bluuebunny/crossref_metadata_2025 huggingface dataset:
Individual Instruction in Ninth Year Algebra
Authors: Stokes C. N.
Published: January 2021

A class of eighteen pupils whose average I. Q. was 93, completes the second semester of algebra without a single failure! On a general test at the end of the course the class ranked fifth among nine fast, one normal, and two slow classes. There were no home assignments. The semester's work was completed by one pupil in ten weeks, the others requiring from ten to eighteen weeks. I want to tell you how it happened.
Current Practice in Junior High School Mathematics
Authors: Worthington Edward H.
Published: January 2021

Since the report of the National Committee on Mathematical Requirements, under the auspices of the Mathematical Association of America, made its appearance we have been more certain of the content of Junior High School Mathematics, although the committee gave no order of topics with specific time allotments of each. A question which arose in my mind last spring was, “What are the Junior High Schools throughout the country definitely teaching in Mathematics?” I, accordingly, wrote to Dr. Glass, of the State Department of Pennsylvania, for a list of twenty-five of the best Junior High Schools in Pennsylvania, exclusive of Philadelphia. Philadelphia was excluded as most of the members of my class were already teaching in Philadelphia and were acquainted with the Philadelphia course of study. We received a directory of the Junior High Schools of Pennsylvania with twenty-five of the best checked by Dr. Glass. Books on Junior High Schools were then scanned for names of Junior High Schools, but with little success as they referred mainly to large school systems and we desired to get in touch with the mathematics departments. We found in the ninth year book of the National Association of Secondary-School Principals, in the directory of members, about forty-five names of Junior High Schools throughout the country.
Use of the Inventory Test in Plane Geometry
Authors: Haerter Leonard D.
Published: January 2021

In the course of the last few years there has been an extensive reorganization of the course of study in mathematics in grades seven, eight, and nine. One phase of this reorganization movement deals with the incorporation of much geometric material. A large amount of simple construction and drawing is being done with the ruler, compasses, and protractor. Through the application of both arithmetic and algebra in the field of geometry the child is becoming familiar with the names and shapes of a large number of plane and solid figures. In addition, many of the simpler notions of geometry are being experimentally obtained by the pupils in these grades.
Drawing for Teachers of Solid Geometry
Authors: Bradshaw John W.
Published: January 2021

In the last article we drew in clinographic axonometry the picture of a right prism with a rhombus for its base. As a second illustration of this method of making pictures, let us consider a regular pyramid whose base is an equilateral triangle ABC and whose altitude h is equal to the edge of the base s, a figure closely resembling the third in the Board's Document. We shall put the prism in such a position that the altitude will be vertical and we may use the plane of the base as our horizontal XY-plane. Then any pair of perpendicular lines in this plane may be taken as X- and Y-axes, but a particular choice will be useful in solving some interesting problems that we shall notice later. So let us choose our X-axis through A parallel to BC and our Y-axis through C perpendicular to BC (Fig. 16). If G is the inter-section of the medians AD and BE of the triangle, this is the point in which the altitude strikes the base. The vertex we shall denote by V, the altitude GV of the pyramid is parallel to the Z- axis.
The Effort to Make Algebra Yield Fruit
Authors: Smith Eugene R. , Rorer Jonathan T. , Cornish W. A.
Published: January 2021

If this analysis is correct it has important bearings on the world-wide effort to give concreteness to algebra. Concreteness as Smith and McMurry have pointed out is to be secured by solving problems where they are found, in their home environment. Abstractness is the sure result of taking things out of their home environment and treating them by themselves.
A Mathematical Contest
Authors: Walker Helen M.
Published: January 2021

The mathematical contest described in this article was originally devised for the entertainment of the Twin City Mathematics Club by the joint efforts of Mr. Myron F. Leslie and the writer, both of whom were then teaching in North High School, Minneapolis, Minn. The Twin City Mathematics Club, a joyous and enthusiastic organization under the leadership of Professor W. D. Reeve, had the custom of devoting its June meeting to an evening of pure fun. At one of these meetings, this contest provided so delightful a bit of entertainment that it is offered here in the hope that it may prove equally interesting to other informal gatherings of teachers and to high school and college mathematics clubs.
How Alice Made Pi Mu Epsilon
Authors: Shaw James B.
Published: January 2021

Alice had learned in her adventures in Wonderland that almost everything was just a game, and could have been played some other way. In her trip through the Looking-glass she had found that things in the world went along about as well backwards as they did forwards. She had developed a rather cynical attitude as to whether anything was certain, and could be relied upon, until she went to High School and studied Algebra and Geometry. In the High School and the Junior College she had come to have a very high regard for Mathematics, the only subject in which one knows what he is talking about and whether what he says is true. She made only A grades, and was not much surprised one day to receive an invitation to a party, which could mean only that she was being rushed for Pi Mu Epsilon. She met a number of her friends there, and did a fair share of the puzzles she was to solve. Evidently she made a good impression, as later she received an invitation to join this honorable society. As part of the initiation, after she had secured the signatures of most of the department, she was to go to the Brownfield woods, and meet the White Babbit who would conduct her examination. The dormice and the caterpillar were to serve as committee.
Objectives in Intermediate Algebra
Authors: Nyberg Joseph A.
Published: January 2021

