bluuebunny/crossref_metadata_2025 huggingface dataset:
Classifying College Students on the Basis of Their Grades in Mathematics
Authors: Taylor S. Helen
Published: January 2021

More than two years ago we reported in the Mathematics Teacher on the progress of an experiment which was then going into its fifth year at the University of Illinois. At the time of the writing of that article, the future policy of the Department of Mathematics in regard to sectioning on the basis of previous grades in mathematics had not yet been determined. Many questions came to us as to the policy adopted and for that reason a more complete report was deemed advisable. No resume of the procedure can be given here as the report in the November, 1931 Mathematics Teacher, gave considerable detail. The results and conclusions are based on four years' work with sixty-six sections of analytic geometry under fifty-five instructors, only eleven instructors repeating in the analytics sections in the four years. Complete statistical data are given for more than fourteen hundred students with incomplete data on two hundred others. The policy of classification as adopted two years ago is now in force, so that the period of time during which such sectioning has been used is seven years.
The Problem of the Poorly Prepared Mathematics Teacher in Our Secondary Schools
Authors: Dawson Lester
Published: January 2021

So large a percentage of college freshmen who have taken all the mathematics the high school has to offer are poorly prepared to continue mathematics that one is moved to ask: “Why not demand well prepared mathematics teachers, if the subject is important enough to be taught?”
Weaknesses of High School Students Who Enter College Mathematics and a Suggested Remedy
Authors: Holroyd Ina E.
Published: January 2021

The subject assigned me was “Weaknesses of High-School Students Who Enter College Mathematics and a Suggested Remedy.” I should like to change this to read “A Few of the Weaknesses … and Suggested Remedies.” There are several remedies for the situation in which we find ourselves. One of the most important I shall venture to suggest before discussing the main topic.
Report of the Commission on Examinations in Mathematics to the College Entrance Examination Board
Authors: Reeve W. D.
Published: January 2021

The “Report of the Commission on Examinations in Mathematics” to the College Entrance Examination Board appearing on pages 154–166 of this issue of The Mathematics Teacher will be of particular interest to all teachers of secondary school mathematics.
Are We Teaching Arithmetic Effectively? A Summary of a Recent Study
Authors: Robinson Arthur E.
Published: January 2021

Arithmetic was introduced into the elementary school in 1548. For 400 years it has held a place of importance in the elementary school curriculum second only to that of reading. Yet in spite of its venerable age, the subject has at no time in its long history been subjected to such severe criticism as that of the past decade. A number of its most outspoken critics would stop little short of dismissing it, as a subject of formal instruction, from the elementary course. Others would let it remain but would insist that its materials be drastically modified and reorganized for the purpose of teaching it to elementary children. Still others would severely reduce its content and postpone the study of what remains to the later grades of the elementary school course.
Different Kinds of Equality
Authors: MacDuffee C. C.
Published: January 2021

When Thomas Jefferson suggested that all men were created free and equal, he raised two interesting questions. The first question, “What is freedom?” is at present being given some thought by the political scientists, so it seems only fair that we should do our part by attempting to answer the second question, “What is equality?”
The Organization of a Course in General Mathematics for the Seventh Grade
Authors: Lankford F. G.
Published: January 2021

During the session 1932–33 four of the seventh grade mathematics teachers in Albemarle County, Virginia, worked with the writer in organizing a general mathematics course for the seventh grade. The study was made possible through the cooperative arrangement existing between these schools and the department of education of the University of Virginia. Three projects were undertaken: First, a systematic and comprehensive analysis was made of the objectives of seventh grade mathematics as controls of content. Second, a catalog of seventh grade pupils' interests was compiled to serve as a point of departure in introducing the units of work to the pupils. Third, the difficulties of seventh grade pupils in common and decimal fractions were ascertained as a basis for remedial work. In its final form, the course contained ten units of work.
A New Deal in Geometry
Authors: Shanholt Henry H.
Published: January 2021

One of the most striking developments in the teaching of geometry in recent years is the change that is taking place in the philosophy underlying the purposes of the course. When we read (1) “Our great aim in the tenth year is to teach the nature of deductive proof and to furnish pupils with a model for an their life thinking”;1 (2) “We believe that geometry may be made the basis of the study of the methods of reasoning which will be of use in any field where the necessary facts are at hand”;2 and (3) “He (the pupil) sees a sequence of theorems built up into a logical system and he sees how this system is constructed, the result being a basis of proved statements which he can use for establishing further proofs, precisely as a lawyer proceeds to construct his case or a speaker to construct an argument,”3 we find that there is the stated objective, if not carried out in reality, which denotes a trend away from rote memory to the development of reasoning.
Report on the Training of Teachers of Mathematics
Authors: Moulton E. J.
Published: January 2021

