bluuebunny/crossref_metadata_2025 huggingface dataset:
Research Department
Authors: Schorling Raleigh
Published: January 2021

This department has proposed two problems with the hope that data bearing on these two questions might be collected from many sources. The April (1922) issue proposed: “To study the relation between general intelligence of pupils and achievement in a demonstrative geometry course.” second problem was stated as follows in the May (1922) issue: “To study the relation between the general intelligence of pupils and achievement in a regular algebra course.” A considerable amount of material has been received for each problem but the data secured are not as complete as they need to be to make possible a reliable study. The chief defect arises through the practice of sending material which neglects to account for pupils who withdraw before the close of the semester (term, or year). It may also prove desirable to indicate what pupils are repeaters and the number of times they have failed the course which they are attempting.
The Unitary Organization of the Mathematics of the Seventh, Eighth, and Ninth Grades
Authors: Breslich E. R.
Published: January 2021

In the traditional courses in mathematics there has been a constant tendency in organization of materials to organize in logical units, i. e., to put together subject-matter which logically belongs together. In studying the material, the pupil concentrates intensely on one topic at a time without giving thought to its relation to other topics or to the course as a whole. Moreover, he does not concentrate fully enough on a single topic to get the experiences necessary to attain complete mastery. For, the unit is simply a lesson on a fact, a process, or a principle, taught and studied on a certain day, without clear connection with other related facts, and without definite insight as to what each fact contributes to the whole. The goal of instruction is ability of the pupil to recite on, or to discuss, the particular lesson taught, before taking up the study of the next lesson. As a result, the pupil may answer satisfactorily questions on each lesson, without being able to recite on the topic as a whole, and without being able to distinguish between the relative values of the parts of a topic. A successful recitation is considered sufficient evidence that a lesson is learned. Tests consist of questions on isolated facts, rather than on the unit as a whole.
Mechanics: Rectilinear Motion of a Point. Gravity.
Authors: Mirick Gordon R.
Published: January 2021

In the last article we were concerned with finding the final velocity, being given the initial velocity, acceleration and the time. We did not consider the distance passed over during any interval of time.
Fate and Freedom
Authors: Korzybski Alfred
Published: January 2021

In this lecture I propose to analyze the principles on which the foundation of the Science and Art of Human Engineering must rest, if we are ever to have such a Science and Art.
The Confusion of Objectives in Secondary Mathematics
Authors: Betz William
Published: January 2021

It is the purpose of this study to consider the transforming influence of recent curriculum theories in the field of secondary mathematics. These theories are vitally affecting mathematical instruction from a standpoint of both quantity and quality. Throughout the discussion, an acquaintance with the older literature of educational aims and values is presupposed. For the sake of brevity, moreover, the familiar, traditional point of view in the teaching of mathematics will be referred to only in a prefatory way.
Oral Work in High School Algebra
Authors: Taylor Miss S. Helen
Published: January 2021

By oral work I refer to all work of which none is written, whether it is actually rehearsed in words or simply performed in thoughts. I shall include all class discussion under oral work, so that I may include what I consider a very valuable part of oral work, the discussion of written work. I qualify this definition by remarking: first, that if the algebraic material is well organized, it is difficult to set off one section as oral and one as written, even for a given pupil; second, work which is suitable for oral work for one pupil is not necessarily so for another, and third, that in practice one passes over the boundary from oral to written work with great frequency and that this is desirable.
Memory and Marks in Mathematics
Authors: Luccock Ethel
Published: January 2021

Last November I read an article in School Science and Mathematics on “The Relation Between Thinking and Memorization in Mathematics.” It was written by Mr. E. W. Atkins of the Carnegie Institute of Technology.
A Project in Mathematics: Two Algebra Classes Build a Railroad
Authors: Smith Donald P.
Published: January 2021

In this project, two classes in mathematics, one of boys and the other of girls, built and operated a railway system. Since it was impossible to obtain the necessary data on any small line in the vicinity of the school, a branch of the New Jersey Central was used. Enough information was available concerning the actual system here to make the project real and possible.
Hotz Algebra Scales in the Pacific Northwest
Authors: Eells Walter Crosby
Published: January 2021

As a result of an address on “Standard Tests in Mathematics” given by the author at the annual meeting of the Inland Empire Council of Teachers of Mathematics at Spokane in April, 1924, a committee on “Standard Tests in Mathematics in the High Schools of the Pacific Northwest” was appointed. He was made chairman, the other members being Professor J. E. Buchanan, Cheney Normal School, representing the normal schools; and Miss Anna Whitney, Yakima High School, representing the secondary schools.
Scales of Notation
Authors: Mirick Gordon R. , Sanford Vera
Published: January 2021