In the Mathematics Teacher for March, 1927, Professor Reeve has presented an interesting and useful list of the objectives in intermediate algebra. Every teacher will find in the list the particular items that the teacher believes should lie included. When a list is as comprehensive as this one, certain practical questions arise: Can all the objectives be reached? Which objectives can be slighted if necessary, and which are most important? Since Professor Reeve suggests that the list serve as a basis for discussion, I present one answer to these questions, an answer based on ten years’ experience with about 500 pupils in classes averaging 37 each.
Some Pedagogical Aspects of Geometry Teaching
Authors: Sykes Mabel
Published: January 2021

Oftentimes things are said that are so fundamentally true that they never grow old.
Assumptions and proofs
Authors: Russell Stabler E.
Published: January 2021

In teaching demonstrative geometry do we aim primarily to develop in our pupils the ability to prove a fixed number of book theorems, or even to prove originals at sight 1 Assuredly, no. We aim rather to give them a clear understanding of the methods and significance of proofs so that they can apply these methods to non-geometric situations. We cannot hope to accomplish this if we devote our attention solely to geometric theorems and originals. It is evident that some of the work of the class must be related consciously to problems from real life which can be treated to advantage by methods of reasoning which the study of geometry has made familiar.
Ability Grouping of Students in Senior High School Mathematics
Authors: Weimar M.Bird
Published: January 2021

Ten years ago the department of mathematics of Wichita High School began grouping students according to ability into three groups—honor, medium, and slow. At first we used an intelligence test as a part of the basis of classification. We have used the Stone Reasoning test, the Otis Intelligence Test, and the Terman Test. With or without an intelligence test we have always used the judgment of the teacher who had the pupils the previous semester and the one receiving the pupils. Not always have we given an intelligence test but we do feel that we lose some of the certainty of placing and at times find our first judgment wrong without the test. A student may be very good in the mechanics of elementary algebra, doing the original reasoning required there in a satisfactory manner, and yet lack the power of analysis required in geometry, advanced algebra, and trigonometry. Students naturally group themselves according to their analytic and reasoning power and an intelligence test discovers this grouping more readily than the regular classroom procedure.
The Maintenance of Fundamental Arithmetical Skills in the Junior High School
Authors: Benz H. E.
Published: January 2021

One underlying assumption of this paper should be stated at the outset in order that the development of the subject may be more readily followed, and in order that those who find themselves unable to agree with this assumption may at once reject any conclusions which may be drawn. That assumption is that arithmetic skills are worth acquiring because of their usefulness in life. Our hypothesis does not necessarily deny the existence of any disciplinary values in arithmetic, nor does it imply a quarrel with those who hold the “rich-present-life-for-the-child” theory of education. It merely insists that one reason for teaching the fundamental skills of arithmetic in the elementary school is that it is the duty of the school to contribute to the future social and civic usefulness and to the happiness, convenience and comfort of the individual by creating in him during the elementary school period the ability to perform accurately and with reasonable dispatch those arithmetical computations which life demands.
The Validation of New Types of Plane Geometry Tests
Authors: Greene Harry A. , Lane Ruth O.
Published: January 2021

feachcrs in all fields of subject matter arc turning to objective tests as the only reliable means of determining the efficiency of their instruction. This interest on the part of the cla sroom teacher has had a most wholesome effect on the recent developments in educational measurements. As teachers themselves become better informed they grow more critical of existing devices, and in many cases have themselves made significant contributions. In fact, a very considerable portion of the material described herein is the product of a classroom teacher working under normal instructional conditions.
Variability and Functionality in High School Mathematics
Authors: Blank Laura
Published: January 2021

The subject of variation as a topic or possibly phase of mathematics is a very important one in the field of the secondary school. In this day, when so much is made of correlations within the general field of mathematics and with other allied fields of science, the study of variation brings out numerous interesting contacts and inter-relations for the pupil, thus impressing him with the great breadth of application of mathematics. Moreover, gradual development of the idea and use of variation establishes certain modes of thought applicable to matters not wholly mathematical and perhaps only relatively quantitative. The concept of variability or functionality is perhaps sufficiently far-reaching in scope and application, if properly studied and emphasized to serve more than any other idea or agency to tend to correlate or unify mathematics.
Value and Logic in Elementary Mathematics
Authors: Durell Fletcher
Published: January 2021

