bluuebunny/crossref_metadata_2025 huggingface dataset:
Do They See the Point?
Authors: Spencer Peter L.
Published: October 2020

DO THEY See the Point? This question has a dual meaning. “The Point” refers both to the actual dot, i.e. the decimal point, and to the “point” or meaning of the expression wherein the decimal point is used. Likewise two forms of seeing are implied. The one has to do with the adequacy of the sense of sight. The other is concerned with ideological understanding and judgments of significance, i.e., insight. The one refers to visual sensitivity. The other to conceptual sensibility. Both are important and worthy of careful consideration.
Perspective in Arithmetic
Authors: Osborn Jesse
Published: October 2020

Many years ago i read Creasy's “Fifteen Decisive Battles of the World.” These were thrilling to me. Before each battle, civilization was pictured as at a crossroads. A momentous issue was to be decided once and for all time.
Utilizing the Strategic Moment In Arithmetic
Authors: Pieters Mary Ballard
Published: October 2020

Billy was four years old. The sand dropped more and more slowly from his dipper as he looked up at the blue sky with the clouds moving quietly over. His voice became softer as he spoke.
“’Twas the Night Before Christmas” (In the First Grade)
Authors: Ambrosius Dorothy S.
Published: October 2020

“’Twas the night before Christmas… ” (100% attention is what I had from my small enraptured listeners.)
Mathematics Education in the Soviet 7-Year School
Authors: Chetverukhin Nikolai F.
Published: October 2020

THE SOVIET INTERMEDIATE SCHOOL (“Mittelschule”) for the development of general knowledge is included in a total school period of 10 years. The first four schoolyears, which are attended by pupils beginning with their 7th year of age, are called the elementary school (“Elementarschule”). At this school one teacher gives the lessons in all subjects. The children learn reading and writing as well as the fundamental operations of arithmetic and they become familiar with the most simple phenomena of nature and society.
Diagnosing Pupil Needs in Arithmetic
Authors: Moore Edwena , Platte DeGroff
Published: October 2020

Too much teaching is done on the basis of assumptions. We assume that our pupils have certain understandings and that they have mastered certain facts. It is easy, in arithmetic, to assume the logical sequence of learning has brought our pupils to us ready to take the next step up the learning ladder. Too often this assumption gets us into difficulties, and, even more, makes arithmetic a frustrating experience for the pupils. However, knowing that our assumptions are untrue is not enough; we need to know how we can pin down the actual accomplishments of our individual pupils in each area of arithmetic.
The Prismoidal Formula
Authors: Buckland G. T.
Published: October 2020

Just as there is a master key made for a series of locks, and just as there are usually short cuts for doing various difficult tasks, there is also a master key in mathematics that has been neglected for many years by teachers of mathematics and for many hundreds of others was never known. The simplicity of a key that is capable of unlocking many other locks which each in turn requires a special key is sometimes amazing, truly so in mathematics.
The Content and Organization of Arithmetic
Authors: Buswell G. T.
Published: October 2020

The content of this paper will be organized into three parts: first, two matters which are basic to any improvements in the arithmetic program, namely, the relation of content to individual differences and the effects of the deferred or stretched-out curriculum; second, some proposed changes at the primary and at the seventh-eighth grade levels; and third, some comments on materials of instruction and preparation of teachers. The issues to be covered are controversial and the reader will undoubtedly supply pros and cons to supplement the discussion given here.
Why Is Arithmetic Not the End?
Authors: Sawyer W. W.
Published: October 2020

In primary school we learn to answer questions like, “What is 3 times 8?” and “If an object cost $8.23, what would 37 such objects cost?” After a bit, someone who was good in arithmetic might be able to add, subtract, multiply and divide any numbers that anybody mentioned. It seems there would be nothing more for such a student to know.
Helping Children Understand Verbal Problems
Authors: Blecha Milo K.
Published: October 2020

It doesn't take any research study or report to tell either teachers or parents that many children have a great deal of difficulty with verbal problems—also referred to as work problems, sentence problems, or story problems. This, of course, is no new or startling situation. Most of us can recall going through the same struggle with these problems a children do today. In fact, many of us still wouldn't do too well with some of the verbal problems in a sixth or seventh grade arithmetic book.
Fundamental Issues in the Teaching of Elementary School Mathematics
Authors: Stone Marshall H.
Published: October 2020

THE COMMITMENT OF OUR NATION to an intensive scientific and technological development puts heavy pressure on our schools and colleges to produce an increased number of graduates well trained to pursue trades, professions, and scientific or academic careers dependent upon mathematical skills and abilities. While this pressure is felt especially in high schools, colleges and universities, its effects are reaching the grade-schools as well. From the stream of students flowing through our educational system we must obtain a greater proportion willing to pursue mathematical studies to more or less advanced levels, and we must in particular guarantee that among the students leaving the grade-schools an increased number will have a taste and inclination for mathematics sufficiently strong for them to study further mathematics in high school. This necessitates an improvement and enrichment of the mathematical elements in grade-school education.
Experiments in the Primary Grades
Authors: Clark Alice
Published: October 2020