Teachers of mathematics will be interested in a report on “The Training of Teachers of Mathematics” published in a recent issue of The American Mathematical Monthly.1 The report was prepared by a group of ten mathematicians serving as a Commission on the Training and Utilization of Advanced Students of Mathematics.2 In December, 1934, it was presented to the Trustees of the Mathematical Association of America by whom it was accepted and approved. The following excerpts from the report may serve to indicate its character.
Generalization as a Method in Teaching Mathematics
Authors: Winger R. M.
Published: January 2021

There is an extensive and rapidly growing literature on the teaching of high school mathematics. It is not the purpose of the present paper to comment on the sins of specific authors, but it may be remarked in passing that many of the current offerings seem inordinately dilute and that numerous doctrines which are exploited as modern and novel appear on closer scrutiny to be old familiar friends decked out in false whiskers and new wigs. One notes too the profusion of those terrible plurals so characteristic of recent pedagogical writing: “attitudes,” “skills,” “techniques,” “procedures,” “outcomes,” “appreciations,” even “understandings.”
Editorials
Authors:   W. D. R.
Published: January 2021

Those who believe that the importance of subject-matter training in mathematics and related fields as a part of the equipment of a teacher should read a recent report of the American Chemical Society's Committee on high school teaching of chemistry which was adopted unanimously at a recent meeting of the Council of the Society in Kansas City, Mo. The report charges that “the high school students now entering our universities and who have entered within the last ten years are much inferior in preparation in mathematics and other fundamental and basic courses to similar students of a generation ago, and the situation is tending, if possible, toward a worse condition.”
Modern Mathematics in Germany
Authors: Threlfall W.
Published: January 2021

Since I am speaking to you about modern German mathematics, I wish to call your attention to a most important subject, namely to the world which surrounds us, and to our scientific knowledge of its extent in space and time. There can be no doubt about the fact that this world we are living in is not the best of all possible worlds. Financial, industrial, and political dieases, you know them just as well on the other side of the great pond as we do on this side. Nevertheless in one respect we are living just now in a golden age. The world of science is in an excellent state and few eras have seen as important successes of mathematics and physics as ours.
News Notes
Authors: Tiedeman H. S.
Published: January 2021

The twenty-first annual meeting of the Mathematical Association of America will be held at Durham and Chapel Hill, North Carolina, on Thursday, December 31, 1936 and Friday, January 1, 1937, in conjunction with the meeting of the American Mathematical Society.
Some Remarks on Approximate Computation
Authors: Babb M. J.
Published: January 2021

It has generally happened in the past that teachers of elementary mathematics have had little or no acquaintance with what is generally called the higher mathematics. Even when a boy went to college he promptly forgot his elementary mathematics, and if by chance he became a teacher in the secondary schools there was no one to advise with him on means of applying what he had learned to the work in hand. Necessarily he drifted into the stereotyped manner of teaching the subject and his college work was only a pleasant memory. The college teachers were often recruited from men who naturally had very little knowledge of the problems of elementary education. Very few would have been able to grasp the point of view of the youthful mind: many were thoroughly ingrossed in their subject and had found ideals of rigidity of statement and proof as far beyond the ken of the elementary schools as they were in advance of the notions of those who intuitively founded the subject wiser than they knew.
Development of the Fundamental Ideas of the Differential Calculus
Authors: Graves G. H.
Published: January 2021

The purpose of this paper is to present the characteristic features of the different methods, by which the differential calculus has been introduced to students beginning the study of the subject.
Trends for Improving Instruction in Mathematics
Authors: Christofferson H. C.
Published: January 2021

Improving instruction in mathematics, the general subject for discussion, is a challenging title which suggests progressive and sane leadership and a constructive program of education. Sometimes the cure for a toothache is to pull the tooth, perhaps too a headache would be relieved by removing the head, orignition trouble in your automobile could be remedied forever by removing the motor. Some administrators would remedy the difficulties with our teaching of mathematics by eliminating mathematic from the curriculum. They would send a child out into this increasingly mathematical and scientific civilization with less and less mathematics and science.
A High School Course in Statistical Methods
Authors: Hausle Eugenie C.
Published: January 2021

When we speak of a course in statistics one usually thinks of a graduate course in some college and in the non-mathematical person it may even provoke a feeling of awe. Can such a course be given to secondary school pupils? The experiment was tried out at the James Monroe High School, New York City.
The Magic Clock
Authors: Heath Royal V.
Published: January 2021

Puzzle problems in elementary algebra generally revolve around the so-called “guessing” of a number.—You are asked to guess a number, then you are told to double it, triple it, or quadruple it, add some other number, subtract another one and so on until you begin to scratch your head.—Then, after you arc practically offguard—you are told what number you guessed.
Can Mathematicians and Educationists Cooperate?
Authors: Havighurst Robert J.
Published: January 2021

