managed to pass to the tenth grade and takes up plane geometry all but assumes that a passing understanding of the subject is his birthright. Perhaps it would be conceded that plane geometry is the first great obstacle to the youth's securing a coveted diploma. Or possibly it might be stated thus: it is in his attack upon this subject in which the frailty of his mental make-up is most in evidence, most pitilessly laid bare, if there is such weakness; or, on the other hand, his power of intellect is here first appreciated by others, and, with great satisfaction, by himself. Hence the instructor of plane geometry to-day who would teach the subject in a forceful and effective manner, developing his pupils, convincing them of its influence, its use and keen intellectual enjoyment, must be forever on his toes inventing and contriving devices and stratagems to teach satisfactorily this large group, less clever, less ambitious, less able, than heretofore, taken in the cross-section. What a wonderful people the citizens of the United States would be intellectually several generations hence if all who attempt a high school education really had the ambition and ability to master it.
Finding Plane Areas by Algebra
Authors: Reynolds Jos B.
Published: January 2021

The wide-awake teacher of mathematics is ever on the alert for opportunitics of vitalizing his subject. He has a keen eye on the lookout for applications which will bring the day's work for the pupil into relation with the field of experience, or which will make use of knowledge acquired in one field to further efforts in others. To some students applications of a subject or method outside of those found in the tmrt studied is a never-failing stimulus to renewed thought and effort. The beginning of a life of research is frequently to be found in such small revelations.
The Lesson of Dependence
Authors: Smith David Eugene
Published: January 2021

Notion of Dependence.-A child in the seventh school year learns how to find the circumference of a circle. He sees no particular reason for learning it; he does not use it, nor is it used in his home. If he enters certain types of industry, he will need it, but probably not otherwise. If his teacher connects it with the speedometer on his father's car, it immediately has some interest; and if it is similarly related to a bicycle, the interest is increased and the way is open to other applications that give reality to the abstract. If the law is expressed algebraically, he learns that c = 2πr, or c = 6.28r approximately, and the concrete again returns to the abstract. If he is told that this is merely a piece of shorthand, his interest is again awakenedawakened by the mystery of a name-he is writing a kind of shorthand, a universal language which is the same in France and Germany and Japan and all the civilized countries of the world.
Geometry Notes
Authors: Moriarty M. M.S.
Published: January 2021

These notes offer clearer statements of some propositions of plane geometry and more consistent treatments of others. They would put some propositions from required lists to exercises. And they look at “rotation-translation.”
Opportunities for Transfer making in Elementary Mathematics
Authors: Jablonower Joseph
Published: January 2021

The title of this article is somewhat misleading. If the article has merit at all, the merit is not in the scientifically established validity of its position. If the reader expects to find here a study of the claims of the different theories concerning transfer of function, he will be disappointed, and had better turn at once to the next article. No references are made here to correlation coefficients, although instances of probable error are frequent.
The Teaching of Proportion in Plane Geometry
Authors: Good Warren R. , Chipman Hope H.
Published: January 2021

The teaching of proportion offers such difficulties in plane geometry that many teachers of recognized excellence do unsatisfactory work in dealing with this topic. Textbook presentations show wide variation, and it is difficult to say which kind of treatment is better. From the books on the teaching of mathematics one expects help with the pedagogy and presentation of the various aspects of algebra and geometry. But the literature concerned with the teaching of ratio and proportion is pitifully meagre.
Stewart's Theorem, with Applications
Authors: Morris Richard
Published: January 2021

The writer will introduce this paper by quoting a sentence from Cajori's History of Mathematics. “While in France the school of G. Monge was creating Modern Geometry, efforts were made in England by Robert Simson (1687-176) and Matthew Stewart (1717-1785) to revive Greek Geometry. The latter was a pupil of Simson and was one of the two prominent mathematicians in Great Britain during the eighteenth century.” Dr. David Eugene Smith speaks of Euclid as the most influential text-book on mathematics ever written. We are grateful to these two men, Simson and Stewart, for their labors in the Renaissance of Geometry.
Generalization
Authors: Lytle Ernest B.
Published: January 2021

