bluuebunny/crossref_metadata_2025 huggingface dataset:
Eleventh Year Mathematics Outline
Authors: Reeve W. D.
Published: January 2021

The Following Outline is based on the assumption that the function concept is the most important idea to be stressed throughout the eleventh year. Instead of beginning the course with the traditional formal review of the ninth year mathematics, the function idea is introduced at once through variation and formulas. Without doubt the fundamental principles of algebra will need to be reviewed, but only as needed in connection with a study of the topics listed in the outline.
An Experiment with the Mathematics of the Eleventh Year
Authors: B. Orleans Joseph
Published: January 2021

T. Percy Nunn, in his Teaching of Algebra, says concerning the position of trigonometry1 "At present it is usual to teach both of these subjects (trigonometry and the calculus) distinct from the algebra and from one another. The reason is easily found. The professional mathematician interested chiefly in perfecting the technique of his subject finds it natural as well as most effective to take a special group of allied methods or allied problems and to develop them as far as he can without concerning himself too greatly about the practical value of his work. Now this systematic exploration of special parts of mathematics is, no doubt, of vital importance for the continued growth of the science. It does not, however, by any means follow that the branches of mathematics should be presented to beginners with the formal elaboration which is the inevitable mark of their treatment as separate subjects..... Taking the case of trigonometry, it becomes evident that the pupil's acquaintance with the tangent, sine, and cosine should begin in the region where arithmetic marches with elementary geometry. As soon as the symbols of the trigonometrical ratios are recognized as capable of entering into formulae and of being manipulated, they should be regarded as belonging to the vocabulary of algebra. There is, indeed, no principle except the invalid one of formal segregation upon which we can include the study of xn and of ax in the algebra course and exclude sin x or tan x. All alike are pieces of symbolism invented for the description and interpretation of facts of the external world. Each represents a typical kind of function. To each corresponds a specific form of curve which may be regarded as the graphic symbol of the function. Both algebra and trigonometry would gain by fusion: the former through an added variety and richness in the illustrations of its main themes; the latter by the removal of the excessive formalism which at present obscures its value and interest for the beginner."
Some Values of the Study of Mathematics
Authors: D. Campbell Alan
Published: January 2021

Probably you have all had experiences like the following. We were having a week of review in a class in algebra. I asked if the students had any questions. One boy asked, "What is this all about?" Another student asked, "What is the use of all this mathematics?"
Algebra and the Development of Reason
Authors: Langer Susanne K.
Published: January 2021

What I wish to say to you today is a general reflection on the subject of high-school algebra. As a layman both in mathematics and in secondary school teaching, I can speak only from two lay points of view—that of the pupil, which meets you at one end of your activity, and that of the philosopher, which you encounter at the other. Consequently I shall begin by talking about the futility and barren, ness of algebra, and end, I hope, by reviewing with you its importance, interess and charm. For it is a peculiarity of the subject that an uninitiate mind can usually see nothing in it but a dry, lifeless discipline, whereas the adept sees in it the apotheosis of human reason. The mean from the former outlook to the latter is your ministry.
An Experiment in Classification of Students in Mathematics
Authors: Taylor S. Helen
Published: January 2021

Beginning in the second semester, February, 1927, and Continuing through four years, the mathematics department of the University of Illinois undertook a study of the effects of classification of students according to their mathematical ability. Several other departments have been interested in the same general problem, but the experiment in mathematics has been more extensive than has any other. It has involved a large number of students and a correspondingly large number of instructors. The experiment has also been extended over a much longer period of time than is usual.
The Tetrahedron and Its Circumscribed Parallelepiped
Authors: Altshiller-Court Nathan
Published: January 2021

Gaspar Monge (1746-1818), like his protector and idol, the Great Napoleon, was a man of humble origin. Time has tarnished the glamor of the victories at Marengo and Austerlitz, and future generations may grow indifferent towards the name of the successful general. However, wisdom-loving humanity will forever cherish the name of Gaspar Monge not only as the father of descriptive geometry, as the great teacher of Poncelet, Brianchon, and Dupin, as the organizer of the famous Ecole Polytechnique, but also for his many brilliant contributions to solid geometry, which he loved—to the exclusion of plane geometry.
Drawing for Teachers of Solid Geometry
Authors: Bradshaw John W.
Published: January 2021

In earlier parts of this discussion1 we have been concerned with the picturing in oblique parallel projection of certain simple solids bounded by plane surfaces. In this part we shall continue the study with a consideration of the simplest curved surfaces, the right circular cylinder and the sphere. The Appendix on “Drawing” (pages 35- 39) of Document No. 108 of the College Entrance Examination Board on Geometry furnishes the outline; the following quotations are taken from this Document. References to figures are to the figures in that document, some of which are reproduced in this article.
An Attempt to Apply the Principles of Progressive Education to the Teaching of Geometry
Authors: Schnell Leroy H.
Published: January 2021