One of the promising things in recent educational history is the growing interest that college and university teachers have been taking in the teaching of mathematics at the secondary school level. As people are coming to realize, we arw in the midst of a reorganization of secondary school education that is of profound importance for the future of America. We are creating a program of general education for youth of secondary school age that is a uniquely American experiment. In such a significant venture it is extremely important that all the parties that have an interest in education should be aware of what is going on and active in directing the course of events. It is a good thing, therefore, that such an important group of the keepers of our cultural heritage as the mathematicians should be taking a hand in directing the reorganization of general education at the secondary level.
Mathematics and Intellectual Abilities
Authors: Baker Harry J.
Published: January 2021

Although your present speaker is not directly engaged in the problems of curriculum, he bas a very strong belief in the importance of mathematics and exact sciences in modern education. In passing, he merely wishes to note that we are living in a modern world requiring exactness, precision, split-second decisions, balance sheets that balance, and bridges that do not collapse. All of these considerations are related in practical ways to present-day education.
Calculating Machines and the Mathematics Teacher
Authors: Horton Evelyn M.
Published: January 2021

The field of the calculating machine is one which should be of interest to every mathematics teacher who is concerned with equipping the student with every possible device to cope with the present trend in complicated educational and commercial figuring.
The Importance of Certain Concepts and Laws of Logic for the Study and Teaching of Geometry
Authors: Lazar Nathan
Published: January 2021

That mathematics is in some way intimately bound up with logic has been recognized since the days of Euclid, who, without explicit formulation, utilized laws of logic in many of his indirect proofs. The important place that mathematics has occupied unchallenged for centuries in the curricula of secondary schools, colleges, and universities is undoubtedly due to an unconscious and unquestioning faith in the power of mathematics to train the mind in logical thinking in other branches of knowledge. With the rise of educational psychology in the beginning of the twentieth century, experimental evidence began to accumulate against the possibility of automatic transfer of training from one subject to another unless “identical elements” were present in both subjects.1 Whereupon a contrary reaction set in. The formulation of the “law of specificity of training” was surely one of the major causes that brought about, in the last decade, the decline of the prestige of mathematics as the irreplaceable preparation for clear thinking and logical reasonmg.
Deferred Arithmetic
Authors: Breuckner Leo J.
Published: January 2021

In this discussion I wish to differentiate between two aspects of the content of the arithmetic curriculum. One aspect may be designated as social arithmetic, which includes those learning experiences whose primary purpose it is to help the pupils to understand the functions and applications of numbers in the affairs of their daily lives and in activities of the community. In these activities the emphasis is on adding meaning and significance to is on adding meaning and significance to experience rather than on teaching pupils how to manipulate number processes. The other aspect of arithmetic may be designated as computational arithmetic. In this work the primary purpose is to present the number facts and processes in a systematic way for the purpose of developing skill in computation and number manipulation. In the ideal program these two aspects of arithmetic, the social and the computational, should supplement each other. However, it is commonly recognized today that in the past the tendency has clearly been to over-emphasize the formal computational aspect of the subject and to place relatively little stress on the social-informational functions of the subject.
The Nature and Place of Objectives in Teaching Geometry
Authors: Breslich E. R.
Published: January 2021

Mathematics in competition with other school subjects.—Up to the year 1910 the popularity of mathematics in the high schools of this country was on the increase. Not only was the number of pupils taking mathematics growing but, there was also a constant gain in the percentage of pupils in mathematics. In 1910 more than half of the pupils took algebra and about one-third took plane geometry. The increase took place in the face of a great deal of adverse criticism which often amounted to attacks on the subject.
The Art of Teaching
Authors: Dodson Norman E.
Published: January 2021

Pedagogically it may be profitable at times to sacrifice historical and independent presentation of topics in elementary mathematics. If better understanding and readier acceptance of a new topic can be secured by its presentation not as a separate and new topic, but as something discovered to help in handling some present problem or topic, it may be wise thus to present the new topic.
Mathematics in a Program of Progressive Education
Authors: Jablonower Joseph
Published: January 2021

It is probably not necessary, but since it may prove prudent to do so, I want, at the outset, to treat of the senses in which the term “progressive school” may be used, and to indicate the way in which I use it in the present brief discussion. I shall want next to indicate the manner in which the progressive school, as I define it, assumes the obligation to make certain investigations in ways of making the work in mathematics more significant to students and their communities. Finally, I shall make mention merely, since time allows no more than mention, of some of the ways in which schools have sought to meet this obligation.
The Coordination of the Teaching of Mathematics
Authors: Levy Sophia H.
Published: January 2021