The inclusion of the topic Scales of Notation in the College Board's requirements in Advanced Algebra is justified not for the intrinsic usefulness of the subject for its practical value is nil, but solely for the insight that it gives into the fortuitous nature of our number system.
Improvement in Algebra Teaching
Authors: McCain A. B.
Published: January 2021

In an article by Harry C. Barber in the October, 1923, number of The Mathematics Teacher there are some very interesting questions asked of the teacher of mathematics about what he is going to do for a ninth grade girl if she comes to his classes for the pupose of studying Algebra. Now I am the teacher and I believe I can answer some of those questions quite satisfactorily without waiting for this fourteen-year-old daughter to become a grandmother, for I feel very certain that if we wait for the final answer to be given by experimenters and psychologists we will allow many generations of fourteen-year-old sons and daughters to become grandparents and yet the answer will not be given to the satisfaction of all.
Some Comments on the First Year Book by the National Council of Teachers of Mathematics
Authors: Johnson J. T.
Published: January 2021

In this age of rapid evolution in methods of teaching mathematics, in text book making and curriculum construction no professionally spirited teacher of mathematics can well afford to be without this comprehensive treatise.
Some Thoughts on Space
Authors: Roe E. D.
Published: January 2021

The statement is frequently made that Kant’s theory of space has been overthrown.
Equations
Authors: Smith Eugene R. , Rorer Jonathan T. , Taylor James M.
Published: January 2021

The statement that two expression denote the same number is called an equality. This name is precise and descriptive; equally so arc identity and equation as names respectively of an unconditional equality and a conditional equality. The beginner in algebra should clearly distinguish between these two kinds of equalities.
Interest of Pupils in High School Mathematics and Factors in Securing It
Authors: Davis Alfred
Published: January 2021

A few years ago attention was attracted to the high percentage of failures among pupils taking high school mathematics. Sometimes as many as 50% or even more would fail in a single class. A little consideration would have convinced the teachers that such a situation must soon attract unfavorable criticism, and that this might be expected from those who were not most favorably disposed towards the subject. At a time when every subject was to be tried and judged, not according to its past achievements, nor according to its future possibilities, but according to present status alone, someone was certain to take a one-eyed view of high school mathematics and condemn it as an unsuitable subject to be required of all high school pupils.
Mathesis
Authors: Brownell Ella
Published: January 2021

The scene is an underground studio or workshop. Incense is burning in a large black kettle hanging from a black tripod at front of stage. A red electric bulb under the kettle is surrounded by sticks of kindling wood. Two large portable blackboards are placed one at each side of front stage. Small table with white paper spread ornamented with black paper figures (circle, trapezoid, triangle, etc.) is concealed behind left blackboard. On the table are the following articles: cardboard cylinder, three ice cream cones filled with sand and having same base and height as cylinder. Two eighteen-inch boxes at right front stage covered with white paper and ornamented with black circles to imitate dice.
Address of Welcome
Authors: Snow WM. B
Published: January 2021

I feel greatly honored at being designated to extend to you this evening the cordial welcome of the School Department of the City of Boston, and I confess to an especial pleasure in being privileged to extend that welcome to the Mathematicians rather than to the Scientists or the Historians or the Classicists or the specialists in English. For although most of my friends in educational circles now think of me as a mere dabbler in the modern languages, I might assert, in the words of Spartacus to the gladiators, that “I was not always thus,” for in the early days of my teaching I foregathered with men who talked of cosines, integrals, quaternions, and transcendental functions; and though our paths long since diverged, I can imagine, in meeting you tonight, something of what one feels when, after many years of happy wedlock with another, he meets again with her who charmed his youth. The names, too, on your program: Mr. Vosburgh and Miss Kee, of our Boston Teachers College; Tyler, of the Institute, whom I first knew when we were boys together in a little New England town; Downey, who taught for years beside me and succeeded me as Headmaster of the English Iligh School; Barber, who has worked with me in both day school and eYening school and whose powers developed in that same English High School in contact with such colleagues as Evans and Wright, and Marsh! Why, the very atmosphere of that school was redolent of mathematics; two thirds of its headmasters were noted mathematicians, and the line runs straight from Emerson and Miles through Thomas Sherwin and Edwin P. Seaver to Walter F. Downey, who is to speak to you tomorrow afternoon. How could I fail to rejoice in finding myself in such company! So, in calling you friends, I almost venture to add “fellow-mathematicians,” for may not Echippus claim kinship with Bucephalus?
The Need for Testing Practices in Curriculum Revision
Authors: Edwards W. M. Herbert
Published: January 2021

Anyone engaged with the problem of curriculum revision is likely to be very distinctly impressed by the literature on the subject where three dimensions are essential to redesigning a curriculum. The three predominately mentioned are first, aims, second, materials and third, methods of teaching. The purpose of this paper is to call attention to the significance in mathematics curriculum revision of a fourth dimension, namely the testing practice at present employed in the mathematics classroom.
Significant Facts in the History of the Metric system for Teachers of Junior and Senior High School Mathematics
Authors: Schreiber Edwin W.
Published: January 2021

