bluuebunny/crossref_metadata_2025 huggingface dataset:
Character-Building Content of Arithmetic
Authors: Green Jenny Lind
Published: January 2021

Arithmetic was introduced into American schools to meet definite social situations of Colonial times. Although a fixed factor in the course of study, it has wandered far from its predestined course. Literally, we have seemed to stress addition, subtraction, multiplication and division at the expense of knowing what to add, subtract, multiply and divide. We have given the impression of emphasizing the fundamentals and their kindred abstractions to the extent of ignoring the fact that it is sometimes necessary for us to decide which of these desirable processes should be used. Sadder still, we have been accused of forgetting to mention in a functional way that one is likely to meet these fundamentals and mathematical accessories in the flesh, and clothed in raiment the like of which was never seen in text-book or classroom.
Tests of Mathematical Ability — Their Scope and Significance
Authors: Rogers Agnes L.
Published: January 2021

Measurement in the field of algebra and geometry is of such recent origin, it may at first glance seem somewhat premature to survey the work so far accomplished. It was only in 1914 that the first tests of ability in high school mathematics were published. The production, however, although so recent, has been so suggestive for future work that the time is undoubtedly propitious for taking stock of the tests at our command and for estimating their significance.
A Psychological Basis for a System of Education with Applications to Mathematics
Authors: Webber W. Paul
Published: January 2021

The aim of this paper is to put in small compass and in non-technical form a theory of education that can be applied directly by the serious teacher, to assist in orienting some questions that are confusing to a considerable number of teachers of mathematics, and to furnish a statement of some of the definite objects that may be accomplished in teaching mathematics. The organization of the material is incidental to a course of lectures on the theory and methods of teaching mathematics given regularly by the writer in the University of Pittsburgh. While some controversial questions are discussed, it is the purpose of the writer to be constructive.
Philosophy and Non-Euclidean Geometry
Authors: Foraker F. A.
Published: January 2021

Leibnitz and Descartes made remarkable contributions to both mathematics and philosophy. Newton obtains a high rank in the history of the former subject, but only a minor place in the history of philosophy, while Kant, who possessed a well-founded knowledge of the science and mathematics of his time, receives one of the foremost positions in the history of philosophy. Upon the basis of these facts, if we neglect a few of the lesser lights, the statement is often made that there is a relationship between the study of mathematics and the study of philosophy, and that he who studies one of them will also find himself a devotee in the pursuit of the other.
Certain Undefined Elements and Tacit Assumptions in the First Book of Euclid’s Elements
Authors: Smith Eugene R. , Gaylord Harry D. , Chambers Geo. Gailey , Breckenridge William E. , Webb Harrison E.
Published: January 2021

For twenty-one centuries the spirit of Euclid has reigned supreme over elementary geometry. For the greater part of this time the terms “Euclid’s Elements” and “Geometry” have been all but synonymous. In no other science save theology has a single book held undisputed sway for unnumbered generations. Educational reformers have often pointed to this universal acceptance of Euclidean authority as an evidence of dead conservatism on the part of teachers. It is due rather to recognition of the unparalleled skill of the great Elementarist, whose text still stands as the best among the thousands which have been written on the subject, and whose methods are so simple and direct as to be well within the abilities of a beginner.
Proposed Syllabus in Algebra
Authors: Wheelock Chas. F.
Published: January 2021

This syllabus in algebra is in the main a reprint of the tentative syllabus issued in February, 1919. A few changes have been made in response to criticisms received.
Comments on the Teaching of Geometry
Authors: Touton Frank C. , _ _
Published: January 2021

Purpose or Problem. — The writer of this paper has each day occasion to visit classes where geometry recitations are in progress in the course of his regular supervision work. Some outstanding features of the recitation work are here mentioned, that good classroom practices may become more common, and that practices of doubtful value may be called in question and, if found lacking, abandoned. Certain methods of work which seem effective in the study-recitation process are here considered in some detail and are recommended for trial and for adoption by those who succeed through their use.
The Relative Emphasis Upon Mechanical Skill and Applications of Elementary Mathematics
Authors: Allen Fiske
Published: January 2021

The teaching of elementary mathematics has two distinct purposes, quite closely connected with each other and yet easily distinguished. The pupil must develop a skill in the manipulation of the symbols of elementary mathematics and he must develop a power to apply them to the solution of life problems. By special emphasis upon either phase of the subject an ability can be developed in it without a corresponding ability in the other phase, and sometimes at the expense of ability in the other phase. It is easy to develop in pupils a high degree of skill in the mechanical processes of computation with almost no ability to decide in a particular problem what process is to be used. And in pioneer days many men were quite able to solve the problems met in daily life though knowing nothing of the use of figures for purposes of computation. It has been very interesting to me to note that pupils in the third and fourth grades, utterly innocent of the use of the symbols in division of fractions, will frequently solve problems involving division of fractious more readily than will those same pupils after they have been taught to “invert the divisor and multiply.” This does not mean that skill in computation with figures stands in the way of solving concrete problems, but that during the time devoted to acquiring the skill they have lost power in thinking number relations, possibly through a transfer of interest.
A Note on the Failure of Educated Persons to Understand Simple Geometrical Facts
Authors: Thorndike Edward L. , _ _
Published: January 2021

