bluuebunny/crossref_metadata_2025 huggingface dataset:
From the editor's desk
Authors: Brydegaard Marguerite
Published: October 2020

We wish to express special appreciation to our referees who review manuscripts and make recommendations concerning publication. In many instances, our referees make suggestions that lead an author to revise his manuscript so that it is suitable for publication. Help such as this is in. valuable. We are grateful for each reviewer.
Why teach division of common fractions?
Authors: Price Jack
Published: October 2020

A few years ago Max Beberman made what he called “a modest proposal.” While it may not have been as startling as Swift's original “modest proposal,” it still was iconoclastic. He suggested that we no longer teach long division. Perhaps the same is true for fractions in general and division of fractions in particular, and we are ready for a third proposal.
Focus on research: Suggestions from research—fractions
Authors: Anderson Rosemary C.
Published: October 2020

Because the manipulation of fractions has been a source of confusion and difficulty for students, researchers have been investigating this topic for many years. This article presents some suggestions taken from research findings which may help elementary school teachers to improve the mathematics program. A list of selected references is included for those who wish to delve more deeply into the research findings.
Graph paper: a versatile visual aid
Authors: Parker Robert
Published: October 2020

In considering the mathematics program for elementary children, it is important for teachers to examine not only mathematical ideas but also the contexts within which such ideas are used. This usually means an examination of visual aids or tools of learning, since instruction in elementary grades depends upon the concrete to explain the abstract. With this in mind, one such tool that deserves special attention is graph, or squared, paper. Until one looks at the many possible uses of this visual aid, it may be taken for granted, and its applications remain sporadic and disconnected. This article is presented for the purpose of showing that graph paper is an educational device having few peers, especially from the points of view of economy, availability, and ease of use. An ordinary compilation of graph paper uses would be helpful to some degree, but what follows is a sequential development from the primary level through the upper elementary grades.
Subtraction of integers—discovered through a game
Authors: Milne Esther
Published: October 2020

This game description was a student's idea of a good problem requiring subtraction.
Prime: a drill in the recognition of prime and composite numbers
Authors: Holdan Gregory
Published: October 2020

Drill has always been of fundamental importance in mathematics for mastering and reinforcing the basic concepts. To discourage the development of unfavorable attitudes towards mathematics, a drill exercise should not become a boring, rote exercise. Instead, drill should be made meaningful for the student so that its contributions become functional in later learning experiences. Whenever drill is disguised in some other not-so-obvious form, such as a game, it tends to be more fruitful.
Message from the President
Authors: Hlavaty Julius H.
Published: October 2020

Here is the message you have been expecting—and you may have wondered why it's been delayed so long.
Attitude toward arithmetic at the fourth- and fifth-grade levels
Authors: Capps Lelon R. , Cox Linda Simon
Published: October 2020

The child's attitude affects what he learns, what he remembers, and what he does. Hence, evaluation of his attitude assumes a fundamental role in guiding his development.1 Dutton concluded that Grades 4–8 have appeared to be the most crucial years in developing an attitude for or against arithmetic.2 Because attitudes are deep within us, they are not always directly expressed, therefore, are not easily compared or observed. This ditliculty in measuring attitudes has led researchers to develop several different instruments for measuring attitudes.
Multiple methods of teaching operations
Authors: D'augustine Charles H.
Published: October 2020

If we are to meet the diversified needs of the disadvantaged as well as the advantaged child the n we must be prepared to employ many teaching techniques in reaching this goal. While educational psychologists have been reporting for many years that not every child learns best by the same method, the basic elementary school texts and methods texts have been slow to reflect this idea. Therefore, this article presents multiple methods, devices, and models relating operations on the set of whole numbers.
The effect of three different methods of implementation of mathematics programs on children's achievement in mathematics
Authors: Greabell Leon
Published: October 2020

A survey of the literature pertaining to modern mathematics education shows that disagreement tends to be the rule rather than the exception. Although there is an overwhelming acceptance and support of the general direction in which the mathematics curriculum is flowing, there are disagreements as to the importance of some of the newer topics such as topology, logic, and probability. Other areas of concern relate to the methodology used and some of the basic philosophical and psychological principles upon which a modern mathematics program is founded.
Bingtac
Authors: Williams Russell L.
Published: October 2020

During the past few years, I have enjoyed reading THE ARITHMETIC TEACHER and THE MATHEMATICS TEACHER very much. Since I am a junior high school mathematics teacher, there are articles in both magazines that are useful and interesting to me. One such article, which dealt with addition and multiplication facts, was “Yahoo—a Game for Fun and Skill” in the April 1967 issue of THE ARITHMETIC TEACHER.1
Editorial comment: As we read
Authors: Inskeep James E.
Published: October 2020