Generalization as a principle of teaching mathematics is often neglected. We are not thinking here of generalization as simply a process of passing from particulars to generals; rather we wish to consider that attitude of mind which continually gives attention to the relations and significance of facts. Learning is a continuous process, a growth, a development, a passing from one thing to something else. In the process of learning there must be concrete particulars; these particulars are the means to intellectual growth and form the material of which knowledge is made. But so long as they remain just isolated particulars they are of little value, they are mere excitations and possible irritations. To be of value these particulars must be related, organized, given meaning and significance. The mere encyclopaedic collection of facts is not our conception of valuable learning; rather it is the interpreting and application of facts, the relation and organization of facts, the careful study of the meaning and significance of particulars which rounds out and carries forward the learning process. This continual seeking for significance and organization is generalization.
The Functions of Intuitive and Demonstrative Geometry
Authors: Blank Laura
Published: January 2021

Intuitive geometry has been extensively emphasized and discussed in the last ten years usually in connection with general mathematics and the junior high school movement and but rarely in its relation to demonstrative geometry. It is useful and important, no so much so in itself, but rather in its connection with demonstrative geometry. Tbe pedagogical books and journals have stressed intuitive geometry emphatically whereas they have briefly discussed demonstrative geometry, due, no doubt, to the fact that the latter subject has held its own for twenty-three hundred years among the subjects of pursuit in a liberal education. What is meant by intuitive geometry? Have the two subjects much in common? What is the field of each? What is the aim, purpose, or objective in the pursuit of each? Where in the school curriculum is the place of each? Are they subjects that can be fused, then taught simultaneously or should they be taught successively? Can one replace the other? It is not my intention to answer each of these questions and put an emphasis of finality upon whatever answers are suggested.
Teaching the Verbal Problem in Intermediate Algebra
Authors: Rudman Barnet
Published: January 2021

None of the pitfalls of algebra is dreaded by the “average” pupil more than the verbal problem. In it he faces a veritable chaos—words, words, words—with no clue, no lead, no rule to show him the way out. And say what one may against the “rule” as a mathematical instrument one must credit it with giving the pupil a sense of security, a vehicle, as it were, to start him on his mental venture. It was no mere accident that the crossword puzzle, when in flower, had such a tremendous hold on the minds of both young and old. The originators of the puzzles were shrewd enough to supplement their problems with many helpful rules and numerous leads, thus achieving results that we, algebra teachers, had good reasons to envy. Equipped with a rule, even the inferior pupil will at least try to factor, or add, or multiply, or divide. He may misapply the rule and come to grief but he is spared a most depressing feeling, that of total helplessness.
Controversies on Mathematics between Wallis, Hobbes and Barrow
Authors: Cajori Florian
Published: January 2021

In the writings of John Wallis, Thomas Hobbes and Isaac Barrow, persons proficient in the dramatic art will find rich material for a mathematical tragedy or comedy. Hobbes, the aged philosopher superficially versed: in all fields human knowledge, presumes to show mere professors of mathematics that a philosopher from his wider outlook easily disposes of problems which had baffled mathematicians or ages-such problems as squaring the circle, trisection of an angle and the duplication of the cube. Wallis, young and ambitious, a highly trained mathematician and gifted also: in the power of satire and ridicule, demolishes Hobbes' geometric structure, leaving no stone unturned1. Barrow, the theologian and mathematician, assuming the position of a superior judge, takes under advisement the various mathematical views advanced by Hobbes and Wallis, and finds something to praise and much to criticise in the philosophy of both. Hobbes the septuagenarian emerges from the conflict battered and torn. Wallis shows little outward evidence of the struggle, but inwardly repents for the mass ridicule which he had heaped upon the aged philosopher; Wallis refuses to have hifi controversial articles against Hobbes included in his collected works. Such in crude outline is the material available for the dramatist. We note a few of the topics discussed by these distinguished seventeenth century thinkers.
The Use of Mathematical History in Teaching
Authors: Hassler J. O.
Published: January 2021

