bluuebunny/crossref_metadata_2025 huggingface dataset:
Editorial comments: As we read
Authors: Hamilton E. W.
Published: October 2020

It seems appropriate that part of the first Fall issue of THE ARITHMETIC TEACHER should deal with a deep and controversial problem. Two articles have to do with the use of physical objects, more particularly, structured materials, for helping children gain command of number. Andrews and Nelson do a good job of presenting the theoretical case, for and against, the early use of such materials. They warn that it is easy to substitute the rote manipulation of things for the rote manipulation of numerals—the former, of course, we recognize as just as undesirable as the latter.
Beginning number experiences and structured materials
Authors: Andrews E. E. , Doyal Nelson L.
Published: October 2020

Few teachers would deny the importance of the role of concrete objects in helping primary children to understand number, number operations, and number relationships. In fact, many teachers believe that at this level the choice of appropriate manipulative material ranks in importance with the choice of an adequate text or workbook. Some teachers are of the opinion that beginning number ideas can be taught most effectively when pupils are provided with a great variety of carefully chosen manipulative and pictorial aids. Others prefer to rely on highly structured materials such as Cuisenaire rods and Stern blocks to provide a concrete vehicle for teaching abstract number concepts.
The Elementary School Principal and Mathematics instruction
Authors: Mcarthur Bill E.
Published: October 2020

Mathematics, unlike reading, writing, spelling, written English, and history is an area in which most children have had considerable experience when first entering school. Because of his inbred acquisitive nature, a child soon develops a need for accounting for his acquisitions and develops a mode for expressing his desire for greater acquisition. He soon avariciously compares what he has with that which someone else has, and, hence, enters the realm of the relationships of numbers, in addition to their mere enumeration. With all this background, a child on entering school is usually quite ready for the various phases of the mathematics program. The school's job, then, is to capitalize on what the child already knows about mathematics and in a sequential manner develop, extend, and enrich his “one-to-one correspondence” of numbers to the degree that he could someday, translate data into mathemat ical equations and formulae to be fed into an electronic brain for use in solving problems in any field. The school's job involves the teacher's understanding of children so that mathematical learning and social usage can be developed right along with the child's attitudes, interests, and feelings.
In the classroom: Using a math caddy to store and display manipulative devices
Authors: Mae Heard Ida
Published: October 2020

For the past two years, our forty-eight elementary principals and their six hundred teachers have worked tirelessly to update our mathematics program. We have tried out new content, have experimented with new organization of traditional content, and have used NDEA funds to purchase a variety of manipulative and graphic aids to motivate the study of mathematics.
Piaget: number and measurement
Authors: Coxford Arthur F.
Published: October 2020

For approximately forty years the French psychologist Jean Piaget and his various collaborators have been producing volumes dealing with the formation of concepts in children. He has intensively studied the concepts of number, geometry, physical causality, space, the world, and reality; also the moral judgment, reasoning, language, and thought of the child. He has published a total of twenty-five books on these subjects, four teen of which are now in English.
Testing the Cuisenaire method
Authors: Lucow William H.
Published: October 2020

The foregoing were some of the conclusions from the MTS (Manitoba Teachers' Society) Cuisenaire arithmetic experiment that involved eight Manitoba schools, sixteen classrooms with their teachers, and upwards of- five hundred children in Grade 3.
In the classroom: Division made easy
Authors: Lung Clarence
Published: October 2020

Division has long been a “bugaboo” to many students due to the uncertainty of finding the correct quotient figure. By using the cumulative quotient method shown in the following illustrations there is no necessity for erasures and reworking the problem when there is an underestimate or an overestimate of the quotient figure. Much of the trial and error method of determining the correct quotient figure is eliminated.
National Council of Teachers of Mathematics: Membership report
Authors: Gates James D.
Published: October 2020

Our membership growth has continued to be large, as indicated by the totals in the report which follows. We can all be proud of the increase of 6,076 members and subscribers. The greatest amount of growth has again been in the institutional subscriptions to The Arithmetic Teacher. The increase here was 29 percent.
Editorial comments: As we read
Authors: Hamilton E. W.
Published: October 2020

Professor Marks opens this issue of The Arithmetic Teacher by probing a tender spot. It is easy to damn the elementary teachcrs for all sorts of shortcomings, the tudents for being dull and disinterested, and the parents for being shortsighted, uninformed, and hardheaded. It is not so easy, at least not so popular, to admit that we in the profession of teacher educrttion may not be equal in quality or quantity, or both, to the task of preparing enough well-trained teachers for the new curriculum that is emerging.
Word problems in elementary mathematics
Authors: Hagaman Adaline P.
Published: October 2020

