bluuebunny/crossref_metadata_2025 huggingface dataset:
Uniform Grading of Examinations in Algebra
Authors: Nyberg Joseph A.
Published: January 2021

About fifteen years ago investigators began calling attention to the great variation in grades that different teachers give an examination paper. If, for example, the pupil is solving the equation 5x − 3(x − 2) = 14 and obtains 5x − 3x − 6 = 14 and then x = 10, shall this work be marked zero because the solution is incorrect or shall the pupil be given some credit for his ability to solve 5x − 3x − 6 = 14 even though the pupil has made an error in obtaining this equation? The object of this paper is to explain a method by which different teachers can grade an examination paper in algebra and all agree on the score.
The Why and the How in Algebra
Authors: Marsh Harry B.
Published: January 2021

One of the most important questions at the basis of mathematicalunderstanding and discovery is contained in the single word, Why. The question Why indicates a most desirable attitudetoward activity in any field of mathematics. It is especially desirable as a class-room attitude. When pupils are in such a state of mind that they wish to know the reasons for various processes and steps, they are at least on the road to real appreciation and enjoyment in mathematics. Unfortunately, so far as this situation is concerned, ours is a large country, and, speaking figuratively, too small a percentage of our pupils are from Missouri by nature. This, however, does not relieve us as teachers from doing all in our power to stimulate in the minds of our boys and girls the spirit of curiosity and inquiry. We should create and constantly encourage the questioning and even the challenging attitude that must ever know the reason why. We must realize that to be alive and alert, a class must be interested and active and that we are always more interested in activities in which we have a share. Hence it is important not only to secure a questioning attitude but also to translate that attitude into actual class discussion and participation. Only under such circumstances can the best and most constructive progress be made.
Is Geometry Possible?
Authors: Statham Jeanette F.
Published: January 2021

The attitude of many teachers toward geometry, as shown by frequent discussions of this subject, might make some students even more reluctant to take it up than they are now. Students pass along the word that geometry is hard and most sophomores apparently try to avoid one of the most beneficial subjects in the high school curriculum. If they could approach it with unprejudiced minds, avoiding the deadly “complex” which many of them talk about with delight, the teacher's task would be much easier.
Suppose There Were No Mathematics
Authors: Clark R. F.
Published: January 2021

Henry Jones, section 519, sat at home in his room studying his Math. 5. His father, a successful C.E., president of one of the large construction companies, stepped into his room and asked how his work was going. Henry said that it wasn't going very well. He couldn't see why he should study mathematics. “I don't need it. It hasn't any value.” His father replied, “Think it over. Suppose there were no mathematics. What about our civilization?”
The Need for More Adequate Measurements of Achievement in Arithmetic
Authors: Sangren Paul V.
Published: January 2021

Complexity of Abilities in Arithmetic,—In all attempts at measurement the primary problem is that of defining the ability, quality, or factor to be measured. In this respect the abilities in arithmetic offer no exception. When the question is raised as to the exact meaning of that which we call arithmetical ability the most capable student of the psychology of arithmetic must “side-step” with a statement which attempts to state the various directions in which the abilities in arithmetic function. One does not need to be a careful student of Education, Psychology or Mathematics to be aware of the fact that it is impossible to point out a particular mental activity or mental product and say, “This alone is arithmetic or the exercise of arithmetical ability.”
An Analysis of the Learning—Units in N Processes in Algebra
Authors: Pease Glenn R.
Published: January 2021

In the face of continued agitation for curricular reVIsron, looking toward the “Practical” in all lines of ccondary school subjects, it may, at first thought, seem a bit archaic to propose a study of the purely abstract elements involved in the fundamental functions of beginning algebm. Such a study is desirable, however, because the mastery of these abstract principles is an absolute prerequisite to successful problem solving in the field which the curriculum revisors point out as proper material for first year algebra. Such necessity for mastery of the abstract problem preliminary to verbal problem solving is recognized by Judd,1 Rugg and Clark,2 and other investigators. H. E. Dow 3 points out the fact that in nine of the most widely used textbooks, 80 percent of the problems offered are abstract problems, and only 20 percent are verbal problems.
Remedial work in High School Mathematics
Authors: Whitcraft L. H.
Published: January 2021

Teachers of high school mathematics are confronted with the fact that there are more failures in the mathematics of the secondary school than in any other subject in the secondary school curriculum. These failures may be traced to some one of the following factors; (1) the materials of mathematics, consisting of the textbook, practice exercises, and special devices; (2) the teacher's method of instruction and manner of presenting the subject matter to the pupils; or (3) the methods and processes of the pupils themselves. Now that the teachers of mathematics realize that there is a great amount of criticism due the department of mathematics what are they going to do about it? The answer should be the same as the elementary teachers have given to the criticisms which have come to them-give remedial work.
Relating Art and Mathematics
Authors: Luella Weir Bertha
Published: January 2021