For several centuries subject matter was considered the only thing of importance in a course in mathematics. Then came a demand for the teaching of the applications of mathematics. Consequently there was written into our textbooks various types of applied problems. In the old order of things it was considered sufficient for the pupil to prove as an exercise-theorem that if the diagonals of a parallelogram are equal the figure is a rectangle. Now we suggest in connection with this exercise that a boy may test his accuracy in laying out a rectangular tennis court by measuring the diagonals. In more recent years we have also come to the realization that there is educational value in knowing the history of the subject; consequently we tell the pupil how and when the human race first discovered and proved this important fact about parallelograms with equal diagonals-or any other important and useful part of mathematics. So, in the last quarter of a century, we find the history of mathematics creeping into our high school textbooks. Let us consider then what value may be found in the history of mathematics, either in high school or college teaching, and how we may make use of mathematical history in teaching.
The Cultural Value of Mathematics
Authors: Rankin W. W.
Published: January 2021

Culture is an intelligent interest in the past, present, and future achievements of man. Surely there is no one who will say that culture is less than this.
Proving the Equkaity of the Base Angles of an Isosceles Triangle
Authors: Nyberg Joseph A.
Published: January 2021

In a recent paper (A Different Beginning for Plane Geometry, by H. C. Christofferson, MATHEMATICS TEACHER, Dec., 1928) much emphasis is placed on the fact that the existence of an angle bisector must be assumed in proving that tho base angles of an isosceles triangle are equal. Because of this assumption it is argued that, we could better begin by assuming triangles congruent if the corresponding sides are equal. The following is a proof of the equality of the base angles of an isosceles triangle without the use of tho angle bisector. Since the quqestion seems important I present the proof with some detail. Step 4 is the significant step.
Teaching Geometry into Its Rightful Place
Authors: Hassler J. O.
Published: January 2021

During the last ten years there has been much concern over geometry's losing its place in the high school curriculum and a consequent loss by high school pupils of a vital element in their educational training. Attacks by educationists on the hitherto impregnable position of geometry in the curriculum has drawn the fire of its ardent supporters. Organizations of teachers have sent out questionnaries to citizens in all walks of life to get evidence on the value of mathematics in their professions and business. Much has been written about the educational value of mathematical training. We have “boosted” mathematics to such a degree by saying nice things about it that a “highpowered” chamber of commerce might well take lessons of us.
A Mathematical Nightmare
Authors: Skerrett Josephine
Published: January 2021

As a member of the Mathematics Club, I do not come before you to solicit your membership. Instead, it is my purpose and intent to prepare your minds for the little sketch which will follow me.
Handling Problems in Arithmetic by Type
Authors: Moore Clark D.
Published: January 2021

Since it is a lamentable fact that pupils are not able to solve the variety of problems that is expected of them it behooves us to make an effort to enable them to do this. Every test and examination that we give show startling results, and we wonder if much of our teaching is not in vain.
Creating Interest in Mathematics through Special Topics
Authors: Hansen Lena B.
Published: January 2021

For a Number of years every student taking mathematics in our senior high school has been required to develop some special assignment in the form of a booklet or poster. To be up to date we are now calling these assignments "projects." At the close of the year the best of these are sent to our annual school exhibition. These projects have been the means of creating greater interest in mathematics without in any way lowering the standard for the regular work.
A Fallacy in Geometry Reasoning
Authors: Christofferson H. C.
Published: January 2021

In the mathematics teacher for December, 1928, I attempted to expose a weakness in the usual proofs of beginning geometry and advocated a new and slightly different beginning which at the same time bas the virtue of being more simple. The usual order of proofs is (1) congruence by side-angle-side; (2) congruence by angle-sideangle; (3) the theorem that the angles opposite the equal sides of an isosceles triangle are equal; (4) congruence by three sides; and (5) sometime later, the construction of an angle bisector and of an angle equal to a given angle. We are concerned here with only (3), (4), and (5).
The Slide Rule as a Check in Trignometry
Authors: Breckenridge Wm.E.
Published: January 2021

For some years the use of the slide rule as a check in trigonometry has been allowed in the Regents' Examinations of New York State provided that all the computation work appears on the answer paper. The State Education Department insists that the students of trigonometry be trained in the use of tables of natural and logarithmic functions. This training is tested by the requirement that all computation work appear on the answer paper. Having tested this part of the work, the Department encourages the student to check his work as any engineer would do-by the slide rule. The procedure is:

(1) Solve the triangle by logarithms.