Teachers know that children learn best when they understand the meaning of what they are learning, in terms of their own experiences and interests. There are two kinds of meanings in arithmetic. One is the intrinsic meaning of the quantitative relationships Which underlie mathematical thinking. The other is the functional meaning, connected with children's experiences. Both kinds of understanding are essential in arithmetic teaching. The intrinsic involves the abstract meanings of elementary mathematics, and the functional applies arithmetic to practical, concrete situations
In the Classroom: Multiplication in black and white
Authors: Glanzel Elizabeth V.
Published: October 2020

A table, as defined by Webster's New Collegiate Dictionary, is “any collection and arrangement in a condensed form, for ready reference, … measures, numbers, etc.” The multiplication tables lend themselves artfully to this definition when they are set up to form areas of black and white on graph paper. Many interesting and helpful relationships can be explored by children as they study the multiplication tables in pattern.
A time for precision
Authors: Schminke C.W.
Published: October 2020

During the 39th annual meeting of the National Council of Teachers of Mathematics at Chicago, Illinois, in 1961, Professor Ben Sueltz delivered an address in which he evidenced concern about what mathematics in the elementary school should be, and who should make decisions concerning what it should be. The title of his address was “A Time for Decision.”2
Topics in geometry and point set topology—a pilot study
Authors: D'augustine Charles H.
Published: October 2020

There is evidence that children develop certain ideas and concepts fundamental to geometry and topology long before they understand such concepts as one-to-one correspondence and number associated with a set. Jean Piaget2 discovered that even at the age of three years a child could distinguish a simple closed curve from a non-simple closed curve. Suppes and Hawley,3 working with primary school students, found that many of Euclid's concepts, which could be discovered by construction, were both teachable and stimulating.
Preparing solidly for algebra… using prime numbers
Authors: Leonard W.A.
Published: October 2020

It was once suggested that beginning the study of freshman high school algebra is not totally unlike embarking upon the sea of matrimony. Both are milestones in one's life, involving opportunities for excitement, adventure, growth, and rich and lasting reward; but, nonetheless, both tend to necessitate some different approaches to problems, some new ways of thinking, and certainly, in more than a few cases, some amount of adjustment. Without intending to attach social implication to algebra, we as teachers cannot fail to recognize that the first exposure to high school algebra can be a foreboding experience to many elementary school graduates, particularly in the light of the statistical evidence for the high fatality rate of students taking algebra for the first time.
Participation of young children in mathematics
Authors: Korey Ruth Anne
Published: October 2020

Ever since primary arithmetic abandoned the paper-and-pencil standard, teachers have been concerned with problems of inattention and restless behavior during the mathematics period.
How well are colleges preparing teachers for modern mathematics?
Authors: Melson Ruth
Published: October 2020

It is well known throughout most of the country that the public schools have had to make changes in the content of their courses, particularly offerings in mathematics, because of the vast increase in knowledge and changes in emphasis in various disciplines. The schools have been forced to retrain their teachers or make the teachers themselves responsible for securing additional education, so that the new content and the new approaches to teaching the new content, can be used successfully. Through in-service institutes and courses, teachers have, in many cases, been markedly helped in their desire to become up-to-date in the subject matter for which they are responsible. Unfortunately, it is necessary for schools to employ from 5 to 44 percent new staff members each year. The question arises, “Are the newcomers prepared in modern content to teach the up-dated courses now being offered in our schools?”
The mathematics education of elementary school teachers: pre-service and in-service
Authors: Weaver J. Fred
Published: October 2020

The mathematics education of elementary school teachers is not a new problem, nor has it been a problem of limited or superficial concern. A few years ago in The Arithmetic Teacher Jack N. Snarks summarized concisely a number of attacks upon this problem,1 citing references from 19-19 through 1959.* Concern over the problem was voiced by several writers prior to 19-19. Now, within tbe past several years, intensified attention has been given to the mathematics education of elementary school teachers.
Developing generalizations with topological net problems
Authors: D'augustine Charles H.
Published: October 2020

Topological net “games” are being included in contemporary junior high and elementary school mathematics texts. The “game” aspect is of questionable pedagogical soundness. Wouldn't these topics be of more value to the student if they were introduced systematically and in such a way as to lead the student to make certain logical generalizations? Wouldn't these topics be of more value to the student if he “possessed” certain generalizations which would enable him to create and solve highly sophisticated net problems independently.
The preschool child's concept of number
Authors: Brace Alec , Doyal Nelson L.
Published: October 2020

Teachers of elementary school mathematics realize more than ever before how important it is that the child develop an understanding of mathematical relationships and principles. So, to establish a firm foundation for higher order mathematical ideas, the first-grade teacher attempts to give increased emphasis to experiences which facilitate the growth of the concept of number and correspondingly less emphasis to those activities which involve rote memorization of number symbols and facts. Providing adequate experiences of this kind depends, in large measure, on the teacher's knowledge of which aspects of the number concept have been developed in preschool years.
Games and programmed instruction
Authors: Allen Layman E.
Published: October 2020