For some time teachers of mathematics have been verbalizing the ideals and principles of progressive education and at the same time have proceeded to conduct their teaching along conventional lines. No one familiar with the common practices of the classroom will deny the statement that instruction in mathematics has been largely concerned with subject matter acquisition, and the “mastery” of skills unconnected with their value and meaning in life situations. Nevertheless there are indications of a mild revolt against outworn methods in the teaching of mathematics. Furthermore there is increasing dissatisfaction with a curriculum unadjusted to the needs and abilities of the individual child. There is a growing conviction, that will sooner or later be translated into widespread action, that the mass instruction technique, with all it implies, is inimical to the best interests of the child.
A Play, “The Case of Matthew Mattix”
Authors: Smith Alice K.
Published: January 2021

Scene I. Living-room of the Work home. It is late in the afternoon of a spring day of the early 1930's.
Supplementary Projects: Procedure
Authors: Georges J. S.
Published: January 2021

In a previous paper1 the purpose of supplementary projects in mathematics was discussed. The present paper outlines a suggested procedure which teachers of mathematics may find useful in directing supplementary project work in their classes. The procedure was used successfully at the University High School, the University of Chicago, where for a number of years the author was in charge of supplementary project work in the department of mathematics.
The Incommensurables of Geometry
Authors: Browne E. T.
Published: January 2021

It is not known when man first began to count. Even the lower animals have a so-called number sense which enables them to distinguish certain numbers from others. For example, it is said that a crow can distinguish three from four; and as the German mathematician Hanckel puts it “Even a duck can count her young.” Certain it is that as far back as we have any records, man has known how to count. From this process of counting there arose the positive integers, or natural numbers.
Evaluating “The Mathematics Teacher”
Authors: McCullough Constance
Published: January 2021

The professional journal in the special subject matter fields has varied functions to perform in the service of education. It must endeavor to strike a balance between the professional and the scholarly interests of its subscribers. For the teacher it presents materials for classroom use and methods of teaching with a view to improving instructional procedures. By discussing the aims of education and the contribution of the particular subject to the fulfillment of them, it provides a guiding philosophy for the direction of the teacher's efforts, and a basis for curriculum construction and revision for those charged with supervisory or administrative responsibility.
Algebra as a Language
Authors: Sweedler Esther D.
Published: January 2021

Words, words and some more words—objectives to be attained in the teaching of mathematics—courage for truth, reverence, the will to perfection—so states the report of the Standing Committee on Mathematics. One of my colleagues remarked that the committee has taken the objectives for an airplane ride. How about getting down to earth?
Pierre-Simon Laplace
Authors: Sanford Vera
Published: January 2021

The work of Laplace is of such an advanced character that it is prudent in this sketch to concentrate on the details of his career and his character and to give only brief mention of his contributions to mathematics.
Abstracts of Recent Articles on Mathematical Topics in Other Periodicals
Authors: Lazar Nathan
Published: January 2021

1. Linn, Marguerite. An experimental comparison of two methods of teaching elementary algebra. School Science and Mathematics. 34: 9 3-5. December 1934.
The Congruence Theorems by a New Proof
Authors: Christofferson H. C.
Published: January 2021

A Recent Book * on professionalized geometry suggests that the congruence theorems can all be proved by the use of a construction postulate instead of the old superposition method. Aside from the philosophical arguments against superposition and the hypothetical constructions involved in the usual sequence, the chief objection to superposition seems to be a pedagogical one. Every theorem serves two functions: a pattern to be followed in proving other propositions, and a general law or principle which can itself be used in proving other propositions. Whatever value the proof by superposition may have as a pattern proof, must at once be destroyed since it is not a desirable method. In fact most teachers have had the experience of having a pupil try to prove exercises by superposition after he has been subjected to the use of superposition in the congruence theorems. The teacher has then been forced to advocate the abandonment of the superposition technique and the substitution of a technique more generally useful.
The Mathematics Laboratory–A Device for Vitalizing Mathematics
Authors: Ramseyer John A.
Published: January 2021

Mathematics as traditionally taught has met with considerable disfavor among educators and in many cases it has been found to be impracticable. While this may be true evidence does not point to any inherent weakness in mathematics itself. Rather, it has shown that mathematics is a very necessary part of our civilization and, as such, it rightfully deserves a place in the curriculum of our schools. Evidence does point, however, to the fact that the teaching of mathematics is at fault.
Reduction of Angles in Trigonometry
Authors: Dehn Edgar
Published: January 2021

I want to explain in this article a rule for reducing angles which I have used in my classes for many years.
The Future of Geometry
Authors: Joseph Margaret
Published: January 2021