(2) Check to 3 significant figures by the slide rule.

(3) If time allows, check to 5 significant figures by the usual logarithmic check or the check of natural functions.
The Value of Pupils ' Examination Papers to the Teacher
Authors: Orleans Joseph B.
Published: January 2021

For Many Years teachers have been composing examinations in algebra and in geometry and pupils have been writing the answers to the questions. For many years also the teachers have been permitting the pupils to look over the corrected papers and have been explaining to the class as a whole the errors made by the individuals, while the pupils have been trying to find out why the mark recorded in the upper left hand corner in red or in blue is not more than it happens to be. The teachers have religiously entered the marks in their rating books, in order to consult them most conscientiously in determining the numerical evaluation of the pupils' achievement at the end of the set marking periods in accordance with the regulations of the schools. Individual teachers have at times, no doubt, introduced innovations into their school routine and have tried to learn as much from the examinations as possible; but, in general, from the point of view both of the teacher and of the pupil the examinations have been useless gestures, i.e., as far as the use of the written papers is concerned as an integral part of the classroom work.
Individual Work in Plane Geometry
Authors: Zant Jas. H
Published: January 2021

In the October 1929 number of the Mathematics Teacher there appeared a report of individual work done in ninth grade algebra1. The following report may be of interest as a description of an attempt to teach plane geometry by an individual instruction method. It was used in the Russell High School of the Southeastern State Teachers College, Durant, Oklahoma during the winter and spring of 1927-28. The class used was composed of about twentyfive members which were all the pupils taking geometry in this particular school. The text book in use was the state adopted text of Oklahoma, Newell and Harper's Plane Geometry, published by RowPeterson and Company.
Thither Algebra
Authors: Stroup P.
Published: January 2021

The Recent Article by Mr. Betz is a classic of timeliness and wisdom. It arouses the faintly breathing hope that something may yet be done. Mark Twain's remark about the weather might well be applied to the situation in mathematics. There is still however an observation which is perhaps worth making. Our splendid physical prosperity must have some educational basis which is partially responsible for it. Now surely if there is a weakness in our present national development it is spiritual rather than material, it is in culture rather than in mechanical advances. So we are compelled to ask those who raise the cry that we have not taught mathematics efficiently enough just what they have a right to expect. They have set up certain expectations for various stages of mathematical development in the child and have been disappointed to test and find their expectations are not met. Perhaps they were optimistic rather than wise. The technical schools may claim all the credit but it still leaves nothing to complain about as far as the mechanical side of our celebrated prosperity is concerned. The thing that we need most to be concerned about is whether those that succeeded in mathematics furnished a smaller per cent of bootleggers and divorcees than those who failed. I have no statistics to offer but I have always pursued my work as a teacher of elementary algebra and geometry encouraged by the hope that if my students were led to think straighter in mathematics they would have a greater chance of leading useful happy lives. No one has come right out and said that the faulty teaching of algebra and the rest of the debatable high school subjects were responsible for the increase in crime except perhaps Henry Ford with his announcement of millions for education. His proposals do not sound feasible enough as a general solution to warrant our sitting back and waiting for his specifications for the reforming of our high schools.
Some Difficult Problems
Authors: A. Zeller Karl
Published: January 2021