Do the new ideas really help the children learn, or are they just more dramatic? If a teacher tries to teach arithmetic using some of the new materials, whether or not she continues to use them, her thinking about her own methods has been stimulated. She can evaluate her teaching in a new light. She can judge her teaching in a more scientific way, having experimented, observed, and drawn her own conclusions.
Providing for the Gifted Child
Authors: Panek Alice
Published: October 2020

The gifted child is that endowed individual, who, according to Dr. Lewis Terman of Stanford University, is generally superior in all physical traits, well-adjusted socially, and has a unique superiority over the average in intelligence—“the ability to carry on abstract thinking, to use abstract symbols in the solution of all kinds of problems.” This includes about 1 to 2% of the population having I.Q.s of 130 and above.
“Plus” Work for “Plus” Pupils
Authors: Lewis Eunice , Plath Ernest C.
Published: October 2020

One plus one equals “10” for the members of a special arithmetic class at the University School, College of Education, Norman, Oklahoma. Of course, the members of this class were working with a number system of base two, commonly referred to as the binary system. Students also readily stated that three plus three equals “12” if the base is four. Changing the base number was not only fascinating to these highly talented fifth and sixth grade youngsters, but also provided a launching platform for the development of complicated formulas (patterns to them) which are normally developed in a second year high-school algebra course.
A Gifted Underachiever in Arithmetic: A Case Study
Authors: Isaacs Ann F.
Published: October 2020

The data presented in the history which follows is of interest from three points of view. First, a majority of the reports in the literature on the “gifted” devoted to the development of children with superior endowment stress the fact that superiority is not unitary. Gifted children tend to exceed the norm in all areas. A study of gifted twin boys (2) illustrates this point of view. Secondly, various studies have attempted to show that students of education are not comparable in endowment to students in other fields. Wolfle (3) in exploring some thirty fields of endeavor has shown that the combined fields of physical education and general education contained the fewest number of cases on the high end of the distribution curve. The subject of this study tends to be an exception to both of the above since she has a problem, and though of very superior intelligence is the offspring of educators, also of very superior intelligence.
Stocks as Investments
Authors: Ganley Thomas J.
Published: October 2020

My stock went up 7¼ in the last five days.” An eighth grade boy had just fin ished reporting on a company listed on the New York Stock Exchange that he had been keeping a record of as part of his class's assignment on a unit about “Investments and Savings.”
The Madison Project
Authors: Lutz Marie
Published: October 2020

“Mrs. Downing, why didn't you teach me signed numbers the way you are teaching them to my brother? He knows them better than I do! He helps me!”
Some Important Features of European Arithmetic Programs
Authors: Schutter Charles H.
Published: October 2020

An examination of arithmetic books from twenty European countries reveals some interesting practices, the most noteworthy of which are listed in this article. (A more complete and detailed analysis of those textbooks will be found in the recently published booklet, Teaching the Third R, a Comparative Study of American and European Textbooks in Arithmetic, produced by the Council for Basic Education, 725 Fifteenth Street, N. W., Washington 5, D. C.)
Mathematical Ability and Masculinity
Authors: Lambert Philip
Published: October 2020

The idea that men are Better than women at mathematics has been widespread. Many writers on education have taken it for granted; a few have tried to prove it. Unfortunately, the general acceptance of this assumption distorts the test results; achievement rather than innate ability is measured. A comparison of the scores of men and women on various kinds of arithmetic tests is not conclusive, since ability to do arithmetic is partly the result of past and present interest in the subject. Even at an early age, boys are expected to be interested in mathematics. Girls, on the other hand, though they may have equal ability, may be discouraged from learning by the prevailing idea that mathematics is a masculine field.
Algebra in Grade Five
Authors: Sawyer W. W.
Published: October 2020

I should like to make known to arithmetic teachers an experiment that I have been and am still conducting. Experiment is perhaps the wrong word. In Europe, as a matter of course, the abler students begin algebra at 10 or 11 years of age. American students are just as intelligent, and I never had any doubt that they would be able to do the same. So perhaps it should be called a demonstration rather than an experiment.
Measuring the Meanings of Arithmetic
Authors: Koenker Robert H.
Published: October 2020

The meaningful method of teaching arithmetic is generally accepted by most teachers and professional educators, but to the best of the writer's knowledge few, if any, attempts have been made to measure the meanings of arithmetic. Standardized and teacher-made tests in the field of arithmetic usually measure abstract computational skills only. If we are to teach by the meaningful method then we should test to discover if the child comprehends the meanings and understandings inherent in our number system. The fact that a child can give the correct answer to the computation 25+38 indicates that he knows how to obtain the correct answer but does not necessarily indicate that he understands what he did to obtain the correct answer.
The Teaching of Roman Numerals
Authors: Porter Richard D.
Published: October 2020

The teaching of roman numerals seems always to be minimized and occasionally skipped altogether in both elementary and secondary school mathematics. Is this current lack of attention to Roman numerals due to a decline in their importance—or is it possible that this lack of attention is due to the relative difficulty of teaching Roman numerals in relation to more conventional subject matter in mathematics?
Teaching Square Root Meaningfully in Grade 8
Authors: DeGraff Homer R.
Published: October 2020