Teachers of mathematics are often confronted with pupils asking, “Why should I study mathematics?” or “Where shall I ever use geometry?” Such statements made by pupils are easily answered by any mathematician; so are of little concern. The real problem lies in the criticism from adults, for many of our fellow teachers and executives believe that mathematics should have no place in the new curriculum. Just what should be taught in its place has not been determined, for their criticism is of the destructive type, not the constructive. It is only natural that every teacher should feel that his specialty is of importance, so regardless of all the unfavorable comments some people make about mathematics, I still feel that it should be studied by all pupils capable of doing high school work.
A Message from Honorary President H. E. Slaught
Authors: Slaught H. E.
Published: January 2021

Sixteen years ago when the National Committee disbanded, its inspired leader, the late Professor J. W. Young, expressed the hope that representatives of the hundred or more clubs and mathematical organizations in the high schools throughout the country, whose loyal cooperation has been so helpful to the Committee, the hope, I say, that these same workers and many others would band themselves together to perpetuate the spirit of that Committee's remarkable report.
The Social-Civic Contributions of Business Mathematics
Authors: Kinney Lucien B.
Published: January 2021

It has been recognized for some time that students who are being educated for business require some special training in mathematics. Commercial arithmetic was among the first of the so-called practical subjects to be introduced into our secondary schools. It still remains one of the most important of the commercial subjects, in terms of enrollment, in the public and private secondary schools. If it has not made the contributions to the total education of the pupil that might have been expected of it, it is because, in common with other secondary school subjects it has suffered from a failure to define the major purposes of the course in the proper relationship to the aims of all education. When we consider the function of mathematics in the commercial curriculum, our questions must be somewhat as follows:
Recent Changes in Point of View Relating to the Teaching of Arithmetic
Authors: Bond E. A.
Published: January 2021

In many school subjects tradition is being routed by scientific studies in education. The teaching of arithmetic is at present a most active field in a most active period of education. In 1924, Buswell and Judd summarized the investigations relating to the teaching of arithmetic that had been reported at that time. Since then, more than four times as many experiments have been made as were available at that time. Moreover, the rate of the appearance of investigations is still increasing. The findings of these studies have caused us, who work in this field, to reorganize our philosophy and our classroom procedure to be in conformity with the evidence that is now available. This reorganization has taken various forms. In the main, the reorganization in arithmetic has occurred along three lines, namely: the broadening of the aims, the selection of learning exercises because of their social use, and the arrangement of these exercises in the order of ease for learning. I want to examine with you those recent changes in point of view and in classroom practices that I judge most important.
Let's Check the Hypothesis
Authors: Olds Edwin G.
Published: January 2021

It is quite generally recognized that, while the world needs mathematics more and more, the schools teach it less and less. The principal reasons offered to explain the loss of popularity of mathematics as a school subject are that it is badly taught and that the teaching materials are poorly selected. The chief values claimed for mathematics by its supporters are its utility and its preeminence as a mode of thought.
Out of the Past
Authors: Florence Brooks Miller
Published: January 2021

As opportunities presented themselves, historical bits of information were inj ected into the program of a ninth grade algebra class. Among these were the development of our number system, and the use of mechanical devices, from very early times up to the present, to aid man in keeping track of things as well as to calculate.
The Art of Teaching
Authors: Morris Daniel Luzon
Published: January 2021

After a person has passed through the “discipline” of plane geometry, solid geometry, and trigonometry, he sometimes realizes the transcendent beauty of plane geometry. Why should he not realize this while he is learning it?
News Notes
Authors: Kelly Mary , Tiedeman H. G.
Published: January 2021

The annual open luncheon meeting sponsored jointly by the Association of Mathematics Chairmen and the Association of Teachers of Mathematics of New York City will be held on Saturday, March 12, 1938, at 12:30 P.M., at the Essex House, 160 Central Park South, New York City.
Editorials
Authors:   W.D.R.
Published: January 2021

We have repeatedly had letters from teachers of mathematics from various parts of the country who write somewhat as follows: “Since the high school library has now ordered The Mathematics Teacher, I wish to discontinue my subscription.” Now we realize that the main purpose of the magazine will be served if it is read and appreciated by teachers of mathematics whether they pay for membership in the National Council or not. However, just imagine what would happen to The National Council of Teachers of Mathematics if we all took that attitude. The official journal would have to close up its business and what little money the Council is able to save from subscriptions and the sale of yearbooks would no longer be available. This would mean that our annual meetings would cease and that we could no longer help to subsidize such important studies as the one that is now being made by The National Arithmetic Committee of which Professor R. L. Morton of Ohio University is Chairman. This Committee is entirely financed by the National Council. Moreover, the National Council has been largely responsible for starting the Joint Cmmnission of the Mathematical A ssociation of America and the National Council of Teachers of Mathematics on “The Place of Mathematics in Secondary Education.” The report of this Commission will constitute the Fourteenth Yearbook of the National Council in 1939.
The Art of Teaching
Authors: Richard Dickter M.
Published: January 2021