About fifteen years ago our National Government brought suit for the dissolution of the United States Steel Corporation on the ground that this organization was a combination in restraint of trade and therefore was operating in violation of the Sherman Anti-Trust Law. In the year 1919 the final decision in this case was made by the Supreme Court of the United States.
Recreations for the Mathematics Club
Authors: Bentley Byron
Published: January 2021

Now that the subject of extraclass activities is receiving prominent mention in the field of secondary education, the Mathematics Club is assuming a position of larger importance in the affairs of the school. As with any such organization, however, its value will depend chiefly upon the effectiveness of its programs. Outside speakers will at times be unavailable, business will drag, and even student orators have been known to neglect to prepare themselves upon such weighty topics as "The Life of Pythagoras" or "The Einstein Theory." To enliven the meetings as well as make for constructive accomplishment the recreation has its place.
Some Difficulties Involved in Solving Verbal Problems in Elementary Algebra
Authors: Clem Orlie M. , Hendershot Bertha Adams
Published: January 2021

What difficulties do pupils meet in solving verbal problems in elementary algebra? Can these difficulties be classified or analyzed? Do these difficulties indicate specific weaknesses in teaching? Do they provide suggestions for remedial teaching? The study here reported was conducted in order to answer these questions in terms of certain typical classroom situations.
Mathmatics as a Fine Art
Authors: Shaw James Byrnie
Published: January 2021

Mathematics studies a vast world of objects and their transformations, their static and dynamic characters, intricate and tangled, yet systematic and ordered to a degree far greater than that of any other known world. This world has been created by the mind of man, partly in order to enable him to handle the world of phenomena, but mostly for the elegant beauty of its objects. The mathematician is an artist whose material is more subtle than stone or paint, tone or words. Of late he has made a thorough study of what he really does and what he really studies, and has concluded that he has always exercised a creative function of his mind. He has come to see that the rainbow which lures him on for the pot of gold is one of his own making, and the gold he finds was fused in his own crucibles. Indeed he is able to point out to the scientist that most of what he too is concerned with, is of the same character, and that he too works for the aesthetic satisfaction he gets. It is this character of mathematics which we shall consider for a few minutes. And first let us look at a few peaks in its history.
A Study of Certain Mathematical Abilities in High School Physics
Authors: Carter William Ray
Published: January 2021

The problem of the functioning of the mathematical training of the student in high school physics has received much attention during the past decade. This attention has ranged from magazine articles advocating the demathematizing of high school physics to carefully planned studies to determine the kind and amount of mathematics needed in the course. There has been much difference of opinion as to whether or not too much emphasis has been placed upon the mathematical aspects of the subject. The earlier discussions were much concerned with this phase of the problem, but not much was done to settle the question on an objective basis. Hughes has summarized the arguments on both sides of this question and has presented certain conclusions regarding this controversy.1
The Problem of Individual Differences in Mathematics Classes
Authors: Sykes Mabel
Published: January 2021

This study was undertaken in connection with sabbatical leave from one of the Chicago high schools and covers over fifty schools, twenty-five of which were visited by the writer. The facts concerning the others were obtained from replies to letters.
Mathematics and Social Science
Authors: Prendergast Ella M.
Published: January 2021

Having felt for some years the increasing lack of co-ordination among the departmentalized units of the junior high school, the writer unexpectedly received an impetus toward active work on this problem as related to mathematics, during the progress of a graduate course in the “Teaching of Mathematics,” taken at the University of Southern California under Dr. Myrtie Collier. Through her encouragement and under her helpful supervision, some experimental investigations were started which it is hoped may have their small share in turning professional thought toward correlation of subjects in a definite and constructive manner.
Real Life Experiences in the School
Authors: Botsford Stephen J.
Published: January 2021

Do we want “real life experiences” in our schools? This problem is one that many educators are discussing and is the subject for many experiments. For some time, led by Professor Kilpatrick of Teachers' College, the proponents of this method of education appeared to have the best of the argument. However, the opposition is meeting the issue so that the contest is by no means one sided and final conclusions may never be reached. There seems to be no doubt but that “experience is the best teacher,” and it all depends upon what is to be taught whether or not “life experience” should be the method used.
Mathematics Teams to Motivate Drill Work in Junior High Schools
Authors: Kessler R. V.
Published: January 2021

The junior high school student is gregarious. He is plastic, he is energetic, he is ambitious, and he is quite sensible. His gregariousness, his desire for group work and competition is, however, his outstanding quality. He enjoys all kinds of team work, and he likes to have a definite goal toward which to work. An appreciation of these truths furnishes the key to well motivated and successful work in mathematics.
The Training of Candidates for Teaching in Secondary Schools, Especially in Prussia
Authors: Wolff Georg , Beyer Arthur
Published: January 2021