Square root can bestbe taught at the eighth grade level as part of the unit on the area of rectangles (and squares). The system though basically the same as the expansion of (a+b)2 taught in ninth grade, leads to quicker and more complete comprehension of the square root algorithm. The diagrams which follow will illustrate both the similarity and the differences.
A One-Handed Clock
Authors: Clark Caroline Hatton
Published: October 2020

In teaching kindergarten or first-grade children to tell time, it is helpful to begin with a clock which has only one hand, the hour-hand. Children arc ready to use such a clock as soon as they recognize the numerals 1 to 12. They can associate the time at which the hand points to 9, as time for school; the time at which it points to 12, as time for lunch. Similarly other critical hours of their day can be poi nted out on the clock.
Teaching Measurement in a Meaningful Way
Authors: Parker Helen C.
Published: October 2020

A true “Understanding of Numbers” was realized through an arithmetic project carried out by a sixth grade class and their teacher at School Nine in Yonkers, New York. This sixth grade had charge of the Safety Patrol of the school. They were assisted by other upper grade pupils. For safety reasons there was a definite need to establish positions for patrols. It was necessary that a map be made to indicate crossings, bus stops, entrances, class positions, steps, and other possible situations in this setting.
Arithmetic Instruction is Improving
Authors: Peterson Joyce
Published: October 2020

Arithmetic instruction is no longer made up of formal lesson plans and courses of study which provide for teaching addition and subtraction in the first and second grades, multiplication in the third, and division in the fourth. The emphasis now is on the understanding of the meanings in arithmetic based on discovery rather than mechanical, manipulative skill. In the past, the majority of students developed a fear for many of the specific processes before they ever attempted them. For example, long division and fractions held the reputation of being in the realm of extremely difficult tasks to master. Has not this been one major cause of the dislike, dread, and fear on the part of many students for arithmetic?
Don't Move the Point, Move the Number
Authors: Swart William L.
Published: October 2020

One of the Most Difficult tasks in the world of mathematics, or any field is to change the vocabulary.
Ali's Four Weights
Authors: Williams Allan S.
Published: October 2020

Once a week, our seventh grade Arithmetic class is given mathematical puzzles. Some of these puzzles are easy and some are hard. Some challenge the student's logic, some test their ingenuity, some amuse, and of course, some confuse.
“Interest with Interest”
Authors: Schlichting Minnie
Published: October 2020

The computation of interest is a perennial instructional “headache” for the arithmetic teacher. There are several different methods of finding the amount of interest, but the 60-day method is the one which is used most frequently. Advocates cl aim that this method is short, and indeed it is, so long as the rate is 6 per cent and the in terest is to cover 60 days. But try to convince students that the 60-day method is shorter when the ra te is 5 per cent and the time is 96 days!
Editorial comments: About the articles
Authors: Hamilton E. W.
Published: October 2020

The articles in this issue deal with several aspects of the modernizing and mathematizing process now gaining momentum in arithmetic instruction. Davis' report of a suggested sequence for the training of elementary-mathematics teachers should make us sit up and take notice. How many present teachers could qualify? How many institutions offer such a program? We seem headed toward special teachers in arithmetic. Do people realize and accept this?
A case in point: Is it wise to insist upon correct usage of numeral and number at the elementary level?
Authors: Peterson Wayne
Published: October 2020

When mathematics is taught, wrote George Boehm, “it is presented mainly as a collection of slightly related techniques and manipulations. The profound, yet simple, concepts get little attention. If art appreciation were taught in the same way, it would consist mostly of learning how to chip stone and mix paints.”
Highlights of a summer conference
Authors: Davis Catherine Linn
Published: October 2020

Across the nation today teachers and students are being offered an opportunity for professional inspiration and growth under condi tions unique to our times. Under t he auspices of theN ational Science Foundation, an increasing number of universities and colleges a re conducting institutes and conferences in science and mathematics. Participants in these institutes receive stipends that make it financially possible, and often profitable, for them to attend. In many instances, they receive college credit toward advanced degrees for the comse work involved.
The use of models in the teaching of mathematics
Authors: Osborn Roger
Published: October 2020

Instructional materials make up an important part of the equipment of the effective teacher of elementary- or secondary- school mathematics. The distinction between number and numeral is being made with increasing consistency and emphasis in programs of mathematics instruction being currently evolved. The development of this concept may, for many teachers, point up a need for new evaluation of the role of instructional materials in the classroom. The importance of the fact that the name of a thing and the thing itself are not the same has become more and more evident in mathematics programs as teachers con ider numerals as symbols we use to denote numbers.
Notice of Annual Business Meeting
Authors: Ahrendt M. H.
Published: October 2020

The Annual Business Meeting will be held at the Conrad Hilton Hotel in Chicago on April 6, 1961. This meeting will be one of special significance to the members of the Council, for at this time proposed amendments to both the Bylaws and the Articles of Incorporation will be presented.
Editorial comments: About the articles
Authors: Hamilton E. W.
Published: October 2020