It was down in old Mexico that I had my first real introduction to the metric system. 'Tis true I had met the meter and her children, centimeter, millimeter, and little micron, in a formal way whiJe busy in the laboratories at the university in my undergraduate clays-but it was a cold and scientific acquaintance. Under a warm southern sky, with the sun doing its full share to brighten the picture, I read in no uncertain letters on a freshly painted sign which was posted on a little rail way station in old Sonora: "To Calexico, 33.5 Km." So here upon a common road (not a royal one) Kilometer and I met face to face. From that friendly meeting of a member of the metric system a desire was kindled within me to know more about the family history of the meter, and since that time (1913) I have picked up some interesting facts covering the whole family, some of which it is my purpose to relate at this time.
Socialized Mathematics
Authors: Klopp W. J.
Published: January 2021

Much is being written about mathematical objectives to be realized in courses offered in secondary schools and much stress is laid upon the modern trends in mathematical teaching outcomes.
Professional Preparation and Growth in Secondary School Mathematics
Authors: Blank Laura
Published: January 2021

However Inadequate one finds his undergraduate preparation in mathematics, once he is settled in the work of teaching secondary school mathematics, there is little excuse for his failure to pursue some very definite plan for professional growth. It is true, one can fulfill the conditions of his contract, he can acquire even a sort of proficiency, as an instructor, drawing solely from the fund of information and training of his college days, coupled with his gradually acquired experience. This same instructor, after he has developed a genuine enthusiasm in his subject, a constant watchfulness for allied interests, associations and contacts, after he has pursued some externally directed or self directed study of some branch of mathematics for several years, he rapidly becomes a very valuable member of a department of mathematics.
Criticism of Dr. Bowden's «Consumers Uses of Arithemetic»
Authors: Roth William E.
Published: January 2021

DR. A. O. Bowden in a dissertation on “Consumers Uses of Arithmetic”1 aims to determine those types of arithmetical knowledge “which may be universally required of all the public elementary school population.” (p. 1) His estimMe is based on questionnaires: first he submitted a questionnaire containing 345 problems of the kinds commonly found in elementary school arithmetics to 42 persons in three cities; then on the basis of these 42 returns he prepared a new questionnaire containing 123 of his original 345 problems. On the latter he received 640 returns which he considered as properly executed; thus giving him in all the 682 returns on 123 problems that form the basis of his study. Those filling out the second questionnaire were instructed that they were “not to solve the problems, but check whether you (they) have ever used the kind of arithmetic needed to solve them.” (p 67) The uses aside from business or vocational needs were to be checked either “yes” or “no” under each of the seven headings: buying at store, making change, reading of newspapers and magazines, investing of savings, letter writing, etc., income tax sheets, traveling. Then he has “arbitrarily taken for granted that less than 25 per cent use by the adult population warrants our discarding certain types of problems from elementary school textbooks.” (p. 48) And he concludes that of the original eighteen categories of problems covered by his first questionnaire only eight remain.
Roman Numerals
Authors: Sanford Vera
Published: January 2021

When a thing that has had a wide use is finally restricted to a narrow field, it often happens that it becomes stereotyped, and generally it ceases to develop further. This has been the case with Roman numerals. After upwards of two thousand years. of active life, they have been relegated to a few uses, and we, familiar with the conventional rules under which they now operate, are astonished when we realize that they have ever differed from their present form.
Sources of Program Material and Some Types of Program Work Which Might Be Undertaken by High School Mathematics Clubs
Authors: Hoag Ruth
Published: January 2021

The following suggestions for work of high school mathematics clubs are listed under seven headings: (1) Projects; (2) Demonstrations and Experiments; (3) Skits, Plays, and Dialogues; (4) Games; (5) Field Trips and Field Work; (6) Outside Speakers; and (7) Topics for Group or Individual Presentation. A project may be initiated and carried forward in addition to a diversified or unified program meeting if desired. Such projects can aid in allowing the club work to parallel and grow out of curricular work.
A Technique for Introducing General Number and Algebraic Representation of Operation
Authors: Brechbill Henry
Published: January 2021

The majority of algebra teachers and textbooks open their beginning courses in this subject with the treatment of formulas. While the wisdom of introducing the course with so abstract a topic is open to question, it is not the purpose of this article to contend for a departure from the usual practice, but rather to point out certain pupil difficulties and to suggest ways of overcoming them.
John Wesley Young
Authors: Sanford Vera
Published: January 2021