The problem of forgetting, particularly where specific skills are involved, is always a discouraging one. One teaches a unit of work, and, unless the skills learned in this unit are used in the next unit, the students forget them. That is always a pity, and becomes more than that if the skills learned earlier in the term are needed later in connection with new work. It is necessary to review periodically, and certainly just before a previously learned skill is to be used again. The efficacy of these periodic reviews is likewise problematical. Let us say that, during the review, the student regains his lost skill, but it is soon forgotten again unless used. Moreover, when the course of study is a crowded one, as is usually the case, it is difficult to spare the time for these reviews.
The Professional Preparation of Mathematics Teachers
Authors: Wren F. L.
Published: January 2021

What is a profession? What is meant by professional preparation? A profession is a calling or occupation in which one has acquired significant knowledge and information which he uses in the instruction, guidance, and service of his fellowman. There are two equally important aspects of any true profession, namely, significant knowledge and effective technique. One cannot be efficiently professional if there is any distinct weakness in either aspect. A truly functional program of professional preparation must therefore place emphasis on the acquiring of knowledge significant to a chosen profession and also on the acquaintance with and use of the more efficient techniques of that profession.
Shall We Accept the Two Years of Required Academic Mathematics as a Right, a Ritual, or a Challenge?
Authors: Sumner Ruth G.
Published: January 2021

To present this question to a meeting of this kind seems rather like bearing coals to Newcastle. The mere fact that we have gathered here from all parts of the United States is in itself an answer to the question as far as you and I are concerned. That year after year these meetings are possible is because of our one interest in common, namely mathematics, and surely this is indicative of the fact that we have felt the challenge and are seeking an answer. Relatively speaking, however, we are a very small portion of that great body of teachers of mathematics. This brings us to the question, are we content to sit back and do nothing after having felt the challenge? To ask that question is more or less like the old darky camp meeting song with its repetition of “Has you been redeemed? Has you been redeemed?” and the every ready response, “Yas Lawd.” We have come to this camp meeting either because we are seeking the light or because we have been redeemed or think we have. But have we? I wonder how many of us are active converts and how many are merely passive onlookers. The trouble is that just as the newly made convert either must take an active interest in his church or he is apt to fall from grace, so with us we either go forward or we fall back into old practices. That is one of the laws of human nature. I sometimes wonder how many of us, the lay members of our profession, are content to go through the exhilaration of being led to see the light only to drop back into the old rut once more. We forget the temporary thrill we received until the next camp meeting and then once more seek the mercy seat with the same lack of change. It becomes a rhythmic cycle of repentance and back sliding which is repeated over and over again.
The Art of Teaching: Analytic Geometry and Trigonometry in Second Year Algebra
Authors: Gottschalk Winston M.
Published: January 2021

ln preparatory school the modern trend is to begin geometry in the latter half of the second year, finishing algebra in the third year. In smaller schools such as ours a student sometimes takes geometry and second year algebra simultaneously. Such arrangements give a welcome opportunity to bring out the union of the two subjects in analytic geometry. My experience has been that such procedure is easily carried out and that the interest of the students is aroused. Then, too, certain phases of both subject are given meaning and the student is prepared for the geometric illustrations of annlysis, so helpful in studying calculus.
The Value of Simplification
Authors: Ely E. E.
Published: January 2021

An Excellent article in the November issue, by Professor Davis, concludes with the surprising remark, “We hope you will not break faith with us (the teachers of science) by making your mathematics courses so easy that they mean nothing.” The surprise is engendered by the fact that the article shows to what extent mathematics has been made meaningless by too much complexity, too much undigested matter, too much practice on routine problems, and far too little attention to the derivation and meaning of the formulas which the pupils are allowed to copy instead of deriving those formulas for themselves.
Two Important Deliberative Reports Concerned with Mathematics in the Schools
Authors: Douglass Harl R.
Published: January 2021

It is rare indeed that in any year there would appear two deliberative reports of national committees in any field as challenging as “Mathematics in General Education”1 and “The Place of Mathematics in Secondary Education.”2
The American Way of Thinking About the Value of Mathematics as Revealed by Ten of Our Great Leaders
Authors: Schreiber Edwin W.
Published: January 2021

Benjamin Franklin (1706-1709), American statesman, printer and physicist:
What Specialized Knowledge Should the Teacher Training Program Provide in the Field of Geometry?
Authors: Edwards P. D.
Published: January 2021