As you read this month's issue of The Arithmetic Teacher, the winter reports of below zero weather have become memories. Perhaps you Jive in a mild climate and “below ze ro” has but academic interest for you. In many of our warm desert locations, the visitor is sure to observe signs that indicate he is driving “below sea level.” In any part of the country, a student may view with alarm the fact that his grade is below the average for the class. In each of these instances, some idea of direction, point of origin, and a number scale are involved. The integers provide the abstraction we need for these physical models. For the primary grade teacher, knowledge of the integers is prerequisite to introducing them informally. The junior high school teacher wrestles with the problem of making the integers and operations with them seem “reasonable” to his students. This issue of the journal emphasizes these important numbers.
Adding integers using only the concepts of one-to-one correspondence and counting
Authors: Sherzer Laurence
Published: October 2020

The following is a method for teaching the addition of integers which requires only that the students have developed the concepts of one-to-one correspondence and counting. This means that the student need not be familiar with the operations of whole numbers.
IMF for Grades 3 to 6
Authors: Baker Dianne M. , Overholser Jean S.
Published: October 2020

The teacher wore a large gold badge made of a blank notarial seal, with a large gold paper star inside. On the star were ernbossed the letters IMF. A student asked her what the letters meant. She took him aside, explained that IMF was a secret society, and asked him if he would like to belong.
Patterns of geometry
Authors: Farrell Margaret A.
Published: October 2020

Since time immemorial, men have been impressed by the constants that exist in an apparently chaotic world. Nowhere has this appearance of surprising similarities been more frequent than in the field of mathematics. From the recognition that the sum of two odd integers is a n even integer, to the appreciation of geometric forms in nature (e.g., the hexagonal snowflake), man is continually attracted by patterns that stimulate him to classify and to think in terms of analogues. It is evident that instruction that focuses on various recurring stimuli is at least geared to a child's intuitive interest and at best apt to stimulate thought and aid understanding.
What can you do with a geoboard?
Authors: Liedtke Werner
Published: October 2020

A “mathematical problem” that upper elementary pupils might find challenging and enjoy solvi ng could be the construction of their own pegboard (with a friend's, father's, or big brother's help, if necessary).
On computation and drill
Authors: Quast W. G.
Published: October 2020

Computation and drill form the bulwark of the mathematics program in the elementary school— or so many teacher think. Despite the adva nces of “modern” approaches, which emphasize understanding and “meaningful” drill, many Students are still subjected to questionable practices and procedures that serve to undermine the learning of mathematics. Let us examine some of these detrimental procedures and practices.
Problem solving with enthusiasm—the mathematics laboratory
Authors: Schaefer Anne W. , Mauthe Albert H.
Published: October 2020

A promising approach to the teaching of problem solving is the use of the mathematics laboratory. The purpose of the laboratory is to provide children with opportunities to discover mathematical concepts through their active involvement in solving problems. The emphasis is on learning by doing.
From the editor's desk
Authors: Brydegaard Marguerite
Published: October 2020

We wish to express special appreciation to our referees who review manuscripts and make recommendations concerning publication. in many instances, our referees make suggestions that lead an author to revise his manuscript so that it is suitable for publication. Help such as this is invaluable. We are grateful for each reviewer.
Geoboard geometry for preschool children
Authors: Liedtke W. , Kieren T. E.
Published: October 2020

There is increasing emphasis today on preschool experiences in mathematics for children to capitalize on their eagerness to explore and interpret the world around them. This paper explores a wide variety of experiences based upon the use of a geoboard and rubber bands. The geoboard provides many opportunities to acquaint children with geometric concepts. Learning from their own play and from imitation of adults and other children, it is not long before they can recognize, correctly label, and form for themselves many common geometrical figures and instances of geometric properties, as well as such common shapes as letters of the alphabet.
A color-coded method of teaching basic arithmetic concepts and procedures
Authors: Junge Charlotte W. , Green Roberta
Published: October 2020

The method that is explained below was developed by the author in an effort to aid a fifth-grade boy who was severely retarded in arithmetic achievement. All conventional methods of explaining place value, such as the abacus, pocket charts, Cuisenaire rods, etc., were too abstract for this child, and the use of the materials had not led to his developing understanding of concepts.
Recent research contributions to elementary school mathematics
Authors: Riedesel C. Alan
Published: October 2020