In our complicated world of today, when mathematics is needed more than ever before, it is being taught less. The trend towards giving more and more practical courses in secondary schools has created a definite competition for the hours of the school day. Courses in commercial subjects, shop work, and social studies, among others, have been expanded and intensified, while courses in mathematics have been diluted, postponed, or sometimes left out of the program entirely. Mathematics is not at fault, nor are the teachers at fault. The results, as stated by mathematicians, to be attained by the study of the subject are worthy ones, but it is true that these desirable aims are not always being achieved. And since the fault is not with mathematics, it must either be in the content of the courses offered or else in the methods of teaching them. The goal of all teachers in the field should be so to enhance the contents of their courses and so to improve the methods of teaching them that the aims of the study of mathematics will be more clearly realized and that its value will be more generally appreciated. Through coordination of the teaching of mathematics these goals will be more readily attained.
Shall We Defer the Teaching of Algebra to the Tenth Year?*
Authors: Welch Harriet A.
Published: January 2021

In the April number of the monthly bulletin published by the California State Department of Education, there appeared the following statement: “Replies from 324 public high school principals establish that more than half of these institutions have moved algebra from the ninth to the tenth grade. Plane geometry is an eleventh year subject in more than a third of these schools; in some, it is even postponed to the twelfth year.”
The Art of Teaching: Teaching the Subtraction of Signed Numbers
Authors: Katra A. E.
Published: January 2021

Most textbook writers are agreed that the best way to introduce the addition of signed numbers is by the means of a horizontal or vertical scaled line. When the vertical line is used the direction upward is positive while downward is negative, and addition is carried out by placing a marker on the point of the line corresponding to one of the addends and then counting off as many units upwards or downwards as suggested by the other addend. The sum of the two addends is that number on the scaled line where the marker has stopped after the operation.
The National Council Meeting of Teachers of Mathematics Boston, Massachusetts, June 30, July 1, 1941
Authors: Woolsey Edith
Published: January 2021

Another summer meeting of the Council, the seventh convention in cooperation with the N. E. A., has been held and it was one of the most successful that we have had both from the point of view of the fine programs and also the large attendance. The Hotel Vendome served as headquarters for the meeting. The total registration was 324. They came from 33 states, Washington, D. C., and Hawaii.
The Art of Teaching: Classroom Practice in the Teaching of Everyday Mathematics I
Authors: Mejdak Raymond J.
Published: January 2021

Probably the hardest thing for the teacher of Mathematics is to get the nonmathematical-minded pupils to think mathematically. The teacher of Algebra knows how difficult it is for pupils to transfer arithmetical thought into algebraic thought. Likewise the teacher of Geometry, in his attempt to develop a logical sequence of thought in the minds of pupils, encounters much difficulty. The teacher of Everyday Mathematics is not immune from similar trouble. The teachers of Mathematics are constantly endeavoring to instill into the mind of pupils the principles that make for the development of the powers of reasoning.
Why Mathematics
Authors: Record Richard
Published: January 2021

The advantages of studying mathematics are many, and are so numerous and in some cases so subtle that one can scarcely recognize them. Mathematics is an exact science, an art, the beauty and value of which cannot be reckoned in terms of dollars and cents or any other exact standard by which we judge values today.
The Art Of Teaching: Teaching Logarithms
Authors: Harper J. P.
Published: January 2021

The importance and utility of logarithms cannot be denied by anyone who has any familiarity with them. However, the extent to which logarithms are used does not at all seem to compare to the advantage they hold over other methods of computation. Not many teachers of chemistry and physics, for example, in the colleges encourage their students to use logarithms where they would be of such great advantage as a time saver. Many students use logarithms in these courses but many more do not as they lack confidence in their ability to handle them and lack an understanding of the real significance of logarithms and hence continue to plod laboriously through the tedious processes of arithmetic division, multiplication and extraction of roots.
Mathematics in Present Day Industry
Authors: Kadushin J.
Published: January 2021

We are accustomed to thinking of mathematics as a formal theoretical science. As such, it is a most necessary tool for the physicist, the astronomer and other scientists engaged in profound scientific research.
Vitalizing Mathematics through Classroom Atmosphere
Authors: Heard Ida Mae
Published: January 2021

Have you tried “face lifting” on your mathematics classroom? We did and with most gratifying results.
A Proposal for Mathematics Education in the Secondary Schools of the United States
Authors: Reeve William D.
Published: January 2021

The fact that mathematics is so important is not surprising to one who is properly informed as to the contributions which it has made to the other great fields of knowledge, but many people, including some of our general educators, arc still unaware of the strategic place which mathematics really occupies in world affairs today. It should be the business of those of us who are interested primarily in the subject to help to make clear just where and how mathematics can be of real service to the other great branches of learning and what can be done to secure these services by a better teaching of mathematics in the schools. The war emergency has brought out the great importance of mathematics, but even a war is not enough to convince some people as to the value of mathematics in the education of American citizens.
Bobby Learns His Numerals
Authors: Potwine Elizabeth B.
Published: January 2021