The following was given, as the third in order of a set of eight paragraphs to be read, to twenty-seven adult students in a Summer Session course in Mental Tests.
Arithmetic in the High School
Authors: Dake L. Gilbert
Published: January 2021

The object of this paper is to call attention to some tendencies in the American High School which the writer considers dangerous to the coining generations of high school graduates. It is a plea for a more extended study of practical mathematics. In presenting his view the writer may seem critical and, at times, harsh and radical. He believes, however, that the times are harsh, and require more or less radical statements to cause a change in the present drift of the high school curriculum.
The Psychology of Problem Solving
Authors: Thorndike Edward L.
Published: January 2021

One reason for the great value attached to solving these verbal problems is a confusion of their value as training with their value as tests, and a misunderstanding of what they test. The ability to organize a set of facts in an equation or set of equations such that solving will produce the desired answer is very closely correlated with general intelligence of the scholarly type. The pupils who can do it well rank high in intellect and scholarship. So it is natural to infer that doing it creates and improves the ability.
Romance in Science
Authors: Miller Bessie Irving
Published: January 2021

At the beginning of the second semester of this year we opened a two-hour course, popularly called “Browse,” with a description of a sleek, cream-colored Jersey, standing in deep grass and pausing, after a lucious bite, to gaze meditatively over the landscape. Before the spring vacation, in that same course, I gave an examination on the content of the Einstein Theory and its relation to the Newtonian Theory. Why, how, and with what results I made that transition are the subjects of this paper.
The Future Development of Mathematical Education
Authors: Moore Charles N.
Published: January 2021

You have already heard this afternoon of the work of two organizations that have been and are actively interested in the improvement of mathematical education. You have also had presented to you programs for adapting mathematical instruction to the needs of two rather recent types of school organization. It is apparent from this afternoon's discussion alone that the teachers of mathematics here and throughout the country are alive to their opportunities and their responsibilities. They realize the great service to society which they can perform by selecting from the vast store of mathematical knowledge those elementary methods and processes that are of widest use in the modern world, organizing them into coherent courses, and presenting them effectively to their classes. It is apparent to the careful observer that existing mathematical courses have not been constructed with due regard to the relative importance for the general student of the different mathematical methods and principles that are available for instruction in school and college. Our courses have been arranged primarily for the benefit of those who will continue their mathematical education. That they do contain much material of great use to the general student arises from the fortunate circumstances that most of the processes in elementary mathematics have some important applications in the world of to-day. But the conscientious teacher of mathematics will not allow his good fortune in this respect to paralyze his initiative. If we can add considerably to the usefulness of our courses by reorganizing them, by all means let us do it. It is certainly our duty and it should be our pleasure.
An Experiment in Classification of Pupils in Algebra
Authors: Price Miss L.
Published: January 2021

It is the purpose of this paper to describe an experiment which is being conducted at the New Trier Township High School, in segregating Freshmen into slow-moving, normal and accelerated classes in Algebra, an experiment which is undoubtedly being duplicated in other schools. We are describing our experiment with the hope of bringing about a discussion as to the advisability of such classes, best method of conducting them, subject-matter to be taught, and results that may be expected.
The Thorndike Philosophy of Teaching the Processes and Principles of Arithmetic
Authors: Bailey Middlesex A.
Published: January 2021

The object of this article is to review the Thorndike system of teaching the processes and principles of arithmetic as explained in the “Psychology of Arithmetic” (P), “The New Methods of Arithmetic” (M), and “The Three-Book Series of Arithmetics (I, II, III), with the hope, by retaining the good and replacing the bad, of finding a better system.
Public Honors for Mathematical Contributions
Authors: Miller G. A.
Published: January 2021

The student who is considering the question of preparing himself for a mathematical career is naturally interested in the possible public honors for important contributions along this line. He is probably aware that the Ph.D. degree is supposed to imply such contributions, but he may not have heard much about the public honors which normally follow this degree in ease a man continues to make contributions of high order. It is evident that society should be so organized as to encourage such contributions for after the start has been made under the inspiration of the Ph.D. degree still better results may normally be expected from the more mature later efforts if they are sufficiently strenuous and prolonged.
News and Notes
Authors: Averill P. W. , Emerson Josephine B. , Hart Howard F. , Schuster Carl N. , Webb Harrison E.
Published: January 2021