Teachers of mathematics in secondary schools in this country have been fortunate in having the help and leadership of certain few scholars of pure mathematics who, like Felix Klein in Germany, have been keenly interested in the problems of the elementary field. These men are rare, for such work requires unusual gifts. Of the group, the late Prof. J. W. Young was an outstanding member.
A Study of Certain Mathematical Abilities in High School Physics
Authors: Carter William Ray
Published: January 2021

The results from the five tests used in this study are presented in detail in the preceding part with but little comment or interpretation. A brief description of the distribution of first semester marks in physics is also included. It is now necessary to make further interpretations of these results in the light of the purposes of this study as they are stated in Part II.
Mathematical Induction
Authors: Garver Raymond
Published: January 2021

The student in college algebra does not ordinarily have the opportunity to see very clearly the importance and wide applicability of proofs by mathematical induction. He uses the method in summing certain series to n terms, and in the proof of the binomial theorem for positive integral exponents, and then drops it, usually with a sigh of relief. Consequently in a recent more advanced course in algebra I thought it worth while to devote some little time to a study of various applications of the method. The list of applications which was thus obtained may, I hope, be of sufficient interest to warrant its presentation to readers of The Mathematics Teacher. Of course, the list is obviously not complete; there are many examples from higher mathematics which I did not desire to include. I wanted only problems which the students could work through. I should say that in the class presentation I used none of the references to Dickson's Modern Algebraic Theories, and not all of those to Bôcher's Higher Algebra. However, these are standard sources, and some readers may be interested in the use they make of induction.
Should Mathematics Teachers Seek to Know the Needs of Society?
Authors: Merton Taylor Goodrich M.A.
Published: January 2021

The article “improving America's Mathematics” in the issue of last May of The Mathematics Teacher opened with an illustration so striking that its fallacy was well hidden. It stated in substance that a doctor does not go out on the street and ask different people what kind of pills they have been taking in order to prescribe for his patients. There are many who do not agree with the inferences and conclusions made in that article from that clever but obvious statement.
New Books
Authors: Sanford Vera
Published: January 2021

This new text for classes in second-year algebra is intendent to meet the requirements of the College Entrance Examination Board and the New York Regents. The arrangements of topics, the method of presentation, and the proportioned treatment reveal a book planned to be of assistance for the efficient teaching of algebra and, with regard to the student, a book planned for a logical, practical and pleasant study course.
Scientific Investigations oF the Teaching of High School Mathematics Reported in 1932
Authors: Benz H. E.
Published: January 2021

About a year ago the present writer prepared a summary of scientific investigations of the teaching of high school mathematics. This summary was published as a chapter in the Eighth Yearbook of the National Council of Teachers of Mathematics, and included material from 132 references selected chiefly because they met the usual criteria of scientific research. The present report represents an effort to bring this summary down to date by reporting similar studies which were published during 1932. The same classification is used in order to make it easy for the supplement to conform to the original report.
Central Objectives of the Educational Process
Authors: Webb Harrison E.
Published: January 2021

In a previous article (Newark School Bulletin, November 1931) the writer has considered various social aims in education. The process by which any or all of these commendable purposes are to be attained is of course immediately present to the social consciousness. In general it may be stated that the desideratum in behalf of the young person undergoing education is the possession of useful knowledge. This is to take a static view of the educational scheme. The corresponding dynamic outlook had better be phrased as the capacity for intelligent service. Many books and articles have been written, and countless sermons have been preached, to enforce the importance of the difference between these two lines of approach to the educational problem. The distinction, however, is for the present purposes academic, in that in the last analysis either phrase connotes the other in the realm of practicality. As applied to a particular subject or topic, all worth-while knowledge is serviceable, and the intelligent solution of a particular problem is the useful one.
The Plane Geometry Scholarship Tests in Ohio
Authors: Christofferson H. C.
Published: January 2021

There are at least three parts to the Scholarship program carried on by the State Department of Education in Ohio under the leadership of Ray G. Wood: the Every Pupil Test program in December and April of each year, the State Scholarship Contest in May, and the General Scholarship Test for High School Seniors usually given in March each year. This report is concerned with the Every Pupil Test program only and largely with the geometry test results for December 1930 and 1931. These results have been carefully diagnosed and presented in two bulletins entitled, “The Learning and Teaching of Geometry”1 and “The Ohio Survey of Elementary Mathematics.”2 It shall be the purpose of this paper to present some of the most striking results given in those bulletins.
Mathematics Exhibit – World's Fair, Chicago
Authors: Moore Lillian
Published: January 2021

The mathematics exhibit at the century of crogress exhibition in chicago during the summer of 1933 consisted of two sections: A) an immense octagonal prism, on the lateral faces of which were notations concerning the various subdivisions of mathematics together with slides, illustrating the development and history of algebra and geometry; B) a collection of nineteen exhibits, illustrating various interesting mathematical principles and practical applications of mathematics.
How is it Possible to Make Elementary Algebra More Real to the Pupil?
Authors: Wanenmacher Alberta S.
Published: January 2021