In the January 1970 issue of The Arithmetic Teacher, Burns and Davis reflected upon selected pioneer researches in elementary school mathematics.
Science and mathematics: 1970s—a decade of change
Authors: Mayor John R.
Published: October 2020

Learning to live with change and enjoy it will almost certainly be the major challenge to teachers of the 1970s, even though the past quarter-century has been preparing us for it. The founders of the National Council of Teachers of Mathematics were wise indeed to have chosen 1920 for the year of beginning so that we could, just 50 years later, engage in that happy and wholesome practice of our society— honor the past, examine the how and why of it, and prepare for greater tasks ahead. It is difficult to imagine a more appropriate time than 1970 to do this.
A study of behavioral performances within the structure of multiplication
Authors: Grafft William
Published: October 2020

Structure in mathematics refers to the concepts, principles, generalizations, and sets of relationships which are central to the field and which serve to integrate the many parts so that they constitute a unified body. Today, the newer programs in mathematics attempt to help students sense this structure of the field.
Mental mathematics counts
Authors: Austin John C.
Published: October 2020

The incorporation of mental mathematics in the instructional framework has made a difference in the mathematical ability of students attending the Queens Intermediate School in Pasadena, Texas. Mrs. Margaret Lamar's seventh- and eighth-grade classes have set aside the major portion of one class period a week for mental mathematics exercises. The students are assigned problems to bring to class for that day. The problems are to include the concepts that the class has learned and are engaged in at the time. An example of a typical problem is as follows: Begin with 8, add 4, multiply by 2, subtract 6, divide by 3, subtract 2, extract the square root, multiply by 32, multiply by 10, and subtract 5. Answer: 175. This activity, often conducted on a competitive basis, has been given credit for the school's winning every interdistrict number-sense contest for the past four years. A research study conducted recently further validates this method of instruction. A random sample of one hundred boys and one hundred girls who attended the Queens Intermediate School was designated the experimental group. They were statistically compared to a similar sample of students from the same attendance area that was designated as the control group. The control group attended the traditional junior high school two years earlier than the experimental group and received a traditional mathematics program without a systematic instruction in mental mathematics.
Forum on teacher preparation: Games and algorithms—a new view in elementary school mathematics for teachers
Authors: Mueller Francis J.
Published: October 2020

Did you know that an in-service program, even a mathematics in-service program, can be fun? Did you know that a mathematics program can be relevant, even for elementary school teachers? Some people feel that elementary school teachers generally do not like mathematics and that this cannot be changed. The Maryland State Department of Education has joined force with the University of Maryland to develop the Maryland Elementary Mathematics In-Service Program (MEMIP). This program has been built on the belief that in-service programs can be fun and relevant, and that elementary school teacher can learn and enjoy mathematics. Support for MEMIP has come from both the U.S. Office of Education and the National Science Foundation.
In the Classroom: Creating mathematics with a geoboard
Authors: Wells Peter
Published: October 2020

A nine-pin geoboard is easily constructed from ⅜inch plywood and ⅝-inch panel pins, the pins being about two inches apart. A large quantity of colored elastic bands is also needed.
Statements from the past
Authors: Suydam Marilyn N.
Published: October 2020

A study of textbooks written about the teaching of elementary school mathematics during the past hundred years is an enlightening process—and an enjoyable one! Some of the statements made by these educators indicate a degree of romanticism, others stress then-current psychological beliefs, while still others are universal generalizations. Perhaps teachers will find the following samples provocative.
The angle mirror indoors
Authors: Hart Alice G.
Published: October 2020

On a bright sunny Saturday, twenty-two teachers participating in an in-service course did outdoor mathematics. One of the problems involved the use of the 45† angle mirror. (Read the article: “The angle mirror outdoors” by Lauren Woodby in the April is ue of The Arithmetic Teacher.) Each teacher was to use his own homemade angle mirror to line up the image of the image of the first pole with the “real” second pole, plant his marking pin in the ground under the angle mirror. and stretch string from the first ranging pole to his marking pin, and thence to the second pole.
Focus on research: Researching research questions
Authors: Alan Riedesel C. , Pikaart Len
Published: October 2020

Research usually begins with a need to find the answer to some question concerning variable. Some questions are very broad and require a host of subqucstions as a means of answering the larger question. Other questions are specific enough for an individual researcher or a small team of researcher to handle. Still other questions are beyond the scope of most research projects.
In the classroom: Popsicle sticks and flying polygons
Authors: Lund Charles
Published: October 2020