If, As The writers of our year book would have us believe, it is certain that the schools of our day do not know how to teach arithmetic successfully; if our present day civilization is one which depends on the universal recognition of the importance of the idea of precision, since precision is the soul of science and commerce; if number is an ever guiding principle of life; if the number system has changed the life of men and is a mode of thinking that cultivates a general idea of regularity, arrangement and order in all thinking; if the number system, formulas of Algebra and Geometry have helped the race to organize and arrange the world in which we live; if mathematics is linked up with a large number of the branches of human knowledge; if every educated man or woman should know what mathematics means, what its greatest uses are, and something of its soul; if it enters into the making of a good citizen because of its value as a mental discipline; if the contact with absolute truth, the style of reasoning, the habit of rigorous thinking, the love for beauty develops transferable power for independent investigation and gives a keener insight into life; if these should emerge in the mind of the student, the conception of an ordered, lawful universe, a universe in which the reign of law is absolute; then these facts make the teaching of mathematics a problem that challenges our skill and study, and makes our work top the pinnacle of life service.
Human Elements in Mathematics
Authors: Browne E. T.
Published: January 2021

Some years ago when the proposal was made in a certain liberal arts college that mathematics be no longer a required subject, the professor of philosophy said to me:
Values of Primal Mathematical Concepts: a Picture
Authors: Durell Fletcher
Published: January 2021

The progress of mathematics during the past one hundred years or so has been characterized by two principal movements.
Mathematical Powers
Authors: Rankin W. W.
Published: January 2021

A Complete answer as to what constitutes mathematical ability awaits some unborn triadic genius, who is at once philosopher, psychologist, and mathematician. The mathematicians say, we think; the psychologist inquires, how do you think? the philosopher asks, what do you think? And still we await the triadic genius. In the meantime if our classification is mathematician, remember, we think; and furthermore we must keep it up while waiting for the unborn genius.
A Seventh Grade Mathematics Class Bank
Authors: Day Robertson Georgia
Published: January 2021

One of the variations from our regular classroom methods this year, which proved unusually interesting to both pupils and teacher, was our way of handling the unit in banking in the seventh grade of the Training School Junior High. Mathematics teachers, who are looking for schemes to quicken and lighten the steps of boys and girls on their way to the mathematics room, may be interested in our little device and it can be used without any equipment beyond the ordinary classroom.
Arithmetic in Teacher Training
Authors: Sueltz Ben
Published: January 2021

Except for the fact that arithmetic is a subject for study in all or nearly all of our elementary schools we perhaps would not be spending any of our valuable time in the teacher training institutions in preparing the neophyte teachers for the rather serious task of teaching arithmetic. Isn't it curious that arithmetic is being taught so prominently in our elementary levels of instruction? Have not we all heard reformers say that all the arithmetic needed by the average citizen can be learned in six months? Why then do we spend eleven and six-tenths per cent of the school time in grades one to six in the study of arithmetic? 1 The writer does not wish to enter fully into the arguments of this controversial question but in order to give an historical setting for the material which will be presented later, it seems wise to point out at this time that arithmetic was once considered too vulgar to be included in the elementary school curriculum. A fuller discussion of the beginnings of arithmetic as a school subject would show how our term arithmetic gradually came to include both ancient arithmetic (theoretical work with numbers) and logistic (practical calculation) and how for a long time the schools of non-commercial Europe looked at this study as one to be pursued by only that menial class of people who stooped so low as to gain a living through barter and commerce. Also an historical consideration would show how arithmetic grew in prominence and importance as the industrial revolution began to peacefully transform the point of view of the Western world from which we have taken our heritage of social institutions as well as of our physical beings.
In What Respects Should a Child at the End of a Year of Geometry Be Different from What He Was at the Beginning of the Year as a Result of the Training He Receives?
Authors: C. Byrne Margaret
Published: January 2021

A formidable title, is it not? And when you say “a child,” what child do you mean?—the child gifted in mathematics, the average, or the low I.Q.? And when you ask how he is to be different, do you mean “measurably different?” And when you append “as a result of the training he receives,” do you not really call for a systematic study of a geometry group and a control group?
Improving America's Mathematics
Authors: Barber Harry C.
Published: January 2021

I begin with a protest against a point of view. It is held in certain quarters that the way to improve America's mathematics is to go to the man in the street and to learn from him what mathematics he is using today, and then to teach that mathematics in school. The mathematics used by the ordinary citizen in the pursuit of his ordinary tasks is the mathematics to teach, and it is all the mathematics that ought to be taught, to the ordinary citizen. That sounds plausible does it not?
Practical Application of Mathematics to Engineering Problems
Authors: Cole Harry
Published: January 2021