The two lead articles in this issue, those by Rose and Rose and by Aileen Shine, deal with different aspects of the question, “What effects do intelligence and back-ground experience have on success in arithmetic?– These articles should be of interest to both the teachers and the parents of children who are not succeeding in arithmetic.
The number line in the primary grades
Authors: Ashlock Robert B.
Published: October 2020

If new arithmetic processes are to be introduced successfully in the primary grades, pupils must understand the number system thoroughly. The number line can often be used to deepen understandings, through experiences which follow initial concrete manipulation but precede the more abst ract computational problems.
Creating mathematicians*: Poeta fit non nascitur
Authors: Lansdown Brenda
Published: October 2020

Much foundation and industrial money is spent on searching out existing talent. Perhaps a more democratic approach to conserving our national intellectual resources is to take the view that we can create talent.
Developing concepts of time and temperature: The use of daily ceremonies in the primary grades
Authors: Heard Ida Mae
Published: October 2020

A well-balanced program in mathematics for the primary grades includes many opportunities for children to acquire concepts of measurement. Some teachers achieve this balance by reserving one day of each week for developing measurement ideas. Other teachers schedule some measurement experiences and capitalize on any unexpected situation that arises. Quite a number of teachers depend on the repetition of some worthwhile daily experience to give meaning to some phase of measurement, such as time or temperature.
Editorial comments: As we read
Authors: Hamilton E. W.
Published: October 2020

Problem-solving, the ultimate goal of most education, is not limited to arithmetic nor even to the whole of mathematics. As arithmetic teachers, we profess to deal with the quantitative and spatial aspects of the common problem that man encounters in his effort to adjust to or to control his environment.
Projects make mathematics more interesting
Authors: Haggerty John B.
Published: October 2020

In a recent survey the U.S. Office of Education asked mathematics teachers to rate according to preference a number of items of equipment which they had used for mathematics classes. Mathematical models led the list.
Dividing by zero
Authors: Bender Marvin L.
Published: October 2020

The questions surrounding the idea of dividing by zero are recurrent and perplexing. Attempts to answer the questions are often based on semantic confusion between “nothing” and “Zero,” but zero is not nothing. As we know, zero is a number, in particular it is the cardinal number of the empty set. Zero is the number that tells us how many we have of something when we don't have any at all. Nothing is the state of nonexistence itself. Most dictionaries lend aid and comfort to this confusion by equating the two concepts in definitions. An error is often made by assuming that the opposite of nothing is anything. It would seem much more reasonable to let everything or something be the opposite of nothing.
The metric system IS simple!
Authors: Pray Richard H.
Published: October 2020

With all the clamor about the United States being “first” in space, science, and other related areas, the people of the country have already relegated themselves to one technological “last.” Every nation in the world with the exception of the United States and England has switched to the easier metric system of measurement.
More on divisibility by seven and thirteen
Authors: Cunningham George S.
Published: October 2020

In his article, Divisibility by Seven and Thirteen, in the November, 1958 issue of THE ARITHMETIC TEACHER, Mueller derives and states rules for testing divisibility of whole numbers by seven and by thirteen. These rules are presumably designed to take less time than division, since they are in answer to Yearout's earlier statement that there are no simple rules for divisibility by seven.
The versatile number runner
Authors: Michalov Mary
Published: October 2020

The number runner is a simple arithmetic device that can be used with amazing success in the primary and intermediate grades to develop meaningful arithmetic concepts. The unbroken line of uniformly sized numbers and symbols lends itself to pupil discovery of many number relationships and patterns. The opportunity of handling the runner, of visualizing the arrangement of numbers in sequence, and of discovering number. ecrets results in keen understanding and in a photographic retention of number values, number facts and pattems, and arithmetic processes.
Experimental projects and research: The Greater Cleveland Mathematics Program
Authors: Weaver J. Fred , Gundlach B. H.
Published: October 2020

The G.C.M.P. attempts to lead its students to t he challenging and exciting phases of mathematics-in-the-making by having them rediscover the fundamental patterns and by having them re-create the basic symbolism, thus making the learning of mathematics to a large extent selfmotivating. Problem situations are presented to students as if they had not been explored already by the great geniuses of the past and present. These situations are presented in such a manner that pattern discovery has a good chance of taking place almost spontaneously; then students are guided to a point where the established symbolism for the rediscovered pattern seems almost a necesity. It is hoped that students will come away with the feeling that they, for themselves, have seen the relations, invented the symbols, put them together in meaningful sentences, and, in general, have had a genuine part in making this or that piece of mathematics.
Reviews: Books and materials
Authors: Rudd Lonie
Published: October 2020

The Story of Mathematics: Geometry for the Young Scientist, Hy Ruchlis and Jack Engelhardt. Irvington-on-Hudson: Harvey House, 1958. Cloth, 148 pp., $2.95.
Geometry in the grades
Authors: Brune Irvin H.
Published: October 2020