In the teaching of a unit on basic ideas from geometry to children in grades 5–8, Popsicle sticks can be used to create a motivating, “hands-on,” laboratory exercies. The following exercics have been used with children in both the United States and the Netherlands, and the message of identification of polygons and patterns in mathematics has been put across each time. The flying polygon puzzles and a few sample solutions are illustrated in figure 1.
Mathematical systems and their relationships to the real world
Authors: Brumfiel Charles
Published: October 2020

Let us examine carefully the relationships between the abstract mathematical system of rational numbers and the uses we make of this system as we deal with the real world. The study of these relationships is probably the chief responsibility of elementary school arithmetic teachers.
Dividing fractions with fraction wheels
Authors: Hales Barbara Budzynski , Nelson Marvin N.
Published: October 2020

Despite the numerous instructional media and teaching devices that have come into being to provide concrete and pictorial experiences for learning mathematical concepts, the division of fractional numbers is lacking in these aids. Although the process of division of fractional numbers is relatively easy to teach, only carefully selected terminology, supported by a variety of concrete methods to illustrate the process, can create a real understanding of what is actually happening when one fraction is divided by another.
Scrutinizing number charts
Authors: Paul Goldenberg E.
Published: October 2020

One of the goals of any complete educational program for children is the encouragement of a child's natural curiosity about the world and the development of his ability to recognize the patterns and regularities of the universe about him. Mathematics classes offer an opportunity almost unequalled by any other current curriculum to serve this goal because of the frequency with which very compelling patterns emerge in the midst of rather ordinary-looking work. This paper presents some activities as an example of the kind of mathematical research that young children can enjoy. The object of this close scrutiny is the humble number chart (sometimes called a hundred-chart or number lattice) that appears commonly in texts, viual aids, and some manipulative materials.
In the classroom: Understanding place value
Authors: Ziesche Shirley S.
Published: October 2020

Have your pupils ever had difficulty understanding place value? Perhaps my discovery could help you, too.
It's not how new you make it, but how you make it new
Authors: Wren F. Lynwood
Published: October 2020

Before the “;mathematics revolution” of some fifteen years ago, the emphasis of instruction in school mathematics was almost entirely on the “how” of manipulation. Little or no attention was paid to the “what” and “why” of understanding. Since then the efforts of committees and of individual teachers have effected changes both in curriculum content and in teaching techniques. These cha nges were designed to make basic understanding, as well as significant manipula tion, a fundamental responsibility of all levels of instruction. No longer is the teaching of mathematics designed to result merely in a catalog of rules for mechanical application. Ra ther, it is designed to develop, a long with a facility in use, a comprehe nsion of and an appreciation for bas ic concepts. Further, it is designed to develop an understanding of the purpose and function of opera tional procedures that they may serve as resource reser voirs for intelligent attack on problem situations whenever and however they may occur. Thus the underlying philosophy of this new emphasis in instruction is to present mathematics as an important, logically structured segment of our cultural heritage rather than as a tool kit of rules, formulas, and assorted mnemonics.
The computer revolution needs YOU!
Authors: Travers Kenneth J. , Knaupp Jonathan E.
Published: October 2020

Of the making of revolutions there appears to be no end. The 1960s will surely be remembered by mathematics teachers as the decade of the new mathematics. New terminology, new courses, new approaches to teaching, bomba rded us during those years with seemingly increasing frequency. But the task of shoring up the school mathematics program to come in line more closely with the kind of educational diet required by tomorrow's citizens has really just begun. The computer revolution is now upon us.
Why can't Johnny cipher?
Authors: Henry Boyd
Published: October 2020

Perhaps Johnny can't do his arithmetic because Johnny can't read-can't read the notation, that is. His teacher may be quite unaware that this is the source of his difficulties in arithmetic. The symbols that we use in mathematics to denote the number of elements in a set, to denote certain operations, and to denote various relations are concise, efficient, and usable. But if a child cannot understand the meaning of these symbols, they say little to him. This simple fact is likely to be overlooked by many teachers in the intermediate grades and in junior and senior high school.
Will the set of children …?
Authors: Steinberg Zina
Published: October 2020

In discussing why a study of sets is important, Z. P. Dienes and E. W. Golding say, “If we aim at a deeper understanding of number in the child's learning, then the preparation for number must also be at a greater depth.”1
National Assessment in Mathematics
Authors: Foreman Dale I. , Mehrens William A.
Published: October 2020

The development of the mathematics area of National Assessment is now in the final stage before the assessment. The actual field administration is scheduled to begin in the fall of 1972. This article is a report of the objective and exercise development in the mathematics area that has taken place between 1964 and the present date.
What happened to elementary school arithmetic?
Authors: Brown Gerald W.
Published: October 2020