The following scenes from the history of number were written for presentation by students of junior, and of first year senior, high school age. They do not pretend to give a complete account of the development of the number system. They were given in a twenty minute assembly period, and, for dramatic purposes, we chose to represent the characters as children of the age of the actors and to make the action swift rather than the treatment of the subject complete.
The Art of Teaching: A Mathematics Class Takes Music Lessons
Authors: Cronbach Lee J.
Published: January 2021

A Piano in a prominent place in the front of the geometry classroom rather astonished several classes at Fresno High School one day this spring. Their amazement grew as they perceived a table loaded with tuning forks, a sonometer, and a violin.
The Graphical Solution of Mixture Problems
Authors: Calvert Ralph
Published: January 2021

Recently while discussing the graphical solution of certain problems with a class in college algebra, the idea occurred to me that mixture problems might be solved in this manner. The following discussion is meant to serve only as an introduction for those who have not met this type of solution before.
Mathematics for Production and War
Authors: Whyburn William M.
Published: January 2021

The advent of the present war and its consequent demand for greatly accelerated production of the materials of peace and war has forcefully redirected many elements of the thinking of the American people. The highly technical character of the warfare and the complicated structure of the implements used have combined to create an urgent, if not emergency, demand for speedy, thorough, and widespread training in the fundamental mathematics which is basic in the construction and use of practically every tool of modern warfare. Young men entering any branch of armed service find that mastery of some mathematics is absolutely necessary for any work that is given them, and their usefulness in the service is directly proportional to the extent of their skill in the use of mathematics. Men and women with employment in the war industries are likewise confronted with the necessity of using this subject, at least through trigonometry, in almost any task that is assigned to them. Boys and girls looking to service either in the war industries or with the armed forces are advised that any proper preparation for such service must include mastery of as many basic mathematical skills as possible.
Early American Geometry
Authors: Jones Phillip S.
Published: January 2021

Prior to 1820 there were fourteen different books published in America which could be classified under the heading, “Works Dealing with Geometry and Mensuration” as shown in a bibliography recently published by L. C. Karpinski.1 Of this number, however, only three could be classified with what might be called demonstrative geometry, the rest being works in mensuration and surveying, such as “Hawney's Complete Measurer” (1801), the first book dealing with geometry printed in America.
A Grooved Mechanism
Authors: Yates Robert C.
Published: January 2021

In an article, You Can Make Them (Mathematics Teacher, April, 1942, pp. 182-3), Miss Clara 0. Larson lists a few devices as aids in the teaching of geometry. I wish to remark upon some unmentioned properties 0f several of these devices, not with the hope that my remarks may be transplanted directly into the high school classroom, but that they may serve to deepen the understanding of the teacher.
Basic Mathematics—A Key to Democracy
Authors: Mansfield Ralph
Published: January 2021

Many reasons have been advanced for the need of a universal language. The latest development advanced to meet this need is Basic English—a language based on 850 words and with no less a proponent than the Prime Minister of England. Among the many reasons given for the need of a universal language, the principal one is that such a language offers a common medium for the exchange of thought the world over, and through such a medium it may be possible to introduce democracy to many beleagured peoples.
The Art of Teaching: The Use of Models in the Teaching of Plane Geometry
Authors: Burns Frances M.
Published: January 2021

The use of models in the teaching of solid geometry has long been an accepted practice, but in plane geometry they have found little favor. Although not complicated by a third dimension, many of the relationships of plane geometry are difficult for beginning students to understand. The visual impression created by a model often clarifies the meaning of a proposition or leads to a generalization. The purpose of this article is not to present a case to justify their use, but rather to indicate some ways in which the writer's plane geometry classes have found them helpful.
Why Teach Mathematics?
Authors: Engen H. Van
Published: January 2021

During the past decade, certain areas in the curricula of the common school have been relatively static while other areas have been modified, in some cases, to the extreme. In the first few grades of the elementary school one finds numerous changes that have taken place and are still taking place. Many of these changes are indeed significant, particularly in arithmetic. In the middle elementary grades one finds a diminishing of the number and importance of the changes as compared with those of the lower grades. Again in the junior high school much has been done to adapt materials to the needs of the age. In mathematics adjustments have been made particularly at this level. Yet in spite of the fact that the mathematics of the junior high school has been modified to meet the needs of general education, one finds the attacks continuing, especially those directed at tenth grade mathematics which has not been altered as much as the ninth grade program.
Using Geometry in Algebra
Authors: White John H.
Published: January 2021