The proper study of mankind is geometry. Tiny Timothy chose a nickel rather than a dime, but it was worldly wisdom, rather t han geometric sense, that he lacked. Timothy's grandfather, however, who was shrewd in money matters, be lieved that three-foot cubes rather than three-foot spheres should adorn the new courthouse. He smmised that the cubes, covered only on five faces, would require Jess gold leaf to gild. His geometric guess was almost as naive as Timothy's money muddle.
A spark of enthusiasm
Authors: Powell Lucile B.
Published: October 2020

For some time, my fifth-grade classes have felt that arithmetic was a very dull subject. There is need for repetition and drill on the same work children have studied in the second, third, and fourth grades. of course, pupils need, in varying degrees, this drill and review. Because of a deep interest and enthusiasm for mathematics, I wanted to convey this feeling to my fifth-grade pupils. An elementary teacher feels a responsibility to cover the required material in the textbook, for she does not consider herself qualified to select the material that may be omitted. Thus, I began to use a variation of the “contract type” teaching plan. This plan has been used for three years, changing and adapting to meet the needs of the class and the individual pupils within the class.
Tease them to think
Authors: Jennings Thomas J.
Published: October 2020

Individualizing instruction is a constant concern of all teachers. The following article offers no panacea, but it does suggest a method by which youngsters, in spare moments, may explore a fascinating area in arithmetic—an area that might other, wise be used for less profitable pursuits.
Some new approaches to old arithmetic
Authors: Rivera Emilio
Published: October 2020

Let's examine our arithmetic programs. Do we restrict children's growth in this area because of our own limitations? Are we afraid of arithmetic? Perhaps we can't understand some of the very things which we expect youngsters to absorb. Are we, inadvertently, undermining children's understanding of mathematics? Many school districts are devoting a great deal of time and effort to an analysis of questions such as these. Here arc several ideas which can help you discover some approaches which may improve your arithmetic program.
In the classroom: Teaching multiplication facts need not be grim
Authors: Unkel Esther R.
Published: October 2020

A more thorough and quicker mastery of multiplication facts will result if, in the initial learning period, the following two things are established:

1 discovering the facts by the children and

2 the use of concrete objects.
Report of the Membership Committee
Authors: Rogers Mary C.
Published: October 2020

You who were present at the Thirtyeighth Annual Meeting of The National Council of Teachers of Mathematics in April, 1960, will remember the remarkable membership growth which we were able to report and the enthusiasm with which it was received throughout the convention. The combined efforts of the personnel of a great organization working toward a common goal had brought about results far beyond expectations.
Fingerprints
Authors: Seeger Raymond J.
Published: October 2020

Nowadays you can hardly pick up a newspaper without reading about digital computing machines. The very first such computing machines, of course, were really our ten finger (the Latin word for finger is digitus). Every once in a while I find myself still using my fingers when I wish to see if I have enough places for the people at a party, or to know how many blocks there are from C to K Streets. Do you know the trick of multiplying numbers between 5 and 9 by the use of your fingers? Let us multiply 9 by 7. On one band turn down four fingers, the differerence between 5 and 9; on the other hand, turn down two fingers, the difference between 5 and 7. Now add all the fingers that are turned down (4 and 2), and multiply those that are not turned down on each hand (1 by 3); you get G and 3, respectively. The number is 63. (Thoe of you in the seventh grade might like to discuss with your teacher why this rule always works.)
Other number systems—aids to understanding mathematics
Authors: Willerding Margaret F.
Published: October 2020

What is to be done with the student who reaches high school and is still unable to handle whole numbers and fractions satisfactorily?
Editorial comments: From the editor's desk
Authors: Gibb E. Glenadine
Published: October 2020

With this issue we are ready to bind together a nother volume of THE ARITHMATIC TEACHER Throughout the year this journal has brought its readers various points of view on curriculum, teacher education, and a pproaches to the teaching of mathematics. It ha been a reporter, reporting the results of research in elementary-school mathematics, noting the implication of these studies for making decisions about the future of mathematics in our elementary schools. It has been a teacher through its pages on which various topics in mathematics were presented. It has served as a source of information about new research, ongoing experimental program, tested ideas to be used in the classroom, and reviews and listing of new books and other teaching materials.
Editorial comments: As we read
Authors: Hamilton E.W.
Published: October 2020

Dr. John Clark is one of the respected elder statesmen of mathematics education. It is with considerable satisfaction that we publish, in this issue, his summary of present progress and his prediction as to the trends we will follow in the decade ahead.
E pluribus unum—a brief discussion on the “law of one”
Authors: Reckzeh John K. , Duncan Ernest R.
Published: October 2020

Next to discovering something new, there is probably nothing that pleases a mathematician as much as discovering that an apparently obvious fact is of fundamental significance.
Discovering bar graphs by degrees
Authors: Jennings Thomas J.
Published: October 2020

Quite frequently youngsters are capable of learning a great deal more than we suspect, if they become actively involved in a discovery approach to the subject. A heterogeneous class of children who had just finished third grade helped illustrate this belief.
Evaluation of a mathematics program
Authors: Madaus George F.
Published: October 2020