The answer to the question above is of course dependent on the amount of time allowed for the study of geometry. I shall discuss the courses which we offer at Ball State Teachers College and the objectives in each course.
What Price Enrichment?
Authors: Hassler J. O.
Published: January 2021

Many words have invaded our national educational domain in recent times like fifth columnists to entice us, disarm us, and in every way cripple us in our national preparedness campaign against ignorance and inefficiency. One of these is the word enrich, with its breed of derivatives like enriched, enrichment, etc. It is a sweet sounding word. When rolled under the tongue of an enthusiastic representative of “Progressive Education,” it has had marvelous effect. We have become attached to it and have welcomed it into our educational literature. Webster gives two definitions: (1) To increase the value of, and (2) to adorn or make more ornamental. We have had enriched curricula, enrichment programs, and what not. Some produce increased values. Some just adorn. It is my purpose to point out what I consider some “disenriched” and disastrous consequences of our short sighted friendliness with this seductive invader.
Teaching the Laws of Algebra, or Mathematics Is a Language
Authors: Denbow Carl
Published: January 2021

In recent years the old definition-ruledrill method of teaching algebra has given way. The concise, deductive systems inspired by Euclid have been “kicked upstairs” to the college or post-graduate level.
Service of Mathematics to Nurses
Authors: Hendricks Adeline
Published: January 2021

Before talking directly on the subject assigned me, I believe I should briefly outline the growth of nursing education in the United States of America.
“Lord, Deliver Us from Our Friends”
Authors: Seidlin Joseph
Published: January 2021

The place of Mathematics in the curricula of our secondary schools has been variously defended and attacked. In other words, mathematics has “friends” as well as “enemies.” It seems that the cause of mathematics suffers more from the attempts of some of its friends to save it, than from the attempts of some of its enemies to destroy it.
The Art Of Teaching: You Can Make Them
Authors: Larson Clara O.
Published: January 2021

To handle things or to touch them gives a significance and concreteness that no amount of looking, drawing or thinking can give. For optional work in my plane geometry classes some of the boys made models, some from old erector sets and some from wood.
The High School Training Most Desirable for Prospective Students of Engineering
Authors: Fort Tomlinson
Published: January 2021

The dilemma in which this stalwart son of Italy found himself need never be confronted by the teacher of secondary school mathematics so far as the training of prospective students of engineering is concerned. It is my belief that the mathematics to be taught to the would-be engineer is substantially the same as that to be taught to anybody else and we are not confronted by the necessity of neglecting our engineers in order to rater to the wants of some other substantial group of students.
Vitalizing Junior High School Mathematics for Non-College Students
Authors: Rogers Mary
Published: January 2021

It is interesting to note that in contrast to the now apparent decrease in Elementary School enrollments, our Seccondary Schools continue to grow. Statistics show an increase of nearly 2,000,000 pupils during the past decade, to an all time high of 6,650,000 in 1940-41. We are told that the tendency for an increasingly large proportion of our young people to remain in school through the Senior High School will doubtless maintain this high enrollment for some time to come.
The Reorganization of Mathematics for the Emergency
Authors: Kinney L. B.
Published: January 2021

With mathematics heading the list of requirements for almost every function connected with the emergency, there are few who question the significance of that field. The potential contributions of mathematics are clearly recognized, and immediate results demanded. The responsibility for seeing the problem as a whole, and defining the present role of mathematics in the educational program, falls directly on those interested in the teaching of mathematics.
A Study of Weights and Measures(Another View)
Authors: Johnson J. T.
Published: January 2021

The article on “A Study of Weights and Measures” by Gertrude Cushing Yorke in the March issue of The Mathematics Teacher deserves an answer as it contains statements that may mislead those not familiar with the metric system —its advantages and its progress.
Enriching Plane Geometry with Air Navigation
Authors: Schor Harry
Published: January 2021

Dead reckoning leans heavily on the theorems and constructions of plane geometry. The connection between the two is, however, rarely emphasized. It is the opinion of this author that the teacher of plane geometry can use the problems of dead reckoning to enrich his course and help prepare his students for the air age. Many of the following suggestions can be used in the classroom, others in the Mathematics Club.
The Art of Teaching: Functioning Mathematics
Authors: Altwerger Samuel I.
Published: January 2021

High school students and graduates in increasing numbers read technical manuals, pamphlets, periodicals, and handbooks. Much of this material contains a substantial amount of mathematics and references to mathematics. Yet the mathematical education, even a four years education, in the secondary school has been and is insufficient to meet their needs. The war has brought this sharply to our attention.
Some Thoughts on Placing the Decimal Point in Quotients
Authors: Brown Claude H.
Published: January 2021