A very important problem in junior high school mathematics is to find concrete materials for the cultural values of mathematics, such as the appreciation of its beauty and to constructively develop the imagination of the pupil. Marie Gugle 's article on Dynamic Symmetry in "The Third Yearbook of the National Council" inspired me to introduce the root-two rectangle in connection with the work in square root and the Pythagorean Theorem.
Rebuilding Geometry
Authors: George W. Evans
Published: January 2021

Three or four years ago the National Council published a review of progress in the teaching of mathematics during the preceding twentyfive years. Among the contributions to that end was the reprinting of an address made to the American Mathematical Society in 1902 by its President, E. H. Moore.
Tenth Year Mathematics Outline
Authors: Reeve W.D.
Published: January 2021

A Great Many teachers of geometry are recommending a combination course of plane and solid geometry, one year in length. The attitude of the National Committee favors such a course, as will be seen in these quotations from its recent report.
Problems in the Teaching of Mathematics
Authors: Georges J. S.
Published: January 2021

The Purpose Of This study is to present a systematic classification of the mathematical literature which relates to the problems in the teaching of secondary school mathematics and which has been written during the last three decades. This literature consists of a large number and variety of articles published in numerous educational and mathematical journals, a smaller number of special studies dealing with specific problems, some books on the psychology and teaching of the subject, a few books of a general nature discussing the philosophical aspects of the concepts and principles of elementary mathematics, and unpublished theses. The collection and presentation of this vast material in a connected form is a much needed, though laborious and difficult, task. Its classification will be based upon three distinct, and at the same time inter-related principles: first, that there is a real need for a summary of the problems relating to the teaching of secondary school mathematics; second, that these problems should be analyzed in the light of available literature; and third, that the sources of references dealing with each problem should be brought together.
Home Work or Supervised Study?
Authors: Smith Grace
Published: January 2021

There Seems to be an almost universal agreement among educators that there should be very little home work assignment of mathematics except in the case of special assignments for the removal of disabilities or in the case where the pupil undertakes voluntary projects.
The Efficiency of Decomposition Compared with That of Equal Additions as a Technique in Subtraction of Whole Numbers
Authors: Johnson J. T.
Published: January 2021

In Order to Understand fully the import of this experiment, it is necessary that the reader have clearly in mind the different methods of subtraction.
The Principle of Continuity
Authors: Hennessey Francis P.
Published: January 2021

An interesting and effective manner of conducting a review in plane geometry is to make use of the Principle of Continuity whenever possible. Of the several text-books which I have had the opportunity to consult, relatively few, (D.E. Smith, Seymour, Schultze, and Nyberg) have made reference even indirectly to this important property which weaves many theorems into one. It is difficult to reconcile such an omission with the modern emphasis on functional thinking in mathematics.
The Fourth Dimension:
Authors: Seybold Anice
Published: January 2021

The idea of a fourth dimension seems to have about the same kind of fascination for the lay mind as the famous old problems of duplication of the cube, trisection of the angle, and quadrature of the circle had. Certain things which would follow if we could live in four dimensional space seem quite remarkable to one who has not given the subject enough thought to realize that the actual existence of such space would make it possible to draw four mutually perpendicular lines through a given point, whereas in three dimensional space we can draw only three. These apparent absurdities of four dimensional space appear absurd only when we try to make them conform to our three dimensional experience.
A Testing Program in Elementary algebra and Its Evaluation
Authors: Welton P. L.
Published: January 2021

Itroduction-Results obtained by pupils on various tests and examinations in algebra have been published from time to time. The use of such results and the application of remedial measures to insure better teaching and a higher degree of success on the part of more pupils was outlined, for example, in Mr. J. B. Orleans' article in the March 1930 issue of The Mathematics Teacher.
Significant Digits in Computation with Approximate Numbers
Authors: Bond E. A.
Published: January 2021

Results of operations involving measured quantities are frequently expressed with an indicated degree of precision far beyond that which the approximate nature of the measurements warrants. This is especially true in textbooks both in numerical mathematics and in statistics. Accordingly, it seems to the writer that a study should be made of the number of significant figures that should be retained to express the results of each of the operations involving approximate numbers. This article is an effort to contribute to this problem.
Mathematics as a Liberator of the Spirit
Authors: Anning Norman
Published: January 2021

Standing here within sight of the international boundary may I have a few minutes of your time to pay tribute to two Canadian teachers:
The Need for Being Definite with Respect to Achievement Standards
Authors: Schorling Raleigh
Published: January 2021