At the last meeting of the International Commission on the Teaching of Mathematics in September 1932, Professor Loria of Genoa rightly laid stress upon the fact that in the countries referred to in his report a visible conformity in the theoretical training as well as in the subsequent improvement of teachers of mathematics could be observed. However, with regard to the practical preparation for class work we may speak of a parallelism of the development only with reservation.
Higher Standards for Teachers of Mathematics
Authors: Reeve W. D.
Published: January 2021

The major part of the criticisms of mathematics are due to faulty and antiquated methods of teaching rather than to the inherent difficulty of the subject matter of mathematics itself. Mathematics, if properly taught, would be enjoyed by a large majority of the pupils who study it. Why else do we find so many adults who have gone through our secondary schools with a serious emotional complex against algebra? What can we expect when we reflect that in many localities the athletic coach with little training, if any, in mathematics is assigned to teach an algebra class on the theory that any body can teach algebra? Sometimes it even appears worse than that—someone is assigned to teach algebra because he happens to have a vacant period at the time the algebra class is scheduled.
The Value of Analytics and Calculus in the Secondary School
Authors: Fehr Howard F.
Published: January 2021

“To be more specific, I am opposed to the introduction into the secondary school of the calculus in any form, of projective geometry, of analytic geometry as such, or of any special stress on the concept of function.” Thus Ralph Dennison Beetle1 of Dartmouth College rejects in part the recommendations of the National Committee, which say that “The one great idea which is best adapted to unify the course is that of functional relation” and which also include calculus in every plan of arrangement of material for the twelfth year. Having taught analytics and calculus as such, for the past four years to twelfth year students and having stressed the function concept in the eleventh and twelfth years, I am in direct opposition to Professor Beetle's opinion. In this article are presented some of the advantages that have resulted from this teaching which seem to make it desirable as a required part of the advanced mathematics in the secondary school.
Carl Friedrich Gauss
Authors: Sanford Vera
Published: January 2021

At an early age, Gauss showed unusual ability in mathematics. In fact, some say that he was only three when he corrected his father's calculations of the pay due men working under him. The father was a brick layer and Gauss was brought up in circumstances that barely escaped poverty. At the elementary school in Brunswick, he attracted the attention of an assistant teacher Bartels who was later to become professor of mathematics at Kasan in Russia and then at Dorpat in Germany. At Brunswick, Bartels' duties included cutting quill pens for the younger boys and helping them with their writing. Bartels read mathematics with Gauss and introduced him to the binomial theorem and to infinite series when Gauss was only twelve. Gauss attended the gymnasium in Brunswick and in 1792 with the financial support of the duke of Brunswick who had become interested in him, he went to Caroline College in Brunswick and later to GÖttingen. At Caroline College Gauss worked in mathematics and in languages. When he entered the university in 1795, he had made progress in the theory of least squares, but he was still undecided whether to work in philology or in mathematics. His career to this point has been called his “prehistoric period.” During this time, his study in the theory of numbers was largely experimental—the assembling of many cases, the forming of a rule, the proving of the theorem.
Report of the Commission on Examinations in Mathematics
Authors: Dresden Arnold , Barker Grace S. , Beatley Ralph , Betz William , Longley William R. , Mirick Gordon R. , Smith Rolland R. , Wheeler Anna Pell , Wiener Norbert
Published: January 2021

The Commission has completed its study of the problems submitted to it and embodies its conclusions in the recommendations which follow. Some general observations precede to indicate the fundamental points of view which have guided the discussions of the Commission, and which find expression in the recommendations (sections II and III). Some general comments for the guidance of teachers conclude the report (section IV).
Interesting Detours in Algebraic Instruction
Authors: Bibb S. F.
Published: January 2021

Introduction. If this paper furnishes suggestions for further interesting search, then its purpose will have been fulfilled. Obviously a great amount of absorbing material could be properly mentioned. But included are only a few fascinating problems that have been passed on to the students when an opportunity afforded their demonstration.
The 16th Annual Meeting of the National Council of Teachers of Mathematics, Atlantic City, New Jersey, February 22-23, 1935
Authors: Schreiber Edwin W.
Published: January 2021

Present: J. 0. Hassler, Ralph Beatley, Allan R. Congdon, Edwin W. Schreiber William D. Reeve, Vera Sanford, John P. Everett, Raleigh Schorling, Martha Hildebrandt, H. C. Christofferson, Edith Woolsey; Marie Gugle, past president; Olive A. Key, representing H. C. Barber; and J. T. Johnson, representing Mrs. Elsie Parker J ohson.
A Redefinition of Secondary School Mathematics
Authors: Schnell Leroy H.
Published: January 2021