Those of you who have read the article by Judd in the April 1932 number of The Mathematics Teacher will remember no doubt that he accuses us of not always being efficient in our work. To the question, why students fail in mathematics, he received vague and general answers from mathematics teachers, many of whom were inclined to place the blame for failure entirely upon the students, calling large numbers of them mentally inferior.
Scientific Investigations of the Teaching of High School Mathematics Reported in 1933
Authors: Benz H. E.
Published: January 2021

About two years ago the present writer prepared a summary of the investigations of the teaching of high school mathematics through 1931. This summary was brought through 1932 in an article in this journal last October. The present report continues this summary by reporting similar studies published during 1933.
Joseph Louis Lagrange
Authors: Sanford Vera
Published: January 2021

In the case of Lagrange, we have a man whose interest seemed to lie in other fields until, apparently by accident, his attention was drawn to mathematics which he then studied almost to the exclusion of everything else. Lagrange was of French descent, but for a number of generations his people had been in Turin where representatives of his family held a certain political post in the Sardinian government. Loria notes that this position remained in the family until 1800 from which one concludes that it was abolished when Napoleon's campaigns changed the political organization of Italy.
The Need for a Reorientation of Secondary Mathematics from the College Viewpoint
Authors: Hart William L.
Published: January 2021

In discussing the orientation of secondary mathematics, I shall not consider explicit details about the content of high school courses or about the methodology of their teachers. Moreover, although I shall be speaking from the viewpoint of a teacher of college mathematics, I shall not restrict myself to topics which are of importance only as preparation for college work. Part of my remarks will relate to the matter of teacher morale, and will suggest inferences with respect to the mathematical attitude of those responsible for the administration of the high schools. Another section of my paper will consist of general recommendations about the placement of students in courses in secondary mathematics.
A Proposed National Committee on Arithmetic
Authors: Morton R. L.
Published: January 2021

There are many respects in which books dealing with the teaching of arithmetic disagree. Textbooks designed for the use of children also disagree as to content, the arrangement of the material selected, and the suggested methods of procedure. Some of the disagreements are implied in the following questions which represent more or less random selections from the arithmetic of the elementary school.
The Art of Teaching A New Department
Authors: Sprague James B.
Published: January 2021

Many teachers of elementary algebra find that pupils who take a real interest in learning to perform the four fundamental operations with literal expressions, and who are intrigued by the novelty of using negative numbers are strangely unresponsive when introduced to the solution of verbal problems. Even after an appreciation lesson designed to demonstrate that problem solution is a basic aim of the subject, more than one teacher has been greeted by subdued groans, when announcing that the new assignment is the application of some principle to the solution of problems.
A Brief Professional Philosophy for Teaching of High School Mathematics
Authors: Munch H. F.
Published: January 2021

One of the most important factors in success in teaching is the attitude of the teacher toward his job, toward the pupils, and toward the subject which he teaches, in short, his viewpoint with regard to these factors in the learning situation. You no doubt remember the Biblical quotation (Proverbs 29:18) “Where there is no vision the people perish.” Surely where the teacher has no vision as to his responsibilities, his opportunities, the possibilities of his job, if he has no vision as to the beauties of mathematics, its power, its eternal verity, its universality, its great value in the process of educating young people as citizens of our republic, as members of a family group, for their vocations, or to develop ethical character, the pupils perish. The teacher who has no vision as to the value to the state and to the local community of the young people who como to him for instruction, the teacher who does not sense the wonderful possibilities enshrined in them, who does not comprehend the anxiety of parents and friends for their success and welfare has not the vision to be a teacher.
Mathematics in the Modern Curriculum for Secondary Education
Authors: Wrinkle William L.
Published: January 2021

Two opposing tendencies are normally operative throughout the life of a social institution, the tendency to stabilize and the tendency to change. In a static society, the tendency to change meets successful opposition; in a dynamic society, the tendency of any institution to stabilize becomes the target of criticism and at tack. Twice in the evolution of American secondary education, the dominant institution so successfully resisted change that it was displaced by a new institution designed to better meet the needs of a changed society. Today, public secondary education is again in a period of transition. The advocates of stability and change face each other as traditionalists and progressives.
Experimental Studies of Large Unit and Individualized Plans of Supervised Study of Secondary School Mathematics
Authors: Douglass Harl R.
Published: January 2021

While no one study may furnish the basis for definite or permanent conclusions with respect to the relative value of various proposed plans of directing the study of high school mathematics involving large unit assignments and individualized progress, one may better evaluate the claims made for and against such plans, if one is familiar with the results of those experimental studies which throw light on the question.
A Simplification in Elementary Trigonometry
Authors: Jackson W. H.
Published: January 2021