There are two purposes in this brief discussion: first, to present evidence that there is need for being definite in stating to pupils and parents what changes we are trying to make in pupils during a given period of time; and second, to suggest certain criteria to serve as a basis in securing such a list of essentials.
Maintenance Drills in the Junior High School
Authors: May Lee Dorris , Murray Lee J.
Published: January 2021

A survey test in arithmetic given in a junior high school in Burbank, California, several years ago showed the same condition that many schools have to face — pupils in seventh and eighth grade classes were weak in fundamentals. That such a situation should continue was surely not desired either by the administration or the teachers. The problem, then, was to provide a means of maintaining those computational skills previously learned but usually quickly forgotten. This problem was by no means a local one, as is shown by a statement made by Benz before the Mathematics Section of the Ohio State Educational Conference in 1928:
Mastery of Certain Mathematical Concepts by Pupils at the Junior High School Level
Authors: Henry Butler Charles
Published: January 2021

The investigation which will be reported in the following pages was undertaken mainly for the purpose of finding out to what extent a certain group of mathematical concepts had been mastered by representative groups of pupils upon completion of the seventh, eighth, and ninth grades.
Getting the Most Out of Objective Tests in Mathematics
Authors: Durell Fletcher , Durell Thomas J.
Published: January 2021

In recent years the so-called objective tests have come into wide use and have enjoyed a well deserved popularity. In particular they form a useful auxiliary to what is often termed the new education; that is, those ideas and methods which stress the pupil's self-activity and a more or less democratic form of school administration and classroom procedure.
A Study of Certain Mathematical Abilities in High School Physics
Authors: Carter William Ray
Published: January 2021

The students included in this study were members of the physics classes of thirteen high schools of Missouri during the school year of 1930-31. In selecting the schools which were to co-operate in this study, the Missouri State High School Directory for 1929-30 was used to make a list of the first class high schools offering physics during that year. Letters outlining in detail the nature of the proposed study and asking co-operation in the project were sent to the principals of these schools. The thirteen schools included in this study were the ones from which came the first offers of co-operation. In order to check the results from the Carter test, certain data from the physics classes of the Cleveland High School of St. Louis were used. Data from this school, however, were not used in the main body of this study. There were twenty separate physics classes in the thirteen schools included in this study. The locations of the cooperating schools are shown in Table I.
Preliminary Report of the Committee on Geometry
Authors: Beatley Ralph
Published: January 2021

At the meeting of the National Council in Washington, February 20, 1932 the following motion was passed without dissenting vote: “The National Council of Teachers of Mathematics reaffirm their interest in the question of geometry as expressed at the annual meeting in Detroit, and hope that the Board of Directors will find it possible to initiate and carry forward a study of the whole question of geometry in our schools.” The directors forthwith empowered the new president, Mr. Betz, to appoint a Committee on Geometry; and he, anxious that some work should go forward during the long time necessary for the final organization of this and other committees, selected six members of the National Council for immediate service on the committee, intending to enlarge the membership as soon as possible in order that it might include an even wider range of interest and opinion.
An Idea that Paid: A Play Developed and Acted by An Eighth Grade Class
Authors: Miller Florence Brooks
Published: January 2021

After approximately four weeks spent in a study of the arithmetic used in business by a proprietor of a store, by partners, and also by a stock company, this play was worked up in an eighth grade class. A review of the seventh grade work on Profit and Loss recalled the meaning of wholesale price, retail price, gross profit, overhead expense, net profit, and rate of income. The new work had to do with the forming of a partnership, the sharing of profits and of losses, and the determining of the rate of income; the forming of a stock company with emphasis upon the raising of capital by selling shares of common and preferred stock, the dividing of the net profit among the shareholders of each kind of stock, par as the original value of the stock, buying stock above and below par, and figuring the rate of income of the stockholder.
The Uses of Statistics in the Social Sciences
Authors: Crum W. L.
Published: January 2021

Statistics and statistical methods have become so common a tool of the scientist, both for conducting his research and reporting his findings, that the ordinary layman is in danger of forgetting that statistical theory is a branch of mathematical science and that statistical practice is one type of applied mathematics. This important point should be constantly in the mind of everyone who uses statistics, whether as a producer or as a consumer. Nowhere is the danger of ignoring or forgetting this injunction greater than in the various fields of social science. Whether this is due to the great abundance of factual data and their ostensible bearing upon problems of timely interest, to the supposed necessity of putting reasoning in these fields on a quantitative basis at any cost, to the absence of traditional dominance by mathematical thought processes in these fields, or to other reasons, it is idle to speculate. The essential fact is that statistical workers in social science need particularly to be reminded that the vigorous and growing structure of statistical theory takes its root in mathematics.
Supplementary Projects: Purpose
Authors: Georges J. S.
Published: January 2021