The following preliminary report was submitted by the Committee on Examinations of the Association of Mathematics Teachers of New Jersey, at the regular spring meeting of the association.
Some Varieties of Space
Authors: Martin Emilie N.
Published: January 2021

The purpose of this paper is to make a rapid survey from the standpoint of geometry of some of the more important varieties of space. Of necessity only the most striking of the simpler properties can be brought out, and any theorems given will be stated without proof. The spectacular element that comes from endowing figures in the various spaces with reason, useful as it is for illustration, will be omitted.
Geometry as a Course in Reasoning
Authors: McLaughlin Henry P.
Published: January 2021

How can geometry be reclaimed from its present position in most of our secondary schools as little more than an unsuccessful course in formal mathematical logic, is a question that has engaged the attention of alert teachers for many years. There is a movement on foot at the present time to overhaul the whole of our mathematical teaching in all schools below the college grade which is doing much to improve the situation. As soon as school authorities throughout the country had decided that geometry could and should be taught in the newly organized junior high schools, the problem was put squarely up to mathematics teachers to reorganize the content and methods of this subject. It was quite evident from the start that the old style presentation of mathematical proofs that we call demonstrative geometry would not be understood by pupils below the ninth grade, and there was a sneaking suspicion in the minds of many that it was not too well understood by most pupils above that grade. Accordingly Euclid's organization of the subject matter of geometry was thrown boldly overboard by mathematical committees appointed to study the situation, and a course of study was recommended which was based on the capacities of childrens’ minds rather than on those of the ancient Greek philosophers. Rigid proofs were eliminated and intuitive, observational, inventional, and numerical geometry was substituted.
News and Notes
Authors: Anthony Gertrude L.
Published: January 2021

With Mr. E. L. Thompson of Joliet Township High School presiding, the Mathematics Section of the Central Association met in the Shortridge High School, Indianapolis.
Imagination in Mathematics
Authors: Lovitt W. V.
Published: January 2021

A constructive imagination is one of the most important elements in our life of today. It is the man with an active, vivid imagination who is achieving the apparently impossible.
An Experiment Comparing the Efficiency of General Mathematics with Algebra and Geometry
Authors: Burks W. D.
Published: January 2021

In the fall of 1920, Dr. R. A. Kent, Superintendent of Schools, asked me to conduct an experiment comparing the efficiency of a two-year course in general mathematics with the traditional one-year course in algebra and geometry. We decided to put all students starting mathematics in February, 1921, into general mathematics. There were 63, a few of whom were accelerates and a few poor students, but by far the greater number were failures and had already failed once or twice in mathematics.
Mathematical Games
Authors: Raster Alfreda
Published: January 2021

Most teachers of high school algebra at some time in their careers have to answer the eternal question, “What shall I do today?” And that question usually comes when the teacher is busy with about a million and one other duties. Frequently the teacher is asked to give suggestions to the school mathematics club for a short notice program. At such times the following games may be used to advantage. The rules may be varied at the teacher's pleasure to serve special purposes, or so that they will be better adapted to the teacher's personality. Suggestions for varying these rules to suit different occasions might easily fill a large volume, since the people involved really make the game, adding unwritten rules by the score. The bare rules answer the “what” of the games, rather than the “why, where, when, and how.”
Recent Changes in the Teaching of Algebra
Authors: Nyberg Joseph A.
Published: January 2021

For a time I was undecided whether to make my title “Recent Changes in the Teaching of Algebra” or “Recent Improvements in the Teaching of Algebra.” Finally I concluded that changes would be a safer word than improvements because we may not all think that the changes are improvements. I shall not discuss the content of ninth grade mathematics in general but shall limit myself chiefly to the algebra of the ninth grade, and shall, if time permits, consider two topics: changes in content and changes in classroom methods; that is, what to teach, and how to teach it. The Report of the National Committee and Prof. Thorndike s researches, as presented in his recent book, The Psychology of Algebra, are the two leading influences in changing our work in algebra. We have heard so many favorable comments on the work of the National Committee that I shall assume this afternoon the unpleasant task of calling attention to some of its unfavorable aspects.
What the Tests Do Not Test
Authors: Walker Helen M.
Published: January 2021

The question as to the adequacy of our standard tests of mathematics is only a very modern revision of the ancient and honorable query as to the aims of mathematical education, a subject upon which far wiser people than I have disagreed. It is evident at once that we cannot consistently have one set of goals operative while we teach and another while we test the results of that teaching; we cannot teach mathematics for its character content and test only for mechanical skills. It is of course easier to write a test which will measure dexterity in manipulating fractional equations than one which will measure the “honesty of thinking” about which most of us talk upon occasion, yet if we are to maintain the integrity of our own thinking we must face this dilemma.
A Study of a Pupil's Knowledge of Algebra at the Beginning of His Junior Year in High School
Authors: Mirick Gordon R. , Sanford Vera
Published: January 2021