Games are fun. Good programmed materials can teach well. If the two are combined, some of the results may be interesting. Appropriately done, this may enable us to stimulate and maintain motivation for learning in a way that will be quite useful.
Pre-service and in-service education in mathematics
Authors: Deans Edwina
Published: October 2020

At the outset let us assume that learning mathematics and learning to teach mathematics to elementary school children are continuous processes. It begins when the prospective elementary school teacher is a student in elementary school. It is here that favorable or unfavorable attitudes are developed. It is here that mathematics is first thought of as a body of facts and procedures to be memorized, or as challenging, thought-provoking ways of dealing with quantitative ideas. Learning continues as the prospective teacher takes the high school mathematics courses recommended in an academic program as preparation for successful work in college mathematics.
A Piagetian conservation concept
Authors: Overholt Elbert D.
Published: October 2020

The teaching of the sciences, both physical and mathematical, has received considerable attention in recent years. Numerous conferences have been held and many committees have been formed in an attempt to solve the problem of knowing how, when, and where to present mathematical concepts to children in the most effective manner.
Understanding different number bases
Authors: Rahmlow Harold F.
Published: October 2020

It is now common practice in many of the elementary schools to introduce the students to numeration in bases other than ten so they may appreciate and understand base ten more fully. This paper presents a methodology, or more correctly a teaching aid, for presenting numeration systems using different bases.
Research on elementary school mathematics—1964
Authors: Fred Weaver J.
Published: October 2020

Special Note: At the time this 1964 listing was compiled the December, 1964, issue of Dissertation Abstracts had not been released. Consequently, any studies appearing in that issue are not included in this version of the 1964 listing. Hopefully, it will be possible to insert the studies in question at a later date so that they can be included in the printed 1964 listing.
Editorial comments: Applications and problem solving
Authors: Weaver J. Fred
Published: October 2020

What is “modern mathematics”? What characterizes a “modern mathematics program” for the elementary school?
Have you read?
Authors: Beaird James H.
Published: October 2020

In Educational Comment 1965, edited by Edward B. Wickes and Thomas C. Gibney, College of Education, The University of Toledo (Ohio), appear six articles which give some provocative insight into some fundamental issues of learning theory and mathematics instruction.
The “Object-A-Screen”: a machine for teaching elementary mathematics
Authors: Uncapher Chester L.
Published: October 2020

The “Object-A-Screen” consists of a translucent plastic screen and a panel of low-voltage lights which is shielded to form round dots on the screen when the lights are tumed on. There is a total of eighteen lights, three rows of six each, controlled by a remote panel of switches mounted in the same three-by-six pattern. The position of each switch on the control unit directly corresponds to the position of its related light on the screen. To differentiate among the three rows, each row is a different color: white, yellow, and red, respectively, from top to bottom.
Basic skills in contemporary programs
Authors: Hardgrove Clarence Ethel
Published: October 2020

Some critics of contemporary programs of elementary school mathematics say that the programs neglect computational skills. They say that children are being educated to understand arithmetic but not to do it. Is this a valid criticism? Let us look at the facts.
Measuring arithmetic objectives
Authors: Von Brock Robert
Published: October 2020

One of the difficulties in evaluatiug a child's growth in arithmetic has been that most instruments are based upon computational skills, the assumption being that if a child could manipulate numbers through the basic processes, he understood arithmetic. This assumption was probably adequate a generation ago, but our concern today is more with the understanding of the process than with mere computation. The ability to comprehend, apply, and analyze a rithmetic concepts has become a major factor in developing the elementary school arithmetic program of today.
Multiplication is repeated addition
Authors: Rappaport David
Published: October 2020

In the new elementary school mathematics programs there appears to be a concerted effort to avoid teaching multiplication as repeated addition. This is done for two reasons. First, it is generally believed that multiplication should be considered as an operation that is independent of addition. Second, there is wide pread belief that, although multiplication of whole numbers can be shown as repeated addition, it is not possible to show multiplication of fractions as repeated addition. It is the purpose of this article to show that multiplication of fractions, as well as multiplication of whole numbers, can be taught as repeated addition. Furthermore, it is this writer's belief that the effort to avoid multiplication as addition is psychologicaUy unsound and pedagogically ineffective.
In the classroom: More of moot mathematics
Authors: Muller Adelyn
Published: October 2020

It is rare when the ambiguity of our semantics lends a helping hand to understanding. Here is such a case. The single word moot with all its variant meanings blends to convey the general intent of this article.
A still broader look at method
Authors: Hamilton E. W.
Published: October 2020