One of the outcomes of individualized instruction is enabling the pupil to proceed at his own rate and to complete the unit as an individual task rather than a group task. Individual differences between the rates of learning as well as rates of application often produce a state of affairs in the teaching program that discourages the new teacher using the individualized method of instruction. The bright pupil may complete a unit or an assignment a day, two days, or even a week before the rest of the class. The question arises as to what to do with the bright pupil or the pupil who learns with facility and works rapidly.
Psychology vs. Tradition in the Teaching of Algebra
Authors: Lazar Nathan
Published: January 2021

From the very first day a pupil enters an algebra class it is impressed upon him that there is nothing difficult or mysterious about the subject—that all the operations are patterned after those of arithmetic, and that it is in fact nothing more than a type of arithmetic that employs letters as well as numbers. It is not the purpose of this article to discuss the theoretical relation between these two branches of mathematics or such questions as whether arithmetic derives its underlying principles from algebra or vice versa. There is no doubt however that, from a practical standpoint, the use of arithmetic as a starting point and as a frame of reference will help in the solution of many difficulties that the student of algebra will encounter.
Jean Baptiste le Rond d'Alembert
Authors: Sanford Vera
Published: January 2021

On November 16, 1717, a gendarme found a baby who had been abandoned near the church of Saint Jean le Rond in Paris. The boy was given the name of the church and was boarded out by the parish in the home of a glazier who lived in the vicinity. At a later time, his father made provision for his education, and when he became famous, it is said that his mother tried to get in touch with him, but be refused her overtures and stayed with his foster mother although she was not in entire sympathy with his career. Ball quotes her as saying, “You will be nothing but a philosopher. And what is a philosopher? He is a fool who torments himself during his life so that people will talk about him when he is dead.”
Official Notice
Authors: Schreiber Edwin W.
Published: January 2021

As secretary of the National Council of Teachers of Mathematics, I officially announce the annual election of certain officers of the National Council, said election to take place at Atlantic City, New Jersey, on Friday, February 22, 1935. Article III Section 7, of the by-laws states: “At least two months before the date of the annual meeting, all members shall be given the opportunity through announcement in the official journal to suggest by mail for the guidance of the directors a candidate for each elective office for the ensuing year. At least one month before the annual meeting the secretary of the board of directors shall send to each member an official ballot giving the names of two candidates for each office to be filled. These candidates shall be selected by a nominating committee of the board of which the secretary shall be chairman. The election shall be by mail or in person and shall close on the date of the annual meeting.”
Abstracts of Recent Articles on Mathematical Topics in Other Periodicals
Authors: Lazar Nathan
Published: January 2021

An enthusiastic analysis of the important rôle that mathematics has played in the intellectual history of mankind. The author regrets the diminished time devoted to its study in the elementary school and high school. He is however opposed to the demathematization of algebra and geometry that is commonly practiced to meet the needs of the great mass of students. He proposes instead that school authorities should “permit pupils who show lack of interest or ability and who are a drag on the rest of the class to be transferred to other subjects, say at the end of six or nine weeks.”
The Need for a Reorientation of Secondary School Mathematics from the High School View Point
Authors: Hartung M. L.
Published: January 2021

Three years ago a prominent professor of education in a large eastern University published a book entitled, “Secondary Schools in 1960.” The author assumes the role of prophet, and among his predictions for 1960 are the following: “A very few students in eleventh and twelfth grades take a course in Pre-engineering Mathematics. (But in practice most prospective engineers take all their vocational mathematics in professional schools—as do the followers of nearly all other vocations.…) In marked contrast to the earlier time, it is found that commonly not more than twenty percent of pupils take any mathematics in grades seven to twelve.”
Sales of Books on the Teaching of Arithmetic
Authors: Morton R. L.
Published: January 2021

On several occasions in recent years the writer has heard the remark that if the sales of a book designed for the professional preparation of teachers reached or exceeded five thousand copies within five years of the date of publication, the book was considered a success. Judged by this standard, books on the teaching of arithmetic are rarely unsuccessful.
Transfer of Training and Educational Pseudo-Science
Authors: rata Pedro T.
Published: January 2021