The investigation here reported was undertaken to determine what things in algebra and arithmetic a pupil knows at the be-ginning of his junior year in high school.
Uses of Cardboard
Authors: Lane Miss Ruth
Published: January 2021

All mathematics teachers who read this article have no doubt found various uses for cardboard, probably some of them the same as those I describe, for only part are original with me.
The Interplay of Mathematics and English
Authors: Macdonald Louise Anderson
Published: January 2021

Until my very inspiring associations with the Mathematics teachers of the University, I should have said that the contribution of the department of Mathematics to the department of English lay in the correction of a child's inaccuracies of speech— the troubling verbs, and the no less troubling pronouns. But four years of delightful professional camaraderie with my friends, the mathematicians, have taught me that this correction of verbal errors, while it is a help for which all English teachers are grateful, is by no means the greatest service which the one department renders to the other. No child handicapped from birth by constant association with illiterate minds, ever learns to speak accurately just because he is required by teachers of all departments to stumble again and again over a recitation until he has straightened out his verbs and purified his pronouns. To a child handicapped by environment, accuracy of speech comes only as the result of an inward desire—a yearning, a craving, a passion, for accuracy, In the development of linguistic power as well as in the development of character, we are saved by desire and not by compulsion; we are saved from within and never from without. The correction of a specific inaccuracy, therefore, is a help, to be sure; but it is neither the only nor yet the greatest service rendered, as many of us in our blindness had once supposed it to be.
Suggestions on the Arithmetic Question
Authors: Smith David Eugene
Published: January 2021

The National Committe on Mathematical Requirements served, through its report, to stimulate inquiry on the part of those who know something about the problem of mathematics in the secondary school. The commission appointed by the College Entrance Examination Hoard, through its report, confirmed the important findings of the National Committee, and did much to eliminate the obsolete material in the high-school curriculum and to substitute therefor a more modern type of algebra, geometry, and trigonometry. It will take some time for schools and teachers to adjust the courses in mathematics to meet the recommendations of these bodies, to eliminate the over-drill, to cast out the useless part of the work in the elementary operations, and to realize that trigonometry is a part of algebra and that it can be made much simpler and more interesting than much of the drudgery (as the subject was commonly taught) that it replaces, but the leaven is working and the outcome will be on the right side. It takes time to develop the idea that we should seek quality instead of mere quantity, but our younger generation of teachers is coming rapidly to realize the significance of this idea in a subject, for example, like algebra. The reform would proceed more rapidly if it were not that nearly all of our current tests include a considerable amount of material that has been recommended for elimination by all who have given the subject serious thought. As Professor Upton has recently remarked in the Mathematics Teacher, schools often feel compelled to teach subjects that are obsolete, and possibly even to recognize forms that are incorrect, because of the carelessness shown in preparing many of these tests.
Rule and Reason in Algebra
Authors: Beatley Ralph
Published: January 2021

Miss Young: “Miss Elder, how do you teach — 5 times — 3 equals + 15? 1 have taught algebra for three years now and a lot of my pupils have great trouble in seeing just why — 5 times — 3 gives + 15. They see perfectly well that the rule ‘minus times minus gives plus’ seems to work out all right and they are able to follow the rule in doing their exercises. But I have a feeling that some of the more conscientious among them who are really trying to understand what it is all about are not convinced by my explanations, and that they are beginning to follow rules just so as to get the right answer and to please me. It seems to me that unless I can replace this attitude by a more comprehending one on their part, they will fail to get much of the good which the study of algebra should give them, and will build up a wrong attitude toward mathematics in general.
Some Interesting Side Lights Upon Elementary Mathematics, Introducing a New Expansion of Binomial Theorem
Authors: Meeks L. H.
Published: January 2021

In this article I hope to call attention to certain diversions in the study of elementary mathematics as pursued in high schools today.
The Inductive Method in Junior College Mathematics
Authors: Christofferson H. C.
Published: January 2021

To prove the general case first and then to show the application to specific problems is the usual technique of development of a Mathematical idea. This deductive presentation of mathematical ideas is so concise, so beautiful and so logical that nearly all textbook writers and most teachers enjoy using it. In spite of its universality of use the deductive method of thinking is not the way in which ideas were first discovered, nor is it the way in which they are most easily learned.
Recreational Values Achieved Through Mathematics Clubs in Secondary Schools
Authors: Guglk Marik
Published: January 2021