The recent demand for instruction in navigation has brought out the value of scale drawing in actual computation. In many instances it is possible to secure the answer to a navigation problem by scale drawing in a few minutes whereas calculation by means of logarithms would take much longer and would involve trigonometric manipulations beyond the grasp of the average student. It is true that the answer is not accurate to more than two significant figures, but a pilot seldom requires greater accuracy than this, and to him every second counts.
Changing Philosophies in the Teaching of Mathematics
Authors: Leskow Olive
Published: January 2021

“Mathematics, the schoolboy's horror, is perking up again after a long sabbatical in the educational doghouse.”1 This statement surveys the psychological trends of the teaching of mathematics in the past two centuries. Why was it the “schoolboy's horror”? Why was it in the “educational doghouse”? Why is mathematics again “perking up”? And, will it continue to “perk up” after the war? To answer these questions it is necessary to give thought to the errors of our predecessors so that we will not repeat the same errors and again shove mathematics into the doghouse.
The Solution of Simultaneous Linear Equations
Authors: Conkwright Nelson B. , Heide J. D.
Published: January 2021

The solution of simultaneous linear equations is frequently a cumbersome task, and many schemes have been devised for facilitating the computation. In the procedure to be described in this paper, the computation is limited to the evaluation of determinants of order two. The process developed is believed to offer several advantages not found in other methods.
Why Not Be Sensible About Meaning and Applications?
Authors: Bernard Walter
Published: January 2021

Several articles have been published recently in The Mathematics Teacher on the teaching of meaning. Two of these articles* appear to take opposite sides. Viewing the subject of meaning as a classroom teacher and a former engineer, I am of the opinion that the writers of these articles are both presenting theses of value to us who teach in the elementary and secondary schools. Now I am not stepping into the controversy between Buell and Wheat in the role of peacemaker. Perhaps by the time I am through this paper, both Buell and Wheat will be turning their guns, or pens, on me. I really believe that it is of the utmost importance that we should consider what part meaningful teaching should play in elementary and secondary mathematics.
The Rhumb Line on the Sphere
Authors: Hopkins Mildred
Published: January 2021

Pupils are sometimes interested in computing and comparing the great circle and the rhumb line distances between two arbitrary points on the earth's surface.
The Geometric Form as an Architectural Matrix
Authors: Salit Charles R.
Published: January 2021

Writers in architecture often muse over the origins of—what they prefer to call— certain architectural forms. These forms, according to a seeming consensus of opinion, came into existence by the grace and through the ingenuity of the local architect, he devised them, it is explained, in answer to some pressing demand to meet a specific need. Thus, in Auvergne, southeastern France, he invented coneshaped roofs so as the better to meet the weather conditions peculiar to that region. In the case of the Persian tomb towers, of the eleventh and twelfth centuries A.D., the architect, with no such utilitarian purpose in mind, experienced the inexplainable urge to copy the supposedly conelike tent of the desert nomad. And similarly the Egyptian pyramid, according to architectural writers, were the product of the attempt and travail by the local architects to build for the pharoah a glorious tomb. Some of these writers have even gone out on the limb and described how the pyramid idea was inadvertently discovered by the evidently aimless process of superimposing receding mastabas, as it is supposedly exemplified in the step pyramids of Sakkara and Medum. And so the Mayan pyramids on the American continent had likewise a more or less casual birth, without antecedents or breeding.
Continuous Transformations of Regular Solids
Authors: Baravalle H. v.
Published: January 2021

In the development of modern mathematics transformations of different kinds have gained increasing importance and many new concepts have been derived from their studies, for instance, the concept “Invariance of Functional Form.” From the point of view of mathematical education, transformations provide stimulating material for experimenting, investigating, and for exercises in visualization. In the following article, transformations of regular solids are carried out which have their bearing on crystallography as they keep the angles of the intersecting planes constant and vary their distances, the characteristics of the variations in crystal forms. Through these transformations, relationships between different kinds of solids will become manifest, for instance, between a tetrahedron and a cube, or between an octahedron and a rhombic dodecahedron. In some of the following transformations no less than five different regular and semi-regular solids evolve from one another in a continuous change. Constructions of descriptive geometry furnish the tools to draw the various solids.
Can We Prove 2 Plus 2 Equals 4?
Authors: Byrne Lee
Published: January 2021

As reports are circulating about one campus that no mathematician can prove that 2 plus 2 equals 4, it may be worth while to correct this impression. There are various known ways of formulating the foundations of arithmetic. No one of these formulations would be regarded as satisfactory, unless facts of addition could be proved in its terms, and “2 plus 2 equals 4” could serve as well as anything else to illustrate such a proof.
The Review versus the Telescoped Reteaching of the Work of Preceding Grades
Authors: Morton R. L.
Published: January 2021