The remarkable changes that have occurred recently in elementary mathematics are well known to almost everyone. Rarely has a change in public school curriculum aroused so many. “What is it expected to accomplish?” Or “What will children be able to do after completing six years of new mathematics that they couldn't do after six years of the traditional program?” Of great concern to some is th at this latter question is not being asked- or, if it is being asked, it is not being answered in terms th at are understandable to the public and the teachers.
Forum on teacher preparation: Conceptual mathematical methodology for prospective elementary school teachers
Authors: Brousseau André
Published: October 2020

One who questions a three- or fouryear- old is often surprised at the child's understanding and knowledge of mathematical concepts. Many researchers, among them Davis (1962, p. 57) and Piaget (1953), have concluded that children at an early age, given the proper motivation, references, and catalysts, can grasp mathematical concepts normally delayed until later in their education. In recognition of this finding, and of the impact of television on a child's accumulated knowledge upon entrance into today's elementary schools, teachers must be better prepared. They face a challenge dreamed about but seldom approached before the corning of our present generation of preschoolers.
Things you can try: Subtraction by the “dribble method”
Authors: Hamilton E. W.
Published: October 2020

Most of us have spent some time since our public school days developing shortcuts—labor-saving ways of looking at things—most of which find no place in form al instruction.
Diffy
Authors: Wills Herbert
Published: October 2020

The game DIFFY is an academic game that provides intrinsically interesting drill experiences and allows for individual differences. Moreover, teachers need not construct any of the exercises. The student himself initiates the drill, and the nature of the game provides for variety in the numbers encountered. Thus the activity promotes self-generated drill. This feature is commendable, since students won't run out of material and they become personally involved in their work. Besides automatically adjusting to students of diverse abilities within a given classroom, DIFFY also provides productive academic recreation at every grade level. This flexibility stems from the fact that the game may be played with a variety of numbers: whole numbers, nonnegative rationals, integers, all rationals, or all real numbers.
Mathematics education and the White House Conference on Children
Authors: Smart James R.
Published: October 2020

The White House Conference on Children held in Washington, D.C., 13-18 December, 1970 included representatives from the National Council of Teachers of Mathematics. Some delegates to the conference represented national organizations; others represented geographic regions.
Things you can try: What's the area?
Authors: Rosenberg Howard
Published: October 2020

Do your students really know what squa re measure is? I found that very few of the students in my seventh-grade classes had even an inkling of the concept. In order to give them an introduction to the topic of square measure, I told them to bring a measuring instrument to class. The items they came in with ranged from twelve-inch rulers to yardsticks to tape measures.
A geometric interpretation of certain sums
Authors: Myers Donald E.
Published: October 2020

Elementary school teachers frequently complain that mathematics is abstract and makes too extensive use of symbols. Geometry can help reduce this dependence on symbols. We shall use a story about a famous mathematician to illustrate how some abstractions can be formulated in terms of geometric figures.
Things you can try: Checking the calculated average through subtraction
Authors: Albert Irwin
Published: October 2020

How often have you tried to involve your students in some meaningful practice in adding and subtracting negative numbers? One such application is checking the average through subtraction.
One point of view: Lab Oratory and the generalization gap
Authors: Osborn Alan R.
Published: October 2020

During the past year a number of books have been published that make a strong case fo r the use of a laboratory approach for teaching mathematics. Numerous a rticles in both profession al and lay magazines have advocated a laboratory orientation. Compa rison of NCTM convention programs of today with those of even four years ago indicates a significantly greater interest in activity-based instruc tion. This heightened advocacy is good and appropriate, following on the heels of an extended period of curricul ar revision that emphasized the symbolic and the abstract.
Where are the children?
Authors: Silverman Helene
Published: October 2020

Are we teachers of students or consumers of mathematics equipment? Where are our priorities?
An individualized mathematics program in junior high school
Authors: Ogilvie Lloyd J.
Published: October 2020

The Caledonia, Minnesota, mathematics teachers have devised an individualized mathematics program with the goal of enabling each student to work at his personal rate and at his personal level of achievement. It was hoped that students would cease competing with classmates and begin competing with themselves as they began assuming the responsibility for their own learning. An open-ended program would permit capable students to progress as far as their interest and ability would permit. Students who previously reached mere threshold understanding would gain additional time for better comprehension of the concepts involved by contracting for units of work.
Using research in teaching: Is grouping for mathematics instruction practicable in departmentalized mathematics classes?
Authors: Turkett A. Keith , Purser Jimmy V.
Published: October 2020