For ages mathematics has had the reputation of being the hardest subject in the curriculum. We have often heard of the mathematics grind. Perhaps, of it, more than of other subjects have pupils asked such questions, as “What is it all about?” or “What is the use of studying algebra?”
On the Curriculum of Mathematics
Authors: Schwatt Isaac J.
Published: January 2021

It would appear that the processes of education have been carried on long enough to have established a fixed educational policy. The prevalent conflicting ideas and the present unrest in education indicate, however, that it is only in the beginning of its experimental stage and that educators are not, as yet, agreed on many of the most fundamental questions of their calling.
The National Council in Louisiana-Mississippi
Authors: Slaught H. E.
Published: January 2021

A concerted effort is in progress to establish a branch of the National Council in Louisiana-Mississippi. The sponsors of this program are the officers of the Louisiana-Mississippi Section of the Mathematical Association of America. The annual meeting of this Section, which usually comes at the end of March, has been fixed for March 4-5, 1927, in order to secure the attendance of officers and other members of the National Council who will be returning from the Dallas meeting of the Council which occurs the previous week.
The Four Fundamental Arithmetical Processes in Adults
Authors: Helseth Inga Olla
Published: January 2021

Are the addition, subtraction, multiplication, and division combinations simple and automatic responses on the part of adults? Do they all perform these operations in a somewhat similar manner or has each developed a scheme of his own for getting the acceptable result? Such questions come to the teacher watching closely a class of adults performing the operations.
Romance of Mathematics
Authors: Slaught H. E.
Published: January 2021

It may seem unwarranted to speak of romance in connection with a subject commonly supposed to be as dry and prosaic as mathematics. The dictionary defines a romance as a “fictitious and wonderful tale.” The tale which I am about to relate is indeed wonderful but it is not fictitious—it is true and it is the kind of truth that is stranger than fiction. It is the story of the birth and growth of the number concept in the human race—it is the story of the struggle of humanity to learn to count. We speak glibly of “thousands,” and “millions,” and “billions,” but we should not forget that these concepts are the cumulative heritage of many centuries. Even to-day there are backward tribes in some parts of the world who have no number words beyond “one,” “two,” or “three” and who designate all larger groups under the single word “many.”
Postulates and Sequence in Euclid
Authors: Evans George W.
Published: January 2021

Almost any proposition in geometry is implied by another, already accepted; that may have been implied by still others, but in this regression we finally reach statements that appear not to be dependent upon implication. They are the postulates or definitions upon which all the science of geometry is based— the “first causes.” They are originally the result of analyzing the world outside our minds, to clarify the ideas of the simplest objects in it and of their simplest relations. Some such primary statements can by taking thought be shown to be implied by others. In framing a geometrical system, as Euclid did, it is necessary to choose which of the results of our analysis shall be our postulates or definitions. The choice usually made for elementary geometry to-day is in good part the choice made by Euclid.1 We can, however, be more explicit than he, particularly in regard to the idea of what we call number.
Two Variables
Authors: Farrar Alice W.
Published: January 2021

The two variables about which I wish to speak are skill and understanding. It is very difficult to separate them sufficiently to solve for either in terms of the other, but I feel cpiite sure that the problem of our students’ success in algebra can be satisfactorily solved only in terms of both.
The Teaching of Mathematics in Germany Since the War
Authors: Malsch Fritz , Beatley Ralph
Published: January 2021

The recent political changes which have been taking place in Germany have brought about—among other things—an eager desire for complete reorganization of the educational system of that country. The problems of the new education have occupied the attention of committees and congresses innumerable. Of these the most important is the Reichsschulkonferenz, a national committee, whose report has only recently been published.
Has Algebra Certain Real Values for the High School Student of To-Day?: A Radio Talk
Authors: Perry Winona
Published: January 2021

Why are nearly all of the high school students of to-day asked to include at least one course in algebra on a year's program of study? Is it that one of the uses of algebra is to enable the student to be better prepared to undertake the study of the sciences? A rather large number of instructors in certain science subjects have indicated, on carefully prepared questionnaires, that certain topics in algebra are considered fundamental to the most effective learning of their particular subject. Of immediate importance to us was the series of statements revealing that the easier parts (rather than the long, involved, and difficult aspects) of certain topics were the ones more frequently used in other subjects.
Two Methods of Teaching Geometry: Syllabus VS. TextBook
Authors: Ryan James D.
Published: January 2021

Geometry is intended to be a good course in logical reasoning, and yet, to many, it is a poor course in memory training. Pupils memorize theorems from a textbook (with or without previous explanation by the teacher), recite what they have memorized, but have very great difficulty doing original exercises, even though many of the originals are less difficult than the theorems which have been so glibly recited. Dissatisfied with this situation, many teachers have kept textbooks out of the hands of their pupils, and have taught each theorem as an original. Some issue a printed syllabus of the semester's work; others assign work from day to day, giving the class very little information as to the general direction in which they are going. The general intention in both cases is the same: the pupil must work out each theorem, without at any time seeing it worked iu full in a textbook. Absence of a textbook is the important feature of the syllabus method.
Applications of Indeterminate Equations to Geometry
Authors: Tripp M. O.
Published: January 2021