The French naturalist, Cuvier, was once asked to pass judgment on the following definition: “A crab is a small red fish that walks backward.” Cuvier replied: “The definition is entirely correct except at three points,—the crab is not a fish, it is not red, and it does not walk backward.” Bagley was in the same predicament a few years ago when he was asked to speak at an N. E. A. meeting on the topic, “Modern Educational Theories and Practical Considerations.” In his characteristically satirical mood he developed the proposition beautifully by showing, step by step, that modern educational theory is not modern, that it is not practical, and above all, that it is not educational. We are reminded of these two incidents by the current conception of the problem of transfer of training which is embodied in the phrase, “The Psychology of Transfer of Training.” If we were disposed to be facetious we might paraphrase Cuvier and follow Bagley's example by showing, first, that there is no psychology,—there are only psychologies, second, that in a literal sense transfer of training is a myth, and, finally that the problem of transfer of training is not, educationally speaking, essentially a psychological problem at all. In fact, it is the aim of this paper to attempt a reinterpretation of the problem of transfer of training in the direction of conceiving of it, not as a scientific and more specifically a psychological problem, but fundamentally, though not entirely as an educational and technological question. Hence the title of the article: “Transfer of Training and Educational Pseudo-Science.”
An Attempt at Solving the Problem of Individual Differences
Authors: Murphy Clara D.
Published: January 2021

Four years of Mathematics are offered in Evanston Township High School, as follows: In the first year three courses, called Algebra 1, Mathematics 1, and Business Training; in the second year three courses—Plane Geometry, Mathematics 2, and Bookkeeping; in the third year two coursess—a second year of Algebra and Mathematics 3, which consists of a semester of Algebra and a semester of Solid Geometry; and in the four th year one course, consisting of a semester of Trigonometry and a semester of College Algebra.
Ouantitative Thinking on the Secondary School Level
Authors: Rosander A. C.
Published: January 2021

Introduction. A curious paradox is the contrast between the striking success of mathematical techniques in forming a foundation for, and a method of constant improvement of, our whole industrial civilization; and the complete failure of conventional mathematics to develop any facility in quantitative thinking among the great mass of American people.
Crises in Economics, Education, and Mathematics
Authors: Hedrick E. R.
Published: January 2021

Introduction. That there exists a crisis in our economic life is perhaps more evident than that there exist crises in educational affairs and in the teaching of mathematics in particular. What I desire most tonight is not to bewail these crises, but to discuss their causes and the part that we ourselves may play in such a vital stage in the history of this country of ours. What underlying causes exist? What may be done? What is our own duty?
The Art of Teaching A New Department
Authors: Briggs Dorothy F.
Published: January 2021

I have found it helpful, throughout the course in first year-algebra, to ha vc the tudents formulate problems for themselves, especially for oral practice. Early in the course, as we are developing the idea that, in algebra, a letter represen ts a number, the pupils ask such questions as “When n = 3, what is the value of 2n − 1?” or “If 7a=63, what is the value of a?” Often the pupil stating the problem selects the person to answer it. That student, if answering correctly, asks the next question. Care must be taken, however, to see that opportunity for practice is distributed throughout the class and not monopolized by the more aggressive members.
The Spirit of Education
Authors: Wyeth N. C.
Published: January 2021

In the center of the picture the dense clouds of Ignorance and Prejudice have parted and to the earth bas come an heroic figure symbolizing the Spirit of Education. She holds aloft the flaming torch of enlightenment, which we in AmNica are to carry forward from generation to generation, while open before her lies the Book of Learning. Mercury-like she moves over forward on the winged wheel of Progress.
Why We Teach Mathematics
Authors: Williams K. P.
Published: January 2021

The question which is raised by the title that I have given this paper is one which must have been in the minds of all of you a great many times. At the present you cannot escape it if you would, for it is forced upon you by persons who are insistent that you answer it. And some of these persons have their own answer ready; they will tell you that we teach mathematics because it has become traditional to do so. Such persons may or may not admit that there was at one time a fairly good reason for including certain mathematical instruction a a fundamental part of our school programs, but with a very knowing air they will say that the school must today “go social” in order to save humanity, and they will add that this socialization is being greatly hindered by the dead weight of such traditions as the mathematics one. And you certainly cannot reply that habits and customs often do not stand in our way. We all have complained about them, just as we complain of the Model T Fords which get in front of us on the roads ten years after the last one rolled off the assembly line. This whole question of tradition is a difficult one, but we must not accept uncritically what the rather shallow sociologists who often serve us our educational sociology have to say about it. If we are to appeal to sociologists let us turn to actual for thright students of society. In his Man's Rough Road Keller says this:
Finding Social Mathematics in School Activities
Authors: Noyes Dorothy
Published: January 2021

Judging from a number of the recent articles on high school mathematics it would seem that there is much thinking and considerable experimenting being done on the subject of making mathematics more functional. Mathcmatics has its definite place in our school organization outside of the immediate classroom; a place proportionate to that of other school subjects but which perhaps has not been as evident.
A Generalized Definition Of Limit
Authors: Roe E. D.
Published: January 2021

The object of this paper is to suggest a logical point of view from which a generalization of the definition of limit may be secured.
Special Devices in Teaching Geometry
Authors: Smith Eugene R. , Snook George Aloin , Peck Paul Noble
Published: January 2021