It is generally admitted that consideration should be paid rather to the normal student who forms the bulk of the class than to those few who find the subject particularly easy or particularly hard.
Is the Average Secondary School Pupil able to Acquire a Thorough Knowledge of all the Mathematics Ordinarily Given in these Schools?
Authors: Smith Eugene R. , Babb Maurice J. , Schwatt I. J.
Published: January 2021

Before taking up the subject of our discussion, I ought to state that it has always been with the greatest reluctance that I have felt constrained to criticise the teaching of mathematics in the elementary and secondary schools. The reason for my reluctance is the inequity of the situation. We college teachers have an opportunity to test the knowledge of many who have been taught in the elementary and secondary schools, and on the results of this test, our favorable or unfavorable criticism is based. But the inequity exists because we college teachers constitute ourselves a court of last resort, so to speak. True enough, the college student will be judged by the mental capabilities which he possesses, but very few of them will have to show how much actual knowledge of mathematics they have gained while under our instruction. If we college teachers are unsuccessful with the student, we have the defense that he came to us not fully prepared and that the foundation of his mathematical knowledge was not strong enough to put the superstructure on. However, I feel that there is as much need for improvement in the course of study and the method of teaching of college mathematics as there is of the elementary and secondary mathematics.
An Historical Excursion
Authors: Cook A. J.
Published: January 2021

My youthful education was rather sadly neglected; no doubt, chiefly the result of my own obtuseness. At any rate I seemed to have moved for a long period within the penumbra of mathematics. Some considerable time elapsed, in spite of my interest in the subject, before it became. apparent to me that mathematic was cultural in its quality, that the sciences were, or at least should be, humanities, and that the feud that seemed so often to rage over so-called literary and socalled scientific matters was a battle of prejudice, at least as much as a battle of wits.
The Relative Effectiveness of a Large Unit Plan of Supervised Study and the Daily Recitation Method in the Teaching of Algebra and Geometry
Authors: Hunziker Charles W. , Douglass Harl R.
Published: January 2021

Purpose of Experiment. It was the objective of this investigation to furnish experimental data th rowing light on the question of the relative effectiveness of a plan of supervised study and the conventional daily recitation method. In the supervised study procedure, unit assignments of from four to twenty days were employed. One to three days were spent in making the assignment and preparing the class to attack it. This state was then followed by several days of supervised study in which for the greater part silent individual study was employed though occasional class discussion was used. Each unit was concluded with a “recitation” in the form of an oral discussion or an oral or written quiz over the unit.
Mathematics: A Tool Subject or a System of Thought?
Authors: Griffin F. L.
Published: January 2021

In view of the present widespread discussion of the appropriate place of mathematical studies in contemporary education,1 it seems important to seek a consensus of opinion as to whether mathematics should properly be regarded as a tool subject or as a system of thought.
Geometry and LiFe
Authors: Leisenring Kenneth B.
Published: January 2021

In the general criticisms to which the secondary mathematics curriculum is being subjected the demonstrative geomtry course is perhaps getting the roughest handling. Its position is sometimes made to appear to have little but tradition to support it, and its defenders have sometimes resorted to arguments which have given weight to this appearance.
On the Need of Cooperation Between High School and College Teachers of Mathematics
Authors: Kempner Aubrey
Published: January 2021

It is an honour to be invited to speak to you. Some months ago I talked to my colleagues in the collegiate field about the incredible difficulties in the present high school situation, and pleaded for their cooperation in any form you may desire.1 To you, I need not say much concerning the facts. You are more keenly aware of them than I can be. It would only be carrying owls to Athens. I nstead, I shall attempt a constructive suggestion, without unfriendly criticism of any kind.
Mathematics in Herbart's Philosophy of Education
Authors: Lynch J. A.
Published: January 2021

Mathematicians and mathematical philosophers have often called attention to the fact that mathematical discoveries sometimes seem to anticipate important discoveries in physics. This is usually interpreted as meaning that the universe is “rational at the core” or that it was “created by a mathematician.” Such speculations are extremely enticing; but I wish to make an entirely different application of this interesting observation at the present time.
In Other Periodicals
Authors: Lazar Nathan
Published: January 2021

The following are some of the topics treated: (1) the purpose of plane geometry, (2) the mastery of subject matter, (3) geometric factssum of the angles of a triangle and other polygons, ratio and proportion, Pythagorean Theorem, rigidity of a triangle, area formulas, similari ty, measuring inaccessible distances, principles of construction, navigation, designs and decoration, a rchitecture, nature, (4) precise and accurate use of words, (5) nature of proof, (6) indirect proof, (7) discovering new truths, (8) symmetry of form.
An Experimental Study in Learning to Read Numerals
Authors: Lester R. , Wheeler Viola D.
Published: January 2021