The problem of how to meet the individual needs of learners in heterogeneously grouped classes has plagued educators for generations. Literature is rife with possible administrative solutions to the problem (for example, interclass ability grouping, streaming, the nongraded system, team teaching, and so on); however, action research aimed at providing practical help for the classroom teacher who faces daily classes of pupils whose achievement levels and ability potentials are literally gradelevels apart is not nearly so plenteous.
Auditor's report
Authors: McGivern Raymond H.
Published: October 2020

We have examined the accompanying Balance Sheet of Funds of the National Council of Teachers of Mathematics as of May 31, 1971, the related Statements of General Fund Revenues and Expenses and the Statements of Fund Balances. Our examination was made in accordance with generally accepted auditing standards and accordingly included such tests of the accounting records and such other auditing procedures as we considered necessary in the circumstances.
Building a case for the application of Piaget's theory and research in the classroom
Authors: Inskeep James E.
Published: October 2020

Mathematics education, like all branches of the educative process, is subject to periodic fads. It is possible for mathematics educators to be taken with ideas that appear, have a brief moment of glory, and then are quietly laid to rest. In recent years, Piagetian research has been given hearty acceptance by many educators, to the point where some have suggested that it may be a fad. The purpose of this article is to argue that Piagetian research is worthwhile for the classroom, that its impact has not yet been fully realized, and that it will continue to expand in influence and relevance to mathematics education.
One point of view: The mathematical education of an elementary teacher
Authors: Engen Henry Van
Published: October 2020

A new report on mathematics courses for teachers has been published by the committee on the undergraduate program in mathematics (CUPM).1 the 1961 cupm report2 led to the introduction of new courses for elementary teachers and a flood of textbooks all claiming that they had implemented the spirit of the cupm report. No doubt the next few years will see even more texts making the same claim for the 1971 report of CUPM.
Applying “Madam I'm Adam” to mathematics: A discovery project
Authors: Brown Gerald W.
Published: October 2020

The quotation “Madam, I'm Adam” is recognized as an expression that reads the same forwards and backwards. Perhaps better known is the quip attributed to Napoleon, “Able was I ere I saw Elba.” In language, such expressions are called palindromes.
Things you can try: A game for reviewing basic facts of arithmetic
Authors: Arnsdorf Edward E.
Published: October 2020

A delightful game to use in reviewing addition-subtraction and multiplicationdivision facts for whole numbers has been developed by a Sacramento State College education student, Mary Dunlap.
Things you can try: Rolling tetrahedrons
Authors: Schloff Charles E.
Published: October 2020

The rolling tetrahedron is a polyhedron constructed with a marble inside. The marble protrudes from the base far enough to allow the tetrahedron to roll. The tetrahedron, when pushed gently, will roll smoothly across the floor or table top without any apparent means of moving. Children will be stimulated by the challenge to solve the geometric problems inherent in the construction of the rolling tetrahedron using the straightedge and compass. The problems in construction, and later in racing games, will require careful measurements and may prove to be another practical unit in developing the use of the metric system as a unit of measure.
National Council of Teachers of Mathematics: Annual Financial Report
Authors: Brown Kenneth E. , Begle Edward G. , Egsgard John C. , John Lenore S. , Smart James R. , Gates James D. , Tewell James R.
Published: October 2020

The expenditure requests submitted for budgeting to the Financial Policies Committee greatly exceeded the anticipated receipts. This is not a new problem, but this year the problem was greater than ever before. It is becoming more difficult to find ways of decreasing the expenditures or increasing the revenues. We would be more optimistic about the future financial health of the NCTM if a firmer control were placed on the long-range planning of the two activities that are financially most troublesome: publications and conventions.
The Semantics and Grammar of Arithmetic Language: (Or, What Is “Meaning” in Arithmetic?)
Authors: Allen Hickerson J.
Published: October 2020

Ask a woman to close her eyes and tell you what she visualizes when you say the word handsome. Ask a man to do the same and tell you what be visualizes when you say the word pretty. Now ask both to close their eyes and tell what they visualize when you say two hundred eighty-six.
A Philosophy of Arithmetic Instruction
Authors: Fehr Howard F.
Published: October 2020