Teachers of arithmetic, writers of arithmetic textbooks, and writers of books on the teaching of arithmetic agree that pupils should be taught to solve multiplication problems which involve decimals by multiplying as with integers and then pointing off a number of decimal places in the product equal to the sum of the number of decimal places in the multiplier and the multiplicand. There is also general recognition of the fact that division is the inverse of multiplication.
Arithmetic Achievement of Japanese-Americans
Authors: Pusey Harriet C.
Published: January 2021

There appears to be a general impression that Americans of Japanese ancestry possess unusual aptitude for mathematics. The impression also persists that while students in our schools of this ancestry excel in fundamentals or routine mathematics, they are slow thinkers, therefore, fall behind other American students in reasoning ability.
The Irrationality of √2
Authors: Eves Howard
Published: January 2021

One of the milestones in elementary mathematics is the establishment of the existence of irrational numbers. This is usually accomplished by showing that there exists no rational number x such that x2 = 2, thus proving that √2 is irrational. This particular irrational, the discovery of which is ascribed to the early Pythagoreans, was perhaps the first irrational number to be known, and probably arose in considering the ratio of a diagonal to a side of a square.
General Mathematics
Authors: Tobey William S.
Published: January 2021

During the past four or five years volumes have been written on the reasons for adding general mathematics to the curriculum. Much has been written in general terms on the content of such courses. We are making little progress. We have had years of war with its emphasis on the need for mathematics but relatively little of a fundamental nature has been accomplished. There appears to be a lack of understanding of what needs to be done and how to do it. We have theorized too long. We set up goals and objectives, and then more goals, but just what to do, and how to go about doing it is seldom treated. It is time, yes past time, that we start doing something. Even though we do poorly and make many and serious mistakes we will have created possibilities for correction and improvement. All things must have beginnings and only after a thing exists can it be modified and improved. In our system we began some seventeen years ago to blunder along in an uncharted field, toiling in the belief that with constant analysis of our work we could improve.
The Art of Teaching: A Practical Project in Geometry
Authors: Springsteen Fanny
Published: January 2021

Perhaps one effect of our Pre-induction courses of recent years will be the restoration of mathematics to its rightful place in the school curriculum. In the decade before the War we certainly swung to the far extreme from the spirit of Plato who, more than 2000 years ago founded his Academy in Athens and over the door placed this challenge, “Let None Ignorant of Geometry Enter Here.”
Some Remarks on Air Navigation with Their Implications for Mathematics Teaching
Authors: Rosenbaum Lt. Robert A.
Published: January 2021

The substance of this article was presented as a talk to the Oregon Council of Teachers of Mathematics some time ago. The Okinawa campaign interfered with the preparation of the manuscript in a form suitable for publication; and, by now, many of the illustrations are “ancient history.” The development of loran, for example, is sure to revolutionize navigation and to outmode several of the techniques mentioned in this paper. However, it is not the present purpose to describe modern air navigation; rather is it the aim to discuss a phase of interest to mathematics teachers resulting from the following circumstance: because of the great demand for aerial navigators during the war, it was impossible to choose only those with a mathematical or scientific background for training, even if it had been considered desirable to do so. On the whole, the men whom the Navy used as navigators were intelligent and well-educated, with no special intellectual qualifications which might make them seem natural choices for the job. Their mathematical abilities and training probably approximated the average of college graduates in the U. S. Hence, observations made on this group may be relevant to a discussion of how our schools’ training in mathematics stands up under a “practical” test, and of what features of the training need more emphasis, to judge by shortcomings discovered in the performances of navigators.
Suggestions for Efficiency in Teaching Arithmetic
Authors: Hill Floyd C. , Miller John M.
Published: January 2021

The fact is generally accepted by educators that arithmetic is taught in public schools today for two general primary purposes, namely: (1) to enable future citizens to carry on the business of the everyday world and (2) to do it with the highest degree of efficiency attainable. Our everyday world may be the household of the housewife or it may be the complicated transactions of big business. In either case, the objectives are the same— accurate results in the most efficient manner possible.
Mathematics in a Retail Business
Authors: Stephenson E. C.
Published: January 2021

I have listened with great interest and respect to the discussions of Dr. Jacobson, Mr. Carlton and Mr. Schilling. Truly the adventures into higher mathematics to meet the engineering needs of industry, are of paramount importance to the creation of better products for the use of both producer and consumer.
Let's Do Something for the Gifted in Mathematics
Authors: Johnson Donovan A.
Published: January 2021

For decades educators have insisted on the importance of providing an adequate educational program for the gifted. However, the application of this program in the mathematics classroom has usually been neglected or sporadic. The increasingly critical need for trained scientists no longer permits us to be lackadaisical in using a most precious human resource, the mathematically gifted student.
Devices for a Mathematics Laboratory
Authors: Berger Emil J.
Published: January 2021