As we look back in ancient times, we sometimes wonder how it was possible for the Romans to build that great aqueduct of Rome, their many beautiful and massive edifices, and the bridges in Italy and Gaul without the aid of mathematical analysis or formulas! The same, being true with all ancient culture, the Arabs, the Greeks, the Hindus, and the Chinese, with all their beautiful and massive structures, some of which are standing today, give us the feeling that their architects and engineers had the uncanny feeling of mathematical insight. Through the middle ages many buildings and engineering structures were erected partly with the aid of mathematics and partly with the knowledge and experience of great architects and builders, who certainly had a wonderful sense of proportion and a definite insight of the forces of nature without the reasons therefore. And yet the buildings and structures stand today as mute testimony of the wonderful capacity and ability of the engineers and builders of past ages.
Properties of Squares and Cubes of Arithmetical Numbers
Authors: Theobald John A.
Published: January 2021

Somewhat over a year ago a joke about an eccentric professor made the rounds of nearly every periodical and newspaper of the country. The joke told of a mathematics professor testifying in a police court as a witness of an auto accident. The professor could not remember the license number of the car, but he did remember that he had noted the peculiar coincidence that if the digits of the license number were reversed, and if this result were multiplied by 50, then the sum of the digits would be exactly equal to the cube root of this product.
A Course in Mathematics for Pupils Not Going to College
Authors: Mallory Virgil S.
Published: January 2021

Eight years ago I became interested in organizing a course in mathematics for two classes of pupils: those who elect no mathematics in high school and those who, having elected the regular work, soon find themselves beyond their depth. I am frank in confessing that the original motive was more a desire to improve the teaching of the better students than to aid those in the poorer group. The reasons that led me to do this were probably the same reasons that have led others to establish similar courses in many high schools throughout the United States.
Teaching the Locus Concept in Plane Geometry
Authors: Woodford E. B.
Published: January 2021

After a student has fully mastered a good definition of “locus,” and has solved correctly some fundamental locus problems, he will still have a surprisingly large amount of trouble with originals of this type. Feeling the need of a remedy for this situation, this writer has worked out a series of experiments which enable the student to visualize the required locus. He is then able to construct it with straightedge and compasses. The apparatus is intended as an aid in visualizing the locus and not as a method of construction, except in a few cases. The student should be encouraged to solve the problem experimentally only when he feels the need for experimentation.
Eliakim Hastings Moore
Authors: Smith David Eugene
Published: January 2021

In the death of Professor Moore the country lost a man whose influence upon mathematics and its presentation was more pronounced than is generally realized. Graduating at Yale (A.B., 1883; Ph.D., 1885), he pursued his studies in Berlin (1885-86), returning to accept a tutorship at Yale during the next two years followed by assistant professorship for the same length of time. In 1891 he went to Northwestern University as associate professor, and the following year he was called to Chicago as a professor, becoming the head of the department in 1896. He retired from his professorship in 1931.
Registration at the National Council Meeting
Authors: Schreiber Edwin W.
Published: January 2021

As the 1933 Annual Meeting of The National Council of Teachers of Mathematics at Minneapolis, Minnesota, approaches, the secretary is very anxious that the members, guests and visitors register properly. Four different colored registration cards are used to classify our registration.
Teaching and Learning
Authors: Orleans Joseph B. , Orleans Jacob S.
Published: January 2021

The purpose of teaching is to get pupils to learn. Yet we say that we learn only through learning. Teaching, therefore, means confronting the pupils with situations from which they learn, putting them through experiences which result in the modifications of behavior that we wish to produce.
One Unknown or Two?
Authors: Lazar Nathan
Published: January 2021