Etymologically speaking, to review means to view again. But the second view may be the same view repeated or a different view. The Funk and Wagnalls dictionary calls a review “a second, repeated, or new view.” For teaching purposes, there is a vast difference between a repeated view and a new view. This difference concerns us here.
The Improvement of High School Mathematics Courses as Recommended by the Commission on Post-War Plans
Authors: Zant James H.
Published: January 2021

The Commission on Post-War Plans conceives the problem of improving mathematical instruction as one which should bethought of in its entirety, that is, from grades one through fourteen and not broken into fragments as has been done so often in the past. It is our opinion that the program throughout all of these grades is in need of a thoroughgoing reorganization and the Second Report of the Commission makes a number of specific recommendations which it hopes will be of aid in such a reorganization.
A Testing Program for Mathematics at the Secondary-School Level
Authors: Traxler Arthur E.
Published: January 2021

An important problem related to instruction in mathematics, as in every other subject field, is that of assessing accurately the aptitude and the achievement of individual pupils and of classes. There is imperative need for a teacher to be informed reliably concerning the ability of his students and concerning their mastery of the content of the subject being taught if he is to adapt his instruction to their varying levels, correct their weaknesses, predict their success in advanced courses, and afford them guidance in accordance with their predispositions, attainments, and functioning interests.
The Increasing Importance of Mathematics
Authors: _ _
Published: January 2021

We should like to present to you a point of view which may not have occurred to you before—namely that competence in mathematics widespread among our people is essential for the preservation of our society. Competence in mathematics is necessary not only for the mathematics specialist, but for every one of us who is an active citizen. America and the world are facing enormous problems of progress and survival which are technical in nature and requiring more mathematics from everyone than ever before. It is necessary for some of us to master highly technical mathematics which will be required to solve these problems, and for all of us to know enough mathematics to recognize the problems, to evaluate their importance, and to give support to those who actively endeavor to solve them.
Mathematics in Engineering
Authors: Schilling Robert
Published: January 2021

You have heard and read so much about the urgent need for more scientists, engineers, and mathematicians in our country that I do not need to add to the discussion of the present and future shortage. I am sure all of you want to help in educating more young people for these professions by increasing the interest of your students in mathematics. What you need most is not more statistics but material that you can use in explaining just how mathematics is used in industry and why it is becoming more important with every passing year. Such material I want to present to you here.
The Organization of Instruction in Arithmetic and Basic Mathematics in Selected Secondary Schools
Authors: Irvin Lee
Published: January 2021

During the school-year of 1951-52, the Southern Section of the California Mathematics Council sponsored a research project concerned with the offerings in arithmetic and other non-traditional mathematics courses at the high school level.1 The purpose of the project was two-fold: (1) to discover current practices which might be adapted for use in improving non-traditional mathematics courses at the secondary level and (2) to find bases for making recommendations for the reorganization of the high school mathematics program. The nature of the study, therefore, was that of “action research” such as was recently proposed by the Commission on Life Adjustment Education.
Mathematics Miscellanea
Authors: Jones Phillip S.
Published: January 2021

Many years ago I read an anecdote in which Betsy Ross was supposed to have objected to George Washington to six pointed stars in the proposed new American flag because of some connection with British insignia. When given the explanation that six pointed stars were easier to make, she replied by folding a piece of cloth or paper and with but one snip of her scissors cutting out a perfect five pointed star.
Notes on the History of Mathematics
Authors: Sanford Vera
Published: January 2021

There were three men named Sébastien LeClerc. Sébastien LeClerc the Elder was born in Metz in 1637 and died in Paris in 1714. He is said to have been engraver to Louis XIV. LeClerc's son and pupil Sébastien LeClerc the Younger (1676-1763) was a native of Paris. He was prominent as a painter and as a designer of tapestries. Sébastien Jacques LeClerc (1734-1789) called “LeClerc des Gobelins” was presumably of the same family. These three men were associated with the Hotel des Gobelins, an establishment which had been taken over by Louis XIV to make tapestries and furniture mainly for the court. The life of an artist connected with this institution was a reasonably secure one for the artist received a stipend and living quarters, but the restrictions imposed by those who directed the work must have made such an existence frustrating.
Modern Mathematics and the Gifted Student
Authors: Rees Mina
Published: January 2021

This paper is concerned with the world that confronts the gifted college student of mathematics upon graduation—a world in which employment opportunities are expanding, largely as a result of new emphases in certain fields of mathematical research since the end of World War II. In this article I will describe some of these fields of research, and I will try to indicate very briefly certain elementary aspects of the current activity in mathematics that might challenge the interest of gifted high-school boys and girls. Because I have been asked so frequently about opportunities for women, I shall point out certain mathematical careers in which women have been particularly successful.
The President's Page: Excerpts from a Report of a Committee of the Illinois Section of the M.A.A.
Authors: Mayor John R.
Published: January 2021