Mathematics, with its content, nature, scope, and instruction has been during recent years sharply focused in the eye of the American public. The mathematics curriculum in the schools has undergone, or is about to undergo, major revisions.
In the classroom: The use of overlay charts: A device for teaching some number concepts
Authors: Machlin Ruth
Published: October 2020

The teaching device described is based on a hundred chart and a series of overlays. I used a portable flannel board and inserted several hooks on top from which the overlay papers were suspended. The paper used was 24“ by 18” construction paper. A different color was used for each overlay to make the project attractive to the children. The children were second-graders with an excellent understanding of arithmetic. Counting in multiples, odd and even numbers, and bases other than base 10 were the understandings which were explored with this teaching aid.
Editorial comments: As we read
Authors: Hamilton E. W.
Published: October 2020

Our first article this month is of special interest in that it represents the guest appearance, so to speak, of a professional from another field speaking to us partly as a layman and partly as a psychologist about some of the touchy issues in our business.
In the classroom: Improving understanding of number concepts in third grade
Authors: Steelman Margaret
Published: October 2020

Why does one try new ideas and different gimmicks? In this case I had a few pupils who didn't seem to respond to any method I had ever used before in teaching the number combinations to 20, which is one of the main objectives in third-grade arithmetic. I had tried various work sheets, permitted finger counting, compared number size, and many other devices that I thought would help promote understanding along with memorization and drill.
Multiplication for the slow learner
Authors: Gibney Thomas C.
Published: October 2020

Sectioning for seventh-grade mathematics classes is found in many schools. Most mathematics classes are sectioned according to their reading, science, and/or mathematics ability. Regardless of the basis for the sectioning there are many slow-learner mathematics classes in the seventh grade.
Arithmetic concepts in first grade
Authors: Stutler Mary S.
Published: October 2020

What number concepts should be taught in Grade 1? Why are these concepts placed in Grade 1? What are the trends in arithmetic for Grade 1? These questions have remained in the minds of some of the teachers and the principal in the local school system when the arithmetic texts were reviewed for adoption.
The arithmetic folder: A plan for systematic evaluation of arithmetic instruction
Authors: Schminke Clarence W.
Published: October 2020

Checking to see if pupils have learned what has been taught is thought to be uncommonly easy in arithmetic. For example, little effort is required to determine whether a child can add 23 and 27. Yet, it is quite another matter to determine whether a pupil knows in a certain situation that 23 and 27 are the numbers to be added; whether he has an efficient thought process for adding them; and whether he understands that the order of the addends will not affect the result.
Editorial comments: As we read
Authors: Hamilton E. W.
Published: October 2020

February 20, 1962. American “know how” was demonstrated today. One of the most significant events since the time of Columbus took place, and although I was away from home, I saw parts of the spectacle on various school, restaurant, and hotel TV sets. My heart was with Colonel Glenn, but my attention wandered from time to time to the conversations going on around me, and I didn't like some of the things I heard.
Manipulative materials and arithmetic achievement in grade 1
Authors: Harshman Hardwick W. , Wells David W. , Payne Joseph N.
Published: October 2020

The use of manipulative materials and visual aids in teaching arithmetic is widely accepted by teachers and those concerned with the teaching of arithmetic. The Nationa Defense Education Act is an expression on the national level of a belief in the value of manipulative materials for instruction. While most modern arithmetic programs contain suggestions on the use of visual aids and manipulative materials, much remains to be done in evaluating the effectiveness of selected materials. Cost of materials varies considerably. One main concern of school systems is the cost of materials. Are inexpensive materials as effective as more expensive ones?
The mathematics consultant: A suggestion for improving the elementary mathematics program
Authors: Astle William R.
Published: October 2020

During the past few years there has been a considerable change in the overall academic objective of elementary-school education. The elementary school is no longer a terminal institution. It is emerging as a place where children are prepared for more advanced study in the secondary school. What are the implications of this new objective for elementary mathematics? A professor of mine once said the objective in a mathematics class was to learn mathematics. With this statement I must agree. However, we surely can't teach all of mathematics in one class. It is this author's opinion that we must develop a minimum program of mathematics education for everyone. The objective of this program would be to provide each citizen with the mathematical knowledge to live effectively in our “mathematized” culture. For the average (in ability to learn mathematics) student this program would be of ten years duration; the slower and faster students would reach this minimum goal in more than or less than ten years respectively. I do feel that those faster students who achieve this goal in seven, eight, or nine years should be required to continue studying mathematics at least until the end of t he tenth year in school. I do not intend to investigate the content of such a program, but rat her the implications of such a program for elementary schools.
Two aspects of algebra
Authors: Jordan Anthony M.
Published: October 2020

Currently adaptation of algebra for meaningful learning experiences for children with the numerous enthusiastic innovations (Cuisenaire rods, 2+ □ = 7, etc.) is being explored. The purpose of tllis study is to define two of the fundamental algebraic concepts involved. Just what are the children learning when 6+a=8 is used? What segment of algebra does this useful skill explore?
Factors related to quantitative understanding in the sixth grade
Authors: Muscio Robert D.
Published: October 2020