No topic in elementary algebra is as uniformly relegated to the second term's work as that of simultaneous equations. An examination of 28 textbooks in algebra tends to corroborate the above statement. Although the average number of pages is about 300, that topic appears on pages 225-275.* Assuming that teachers as a rule follow the order of the textbook used, we may safely infer that it is taken up towards the middle of the second term. Incidentally, the belief that the order of topics in a textbook is inviolate is an idea that it would be well to combat. There is more than one correct sequence, and even if we are bound for reasons of economy to the continued use of a certain textbook, we should not be wedded to its order for life.
The Banquet of Angles
Authors: Rosendahl Mary Kathryn
Published: January 2021

Such excitement! All the angles of Geometryville had been invited to a large banquet and the long expected evening had arrived. They came from all parts of the town, some from the corners of rooms and windows, some from the furniture, and some even from the drill pads. All the angles were seated about a huge table covered with many kinds of food. There were delicious triangles surrounded by line-segments, tempting squares of plane surface, many circles filled with arcs and even bisectors and perpendiculars. Everyone was laughing and having a wonderful time.
Alice in Numberland
Authors: Hedges Blanche B.
Published: January 2021

“What is 4 raised to the 4th power?”
Edmund Halley
Authors: Sanford Vera
Published: January 2021

Halley was the only son of a wealthy Londoner. He distinguished himself at St. Paul's School and when he entered Queen's College at Oxford in 1673 he was acquainted with Greek, Latin, and Hebrew. He later had occasion to study Arabic. He was greatly interested in astronomy and before he was twenty he sent to the Royal Society a treatise which had the title Direct and Geometrical Method of finding A phelia and Eccentricity of Planets.
Reading in Mathematics
Authors: Wattawa Virginia
Published: January 2021

Recent studies show that perhaps about twenty per cent of the failures in ninth year algebra may be attributed to the inability of the students to read their problems so as to understand them. What is not so commonly recognized is that the reading of all mathematics is not only harder than the reading involved in the study of non-mathematical subjects, but perhaps requires a special technique which has not been developed. Consequently children experience more difficulty in reading mathematics than teachers realize, for neither in the English classes nor in the mathematics classes does the average child receive adequate training in this type of reading.
Guillaume Francois Antoine de l'Hospital Marquis de St.-Mesme
Authors: Sanford Vera
Published: January 2021

L'Hospital1 seems to have been interested in mathematics from an early age. It is said, for instance, that when fifteen he solved a problem set by Pascal. He served for a time as a cavalry officer, but he soon resigned from the army and returned to Paris. There his money and social position gave him many advantages and he knew or corresponded with many of the mathematicians of his day. It was in a letter to L'Hospital that Leibniz gave his mathematical creed,-"One of the secrets of analysis consists in the characteristic, that is, in the art of skilful employment of the available signs, and you will observe, Sir, by the small enclosure that Vieta and Descartes have not known all the mysteries".2
Mathematics for the Slow Moving Pupil
Authors: Mallory Virgil S.
Published: January 2021

Education and its cost are being subjected to severe criticism and in many sections of the country leadership is in the hands of those who do not have a broad vision for our schools. The number of failures in our schools, their cost in dollars and cents, and more important the effect of failure on the psychology of the child—these things have been frequently studied but are still fertile fields for consideration. It is perfectly possible that one of the by-products of such studies will be an improvement in our teaching. At no point in our educational structure is there greater opportunity for such studies than in the teaching of mathematics. This is particularly true at the present time when our schools are over crowded with pupils who, because of economic conditions, cannot find work. It is further complicated because the problem of over age pupils in the elementary schools has been solved by promoting to the high school pupils whose only credentials for such promotion is their age.
Proofs of Sin (A+B) and Cos (A+B)
Authors: Nyberg Joseph A.
Published: January 2021

1. The proofs of the formulas for sin (A+B) and cos (A+B) in textbooks are interesting because of the way in which the authors have shown the generality of these formulas after proving them for acute angles. One text, for example, after giving the usual geometric proof for two acute angles merely states “The formulas hold true regardless of the size of the angles although the proofs above establish them only for the case where A+B lies between 0° and 90°.” Many of the texts of twenty years ago proved the formulas geometrically for the case where A+B is less than 180°, and then showed that the formulas were still true if A or B was increased by 90°, and hence the formulas were true for all cases.
Jean Bernoulli
Authors: Sanford Vera
Published: January 2021