Various diagnostic studies show that errors in reading numbers are common even through high school. While frequent discussions are found concerning the abstract character of number concepts, educators have paid little attention to the difficulties involved in learning to read numerals, and have limited their investigations largely to a study of eye-movements. Dearborn (6) and Gray (8), using photographic records of eye movements, conclude: first, the time required for reading numerals increases with an increase in the digit lengths of the numerals; second, a single digit is often the unit of perception in the two-digit numerals; and third, in reading numbers the attention is concerned with smaller printed units than when reading words. According to Terry (17), when reading numerals an adult divides the material into much smaller units than when reading words, and seldom apprehends more than two numerals at a time while as many as twelve letters may be grasped at the same time. While this investigator concludes that it requires a different type of memory to keep numbers in mind from that required to recall logically coherent words, Rebert (13) suggests that numerals tend to be read in the same manner as words and that the length of pauses depends largely upon the degree to which the subject is familiar with the numerals.
Status and Trends of Ability Grouping in the State Universities
Authors: O'Quinn Ralph
Published: January 2021

On April 30, 1938, a letter with a brief questionnaire inclosed was sent to heads of mathematics departments in the forty-eight state universities and colleges.
The Two Recent National Reports on Mathematics in General Education
Authors: Potter Mary A.
Published: January 2021

If there were no problems in the teaching of mathematics; if all methods of procedure had been perfectly worked out; if all desirable applications of mathematics were known; if all teachers had been chosen with the greatest skill and had become accomplished artists; if all children had been created with a uniform mental, emotional, moral, and social pattern; if the relative importance of all school subjects had been exactly determined; if the world in which mathematics is used would remain static, then there would be little need of a National Council of Teachers of Mathematics, and Reports would be undesired luxuries.
Mathematics Films
Authors: Hildebrandt E. H. C.
Published: January 2021

At the present time it is generally assumed that the motion picture film can be used to good advantage in teaching the units in the various school subjects. It is, therefore, natural that the teacher of mathematics is led to inquire regarding films which could be so used in the mathematics classroom. The first source for such information is no doubt the latest edition of the Educational Film Catalog.1 In the 1939 edition only three films were listed under the heading Mathematics and one of these, “Visualized Solid Geometry,” was withdrawn from circulation early this year. A second source for the teacher may be found in the catalogues published by the various distributors, copies of which are no doubt on file in the office of the principal or the head of the visual aids department of the local school system. Over half of the state universities have established extension divisions for the distribution of these films and a list of these is found in the Educational Film Catalog as well as at the close of this article. In addition there are a number of private distributors with offices in many of the principal cities.
What Mathematical Knowledge and Abilities for the Teacher of Geometry Should the Teacher Training Program Provide in Fields Other than Geometry?
Authors: Hendrix Gertrude
Published: January 2021

Before one ventures to assert what mathematical knowledge any teacher of any mathematics should have, it is fitting that he remind himself—and others, possibly—that “what knowledge” is only half the problem: Equally arresting is the question of how that knowledge is to be acquired. The knowledge and abilities listed in this paper are necessary, but not sufficient if received as a “hand out.”
Training Teachers of General Mathematics
Authors: Butler C. H.
Published: January 2021

Any discussion of the training of teachers of general mathematics must be approached, I think, through a consideration of what the job implies. This, in turn, involves an examination of the nature and status of the subject and of the reasons for teaching it. It seems appropriate, therefore, at the outset to try to arrive at some acceptable understanding of the meaning of general mathematics and of its place in the educational program.
The Mil as an Angular Unit and Its Importance to the Army
Authors: Burington Richard S.
Published: January 2021

In the Army of the United States, two systems for measuring angles are in wide use; the mil system and the familiar sexagesimal system. In the mil system, the fundamental unit is the mil, where by definition 1600 mils equal one right angle. In contrast, in the sexagesimal system, the fundamental unit is the degree, where 90 degrees equal one right angle. Radian measure is also used to some extent by the Army. Most American mobile artillery units as well as many heavy railway mounts have the scales on their sights, azimuth circles, and quadrants graduated in mils, and some of these units have their scales graduated in both mils and degrees. The mil is also employed to a large extent by the Infantry.
A Presentation of Fractions to Avoid Pitfalls in Arithmetic and Algebra
Authors: Leete Luella E.
Published: January 2021

Fractions probably cause more difficulty than any other subject in the mathematics taught in the elementary schools and the junior and senior high schools. Even the bright pupils in the engineering schools have trouble with fractions. A similarity or uniformity of presentation throughout the grades and high schools may help to steer the students away from the pitfalls which are usually found along the “fraction highway.” It is with this thought in mind that I offer a few suggestion for the presentation of arithmetic and algebraic fractions.
The Art of Teaching: A Device for Teaching Locus
Authors: Amig Margaret C.
Published: January 2021