Mathematics is alarmingly on the defensive. Much that has been traditionally sacred to us is rapidly disappearing from the curriculum. Our past security is vanishing into thin air. The writers of the National Committee Report admitted that, “the subject must, like others, stand or fall on its intrinsic merit or on the estimate of such merit by the authorities responsible at a given time and place.”1 Seven years later Betz stated that, Geometry shares with Algebra and Latin the fate of being on the defensive.”2
A Problem Play
Authors: Cohen Dena
Published: January 2021

The living room scene may be managed by two plain brown screens. In front of these is a table with a chair on each side. The two girls are working with their books and papers piled around. The door at the side may be the right wing of the stage or another screen may form an entrance-exit there.
Testing the Ability to Study
Authors: Orleans Joseph B.
Published: January 2021

Examinations have always been considered an essential element in the education of the young. From the earliest times, school routine has consisted of teaching by the teacher, learning by the pupil, recitation by the pupil and examination by the teacher. Under the monitorial system of instruction in the early part of the nineteenth century one of the duties of the monitor was to examine the pupil periodically and to promote him if he made progress. The lecture-quiz system in the colleges today is essentially an examination system. The recitation method still in vogue in many a classroom in our secondary schools is a form of the examination system. The pupil studies the lesson to which he has been exposed and is then subjected to a brief oral examination to show the teacher to what extent he has mastered the facts that have been taught. Under any system, examinations are held at stated intervals, usually at the end of ten weeks, at the end of fifteen weeks, at the end of a semester, in order that the teacher may measure the achievement of the pupils and record a mark to comply with the regulations of the schools.
News Notes
Authors: Kelly Mary
Published: January 2021

The Wichita Mathematics Association, a new local branch of the National Council of Teachers of Mathematics, held its first meeting of the year October 5th from four to five-thirty at High School—East.
The Development of the Thermometer
Authors: Fretwell Mattie Bell
Published: January 2021

The invention of the thermometer must be attributed to Galileo, who in about the year 1593 made an open-air thermoscope. He never mentions this fact in any of his writings; but since Castelli, one of Galileo's ablest pupils, describes in great detail a thermoscope which Galileo showed him in 1603; and since another student of his, Viviani, reports the invention of this instrument by Galileo shortly after his arrival at the Univrersity of Padua in 1592, there seems to be no valid reason for doubting the statement that Galilro invented such an instrument, which is taken from a letter of Castelli's written in 1638.
The Teaching of Solid Geometry at the University of Vermont
Authors: Nicholson G. H.
Published: January 2021

My teaching experience of solid geometry extends over ten years. During the first few years, I taught the subject as beginners usually do. I selected a textbook, wrote an assignment on the board, the extent of which was decided after the number of propositions to be taught had been carefully divided by the number of lectures to be given during the semester. Each assignment included several exercises. Frequently I would give certain propositions to definite members of the class, either as a home assignment or as a class exercise. These students would put the statement, figure, hypothesis and conclusion on the board. Several would do this each day during the first few minutes, then they would give the formal proof, either orally or in writing. The exercises were dealt with similarly. If the work was not carefully done I would go over it myself. Every now and then I would ask the class to pass in exercises and theorems completely demonstrated; and, when we were studying the last two books, computation problems involving the pyramid, prism, cylinder, cone and sphere were given.
The Art of Teaching
Authors: Kaufman Elliott H.
Published: January 2021

Strange as it may seem, one of the most difficult concepts for the pupil at the junior high school level to grasp in the unit on numerical trigonometry is the location of the three sides of a right triangle, the opposite, the adjacent and the hypotenuse.
The Art of Teaching
Authors: Graham Wallace B.
Published: January 2021

The practice of giving a test at the end of each teaching unit or series of units is an accepted method of instruction. A lengthy justification of this procedure is not my aim in this short article. To achieve some sort of an objective measure of the pupil's ability is probably the most apparent purpose of a test. Whether this rating is of benefit to pupil or teacher is of little importance. To one who has been handling a class group regularly, both the general intelligence and specific subject abilities of each member of the class, are quite evident. A justification of the given mark in the mind of the pupil seems to me to be of definite importance. The test tends to do this, for it minimizes the subjective ranking, thus creating a better understanding between pupil and instructor.
The National Council Committee on Arithmetic
Authors: Morton R. L.
Published: January 2021

In recognition of a growing demand for a committee, nation-wide in its representation, to study and report upon trends in the arithmetic curriculum and in the teaching of arithmetic, The National Council of Teachers of Mathematics in February, 1937, authorized the appointment of a committee on Arithmetic.
Out-of-School Arithmetic of Sixth Grade Children
Authors: Moseley Nicholas
Published: January 2021