During the past year several members of the Editorial Board of The Arithmetic Teacher have written special comments on topics which they deemed important. Nearly all dealt with method from one point of view or another.
Children's perception of mathematical inconsistencies
Authors: Scott Lloyd
Published: October 2020

Existing projects for school mathematics curriculum reform have been occupied principally with the tremendous task of preparing instructional materials. In general, these projects have had neither the time nor the resources to objectively research their contributions. Most of the experimentation which they have undertaken has been confined to the practical consideration of adapting content to the relevant, known characteristics of operating schools. Despite implications to the contrary there is, obviously, no substantial evidence as to the long-term effect of any particular experimental curriculum. These observations notwithstanding, a movement toward the widespread adoption of “experimental” materials for usc in school classrooms is underway, and the trend is not likely to subside in the foreseeable future. In fact, there are such compelling logical and intuitive arguments supporting a modernization of school mathematics that adoption of almost any new program appears reasonable. Though the lack of objective information clearly increases the risk when an experimental curriculum is selected, apparently such risk is regarded as the lesser of evils. Although this position may be realistic, it is clear that an increasing body of information about the new curicula would be welcome grist for the decision-making process. While awaiting the emergence of comprehensive and longitudinal data on the value of tbe various experimental programs, school leaders should enthusiastically endorse any activity designed to produce a bit of information about the new curricula.
Teachers discover new math theorem
Authors: Renzi Helen G. , Cross George C.
Published: October 2020

Who's afraid of modern mathematics? Not the teachers of the Williamstown, Mass., elementary schools who recently stumbled upon what we believe to be a new mathematics theorem. While the theorem itself will not change the course of the world, the circumstances in which it was discovered help to prove the value of the new approach to the teaching of mathematics.
The listening post
Authors: Seal Joan
Published: October 2020

Orten the teacher of arithmetic wishes that she were at least three people: one to lead the class in day-by-day arithmetic growth, one to help the small groups of children who need more work in special areas, and one to lead those who should be working with more advanced concepts.
Being creative with shapes
Authors: Giddings Marie
Published: October 2020

The kindergarten child enters school with an awareness of geometric shapes and designs. He can recognize a circle, a square, and a triangle. Many can recognize a rectangle.
Introducing models for N-dimensional geometry in the elementary school
Authors: Woods Dale , Hoff William E.
Published: October 2020

People, in general, live in a three-dimensional world. For many of them, notions of more than three dimensions are difficult to imagine. To reduce this difficulty, experiences with mathematical models for geometries of more than three dimensions should be provided. In fact, it is believed that such experiences can be provided at the elementary school level.
Cardinal numbers and sets
Authors: Sanders Walter J.
Published: October 2020

Nancy was cleaning out her room, and threw some things she no longer wanted into a heap in the hall outside her door.
Venn diagrams strengthen children's mathematical understanding
Authors: Smith Lewis B.
Published: October 2020

Venn diagraming provides an except ional method of understanding some arithmetic problems that cannot be easily interpreted by traditional mathematical processes. Venn diagrams contribute to a child's ability to see relationships and to interpret data. It helps him construct a model which gives him fuller perception and ability to analyze problem situations.
Letter to the editor
Authors: McCreery Louis R.
Published: October 2020

It seems to me that there is yet another reason, and perhaps the most compelling, for including applications and problem solving in any mathematics program. This reason I would add to J. Fred Weaver's list in the October, 1965, issue of the arithmetic teacher (page 412).
Individualizing instruction in elementary school mathematics for prospective teachers
Authors: Dutton Wilbur H.
Published: October 2020

The importance of teachers' understanding of basic arithmetical and mathematical concepts has been studied by numerous research workers [2, 3, 4, 6].* The understanding teachers have of basic mathematical concepts is closely associated with the ability to present these concepts to children [10]. Considerable research has been done to show the amount of understanding of basic mathematical concepts possessed by prospective elementary school teachers. Most of these studies indicate pronounced inadequacies in teacher understanding, while a few [2, 3, 8] show that some aspects of arithmetic and mathematics are understood quite well. Few studies deal with methods and procedures for overcoming teachers' lack of understanding of these basic concepts.
Possible misunderstandings arising out of Kersh's article on learning by discovery
Authors: Carlow Chester D.
Published: October 2020

In the October, 1965, issue of The Arithmetic Teacher Bert Kerah made a significant contribution to the analysis of the nature of discovery methods of learning (“Learning by discovery: instructional strategies”). Reminding us of the centrality of the withholding aspect of discovery, he made the following important classification regarding information that may be provided and information that may be withheld from the learner.
Editorial comments: As we read
Authors: Inskeep James E.
Published: October 2020