By the time the pupil has reached locus problems (about the beginning of the second semester of plane geometry), he is pretty well acquainted with figures and has learned to observe relationships between their parts—points, lines, and angles. He has been taught to pick the hypothesis out of a statement and draw a figure to illustrate it. With the figure before him, his task is then to discover or to prove certain conclusions about the figure. Locus problems must be approached in a very different way. No description of the figure is presented to the pupil nor is he expected to draw a figure all at once. The problem is to use certain key points or lines in order to locate a set of points which obey certain given conditions. In other words the pupil is to show how a figure grows rather than merely to produce one.
The Problem of Ninth Year Mathematics
Authors: Braverman Benjamin
Published: January 2021

There are obvious reasons why ninth year mathematics has challenged and will continue to challenge the best thought of teachers of secondary mathematics.
An Experimental Comparison of Algebraic Reading Practace and the Solving of Additional Verbal Problems in Tenth Grade Algebra
Authors: Russell David H. , Holmes F. Melville
Published: January 2021

The solution of verbal problems in algebra has always presented difficulties to pupils and teachers. Orlie and Hendershot conclude that “the weakest part of classroom instruction is the teaching of verbal problems” (8:147). Haertter says, “High School pupils who study algebra have greater difficulty in the solution of verbal problems than with the study of any other topic of that subject” (6: 166). In a questionnaire submitted by one of the present writers, fifty-three teachers of algebra in the province of Saskatchewan ranked the solution of verbal problems as the most difficult topic in the algebra they taught.
Learning the Harder Multiplication and Division Facts in a Program Emphasizing Understanding
Authors: Spitzer Herbert F. , Dunfee Maxine
Published: January 2021

A survey of the current literature in the field of arithmetic reveals that much attention is now being given to the development of understanding. There is almost universal agreement among writers that facts should be meaningful and that drill should only be used after understanding has been attained. The use of meaningful procedures is frequently suggested as the method whereby understanding is to be attained. Classroom teachers and others closely associated with children in schools, however, realize that the suggestion “use meaningful procedures” does not go very far in the way of supplying specific methods to be used in teaching. The present paper describes a fourth grade program, in which primary emphasis is put on understanding of facts and processes, and in which learning procedures designed for mastery of facts were given a secondary place in time of introduction and in importance.
A Lesson on the Parabola, with Emphasis on Its Importance in Modern Life
Authors: Camp Chester C.
Published: January 2021

While vacationing in the North Woods of Minnesota last summer I received a letter from your President asking whether I would give a talk before the Mathematics Section of the Nebraska State Teachers Association in October on “The Parabola.” Of course I accepted but when I returned to Lincoln in September I found opposite my name the title, “A Lesson on the Parabola.” The more I thought about it the more I wondered just who it was that this Lesson referred to, whether to the speaker, or to your President, or to the audience—you know if a person learns his lesson he usually doesn't make the same mistake again!
The Mathematics Most Used in the Sciences of Physics, Chemistry, Engineering and Higher Mathematics
Authors: Nickle George H.
Published: January 2021

As a student of mathematics in the secondary school, I accepted the teachings of my teachers as coming from individuals who were skilled in the ways of the world and knew just the things that were best for me to study. In those days, which are not so far past, the pupils did not question the wisdom of the teacher and stay in the class room to argue a point very long. Therefore the teacher was always right.
The Art Of Teaching: Toward Better Graphs
Authors: Eagle Edwin
Published: January 2021

The use of graphical presentation is now wide-spread, and it is becoming increasingly popular and important as a means of prescn ting data and conveying factual information. Even a cursory comparison of today's newspapers, magazines, and scientific and commercial publications with those of a few years ago indicates a definite trend toward an increased use of graphic methods.
Minutes of the Eighth Winter Meeting of the National Council of Teachers of Mathematics
Authors: Schreiber Edwin W.
Published: January 2021

The eighth winter meeting of the National Council was held from December 31, 1941 to January 1, 1942, at Lehigh University, Bethlehem, Pennsylvania. About 200 were in attendance at the various section meetings of the Council and 170 registered.
A Proper Balance Between Social Arithmetic and a Science of Arithmetic
Authors: Bond E. A.
Published: January 2021

I am downright glad to be given this chance to think with you for a few minutes about a subject that has long been nearest my heart. For more than thirty years much of my time and most of my work has been devoted to the problem of improving instruction in arithmetic. Yet at this present moment, I see more real problems ahead than at any previous time during my study. During these years innovations have come and have gone. Some of these changes have made real contributions towards improving the teaching of arithmetic. Others have had to be lived down as have other fads of education.
Arithmetic as Concept Building
Authors: Nordahl Marguerite
Published: January 2021

Before we can think together clearly and profoundly, we shall have to agree what we mean when we use the term arithmetic. Arithmetic has been commonly conceived as synonymous with number.