In DECEMBER and January, 1937–1938, three groups in Grade VI of the Meriden, Connecticut, Public Schools kept “Arithmetic Diaries.” Members of each group recorded day by day how they used arithmetic outside of school. An analysis of the results is given below, but almost more interesting than the tabulations of the actual arithmetic used are the side-lights on the life of many of the children—the time they get up, the time they go to bed, which ones have chores to do, what their allowances are (0–50¢ a week), what the families are buying from the store, what purchasing contests they are in, the games the children play, their reactions to winning and losing. The prize perhaps goes, pathetically, to the child who said, “I used my arithmetic. I went to grandfather's funeral. I counted the cars. There were nine cars.” Or “I went to the store to pay a bill of $5.37. I paid the clerk $2.00 on the bill. How much left on the bill at the store. $3.37 was left.” And “My uncle is paid 850 a month. He asked me how much that was a week and I figured it for him.” The diaries make as fascinating reading as the Lynds' Middletown.
Enrichment Materials for First-Year Algebra
Authors: Starr David W.
Published: January 2021

The place of mathematics in the secondary school curriculum has been a subject of very much discussion the last few years. Just what are the aims of a mathematical education? Let us paraphrase such aims as suggested by J. H. Minnick. We should give each individual such a knowledge of the subject as will enable him to understand the exactness and force with which mathematics works and the parts which it plays in solving the problems of nature and which makes it possible for man to turn the elements of nature to his own use; we should develop such fundamental concepts as will enable the student to express his thoughts more clearly and to understand written and spoken language more readily; we should give to each student such a knowledge of mathematics as will enable him to carry on the work of his future occupation as it is now conducted, as will serve as a basis for future preparation if progress in his work should demand it, as will enable him to find new and better ways of doing his work and to recognize a mathematical situation when be sees it; we should require of each student sufficient mathematics to determine whether he will profit by further study of the subject and to select those who will probably be leaders in mathematical thought; and of the select group we should give enough mathematics to keep open the door of specialization in mathematics and in fields dependent upon mathematics.1
Mathematics in Industrial Chemical Research
Authors: Heckert W. W.
Published: January 2021

As soon as chemists began to make quantitative studies and to look for mathematical relationships among their data they began to make progress at a greatly accelerated rate. This trend toward quantitative treatment has continued. Some of the most fundamental problems of the science, such as those of chemical affinity and reaction velocity, have now begun to respond to mathematical treatment. This trend has made itself felt in the industrial field. It is expected to continue.
Art in Geometry
Authors: Ahern Lorella
Published: January 2021

Art appeals to the emotions. Its inception and final creation are both expressions of the emotions of the artist. Too, it is stimulating to the emotions of all those who enjoy the finished product.
The Educational Value of Logical Geometry
Authors: Blackhurst J. H.
Published: January 2021

The effort involved in attempting to substitute a living concept of education for the static preparation theory of Herbart has resulted in much progress in educational theory and some improvement in educational outcomes. Herbart's contribution to education left faculty discipline without followers except for those who did not know what it was all about. However, as might be expected, this made little or no difference at the time in either curriculum or method. Dewey moved beyond Herbart leaving faculty discipline still farther behind until at the present time faculty discipline is no longer scoffed in theory: it has been all but forgotten. Few educators could tell exactly what it is, or was thought to be. In spite of this fact we are still slaves to its clutches as far as the teaching of logical geometry is concerned.
Analytic Geometry in the High School
Authors: Leary Arthur F.
Published: January 2021

What little work on graphs is included in the usual mathematics course in the high school could readily be extended to include more of the elements of analytic geometry. Most pupils like graphs and find that problems requiring the field of coordinates are easier and more interesting than straight manipulation.
The Lessons Non-Euclidean Geometry Can Teach
Authors: Henderson Kenneth B.
Published: January 2021

So YOU want to teach mathematics! Why you selected college geometry is more than I know because college geometry is about as useless as high school geometry. Seriously now, did the fact that an exterior angle of a triangle equals the sum of the two non-adjacent interior angles ever make any real difference in your behavior? And were you thrilled to find out that a line is tangent to a circle if it is perpendicular to the radius drawn to the point of contact? Let me warn you in advance t hat when you find out a line is perpendicular to a plane if it is perpendicular to all lines in the plane passing through its foot, you will be apathetic. Furthermore, when you prove that the volume of a rectangular solid is really the product of the length, width, and height you will probably be disgusted, for you knew t hat ever since you were in the seventh grade. The fact that you proved it is really silly, isn't it? You have gotten along pretty well so far just taking somebody's, a teacher's or author's, word for it. And after all, what difference does it make whether you assume this is so in the first place or whether you assume something else, and from this prove the theorem for finding this volume. None of you would try to make me believe that you can calculate the area of the floor of this room better than Fred Fable whose schedule conflicts prevented him from being one of your classmates in geometry in high school.
A Simple Blackboard Ellipsograph
Authors: Ruglak Haym K.
Published: January 2021