Anyone who has a learning device which he would like to share with fellow teachers is invited to send this department a description and drawing for publication. Or if that seems too time-consuming, simply pack up the device and mail it. We will be glad to originate the necessary drawings and write an appropriate description. All devices submitted will be returned as soon as possible. Send all communications to Emil J. Berger, Monroe High School, St. Paul. Minnesota.
Statistical Training for Secondary Schools
Authors: Moonan William J.
Published: January 2021

Before we embark upon a discussion of the role of statistics and the statistical method in the curriculum of secondary schools, it is necessary that we have a mutual understanding of certain terms and concepts. In view of the fact that “statistics” means many things to many people, a definition will be proposed so that a basis for discussion may be shared.
A geometric approach to field-goal kicking
Authors: Rising Gerald R.
Published: January 2021

When should a team take a five-yard penalty to get a better angle for kicking a field goal? Here is an interesting use of a well-known geometry theorem.
What is Going On in Your School?: A geometry project at Thornton Township High School
Authors: Harms Ruth J.
Published: January 2021

Some time ago a short paragraph in The Mathematics Teacher about the book, The River Mathematics,1 and its accompanying chart started me seriously thinking about how our classroom could help develop more appreciation for our mathematical heritage. I was hopeful of finding talented art students who were also interested in mathematics and who might enjoy giving our room a bit of atmosphere.
Devices for the Mathematics Classroom: A multi-model demonstration board
Authors: Johnson Donovan A.
Published: January 2021

A versatile demonstration board can be yours for less than $2. And better yet no construction work is required. Buy a piece of hookboard 30 inches square from your local lumberyard or mail-order house. It will cost about 20 cents per square foot. These hookboards have evenly spaced holes in both rows and columns at one-inch intervals.
Notes from the Washington Office: Millions of pages for mathematics education
Authors: Ahrendt M. H.
Published: January 2021

Recently the Publications Division of the NEA, in preparing its annual report, asked us to calculate the number of pages published by The National Council of Teachers of Mathematics during the fiscal year, June 1, 1954 through May 31, 1955. The results of our calculation, given below, rather surprised us. They may interest you too.
Prediction of success in elementary algebra
Authors: Shaw Geraldine Sax
Published: January 2021

An account of the experiences that one school gained while trying to answer the ever-present question, “Who should take algebra?”
What is Going On in Your School?
Authors: Roethig Carl D.
Published: January 2021

For months now, a lot. of publicity has been given to mathematics through the daily and periodical press. Schools have been taken to task for inferior curriculums, their limited offerings, and negligence in stimulating larger and more extensive enrollment. Students have been berated for their indifference toward mathematics and for shying away from studying any further than actually required.
National enrollments in high school mathematics
Authors: Brown Kenneth E.
Published: January 2021

This is a lesson in interpreting statistics of vital interest to those interested in our manpower shortage.
The Technical Manpower shortage— an answer from the high school
Authors: Cooper Theodore S.
Published: January 2021

A high school teacher with a variety of experiences in counseling, curriculum construction, and advising students gives his reactions to some of the pressures put on the high schools to modify their programs.
Historically Speaking,— Irrationals or incommensurables V: their admission to the realm of numbers
Authors: Jones Phillip S.
Published: January 2021

We have seen in earlier notes1 that incommensurable quantities were first discovered in geometric situations and were proved to exist by using the theory of evens and odds. As roots of equations, they were represented by symbols with which operations were performed, and they were approximated by rational numbers. Viete's and Descartes’ literal symbolism helped to free these numbers from what in one sense was a too close association with geometric and physical magnitude.
Mathematical Miscellanea: Roots and logarithms
Authors: Brown Elizabeth F.
Published: January 2021

Any root—integral, fractional, or decimal—of any real number may be found to any desired degree of accuracy by using only the processes of elementary arithmetic and the laws of exponents, not the binomial theorem or Horner's method. The process is self-correcting in that accidental errors are automatically eliminated.
Mathematics in the Junior High School: Teaching the formula for circle area
Authors: Jenkins Jen
Published: January 2021

To make the concept of the formula for the area of the circle an old and accepted one in the minds of gangling, trying-not-to-be-schooled junior high youngsters of today is the goal of many an arithmetic teacher. How far short of his goal he falls is shown in the blank stares the high school teacher faces when he asks his algebra class or geometry class to state the formula.
In What Operations in Arithmetic Should a Pupil be Required to Understand the Reasons for the Steps Taken? In What Operations Should Such a Requirement be Postponed to a Maturer Age?
Authors: Curtis A. M.
Published: January 2021

Our subject is in the form of a question demanding an answer. No definite answer can ever be given in the form of a rule to be followed in teaching children. Children differ so widely in natural aptitude and in rates of development that work adapted to one third of a grade of pupils is not suitable for the remainder of the grade.
concepto de castigo en H.L.A. Hart
Authors: Gragera Junco José Manuel
Published: January 2021