Since the colleges have adopted a more or less uniform standard of entrance requirements, necessitating a high degree of efficiency on the part of the candidates for admission, the burden of preparation falls upon the secondary schools. This raising of the standard on the part of the colleges frequently sorely taxes these schools by requiring a greater amount of work in preparatory subjects without any proportionate increase in the time supposed to be devoted to such preparation. Many of our high schools and private preparatory schools today are doing much of the work that, a decade ago, was considered the function of the first-year college classes. To complete the additional work imposed by this increase in the entrance requirements without slighting any of the subjects is by no means a simple task. The work must be, to a certain extent, condensed and simplified, or special devices resorted to as a means of arousing the student’s interest or directing and conserving his energies.
Testing the Results of the Teaching of Science
Authors: Thorndike Edward L.
Published: January 2021

The topic which I am asked to discuss is one of enormous complexity. The changes in human beings which result from the teaching of science in schools are real, are measurable, and will some day be defined in units of amount as we now define changes in the rate of a moving body or in the density of a gas. But they include thousands of different clements; they vary with every individual; some of them can be demonstrated only long after school is completed; and at present units and scales in which to state changes in knowledge, power, interest, habits, and ideals are mostly matters of faith. An adequate measurement of the changes wrought in one class by one course in physics would be a task comparable to a geological survey of a state or an analysis of all the materials in this building.
Transfer of Training and Reconstruction of Experience
Authors: Orata Pedro T.
Published: January 2021

Transfer of training, like democracy, intelligence, learning, curriculum, and the like, has been defined in a variety of ways. Without taking much space to review these definitions it is safe to say that all of them agree on one general pattern. Thus we may define transfer of training a that proces of using or applying previously acquired information, habit, skill, attitude, or ideal in dealing with a relatively new or novel situation. So defined transfer of training is a fact which both experience and experiment have amply demonstrated, Thorndike to the contrary notwithstanding. That it is also an ideal we have no reason to doubt so long as we have faith in education and so long further as we subscribe to the view that experience, properly acquired and used, is the best teacher. That it is intimately tied up with our concept of democracy cannot be ignored once we agree that democracy, from one view point, is a faith in the average man's ability to use and modify his experience in order to direct the course of his subsequent behavior. Thus, denial of transfer of training means denial of the verdict of experience, of the efficacy of education, and of the soundness and validity of democracy as a guiding ideal. Furthermore, to deny transfer is equivalent to denying to man that quality called intelligence, which separates him from the non-living and the lower forms of life. In final analysis, education, learning, democracy, and the like terms, all haYe their root on the assumption that transfer of training is a fact.
A Few Observations on Robert Recorde and His “Ground of Arts”
Authors: Ebert Emeline R.
Published: January 2021

The Ground of Arts: Teaching the perfect work and practice of Arithmetick both in whole Numbers and Fractions, after a more easie and exact form then in former time hath been set forth
The Relationship Between Silent Reading Ability and First Year Algebra Ability
Authors: Buckingham Guy E.
Published: January 2021

It has been shown by the author1 and his colleagues, Hottenstein, Gilliland and Tucker that a positive relationship exists between one's success in first year Algebra and his ability to eliminate errors in the simple fundamental processes of addition, subtraction, multiplication and division. It has also been shown by the same group2 that these errors persist in the more complex processes of Algebra attempted during the first year.
The Young Paseal
Authors: Bacon Harold Maile
Published: January 2021

Versatility is not inevitably the companion of genius. It is not altogether common to find a man who is at the same time a clever experimental physicist, a creative mathematician, an inventor with an eye to money-making, a gifted writer whose artistry places him among the foremost French stylists, and a religious philosopher of singular originality and ardor. Blaise Pascal was such a man. He could write an important treatise on the vacuum as well as produce those incomparable examples of controversial literature, the famous Provincial Letters. lie invented the first adding machine of practical consequence and tried (in vain) to realize a profit from its sale. In the fragment. of his projected a pology for the Christian Religion, left unfinished by his death at the early age of thirty-nine, are to be found many evidences of his mathematical genius as well as of a remarkable piety and zeal. A clear and complete picture of his early life and education would not only be of rare in terest, but it could not fail to contain many suggestions of value to the modem teacher. It is indeed a pity that such incomplete information is available. The story is soon told, but it is well worth the telling, and perhaps it holds some inspiration or lesson for our own times.
Modern Preparation for Collegey
Authors: Campbell Harold G.
Published: January 2021

Lamenting the uncertainty that jurists sometimes have of the ultimate wisdom of their decisions, Judge Cardozo once remarked upon the peace of mind that must come to the designer of a mighty bridge:
Arithmetic Readiness and Curriculum Construction
Authors: Sueltz Ben A.
Published: January 2021