The simplest and best known method of drawing an ellipse is based on the fundamental theorem in conics that in any ellipse the sum of the focal radii is constant and equal to the major axis of the ellipse. This method is widely used by gardeners in laying out elliptical beds, by pattern-makers, metal workers, artists, and others.
Mathematics for the Modern Junior High School*
Authors: Murray Earl , Ritchie Robert W.
Published: January 2021

A unique feature of this session was the absence of any prepared paper or set speech. Nevertheless, the session was planned carefully and laboriously. Each member of the panel was secured under the arrangement that the session was to be a frank and open discussion of junior high school problems. The chairman prepared mimeographed sheets with suggestions for discussion which were mailed to each panel member about six weeks before the date of the session. Each member responded to these suggestions in writing, sending the material to the chairman, who mimeographed it and returned a copy to each panel member. Because of this, each of us felt acquainted with the others and their viewpoints on the problems, even though we had never seen one another. We did not meet until the hour of the session. The suggested material sent out by the chairman will appear at the first of the discussion under each main topic, rather than appearing here as one document.
Mathematics for Everybody
Authors: MacNeish Agnes
Published: January 2021

Much discussion and experimentation are in process in regard to fitting the high school work in mathematics to the needs of the pupils. Having the right kind of mathematics for everybody is generally recognized as one of the aims of the curriculum. There is accordingly a very great need for a reorganization of high school mathematics with a view to adjusting the offerings of the department to the different levels of ability and preparation occurring among high school students and to the many uses for mathematics in present day living.
Geometry for Everyone
Authors: Davis Kenneth S.
Published: January 2021

There are many geometric relationships and figures in our world that are a part of the experiences of every person, but they escape notice as such because they have not been brought to the attent ion of the observers. Or should it be said, those who do not observe.
New Objectives for Ninth Grade Mathematics
Authors: Willits William
Published: January 2021

I have an interested eye on two of our present ninth grade sections. They were sectioned as average pupils on the basis of their past school performance. The two groups total 87 pupils. Intelligence test scores range from 122 to 84, with a median of 106.
How Shall Geometry Be Taught?
Authors: Waynen M. Van
Published: January 2021

Recent investigations which have compared the merits of the traditional geometry course and the newly inspired course which focuses attention on the principles of logical thought and its application to everyday situations have strongly favored the latter. Results of these studies indicate that pupils of the experimental classes acquire the usually attained geometric achievement while definitely managing to surpass the control classes with scores of nearly two to one in reasoning achievement. However, in spite of these highly satisfactory results, most high schools have done nothing toward adopting the newer techniques which have made them possible.
It All Began Last Winter
Authors: Chayt Edna R.
Published: January 2021

It all began last winter when one of my ninth-grade boys said to me, “Why do we have to study mathematics?” A firm believer in the principle that the best defensive is the offensive, I countered with another question, “Why do you study any subject?” He replied, “Well, history helps you understand what you read in the papers.” “So,” I told him, “does mathematics. Mathematical ideas are just as much a part of an educated person's background as historical ideas.” Well-bred child that he is, he didn't express his disbelief in words, but he didn't have to. I have been refuting the look on his face ever since.
The Place of Experimentation in Plane Geometry
Authors: Sitomer Harry
Published: January 2021

A source of serious errors made by high school students in the plane geometry classroom is the confusion between arriving at conclusions based on observations and those based on reasoning. A student wall state that an angle is a right angle because it looks like that to him. Or he will conclude that two segments are equal because he estimates their lengths to be equal. Too often he fails to understand the nature of his error. He is an ardent believer in the maxim, “Seeing is believing.”
The In-Service Training of Mathematics Teachers
Authors: Blackiston Nanette R.
Published: January 2021

Wm. Lyon Phelps has said, “I love to teach as a painter loves to paint—as a singer loves to sing, as a strong man rejoices to run a race. Teaching is an art—an art so great and so difficult to master that a man or a woman can spend a long life at it, without realizing much more than his limitations and mistakes, and his distance from the ideal.”
Developing the Principle of Continuity in the Teaching of Euclidean Geometry
Authors: Lloyd Daniel B.
Published: January 2021

The development of modern mathematics has depended considerably upon the concept of functionality. Modern mathematicians have used it as the framework for much of their theory in the advanced fields of analysis and higher algebra. Descartes in the seventeenth century founded Cartesianism, an ingenious system whereby geometric loci can be represented algebraically. In this system, known as analytical geometry, any algebraic function corresponds to a geometric locus, and conversely. This algebraic representation of a curve or surface in space laid the ground work for higher geometry, —the analytical treatment of spacial elements. The paramont importance of functionality is thus evident in the entire field of modem mathematics.
Problems of Teaching Mathematics in the Schools of England
Authors: Hooper A.
Published: January 2021