The concept of need pervades all modern theory with regard to learning. Parents and teachers are asked to discover and help the child satisfy his needs. The child's needs are to be at the center of all educational programs. However, there has been little or no suggestion that the child must also sense the need of understanding his parents and teachers and of their guidance and counsel. The school has as its primary task not only to serve the child to satisfy his immediate needs but also to equip him for service to society in his later life. Hence the child has need for that elementary mathematics which is demanded of all people in our free democratic society. Children will recognize some of these needs in their own daily experience, but other needs must be shown the pupils through experience supplied by the teacher.
The Role of a Principal in Teaching Arithmetic
Authors: Newell Laura
Published: October 2020

The life of an elementary school principal is an interesting and challenging one. During the course of a day and all during the year, he receives many genuine satisfactions from his work, as well as sharing many interesting experienes. These experiences and satisfaction come through close contacts with teachers, pupils, and parents. It takes all these groups working togelher to have a good school whose program is responsive to the needs and interests of the children in the community.
Arithmetic Experiences in Grade One
Authors: Jack Dorothy , Hebeler Amanda
Published: October 2020

One Morning Marie announced to her classmates, “We have a new boy baby. Now we have three boys and three girls.”
Requiring Proof of Understanding
Authors: Petty Olan
Published: October 2020

The American School is often criticized for failing to help children develop study habits which enable them to do independent, logical thinking. Teachers of a given grade are inclined to blame instructors of the preceding grade for the child's inability to grapple with simple principles of logic and independence of thought. Complaints concerning the child's lack of ability to solve problems dealing with quantitative situations come from many quarters. Often teachers make the remark: “My children do fairly well with the arithmetical computation involved in solving examples but t hey have much difficulty with the solution of ‘verbal problems’ in arithmetic.” The expression “verbal problems” is generally employed to refer to the word description of a quantitative stituation for which the solution is not indicated. It is to be regretted that arithmetical verbal problems are not solved with less difficulty; however, it is equally regrettable that children do not understand what is involved in the various processes and operations indicated by use of abstract symbols. The fact is that many teachers are not aware of what is actually involved in the several arithmetical operations and processes they attempt to teach. Several practices which may help children to understand better why they do certain things in arithmetic, as well as help them to see what is involved in the fundamental operations performed with the abstract symbols, will be indicated.
How Big Is a Billion?
Authors: Woodby Lauren G.
Published: October 2020

Most Of Us Will Not have the experience of count ing a million dollars, but, if we were to do it using new ten-dollar bank notes, the stack of bills would be about 40 feet high. How long would it take you to count out a billion dollars using one-dollar bills? Assuming that you are fairly skilled in the technique and can count at the rate of 4 every second, you could count $240 in a minute or $14,400 in an hour. It would take you nearly 2 forty-hour weeks to count out a million dollars. If you worked regularly for a year, you could count about 30 million dollars. You would be considering retirement before you finished counting the billion dollars!
How Many Children Are Here Today?
Authors: Instebo Mrs. Esther
Published: October 2020

Numbers Seemed To Become more real to my first graders last fall when we decided to use as counters the self-portraits we had made for open house. It was considered a privilege for one child to point to the portraits with a ruler while another tapped the actual person gently on the shoulder or head. This seemed to establish the one to one relationship so necessary in early rote counting. Each child watched intently to be sure he was tapped as his portrait was pointed out. T he port raits were so real to the children that taking daily attendance became a true number experience very quickly. The inevitable first grade chart story of “We have_______boys, We have girls, We have ________ children.” came easily because the children looked forward to counting their friends each day.
Ideas
Authors: Immerzeel George , Wiederanders Don
Published: October 2020

Each ideas presents activities that are appropriate for use with students at the various levels within the elementary school. Remove the sheets from your arithmetic teacher and reproduce the copies that you need. After you have used an ideas activity sheet with your students, add your comments and file the materials for future use.
Things you can try: Math rummy
Authors: Brown Carolyn R.
Published: October 2020

The card game Math Rummy may help students in your classroom to better understand, identify, and relate equivalent concepts. The game, as described here, relates fractions, decimals, and percents. Additional games can be made by changing the cards to sets of equal sums, equal differences, or combinations of values.
Old MacDonald builds a fence
Authors: Page Robert L.
Published: October 2020

One day while Old MacDonald was out riding, he saw his neighbor, Farmer Brown, busily at work in a field. Wishing to be neighborly and also somewhat curious about his friend's activities, Old MacDonald decided to stop and talk.
Please give us more story problems?
Authors: Snyder Barbara B.
Published: October 2020

Would you please give us some more story problems?”
Mathematics as a core unit
Authors: Morris John L.
Published: October 2020