It is desirable to indicate briefly what this topic implies. What do we mean by arithmetic, by arithmetic readiness, and by a curriculum?
The Art of Teaching A New Department
Authors: Shanok C.
Published: January 2021

I believe that we may accept as axiomatic that one of the greatest sources of difficulty, if not the greatest, for the ordinary algebra student is the solution of verbal problems. It is my firm belief that this difficulty is very largely due—I am almost tempted to say solely due—to the method of attack commonly employed in illustrating the solution of such problems. If I make no mistake, this method of attack smacks considerably of that familiar fallacy, putting the cart before the horse. Bold words, perhaps, but I hope that you too will concur in this sentiment after I have completed my argument.
Mathematics in Relation to Physics
Authors: Bryant Carroll W.
Published: January 2021

Mathematics is undoubtedly applied as extensively in physics as in any other physical science. However, in this discussion, one must not lose sight of the fact that what is said regarding the relationship between mathematics and physics applies equally well to many phases of other physical sciences such as astronomy and various fields of engineering.
Problem Solving in Algebra
Authors: McLeod D.
Published: January 2021

No apology is needed for re-introducing in the pages of The Mathematics Teacher a topic which may be time-worn. The subject of problem solving is a lways in place and ever calls for solution.
Significance, Meaning, Insight—These Three
Authors: Buckingham B. R.
Published: January 2021

Five on six people devoted to education and hence of more than average intelligence are having luncheon. Each has ordered a different meal; each is expecting to settle his own account. The waiter, however, totally disregarding the attempt which has been made to secure separate checks, has brought in but one bill and has placed it before the most prosperous-looking person in the group. You have doubtless participated in such a luncheon. If you have, you remember the comedy which ensues as t hese table companions try to break down the total into the proper amount for each person and assess the tip which each should pay. Meanwhile the waiter who caused all the trouble hovers about, bored or tolerant or supercilious, according to his nature. The comedy is rendered farcical by the fact that everybody talks, nobody thinks, and nobody has the right change.
The Concept of Dependence in the Teaching of Plane Geometry
Authors: Wren F. L.
Published: January 2021

The concept of the interdependence of geometrical magnitudes is by no means new. Although instances of mathematical dependence are to be found scattered throughout the mathematical works of the early Greeks and Egyptians, it was Descartes who formulated the principle that served to crystallize the concept of dependence, or functionality, into one of the most significant of all mathematical concepts. In his new approach to geometry, published in 1637, Descartes introduced a frame of reference consisting of two mutually perpendicular lines as axes and their point of intersection as the point of reference. All points of the plane were then located by means of their respective distances from these axes of reference, a suitable notation for distinguishing between constant and variable distances was set up, and a curve was defined as the locus of a point moving in such a way that certain specified relations between its distances from the respective axes were preserved. Through such a transmutation in geometric technique Descartes was able to definitely systematize the method of applying algebra to the effective study of geometry. Though it was Descartes who devised the technique that has proved so efficient as a key to the study of functional relations, the contributions and extensions made by Leibniz and Newton must not be overlooked. It was, in fact, Leibniz who introduced the word function to designate the magnitudes involved in Descartes’ concept of curves generated by a moving point.
Editorials
Authors:   W.D.R.
Published: January 2021

Miss Martha Hildebrandt is retiring from the presidency of The National Council of Teachers of Mathematics this month after two years of devoted and notable service. Under her leadership the Council has grown not only in numbers but in prestige and influence among school people generally. Anyone who reads her report on the preceding pages of this issue will obtain some idea of the time and energy she has devoted to the cause of mathematics, but only those who have worked closely with her in the organization will know how much she has given of her real self and how unselfishly she gave it. She has been a credit not only to the Council but also to her school where she is a teacher of secondary mathematics. The best that The Mathematics Teacher can do is to wish Miss Hildebrandt a long and rich life wherever she may be. We trust, however, that the National Council may continue to receive her wise advice and that she may have the rare pleasure of seeing us ultimately reach our goal of ten thousand members before many years have passed
Deferred Arithmetic
Authors: Buswell G. T.
Published: January 2021

In looking over the program of this convention I was almost startled to read as the title of one paper “What's Right with Education.” In these days of adverse criticism of practically everything the schools attempt to do, my admiration goes to the man who is willing to defend some of their positive achievements. I almost wish that my topic this morning could be “What's Right with Arithmetic” rather than the topic assigned to me, which, in its very nature, focuses attention on those defects in arithmetic which might justify deferring the subject.
Fugitive Materials
Authors: Mullen Frances A.
Published: January 2021