One of the important problems in secondary instruction in mathematics is to find concrete material for vitalizing the work in elementary algebra and geometry. Frequently the work as given is too abstract for the student, and does not connect closely with his experience. Since the road to the abstract is over the concrete, it is hoped that the illustrative material here offered will make the student's approach to generalized mathematics easier by using much arithmetical work.
Mathematics in Science
Authors: Tyler H. W.
Published: January 2021

I count it an honor, however little deserved, to Have a responsible share in your program. When I received the invitation from the President in esse I had not quite the strength of mind either to decline or to admit that the subject was too big for me. The President in posse in a flank attack made a specious plea about the duty of the head of a department in an institution reputed to be a hotbed of applied mathematics to justify that reputation a plea which it would have been ignominious to disregard. Aware, nevertheless, of my real incompetence to tell you just what part our ancient science really does play in these other more complicated but less interesting modern ones, I have, after trying to show some of you, yesterday, a few exhibits of t ransmigrated mathematics, surreptitiously changed my subject without the permission of either of these presidential potentates to Mathematics as a Modern Science, naturally from the standpoint of a teacher in a school of applied science.
The Position of the High School Teacher of Mathematics
Authors: Evans Griffith C.
Published: January 2021

There are many things that make the present position of the high school teacher unsatisfactory and of doubtful portent for the future. A particular misfortune dogs the teacher of mathematics. Perhaps only a little can be done about it, but we may at least look the situation in the face. Moreover, even if merely small things may be done at present, an awakened public conscience and love of parents for their children may eventually furnish the lever which will change a small movement into a considerable reform. Is there any doubt
Ability Grouping in Mathematical Classes
Authors: Durell Fletcher
Published: January 2021

One of the most striking outcomes of the recent wide use of intelligence tests and the various new-type tests in educational work has been the reyelation of the unexpectedly wide differences in the ability and aptitudes of pupils. Consequent upon this revelation has come the demand that the instruction given to pupils shall be more exactly adapted to their individual capacities and needs.
The Project Method and the Socialized Recitation
Authors: Jablonower Joseph
Published: January 2021

In this paper we propose to consider the Project method and the Socialized Recitation from the point of view of their contribution to pedagogy in general and to the teaching of mathematics in particular. It will be necessary, naturally, to define these terms, and in defining them we shall find clues to the aspects of them that constitute their distinctive and valid contributions as well as to those aspects that we consider their short comings.
A Dirreent Beginning for Plane Geometry
Authors: Christofferson H. C.
Published: January 2021

At a meeting of the Southeastern New York State Teachers Association held at Teachers College, Columbia University. last year. Dr. David Eugene Smith made the statement that there had been nothing new in geometry as it is taught in our high schools since the time ot Euclid, 2200 years ago. Of course there have been minor changes, little tricks and devices, and even an introductory inductive chapter in many books, but the real demonstrative geometry is essentially the same in organization and content as established by that ancient but ingenious master mathematician and logician.
A Reply to “The Position of the High School Teacher of Mathematics”
Authors: Cowley Elizabeth B.
Published: January 2021

The article on the above subject in the October number of this journal presents one point of view quite forcibly. But is that the only point of view? I think that it is not. I wish to present another aspect of this matter by commenting upon certain sentences of the above article which appear in italics below. But before doing so it may be well to indicate my academic status. I have my doctorate in Mathematics. After many consecutive years of teaching calculus and various other branches of mathematics in a large eastern college, I am, by invitation, spending my accumulated years of leave of absence doing research work on the mathematics curriculum of the senior high schools of a large city, and at the same time carrying the full work of a regular teacher of mathematics in a coeducational senior high school. I teach nothing but plane and solid geometry.
A Few Determinants in Building the Course of studey in Mathematics
Authors: Jones Gertrude
Published: January 2021

A casual survey of educational literature reveals the tendency of movements in education to come in waves. The project method, educatioua l measurements, student government, and supervised study are a few of these waves that have been the chief concern of educators until a new wave has rolled in. At present, educators everywhere are riding the wave of curriculum reconstruction, the inevitable result of several factors, among which are the problems presented by the junior high school, the great increase in the senior high school enrolment with its consequent wide variation in ability and interests, and the rapidly changing conditions of modem life. 'This problem of the curriculum is one of vital concern. Professor Thomas Briggs calls the curriculum problem fundamental in education since its content determines the organization of the school, the types of buildings, the methods used, and the value of the school to the community.
College Entrance Requirements in Geometry
Authors: Jackson Dunham
Published: January 2021