What do you think about geometry in the elementary school? Not “as you read,” but before you read, ask yourself how you react to a statement that you need to include geometry in your lesson plan. Perhaps you've already tackled the problem, or you've been teaching geometry for years! You may even think it is unimportant to try to teach geometry to elementary school children. No matter how you react, you will want to take a close look at the articles on geometry in this issue of The Arithmetic Teacher.
Rings and strings
Authors: Major James E.
Published: October 2020

Geometry is now definitely a part of the elementary school mathematics curriculum. It is presented, for the most part, through an intuitive approach rather than an axiomatic approach, with the purpose of providing thinking experiences for the child.
A rationale in the use of variables
Authors: Hajek Roy D.
Published: October 2020

An elementary school introduction to the ideas and topics of algebra has several definite advantages. First, the informal experience with the language and ideas can be used to form a leisurely but correct preparation for later contact when competence and rigor are required. Also, the students can develop a taste for the various kinds of algebraic situations without haste, while the novelty of the material labels the tasks as dessert rather than drab, everyday fare. Most important of all, it has been shown that children can understand the ideas and do enjoy the tasks if they are presented fairly. With these recommendations, topics in informal algebra seem to be logical candidates for inclusion in the elementary curriculum if the difficulties encountered in presenting the material do not offset the advantages and discourage the teachers. These difficulties are of interest to us, since, by examining potentially troublesome areas, we may develop suitable ways to avoid misunderstanding and mistakes.
Developing an understanding of inverse operations
Authors: Mauro Carl
Published: October 2020

The purpose of this activity is to judge how well pupils can apply their knowledge and understanding in unfamiliar situations. Specifically, this is an exercise to evaluate the extent of pupils' comprehension of inverse operations and then continue developing this understanding.
Flow charts for the elementary grades
Authors: Overholser Jean S.
Published: October 2020

The following relay games in arithmetic are suggested as an introduction to flow charts and as practice in the fundamental operations. These games may be adapted for use at any elementary or secondary level.
The eleventh commandment
Authors: Thagoras P.
Published: October 2020

With a resounding rap of the gavel, the judge pronounced the quivering defendant “Guilty!” The punishment was to be enacted immediately!
Discovering what “discovery” means
Authors: Salzer Richard T.
Published: October 2020

In attempting to help both undergraduates and in-service teachers to achieve better understanding of “teaching for discovery.” the author presents his classes with the problem of explaining “why we invert and multiply in the division of fractions.”
Alternate place value schemes for large numbers: a lesson in efficiency of definitions
Authors: Rising Gerald R.
Published: October 2020

It is appropriate to raise in the intermediate- grade or junior high school classroom the question of efficiency of definitions. Examination of this problem can open many doors: it can make students aware of the problems of definition, it can give them some insight into the role of history in mathematical development and the problems history creates, and it can expose them to the availability of alternate routes through mathematics. This last advantage is of greatest importance. Any opportunity a classroom teacher has to show students that there is no single right way is a substantial contribution to their intellectual growth. Two things too seldom questioned in our modern society are pronouncements made by teachers and those recorded in textbooks.
Head-shrinking—an introduction to scale
Authors: Elliott Richard W.
Published: October 2020

At the usual arithmetic time, more giggles of glee than shrieks of horror will greet the teacher's casual announcement, “Today we're going to shrink heads.” Amid the twitters, distribute a sheet of 17″-by-22″ white newsprint and a sheet of 9″-by-12″ construction paper to each pupil, with as many yardsticks as can be borrowed in the building.
Inquiry in mathematics—with children and teachers
Authors: Cohen Donald
Published: October 2020

I would like to share with you two of the most unusual and exciting experiences in my teaching career.
Are almost all children disadvantaged in mathematics?
Authors: Newport John F.
Published: October 2020

Mrs. Mather, sitting across the desk from her son's fifth-grade teacher, said with a smile, “Well, I never was any good in math, so I can't expect Johnny to do much better.” This is probably an oftenrepeated remark at parent-teacher conferences in schools across the nation. True, Mrs. Mather may have done poorly in math when she was in school, and she probably does even less well today. She is in good company, though, since the majority of the adults in this country would probably find seventh-grade mathematics quite a challenge. Why?
Computer-assisted instruction: implications for teacher education
Authors: Riedesel C. Alan , Suydam Marilyn N.
Published: October 2020

There is agreement between mathematicians and educators that future and inservice teachers need a good background in mathematics subject matter. Toward this end many colleges, universities, and school systems have developed content courses for elementary teachers that are very similar to the recommendations of the Committee on Undergraduate Program in Mathematics of the Mathematical Association of America.
A look at triangle congruence
Authors: O'Brien Thomas C.
Published: October 2020

One recent change of great importance in mathematics education is a heightened emphasis on the study of informal (not theorem-proof) geometry throughout the grades. Another change is an increased tendency of mathematics programs to build upon the student's native logic and intuition.
Are elementary school teachers satisfied with their mathematics preparation?
Authors: Reys Robert E.
Published: October 2020