The meaningful approach to the teaching of arithmetic has been widely accepted by educators for more than a decade. The method and content of this approach stress the development of those concepts, generalizations, and understandings inherent in our system of number and measurement. The acceptance has been based largely upon psychological premises since experimental evidence has been meager and oftentimes inconclusive. Additional evidence pertaining to method, content, and role of the learner has been needed to validate, or to criticize, accepted practices in the area of arithmetic instruction.
Order of operations in elementary arithmetic
Authors: Bender Marvin L.
Published: October 2020

We will assume acquaintance with the set of natural numbers N = {1, 2, 3, …} and the set of whole numbers W = {0, 1, 2, 3, …}. The fundamental operations of addition and multiplication, and the related operations of subtraction and division will also be assumed as well known to the reader. It is to be understood that subtraction and division are operations only in a restricted sense, since it is not always possible to subtract or divide in the set of whole numbers. A recognition of a few of the properties of these operations, at least in form if not in name, will be assumed: in particular, the commutative and associative properties of addition and multiplication, and the fact that they do not hold for subtraction and division. Finally, an understanding of the meaning of the relations indicated by =(equal) and ≠ (not equal) will be assumed.
Enrichment materials for school mathematics
Authors: Peeler Harry
Published: October 2020

The term, “enrichment material” means different things to different people. A formal definit ion is unnecessary. In general, I shall use it to mean supplementary topics and aids in mathematics which are of interest to the pupil, which challenge his ability, and which aid in understanding a mathematical principle. Sometimes the material is vertical; i.e., it may be a topic or topics which he would not normally study until later years. Sometimes the material is horizontal; it might be a topic not normally included in the course of study.
Qualitative evaluation
Authors: Robitaille Joseph P.
Published: October 2020

No one will deny that many basic changes are taking place in the mathematical experiences being offered elementary-school pupils. These changes become very dramatic when one compares the differences over a period of a decade or two. Should these changes continue, and it certainly seems likely and desirable, the future will truly be dynamic.
Research on elementary-school mathematics–1961
Authors: Fred Weaver J.
Published: October 2020

This bibliography of research on elementary-school mathematics represents a continuation of a series begun five years ago in The Arithmetic Teacher and brings this series up to date through the calendar year 1961.2
Books and materials
Authors: Hardgrove Clarence Ethel
Published: October 2020

Three book were sent to the writer for appraisal in one composite review. All three have been published as textbooks; all contain the word “arithmetic” in the title; there is little further similarity. The reader may have noticed that alphabetical order of the authors' names has not been observed in the heading of this review. This is not by accident nor error. Books 1 and 2 bear some simila rities to each other, but these two and the third differ as much as Sinbad, the Sailor, and Basbir Ahmed.
Linear measurement and imagination
Authors: Botts Truman
Published: October 2020

No one needs to tell teachers that children have active imaginations. Yet the theme of this first lecture—that mathematics is a thing of the imagination—may seem surprising at first. This is because we are so used to thinking of mathematics as impersonal, coldly logical, cut and dried, hardly a very human activity and certainly not an imaginative one. Nevertheless, I hope we shall see in this lecture that mathematics is in a very essential way imaginative, and that the study of measurement shows this particularly clearly.
Teacher understanding and pupil efficiency in mathematics—a study of relationship
Authors: Bassham Harrell
Published: October 2020

A number of studies have indicated that considerable variation exists among teachers in their understanding of basic mathematical concepts.1 In addition, the mean teacher level of such understanding as evaluated by these investigator has been stated as being undesirably low. In such studies as the foregoing it has been assumed that good teacher understanding of basic mathematical concepts would be necessary in order to promote satisfactory pupil growth in arithmetic, but evidence of an objective nature to either support or refute such an assumption has not been readily available. Evidence has also been lacking concerning possible differences between the gain in achievement by pupils of different levels of intelligence as related to their teacher's understanding of basic mathematical concepts.
A study of mathematical abilities
Authors: Begle E. G.
Published: October 2020

Recent efforts to improve the mathematics curriculum in our schools have led to a flood of new texts and new programs and have, of course, raised the question of how good these are. Opinions are plentiful and strongly held, but little factunJ evidence is at hand. In fact, it would be difficult to obtain such evidence, since many of the virtues (or defects) claimed for the new texts are difficult to measure.
Arithmetic baseball
Authors: Inbody Donald
Published: October 2020

Teachers use many games to provide variety and fun in learning exercises, particularly those of a drill nature. Most of these games have a common failing. They furnish the most practice for the students who need it the least—the better students. The slower pupil is usually eliminated first, and when he is out of the game, he docs not participate, even vicariously.
In the classroom: 4×4 magic squares
Authors: Hewitt Frances
Published: October 2020