A proposal bas been made to the College Entrance Examination Board that it should modify its requirements so as to bring about the more extensive introduction of courses including an appreciable amount of solid geometry in the first year of geometry, in place of a part of the plane geometry ordinarily taught. In response to a request from the Board, a committee has been appointed by the Mathematical Associntion of America and the National Council of Teachers of Mathematics to discuss the feasibility of the proposal.
A One Year Course in Plane and Solid Geometry
Authors: Stone John C.
Published: January 2021

We are here to consider curriculum revision of geometry. It is not only fitting but essential that we review the changes that have been made since the origin of geometry in order to meet the needs of those who are to study it; and that we review the aims and objectives of the course.
Geometry Measures Land
Authors: Ransom W. R.
Published: January 2021

Is algebra just a game, played with letters? This seems to be the opinion held by many students. Moreover, they are often inattentive to the rules of the game, and willing to take a chance of finishing on the winning side.
A Mathematics Exhibit
Authors: Cottell Gregory M.
Published: January 2021

Display Boards And Tables and a poster On which was printed in bold type "Mathematics Exhibit", aroused some curiosity among the students of The Louisville Girls High School last spring. They were accustomed to the exhibits of the art and home economics departments, but a mathematics exhibit! Who ever heard of such?
High School Mathematics Teachers in the United States
Authors: W. Anderson Earl , Eliassen R. H.
Published: January 2021

Prospective Teachers and their advisers are often searching for information regarding the extent to which a specific subject is taught in high schools, the degree to which it is combined with other subjects, and what those other subjects are. It was the purpose or this study to bring together such reported findings relative to the teaching of mathematics.
Some Methods in Professionalized Subject Matter Courses in Mathematics for Teachers College
Authors: E. Kramer Edna
Published: January 2021

As a result of the recent interest and progress in teacher-training in the United States, has come the evolution of the normal school into the teachers college. The development has naturally given rise to the question of what should be done in order that the lengthened course be filled in most profitably. Whether to give additional courses in educational theory and methods of teaching, or to include courses in the content of the various subjects which students plan to teach that is, whether to make the teachers college a normal school of a "larger growth," or to convert it into the equivalent of a liberal arts college, which would lay special stress on the subjects commonly grouped under the heading "Education" — these have been the points under consideration.
Book Propositions in Teaching Geometry
Authors: Horn Aaron
Published: January 2021

The specific objectives to be attained in the teaching of geometry, as typically expressed in the New York State syllabus, are of two kinds: (1) the ability to solve “originals” and (2) the ability to reproduce any of a set of “book propositions.”
On the Teaching of Algebra
Authors: D. Grossman Howard
Published: January 2021

The improvement of the teaching of mathematics is the proper domain of teachers as well as of supervisors. It is on that assumption that the following remarks are made.
The Construction and Validation of a Test of Geometric Aptitude
Authors: Lee J. Murray , May Lee Dorris
Published: January 2021

Is there a need for an instrument of guidance in the field of geometry? The answer from practically all school people who have had to meet the problem is, “Yes.” Geometry was placed in our course of study when the almost sole function of the school was to prepare for college work. It was expected that all pupils should take it as it was considered necessary to their future studies. Furthermore, the students at that time were a highly selected group, only those of high intellectual ability attempting this advanced work. Thus it was not unreasonable to expect all to study geometry with at least a moderate degree of success.
Irrational Quantities
Authors: Phillipi J. F.
Published: January 2021

Having had in my classes in college algebra hundreds of students coming from a variety of preparatory schools, I have come to the conclusion that the subject of irrationals or radicals is a somewhat difficult subject and that any suggestion as to its presentation to students might be welcomed.
Grading Entirely by Tests
Authors: Stroup P.
Published: January 2021

I was much interested in the article by Nelson A. Jackson in the January number of the Mathematics Teacher on “Home work in first year Algebra.” I was not surprised but rather much comforted by statistical confirmation of my suspicion that the inspection of home work is a poor basis for grades. There is a better use for homework and also a better basis for grades. The students correct their own home work or at least are given an opportunity to profit by their own mistakes. Every day the problems are shown to the students correctly solved but after they have had an opportunity to solve them themselves. The usual program is to read the answers to the home work problems and then have some student who has a certain problem solved correctly put it on the board. All are given opportunity to criticize and ask questions. If this gives too much leisure for some, the lesson for the next day is given out and those who are ready go ahead with it. The teacher is constantly on call for any one who wants help; sometimes interrupting the whole group to save time by making a general explanation.
Blaise Pascal
Authors: Sanford Vera
Published: January 2021