Con objeto de establecer las bases de un castigo penal justo, H.L.A. Hart propone una visión alternativa a las versiones tradicionales. El planteamiento de Hart muestra que los enfoques principales no han superado problemas de incuestionable importancia: la justificación moral del castigo penal y su aplicación justa. En este sentido, el trabajo de Hart se sitúa entre el consecuencialismo y el retribucionismo. De esta manera, si un castigo está justificado debe tener buenas consecuencias para la sociedad castigando sólo a quien lo merece. Finalmente, la propuesta de Hart conectará con su concepción del Derecho dando a los individuos las capacidades de guiar su propia vida con previsión, confianza, seguridad y libertad.

In order to establish the basis of a fair criminal punishment, H.L.A. Hart proposes an alternative view to the traditional versions. Hart’s approach shows that the main approaches have not overcome problems of unquestionable importance: the moral justification of criminal punishment and its fair application. In this sense, Hart’s work is between consequentialism and retributivism. In this way if a punishment is to be justified must have good consequences on society punishing only those who deserve it. Finally, Hart’s approach will connect with his own conception of law giving individuals the capacities to guide their own life with foresight, confidence, security and freedom.
Los verbos ‘sentir’ y ‘parecer’ en la obra Nada de Carmen Laforet y su traducción al italiano
Authors: Del Valle Cacela Verónica
Published: January 2021

En el presente trabajo trataremos la dificultad de traducción en italiano que pueden conllevar los verbos ‘sentir’ y ‘parecer’ pues la proximidad lingüística entre ambos idiomas puede suponer un obstáculo a la hora de representar los matices de ambos verbos ya que su frecuencia de uso hace que se encuentren en innumerables expresiones cuyo significado puede ser difícil de delimitar. Para conseguir nuestro objetivo, nos serviremos de la obra Nada de Carmen Laforet y de su última traducción realizada en italiano, de la que tenemos conocimiento, para acercarnos a las variantes de traducción de ambos verbos.

In the present article we shall be concerned with the difficulty of translating the Spanish verbs ‘sentir’ and 'parecer' into Italian since the linguistic proximity between both languages can be an obstacle when it comes to representing the nuances of both verbs. Their frequency of use makes them to be part in uncountable expressions whose meaning can be hard to define. To succeed in our pursuit, Nada by Carmen Laforet and the last translation made in Italian known to us will help us to approach the different translations of both verbs.
Estudio de la inteligencia emocional en escolares de educación primaria: Alcance en el área de educación física
Authors: Sánchez Ortega AG. , Chacón-Cuberos R.
Published: January 2021

La Inteligencia Emocional (IE) se puede considerar una habilidad para conseguir un aprendizaje más significativo, si se lleva a cabo durante los procesos de enseñanza-aprendizaje. Esto es así, ya que, por cada situación que aparezca en el aula durante los procesos de enseñanza, conlleva una o varias emociones desatadas por esas situaciones, y es aquí donde el docente puede reforzar de forma positiva y significativa las dimensiones de esa emoción u emociones surgidas. Tener equilibrio emocional significa tener un buen bienestar físico y mental, puesto que cuanto más saludables sean nuestras emociones, mejor nos vamos a sentir en diferentes situaciones diarias. Por otro lado, realizar una Actividad Física (AF) o cualquier deporte, es beneficioso para el bienestar físico y mental, ya que, realizar actividad física conlleva una serie de emociones positivas en los individuos que la practiquen. Al igual, que emociones positivas, la AF produce emociones negativas, por lo que hemos optado por reforzar y contrarrestar estas emociones durante la práctica de Educación Física (EF) en Educación Primaria, puesto que cuánto antes se redirijan estas emociones, mejor equilibrio emocional y mejor aprendizaje se va a conseguir, y como mejor que realizarlo a partir del área de EF, y promovido por un docente.

Emotional Intelligence (EI) can be considered an ability to achieve more meaningful learning, if carried out during the teaching-learning processes. This is so, since, for each situation that appears in the classroom during the teaching processes, it involves one or several emotions unleashed by those situations, and it is here that the teacher can positively and significantly reinforce the dimensions of that emotion or emotions arisen. Having emotional balance means having a good physical and mental well-being, since the healthier our emotions are, the better we will feel in different daily situations. On the other hand, performing a Physical Activity (AF) or any sport is beneficial for physical and mental well-being, since physical activity involves a series of positive emotions in the individuals who practice it. Like positive emotions, FA produces negative emotions, so we have chosen to reinforce and counteract these emotions during the practice of Physical Education (PE) in Primary Education, since the sooner these emotions are redirected, the better emotional balance and better learning is going to be achieved, and as better than to be done from the area of ​​EF, and promoted by a teacher.