In 1960 the Committee on the Undergraduate Program in Mathematics, the major group influencing the modernization of college mathematics, published their recommendations for the mathematics preparation of elementary school teachers of mathematics.1, 2 Subsequently, statewide conferences for mathematics educators from various educational institutions were conducted under the auspices of the Committee on Undergraduate Programs in Mathematics. In these meetings were discussed the problems of adequately training elementary school teachers of mathematics and possible avenues to an improved mathematics preparatory program. One of the statements issued at each of these meetings concerned the importance of each educational institution's critically examining its own mathematics program for elementary school teachers.
Discovery at the teacher-education level
Authors: Plants Robert W.
Published: October 2020

We have heard much about discovery as a method of teaching the “new arithmetic” to elementary school children. Discovery is as stimulating at the teacher-education level as it is at the elementary school level.
“A rose by any other name ...”
Authors: Junge Charlotte W.
Published: October 2020

The method of checking addition by casting out nines is a very old one, and the problem of helping the student understand “why and how” it works is equally old! The explanation that follows is taken from a book titled Arithmetic reprinted from the Mathematical Textbook edited by President Webber of Cambridge University. It was published in 1812.
Development of critical interpretation of statistics and graphs
Authors: Girard Ruth A.
Published: October 2020

It takes but a cursory examination of a daily newspaper, a current magazine, or a commercially sponsored program on a local television channel to make evident the widespread use, and tremendous impact upon people, of numerical data that have been translated into a graphic representation. lt also takes but a moment of questioning with students to make evident, as well, the implicit trust that many of them give to anything related to numbers as being the inalienable “truth.” Somehow, the transference of statistics to a graph carries with it a factual implication that most students accept as being reportorial rather than editorial. They assume that reading materials from a graph provides numerical answers that are not to be challenged. This is quite similar to the reverence felt for the printed page which makes every word so inviolable that students often answer a question with, “The book says so.”
The NCTM film-text series “Mathematics for Elementary School Teachers”
Authors: Moray Joseph
Published: October 2020

My worst subject has always been mathematics, but I was just getting to be confident about teaching second-grade arithmetic when along comes this ‘new math’ and I'm all shook up again."
Effortless multiplication
Authors: Knigge Wayne
Published: October 2020

The following is to illustrate a method of diagonal placement of subproducts to eliminate the need for mental “carrying” of digits required in the conventional method of multiplication.
Let's use our checkers and checkerboards to teach number bases
Authors: Laganke Lucile
Published: October 2020

In this day of teaching modern mathematics, one notices the tremendous numbers of manipulative materials being manufactured for the sole purpose of teaching number concepts. However, the teacher might find interesting math materials at home.
Just for fun: from arc to time and time to arc
Authors: Ray William J.
Published: October 2020

Some units in the arithmetic, social studies, and science curriculum areas present concepts of meridians and parallels, rotation and revolution, and differences in time zones around the globe. Learning about time zones can be a frustrating experience both for teachers and children unless concepts of arc and time are thoroughly understood.
Editorial feedback
Authors: Zahn Karl
Published: October 2020

I was interested in the “Now Try This in Multiplication” article, published in THE ARITHMETIC TEACHER. I believe children need side trips of this nature to maintain interest and to deepen mathematical understandings. Here are some other interesting diversions that I frequently use with mathematics classes in the Campus Elementary School here at Whitewater.
Editorial comment: As we read
Authors: Inskeep, James E.
Published: October 2020

The child undergoes many dramatic changes d uring the course of his formal education. Nowhere is this so evident as in the transformation that takes place from the prima ry grades to junior high school. This issue of The Arithmetic Teacher is devoted to the dual theme of kindergarten-prima ry and junior high school mathema tics. For those who read cover-to-cover, the contrast in these two a reas will be most evident. The thrill of beginning number concepts coupled with the satisfaction of maturing mathematical problem solving will stand out in delightful juxtaposition.
Preschool arithmetic is important
Authors: Woods Ruth L.
Published: October 2020

Michelle was one of the three-year-olds attending nursery school. She had become interested in arithmetic relationships. So when it became “tomato juice time” in midmorning, she left her play to follow the procedure. There were seventeen children in this nursery, so seventeen glasses of juice were brought in on a tray. Each child in turn came up to the teacher and received his glass of juice. Michelle had watched the teachers check the glasses and send for more when there was not enough. It was in this phase of the program that she was interested. She noted one child drinking a glass. She noted a second child drinking the second glass. When there were still seven glasses to go, she would say, “Is going to be enough,” or “Is not going to be enough,” and go back to her play.
Computer concepts possessed by seventh-grade children
Authors: Wolfe Lee R.
Published: October 2020