Blaise Pascal is known as a philosopher, a physicist, an inventor, and a mathematician, but his varied activities were so closely allied that it is difficult to discuss any one without discussing the others also. It is difficult, too, to speak of the circumstances of his life without constant reference to his father who was a lawyer, and to his two sisters Mme. Perier and Jacqueline.
A Message from the New President of the National Council
Authors: Betz William
Published: January 2021

Just two years ago my worthy predecessor, Dr. John P. Everett, in looking back upon the development of the National Council during the past ten years of its existence, wrote these significant lines:
A Tentative Program for the Policy Committee
Authors: Hassler J. O.
Published: January 2021

This program was outlined first by Mr. Betz, president of the National Council, and revised by the writer who has been appointed chairman of the committee.
Formalism in Mathematical Teaching
Authors: Hedrick E. R.
Published: January 2021

From the very wording of this title of mine—formalism in mathematical teaching—many among you may have inferred that I would decry formalism of every type in the teaching of mathematics. Were I to do so, however, I would needs defame mathematics altogether, for formalism is at the very basis of mathematical procedure. Precise formulation, abstraction, symbolisms, are the life-blood of mathematics, without which it would become anemic, sterile, worthless.
Demonstrative Geometry in the Ninth Year
Authors: Orleans Joseph B.
Published: January 2021

In Chapter III on the Mathematics for Years Seven, Eight and Nine, the Report of the National Committee on Mathematical Requirements contains the following paragraph:
Adapting Instructional Material to Individual Differences in Learning
Authors: Johnson J. T.
Published: January 2021

So far there have been two main teaching methods of dealing with the problem of individual differences in learning, the homogeneous grouping of classes on the basis of ability and the individual instruction method. The earlier attempts at homogeneous grouping were known as the Batavia plan and the Pueblo plan in which groups of students within a class were taught and promoted as groups. It was not until the advent of the intelligence tests that segregation into class groups on the basis of ability began. We now have the well known A, B and C groups or the X, Y and Z groups in many high schools.
The Problem of Mathematical Statistics
Authors: Crathorne A. R.
Published: January 2021

A statistical inquiry is usually made up of three parts, first the collection of the data, second, the analysis of the data and third, its interpretation for the particular purpose in view. The first and third stages depend almost entirely upon the field of investigation. Biological data should be collected and interpreted by a biologist. The collection of economic data should be planned by economists and interpreted by one well acquainted with the field of inquiry. The second stage on the other hand, is in general common to all fields. Whatever may be the subject matter the mathematical analysis has in a great degree the same essential features. Lack of appreciation of this three-fold problem of statistics has led to some extremely doubtful results in statistical analysis. No amount of mathematical training and ability can take the place of the judgment and common sense that comes from a thorough knowledge of the field in which the problem lies. On the other hand much time and energy may be wasted in the analysis of data by lack of understanding of the fundamentals of the mathematical processes used in the investigation. This is usually exhibited in the blind use of formulas without realization of the assumptions and limitations used in their derivation.
The lnfuence of the College Entrance Examinations on the Teaching of Secondary Mathematics
Authors: Whitcraft L. H.
Published: January 2021

A few days ago your speaker was privileged to hear a lecture by Strickland Gillilan, one of America's outstanding humorists. One thing emphasized particularly in that lecture was that facts of today will not be facts tomorrow. During the past few years this has been repeatedly demonstrated. The world has been changing so rapidly that the most of us have found it utterly impossible to make satisfactory adjustments. The data which I shall report in this paper were facts only a short time ago but I cannot vouch for them all as true statements of existing conditions today.
The 14th Annual Meeting of the National Council of Teachers of Mathematics, Minneapolis, February 24-25, 1933
Authors: Schreiber Edwin W.
Published: January 2021

Present: John P. Everett, Martha Hildebrandt, Edwin W. Schreiber, William D. Reeve, Vera Sanford, C. M. Austin, Harry C. Barber, William Betz, Mary S. Sabin, Mary A. Potter, Herbert E. Slaught, C. Louis Thiele, Elsie P. Johnson, Raleigh Schorling. Absent: Mary Kelly, Marie Gugle.
A Study of Davies' University Arithmetic, 1846
Authors: Kunkel Paul V.
Published: January 2021

This study was undertaken to try to answer the following questions: (1) What did our ancestors consider to be the content of arithmetic? (2) Was this more, or less practical than our present content? (3) Are the problems contained in the old arithmetics practical problems, and if so, might they be used as patterns for the construction of problems which would be practical today? (4) What interesting facts and information may be gleaned from the study of this text?
Changes in the Teaching of Geometry and Why We Teach It
Authors: Grant Alice Ann
Published: January 2021

Euclid's methods compared with those of the present day