In every issue of our professional journals and from the speakers’ table at every professional gathering, the teachers of mathematics of this country are adjured to enrich their courses, to vitalize their classes, to motivate their students, by emphasizing the relations of mathematics to current science, industry, and life, by stressing the history of mathematics and its part in the development of civilization, by introducing intriguing puzzles and subtle humor to revive the flagging spirits of our pupils when boredom threatens.
The Nineteenth Annual Meeting of The National Council of Teachers of Mathematics
Authors: Schreiber Edwin W.
Published: January 2021

The 19th Annual Meeting of the National Council of Teachers of Mathematics was held in Atlantic City, New Jersey, February 25–26, 1938. This was the largest of the four Atlantic City meetings—343 registering and some 400 in attendance.
The Mathematics of Elementary Chemical Calculations
Authors: Rogers Charles F.
Published: January 2021

The courses and currents in many contemporary educational pronouncements resemble a mature river, which is full of eddies, uncertainties, shoals, meanderings, and new channels, and which has occasional snags both visible and invisible. Some of these snags can cripple almost any craft that encounters them.
Some Preliminary Considerations Relating to Arithmetic in the Senior High School
Authors: Benz H. E.
Published: January 2021

This paper is concerned with arithmetic as a high school subject. Before proceeding with the argument, it might be well to agree on definitions of terms. For purposes of this discussion, by arithmetic we mean that branch of mathematics which is concerned with numbers, and their application to the quantitative situations of everyday life. Perhaps we will obtain a better impression of what is meant, if we define arithmetic as that branch of mathematics which is generally taught in our elementary schools. However, the term should be delimited further by confining it to those aspects of the subject which are relatively free from algebraic notation, algebraic concepts, and algebraic procedures. At once we are compelled to recognize that under close scrutiny the boundary between arithmetic and algebra disappears. One definition of algebra is “generalized arithmetic”. Perhaps the distinction which is intended here is best brought out by reference to the fact that most persons who are now over 30 years of age studied something which they called arithmetic when they were in the elementary school. It was quite free from such things as x's, equations, negative numbers, coefficients, binomials, etc. Then in the ninth grade such persons made the acquaintance of a new subject, which bore the name of algebra. The definition of arithmetic implied in this paper is that which prevailed in the elementary school of 25 years ago, so far as the scope of the subject-matter is concerned.
Some Factors Which Influence Success in College Algebra
Authors: Marshall M. V.
Published: January 2021

In many colleges the course in freshman mathematics shows a higher mortality rate than any other course. Various reasons have prompted many investigators to study the reasons for this. Some have been interested in ascertaining if the study of mathematics required special abilities; some have been interested in predicting success or failure; some have sought more exact bases for student counselling; and some have been interested in obtaining more exact knowledge of the factors conditioning success or failure. The study here reported is more concerned with the last named purpose than it is with the others.
For Basic Drill in Arithmetic, What Norm or Average Is Satisfactory?
Authors: Wilson Guy M. , Hanley Gertrude L.
Published: January 2021

A 75% grade is the most common passing mark; in some places it is as low as 65% or 70%; in others, as high as 80%, but 75% is decidedly the mode. Of the 206 schools in Odell's study, 3/4 of them have 75% as the passing mark.1 with a 75% passing mark, since the range of scores will, no doubt, go up to near 100% for a few, there may be a class average of 85% or slightly more. What does an 85% class average mean in terms of mastery?
High School Mathematics in the University
Authors: Bacon H. M.
Published: January 2021

In the subject, “High School Mathematics in the Univeristy,” I believe I have found a title which will permit me to discuss almost anything. For it might be interpreted to mean “what mathematics will the high school graduate need if he comes to the university,” or it might be interpreted to mean “what courses in mathematics on the high school level should the university provide for the student who comes with an insufficient mathematics preparation”? Furthermore, although it may not be immediately obvious, I believe that this topic is in close accord with our general theme, “mathematics to meet social needs.” Too often meeting social needs is thought to mean merely dashing about trying to find quick cures for deep-seated and little understood social ills, or making solemn pronouncements about the Social Order, or learning how to keep one's bank balance straight to say nothing of learning how to acquire and keep a bank balance of any kind. But, if we are to make some attempt to solve the great social problems of our day, it is hardly open to question that we must have knowledge, not only about the socalled Social Sciences, but about everything which interests and influences people in their individual and social behavior. This means knowledge of just about everything under the sun. To get this knowledge, and to apply it intelligently to the solution of these problems requires serious and concentrated study. Much of it is most economically secured by studying at a college or university. To pursue such studies effectively, the student cannot dispense with at least some mathematics, and in some fields, he obviously cannot have too much mathematics. And there are even those who will study mathe mathematics for its own sake. However, these are few in number; for, although mathematics is generally referred to as the handmaiden of the sciences, it is usually a case of “often a bridesmaid, but never a bride.”