It was with mixed feelings of surprise, and may I say, of trepidation, that I received an invitation from our Chairman Mr. Melby, to come and address you this afternoon. What qualifications had I that would justify so great an honor as that of addressing a gathering of this nature? Much as I hate to disillusion all those who have ensured a prompt reply to their letters by addressing me as “Professor” I have to admit that I can lay claim to no such lofty title. I am just one of the rank and file, who has spent more than twenty-five years in the classrooms of English Secondary, or High Schools and English private schools. No, I am just a plain, ordinary teacher.
The Teaching Objectives in a First Course in the Calculus
Authors: Parker James E.
Published: January 2021

There is a great deal being said nowadays about course objectives. It is said that the objectives for any course in the curriculum should be clearly defined and that teacher and student alike should be conscious of these objectives at all times. This concern has lead to a re-examination of the objectives for courses taught by the writer. This paper is particularly concerned with the objectives for a first course in differential and integral calculus. Stated briefly, the question at hand is this what are my objectives in teaching a first course in the calculus? Three major objectives are found to be inherent in this case. These are: (1) to give the student an understanding of the fundamental concepts of the calculus and a point of view relative to the historical background out of which these concepts grew; (2) to develop proficiency in the manipulative skills of differentiation and integration; and (3) to develop abilities in making practical applications of the principles learned. A few words will be said about each of these objectives relative to the methods used in attempting to realize them. It is hoped that the following statements will arouse some interest and will bring forth some comments as well as criticisms from individuals more experienced than the writer. In this way the writer, and possibly others, may be greatly helped in setting up goals toward which to work.
The CAA-NYC Aviation Operations Institute
Authors: Moore Lillian
Published: January 2021

The Civil Aeronautics Administration —New York City Aviation Operations Institute was held on April 6th at La Guardia Field, New York City. It was arranged by Mr. O. P. Harwood, Regional Manager of the First Region of the Civil Aeronautics Administration for ninety-eight selected New York City teachers of aeronautics and school administrators, in conjunction with Dr. Frederic Ernst, Associate Superintendent in Charge of High Schools. The Institute program proved to be valuable to the highest possible degree. Teachers who were unable to take advantage of the opportunity offered to gain increased knowledge of aviation operations will undoubtedly be interested in a report of the activities covered during the course of a busy day.
The Art of Teaching: Square Root by Approximation and Division
Authors: Tobey William S.
Published: January 2021

Recently several references have been made to the method of finding square roots by approximation and division. There appears to be a belief among some teachers that this method is longer than the conventional method. This has not been found true in actual tests given to both rapid and slow groups over a period of several years. Finding square roots by approximation and division has been in use fifteen years in the senior high school of Long Branch, New Jersey for two reasons. First, few pupils have come to the senior school during this period with the ability to find the square root of a number despite the fact that several weeks had been devoted to teaching it in an earlier grade. Second, to most pupils, the conventional method is one more example of “mechanical manipulation” and as such has no standing where learning is the goal.
A Method of Self-Instruction for Learning the Thirty-Six Addition Combinations with Sums from Eleven to Eighteen and Their Corresponding Subtraction Facts in Grade II
Authors: Wilburn D. Banks
Published: January 2021

In an earlier article,1 the writer raised the question whether pupils in the primary grades are able to learn the facts of arithmetic largely by their own efforts. He reported a partial answer in a description of the successes of seventy-two pupils in Grade I with a method of self-instruction for learning the forty-five easier addition and subtraction combinations. These pupils learned the combinations through the study of groups. Three methods for studying groups were employed, namely, counting groups, comparing groups, and the analysis and synthesis of groups.
The Effects of Military Training Upon General Education
Authors: Syer Henry W.
Published: January 2021

Hundreds of thousands of words have been printed, in newspapers and magazines throughout the country, commenting, explaining and conjecturing as to what the returning veteran will want and demand. But relatively little thought has been given as to what he may be able to do for us in bringing new information, new ideas and new methods for performing old and familiar tasks.
Mathematics Interest—Fundamental or Not?
Authors: Torrance Paul
Published: January 2021

Several years of teaching mathematics and counseling high school and junior college students has often influenced me to wonder if there is such a thing as a “fundamental” interest in mathematics—or any other subject for that matter, but especially mathematics. Has a student by the time he has reached high school or junior college even acquired such a set of likes and dislikes that he has become the kind of person who cannot become interested in mathematics on the one hand or is the kind who is naturally intensely interested in it on the other hand?
Why Study Mathematics?
Authors: Bond E. A.
Published: January 2021

Two recent experiences of mine had a part in the selection of the topic for this article. The first was an eight page editorial that appeared in a recent issue of Life Magazine on the theme: “War is Teaching U. S. Citizens a Belated Lesson in the Supreme Intellectual Discipline of the Science of Mathematics.” Since books on mathematics are best sellers today, it is probable that teachers of mathematics should better sense the high importance of the work they are doing.