In his painting “Melencolia,” Albrecht Dürer used a fourth order magic square in the upper right hand corner. These 4×4 magic squares were supposed by Renaissance astrologers to combat melancholy. Magical squares are actually very unmagical. They are square arrays of numbers whose sums in all rows, columns, or diagonals are the same. They were called magic squares by the ancients because it was thought that they brought good health and luck.
Experimental projects and research: Mathematical logic for the schools
Authors: Suppes Patrick
Published: October 2020

In general terms the aim of the program is to deepen and extend the mathematical experiences of the able elementary school child at the broadest level of mathematics, the level of methodology and the theory of proof. The approach is through a study of modern mathematical logic, in particular that portion of it which is concerned with the theory of logical inference or the theory of deduction.
Primes and factoring
Authors: Paige Donald D.
Published: October 2020

Since the multiplier and multiplieaml can be interchanged with no effect on the product, it is convenient, to rename these parts and give them both the same name, factor. If we have a product such as 15, we then say that 3 and 5 are fuctors of 15 since 3×5=15. 1×15 = 15 so 1 and 15 are a also factors of 15. Since no other whole numbers multiply to be 15, the only factors of 15 are 1, 3, 5, and 15.
Age of Substance Use Initiation and Sexual Violence Victimization among Female Adolescents
Authors: Muchimba Maureen
Published: October 2020

Objective: In this study, I examined the association between age of substance use initiation and sexual violence (SV) among adolescent girls. Methods: Data were drawn from the 2017 Youth Risk Behavior Survey, and the sample included 7526 girls. Logistic regression was
used to estimate the relationship between age of initiation of alcohol use, marijuana use and cigarette smoking, and SV, assessed by forced sexual intercourse and experiencing SV. Results: A dose-response association was observed between age of substance use initiation and SV. Across
all 3 substance use variables and for both SV outcomes, those who initiated substance use before age 15 were more likely to experience SV than those who initiated at or after age 15, who, in turn, had a higher likelihood of experiencing SV than those who had never initiated substance use.
Conclusion: Early initiation of substance use may be a meaningful marker of risk for SV victimization in later adolescence. SV prevention programs could use early initiation of substance use to identify adolescents who are at increased risk for SV and provide them with targeted interventions.
To be more effective, primary prevention of SV may need to begin targeting substance use in early adolescence.
Kronik
Authors: Philipson Lotte
Published: October 2020

Indhold: Danske kulturtidsskrifter søgbare elektronisk; Det kongelige Biblioteks Danske Afde­ling modtager gennem pligtaflevering fra bogtrykkere alle tidsskrifter, der trykkes i landet, og registrerer og katalogiserer dem til Den danske Nationalbibliografis to hovedfortegnelser Dansk Bogforteg­nelse og Dansk Periodicafortegnelse; REX; "Kogebogen"; Efterlysning -Dusør kr. 50.000; Natten til den 22. oktober 1995 ramtes Det kongelige Biblioteks mindeudstil­ling i anledning af 50-året for Danmarks befrielse "Illegale tryk" i bibliotekets for­hal af et groft og frækt indbrud.  Tyven -eller tyvene -undslap på trods af alarmsystem og vagtalarmering med modstandsmanden Eigil Larsens eget eksemplar af den såkaldte "kogebog"; Fiolstræde til Frederiksberg;  Den 12 .. febr. 1996 åbnede Det konge­lige Biblioteks nærbibliotek for sam­fundsvidenskaber og jura i de midlerti­dige lokaler på Kronprinsesse Sofies vej 35 på Frederiksberg; Erhvervelser; Besøg; Lån til Udstillinger; Frimærkehandler og jernbanehistoriker Peer Olav Thomassens Fond; Personalia
Kronik
Authors: Philipson Lotte
Published: October 2020

Indhold: Ny lov om Pligtaflevering; Farvel til de islandske håndskrifter; Stiorn-håndskriftet; Flatøbogen; Kongebogen (Codex Regi­us); Den Arnamagnæanske Samling; Fund og Forskning 1997; Dania Polyglotta; Index Translationum; Erhvervelser; Udlån til udstillinger; Personalia;
Kronik
Authors: Philipson Lotte
Published: October 2020

Indhold: Fiolstrædeprojektet - nye funktioner i historiske rammer;  Det Kongelige Biblioteks "nye" fakutetbibliotek; Indvielsen af "Fisken" på Havnefronten; International bibliotekskonference i Danmark 29. aug. - S. sept. 1997; IFLA; Land og Folk; Erhvervelser; Personalia;
Kronik
Authors: Philipson Lotte
Published: October 2020

Indhold: Nyt bibliotekssystem - ALEPH 500; REX; Z39.50, Web interface og Windows clienter; Erhvervelser; Udstillinger; Besøg; Personalia;
Kronik
Authors: Leergaard Joan
Published: October 2020

Indhold: H.O. Lange-Prisen; Det Kongelige Bibliotek og G .E. C. Gad NS har indstiftet en forskningsformidlingspris i H.O. Langes navn; Bibliotheca Danica på nettet; Kulturnatten; Bind VI af Danske Provinstryk; Udstillinger ; Efterårsudstillingen 2001: 13 rigtige? -Danske Nobelpriser gennem 100 år; Erhvervelser;