References to instances of and the desirability of cooperation between secondary school and college teachers of mathematics have appeared on this Page several times in the past eighteen months. The National Council wishes to encourage these activities in every way possible. As a means of doing this and, more importantly, of bringing to a wider audience some sound recommendations on this problem, this Page is given to excerpts from a Report of a committee of the Illinois Section of the Association. The Report was presented to the Illinois Section May 9, 1953. Members of the Committee which prepared the Report were: Franz E. Hohn, University of Illinois, Chairman; Mary Entsminger, Laboratory School, Southern Illinois University, Carbondale; Martha Hildebrandt, Proviso Township High School, Maywood; Alice Seybold, North Central College, Naperville; and Henry Swain, New Trier Township High School, Winnetka.
Notes from the Washington office: The National Council is big business
Authors: Ahrendt M. H.
Published: January 2021

It is likely that very few members of The National Council of Teachers of Mathematics have a real conception of how big and complex their organization is. If you compare the Council with many other similar organizations, you will realize that the Council is rapidly becoming “big business.” You may be interested in seeing part of our financial picture and learning how our funds are handled.
Mathematical Miscellanea: Statistics and baby chicks
Authors: Shuster John G.
Published: January 2021

Seventy-five years ago my grandfather shipped from Frenchtown what is considered to be the first shipment of baby chickens on record. The chickens went to California, and in spite of the distance only around 12% died. The baby chicken industry is now a multimillion-dollar industry.
Devices for a Mathematics Classroom: A paper model for solid geometry
Authors: Saupe Ethel
Published: January 2021

Anyone who has a learning aid which he would like to share with fellow teachers is invited to send this department a description and drawing for publication. 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.
Memorabilia Mathematica: The mysterious number PHI
Authors: Stephen Sister Marie
Published: January 2021

The imagination is the storehouse of forms received through the senses, the reproductive and creative instrument of man's great desires and dreams; a little bit of body—a little bit of spirit. This quality makes the education of the imagination a vital necessity in the preservation of the integrity of youth.
Mathematical Miscellanea: Odd and even—a game
Authors: Nygaard P. H.
Published: January 2021

There are two well-known mathematical recreations that start with a square framework consisting of three rows and three columns, each with three cells. In one of these the problem is to form a “Magic Square” by inserting into the spaces the digits 1 to 9 so that the sum in each row, column, and diagonal is exactly 15.
Points and Viewpoints: The National Council and the classroom teacher
Authors: Wilcox Marie S.
Published: January 2021

A column of unofficial comment
Devices for the Mathematics Classroom: Illustrating simple transformations
Authors: Koenen William
Published: January 2021

Described in this note is a device which may be used to illustrate several simple transformations that can be applied to mathematical functions.
An introduction to negative integers
Authors: Brumfiel Charles
Published: January 2021

A new algebra for the secondary schools will require new methods.
Tips for Beginners: Interpretation of the hypothesis in terms of the figure
Authors: Garstens Helen L.
Published: January 2021

It is frequently difficult for the beginning geometry student to interpret the facts of the hypothesis in terms of the figure for an exercise. A practice used extensively to assist the student with this difficulty, consists of marking, in likecolored chalk, those parts of the diagram either explicitly stated as equal or inferred so by definition. Thus if RC bisects angle R in Figure 1, the student may mark angle 1 and angle 2 with the same number of like-colored arcs, because “bisects” means to divide into two equal parts. The advantages of such a technique seem obvious enough. However, even when the student knows that “bisects” means to divide into two equal parts, he may err in choosing the correct equal parts in the figure. Thus in Figure 2, if BC is given as the bisector of DE, often the beginning student is uncertain as to which of the line segments, BC or DE, is bisected, or whether both are bisected I He may therefore, incorrectly mark BA equal to AC or mark all four segments equal, though he is aware of the correct definition of “bisect.”
What do we mean?
Authors: Rourke Robert E. K. , Rosskopf Myron F.
Published: January 2021

An examination of the meaning of (1) some key mathematical words frequently used in mathematics classes, and (2) some words not so frequently used but which are rapidly becoming known and used in secondary circles.
Historically Speaking,— From ancient China 'til today!
Authors: Jones Phillip S.
Published: January 2021

Sun-Tsu, a Chinese of the first century A.D., proposed the problem of finding a number which when divided by 3, 5, and 7 would give the remainders 2, 3, 2 respectively. He gave in verse a rule for this problem which is equivalent to saying that 23 +3.5.7 n is a solution for all integral values of n.
Reviews and evaluations
Authors: Crumley Richard D.
Published: January 2021

Calculus, Jack R. Britton, New York, Rinehart and Co., 1956. Cloth, xiv+584 pp., $6.50.