American society is rapidly becoming computer-oriented, and this fact has implications for the school curriculum. It is safe to predict that the basic concepts of computer science will eventually become a part of the elementary and secondary curriculum.
The relationship of conservation of numerousness to problem-solving abilities of first-grade children
Authors: Steffe Leslie P.
Published: October 2020

Why do some children do better in firstgrade arithmetic than others? Assuming all children want to learn, an obvious answer is that some children possess more ability than their less fortunate peers. True, but a crucial question is, what kind of ability? One type of ability is the ability to conserve numerousness, which has been emphasized by Piaget.
Enrichment with exponents
Authors: McCallon Earl L. , Cowan Paul J.
Published: October 2020

An interesting enrichment activity for the upper elementary grades can be built around exponents and the subtraction operation. The procedure consists of the following steps. Assume a set of counting numbers, such as the first six. Raise each number to any power and take successive differences equal to the exponent used. If the set of numbers meets certain requirements, a constant, which can be predicted, will be obtained.
Geometric proofs of the irrationality of √2
Authors: Beckenbach Edwin F.
Published: October 2020

In this article we discuss geometric proofs of the irrationality of V2. The article pertains to the editorial note in The Arithmetic Teacher, XIV (April l967), 262.
Survey research in elementary school mathematics
Authors: Riedesel C. Alan
Published: October 2020

More than one fourth of journal-published research reports dealing with elementary school mathematics present results of a survey. These range in scope from surveys conducted by individual teachers to the ambitious International Study of Achievement in Mathematics.1 Surveys are used to study presently existing facts, opinions, motivations, behaviors, and attitudes. Surveys may be conducted in two ways, by census or by sample. A teacher may wish to conduct a census survey of all child ren in her room, while a supervisor may attempt to find information by sampling pupils in the district. Both kinds are helpful in finding the status of the mathematics program and in observing pupil and teacher behavior concerned with mathematics.
A note on multiplying fractions
Authors: Romberg Thomas A.
Published: October 2020

While working on the scoring rules for a test on multiplying fractions in the 6th Grade NLSMA Battery,* it was observed that even though most students know and can apply the basic definition for multiplying fractions,
Logarithms for ten-year-olds
Authors: Carroll Emma C.
Published: October 2020

Great inventions from the history of mathematics are finding a real place in mathematics for the elementary school. One such idea—Napier's conception of logarithms as a comparison between two moving points, one generating an arithmetical and the other a geometric progression—developed into a challenging activity for my fourth- and fifth-graders. When they witnessed the simplicity and beauty of reducing difficult multiplication and division into easy addition and subtraction through a simple “log” table, eager experimenters took over, tried the “logs,” checked results with the more cumbersome multiplication and division, and raced home with “log” table copies to share the magic with parents.
Enjoy the mathematics you teach
Authors: Johnson Donovan A.
Published: October 2020

Mathematics is a many-splcndored subject. It is full of surprises, new ideas, anti beautiful patlcrns. At the same time it has a power, a uniqueness, a mystery that may be a fascination or a frustration. If mathematics is such a remarkable subject, then we should enjoy learning it and teaching it to children who are the future scientists and citizens of our land. This enjoyment is the key to success in teaching mathematics.
A method for converting from one nondecimal base to another
Authors: Smith Joe K.
Published: October 2020

In a study of numeration systems with different bases, one frequently encounters the problem of converting from one nondecimal system to another nondecimal system. The problem is often resolved by converting from the first system to the decimal system and then from the decimal system to the second nondecimal system.
Intermediate versus maximal guidance—a pilot study
Authors: Bassler Otto C.
Published: October 2020

According to Kersh, 1 three major claims have been made in favor of the discovery method of teaching. It is argued that the student who learns by discovery—
Elementary teachers’ ability to understand concepts used in new mathematics curricula
Authors: Kipps Carol
Published: October 2020

Today there is widespread concern for helping e leme nta ry school teachers acquire new mathematical knowledge. This is reflected in the vast number of inservice programs being conducted across the country. As yet, however, there has been no gene ral agreement on important goals or reasonable levels of achievement to be expected after a series of prescribed in-service experiences. Characteristically there has been no attempt to find out how much of the new mathematics curricula elementary school teachers understand.
An adventure in division
Authors: Stephens Lois
Published: October 2020

The adventure upon which you arc about to embark requires some computation, so before reading any further, get a pencil and some scratch paper. Ready? Here we go!
Changing bases without using base ten
Authors: Husk James W.
Published: October 2020

It was 9:30A.M. The class had just completed a unit on the various numeration systems when my attention was attracted by a student near the window. To my inquisitive look, Jeff responded, “Is there any way to change a number from one base to a different base without changing it to base ten first?”
Computers Teach Math
Authors: Ackerman Judy
Published: October 2020