The Bernoulli Family presents an interesting study in the inheritance of ability in mathematics. At least nine members of the group were conspicuous for this quality. In the first generation of these prominent scholars were Jacques Bernoulli (1654-1705) professor of mathematics at Basel, and Jean (1667-1748) professor at Groningen (1695-1705) and succeeding his brother Jacques at Basel (1705-1748).
Some Considerations Appertaining to the Content of High School Mathematics
Authors: Mirick Gordon R.
Published: January 2021

Recent years have witnessed a change in the content of courses in mathematics for the seventh, eighth and ninth grades. There has been a change not only in content but in the point of view in the teaching of the subject. A study of the mathematics courses offered to first-year students in our various colleges reveals two important changes. First, the elements of analytic geometry and of the calculus are introduced earlier, and second, there is much less emphasis on Euclidean solid geometry. Pupils who do not take this subject in high school often miss it in college, for the number of colleges offering a course in Euclidean solid geometry is fast diminishing.
Advanced Mathematics in the Secondary School
Authors: Beetle Ralph Dennison
Published: January 2021

In response to a widespread desire expressed by both colleges and schools that the courses in advanced mathematics be revised, the College Board has appointed a committee to act in the matter. Since this committee will endeavor to produce results satisfactory to the majority of the constituency which it represents, it behooves us, both individually and collectively, to formulate well-considered answers to the question: What is the most desirable content of the secondary school courses in advanced mathematics?
Mnemonic Devices—Old and New
Authors: Barkan Samuel H.
Published: January 2021

Although in the mathematics teaching of to day we stress reasoning and thought, we find it convenient sometimes to have our pupils memorize facts that are used frequently. To assist our pupils in retaining these facts, most teachers use devices of various sorts. May I mention a few of the most common tricks that I have used with success?
Mathematics: A Forgotten Subject in Present-Day Schools
Authors: Glover Ira Russell
Published: January 2021

It is apparent to anyone who looks into the matter that mathematics and the teaching of it in the United States are in a slump, and that conditions hold no promise of improvement. If the present unsatisfactory state of the subject were a new thing, we could hope that interest in it might revive with a general revival of economic prosperity and educational expansion. Such, however, is not the case; the decline has been gradual and extended, in fact, over more than a decade. Mathematics is being neglected—relegated to a position of secondary importance which it certainly does not merit—in secondary school curricula, and, to a slightly lesser degree, in that of the colleges. For all of this, a variety of reasons doubtlessly can be found.
Leonard Euler
Authors: Sanford Vera
Published: January 2021

The fact that Euler was born at Basel and died at St. Petersburg suggests a connection with the Bernoulli family.* This was the case. Euler's father had studied under Jacques Bernoulli, Euler studied under Jean. At the suggestion of Daniel and Nicholas Bernoulli, Catherine I of Russia invited Euler to come to St. Petersburg in 1727, and in 17 33, Euler succeeded Daniel Bernoulli as professor of mathematics in the Academy of Science there.
A Study of Prognosis of Probable Success in Algebra and in Geometry (continued)
Authors: Orleans Joseph B.
Published: January 2021

The specific ability test in algebra2 used in this study consists of a short preliminary part of thirteen questions in arithmetic, eleven short lessons, each followed by an exercise based on the lesson, and a summary test at the end. The topics covered in these lessons are the use of letters for numbers, the use and the meaning of the exponent, like and unlike terms, algebraic representation, signed numbers and the solution of simple problems.
Diagrams in Algebra
Authors: Dresden Arnold
Published: January 2021

The statement that “In geometry we prove things, in algebra we do things” represents a point of view not infrequently taken by young people who, after four years' study of mathematics in the high schools, have undertaken a period of further study in college. And woe to the teacher of college freshmen who attempts to extend to his college classes in freshman algebra the pernicious habit of persistently asking “Why?” Many of his students get hopelessly lost from the start.