In order to maintain a high degree of interest in my sixth-grade mathematics classes, I decided to introduce a year-long class project. Each child belongs to a committee and is able to help with the work.
Making and using graphs in the kindergarten mathematics program
Authors: Heard Ida Mae
Published: October 2020

During the 1967/8 school term, the writer used a faculty research grant to initiate a modern mathematics program in the morning kindergarten class at the Laboratory School of North Texas State University at Denton. This was the first time a structured mathematics program at the kindergarten level had been tried at the Laboratory School. The kindergarten teacher, Mrs. Margaret Eden, worked closely with the author in planning learning activities and in selecting materials of instruction. The college students in the writer's courses entered wholeheartedly into the spirit of our adventure—“Operation Kindergarten.” They made charts and maoipulative materials to be used by the children and the investigator.
A physical model for teaching multiplication of integers
Authors: Hill Warren H.
Published: October 2020

One of the pedagogical pitfalls involved in teaching the multiplication of integers is the scarcity of physical models that can be used to illustrate their product. This problem becomes even more acute if a phyiscal model that makes use of a number line is desired. If the students have previously encountered the operations of addition and subtraction of integers using a number line, then the desirability of developing the operation of multiplication in a similar setting is obvious. Many of the more common physical models that can be used to represent the product of positive and negative integers are unsuitable for interpretation on a number line. Partial success is possible in the cases of the product of two positive integers and the product of a positive and a negative integer. But, how does one illustrate that the product of two negative integers is equal to a positive integer?
From the editor's desk
Authors: Brydegaard Marguerite
Published: October 2020

What types of articles are of special interest to the readers of The Arithmetic Teacher? Many letters from our readers direct our attention to this question. Some correspondents ask permission to reprint specific articles for groups of teachers in workshops, conferences, and discussion groups. Authors of forthcoming textbooks ask permission to reprint entire or selected portions of articles. Letters written to the editor indicate reaction to specific articles. On the basis of this communication, we can make some general comments.
Editorial comment: As we read
Authors: Inskeep James E.
Published: October 2020

Mathematics—queen of the sciences! But who serves and pays allegiance to this monarch? Is it not he who has bad a rich background and full range of experience? Many are denied the pleasures of mathematics simply for Jack of this experience. Those who are denied may not know what they have missed. Yet how rich is the life of one who appreciates the beauty, form, and even “application” of the varied forms of mathematics!
Who won the international contest?
Authors: Willoughby Stephen S.
Published: October 2020

In March of 1967 newspapers and magazines reported the results of the International Study of Achievement in Mathematics, edited by Torsten Husen. From the news accounts, it was clear that the teaching of mathematics in this country is inferior and that in Japan it is excellent. In fact, several of our most respected news writers suggested that we begin teaching our children to use the soroban (Japanese version of the abacus). News media all over the country referred to the report and viewed its results with alarm.
More about mathematics in the kindergarten
Authors: Schlinsog George W.
Published: October 2020

When one attempts to write an article on a given topic it is a good practice to examine the literature to see what others are writing. If, however, the topic happens to be mathematics in the kindergarten, there is not much literature to examine. The editors of The Arithmetic Teacher are doing their part to correct this situation. In April 1967 they published an article outlining mathematical concepts appropriate for development in the kindergarten.1 The January issue of this year included several articles devoted to kindergarten and preschool mathematics.
Arithmetic card games
Authors: Hunt Martin H.
Published: October 2020

We all realize how important it is to provide youngsters with a variety of reinforcing opportunities that promote the acquisition of a knowledge of number facts. Playing arithmetic card games that have been adapted from games familiar to children and young adults not only is an enjoyable social experience for pupils, but serves as an interesting school or home activity that enhances facility with the number facts.
Problem solving and the development of cognitive structure
Authors: O'brien Thomas C. , Shapiro Bernard J.
Published: October 2020

A basic purpose of teaching mathematics is to develop a learner's problemsolving behavior. On the other hand, knowledge of mathematical ideas can evolve from problem-solving activities of the learner. As indicated by Piaget, the building of cognitive structure is a process of evolution by stages from sensorimotor activities through concrete operations to formal operations (mental operations not directly rooted in physical experience). The purpose of the following introduction is to consider two of the many implications that Piaget's findings have for educational practice, and then to relate these implications to a problem-solving activity that the teacher may wish to try with his class.
A new role for the teacher
Authors: Kaye G. A.
Published: October 2020

Should algebra be introduced in the sixth grade? Should we teach calculus in the twelfth grade? Should geometry be taught from a transformation or vector approach rather than from a Euclidean viewpoint? These and many similar questions are being and have been asked for many years by mathematics educators, and they all miss the point. We have been far too concerned about mathematics and not concerned nearly enough about students!