The subject of stocks and bonds is one of the most difficult topics in the mathematics curriculum to make relevant to students. This is due primarily to two reasons: (1) it is a subject that is not needed until adulthood, and (2) many teachers do not fully understand the subject.
Probability with marbles and a juice container
Authors: Higgins James E.
Published: October 2020

Probability is too often omitted from the elementary mathematics curriculum. Recent experiences using probability with elementary students, both primary and intermediate, indicate that such a topic increases mathematical understanding and teaches mathematical thinking-two worthy goals of a modern curriculum. Here is an activity that fifth- and sixthgrade students enjoy.
From a panelist's perspective
Authors: Suydam Marilyn N.
Published: October 2020

As this issue of the arithmetic teacher is being prepared for the printers — December 1972—Congress has not yet established the metric system as the official measurement system of the United States. It is possible, of course, that Congress will act the very week that you receive this issue, and Congress may not act favorably on the metric system bill. This does not seem likelybut is it “likely” that the United States would have procrastinated for almost 200 years already?
Schools are going metric
Authors: Helgren Fred J.
Published: October 2020

Forget the length of King Edgar's foot, the length from the nose to the tip of the finger, the length of three barley corns laid end to end, tbe amount of land tha t ca n be plowed by a yoke of oxen in one day. F orget, if you have not already done so, the number of square feet in an acre, the difference between a dry quart and a liquid quart, the number of pecks in a bushel, and all the rest of the system of measures that are learned with difficulty and forgotten with the greatest of ease.
Things you can try: Crazy fractions: An equivalence game
Authors: Carlisle Earnest
Published: October 2020

The game “Crazy Fractions” is useful in helping fifth and sixth graders learn equivalent fractions and the renaming of whole numbers as fractions.
A giant step for NCTM
Authors: Schult Veryl
Published: October 2020

An NCTM Headquarters Building! A few short years ago such a thing would have been thought impossible! A “giant step for mankind” was taken in 1969 when astronauts first set foot on the moon, and what seemed a comparable “giant step for NCTM” was taken in 1973 when NCTM stepped into its own building.
Gas station map mathematics
Authors: Allison William M.
Published: October 2020

The next time you fill up your car with gas, pick up some free teaching materials. Ask the gas station attendant for a supply of highway maps for use in your mathematics class. You need not be hesitant about asking. Oil corporations consider highway maps as promotional literature, and you are going to promote better mathematics education.
Wind rose, the beautiful circle
Authors: Krause Marina C.
Published: October 2020

Teachers today are continually seeking ways to enrich the mathematics curriculum. Student interest may be challenged by the story of man's most effective means of shrinking space, mapping. Mapping opens a world of mathematics, exploration, and art to the student-the wind rose is an example.
Teaching the metric system as part of compulsory conversion in the United States
Authors: Hawkins Vincent J.
Published: October 2020

There is no doubt that the metric system is rapidly becoming the standard system of measures for the entire world. Over ninety percent of the countries have already adopted the system. Even England, from whom we inherited our customary system of weights and measures, is more than halfway through its own ten-year program of conversion.
One point of view: Geometry in the elementary school
Authors: Van Engen Henry
Published: October 2020

This issue of the arithmetic teacher presents a point of view relating to a geometry program for the elementary and middle schools and a program for teachers of elementary schools. The positions presented in the subsequent articles were prepared independently–it is not a committee report–and yet, there is a surprising unanimity about several important aspects of a geometry program for our schools of the future. There are at least th ree points of agreement presented in the following articles that stand out.
Geometric activities for early childhood education
Authors: Immerzeel George
Published: October 2020

A class of first graders was working on a geometry Jesson in which they were to arrange a basic set of geometric blocks like the arrangements shown on a screen in front of the classroom. Three students in the group were noticeably successful in completing the task. They were not only highly successful in the interpretive aspects of the activity, but they were also able to verbally justify their selection of particular blocks, even when the decision required considerable deductive reasoning. Their teacher pointed out that these three students were all in the lowest reading group in the class.
Mathematics in the study of African culture
Authors: Zaslavsky Claudia
Published: October 2020

What do we know about the development and applications of mathematics in Africa, outside of ancient Egypt? My attempts to discover the answer to this question Jed me to a field of research that has barely been touched by mathematical historians. In fact, the treatment of Africa in the books on the history of mathematics leaves one with the impression that Africans could barely count before the advent of Europeans.
Kaleidoscopes and mathematics
Authors: Orans Sylvia
Published: October 2020

In 1816 Sir David Brewster, a British physicist, invented an instrument which today continues to excite children and adults of all ages. Using three Greek words— kalos (“beautiful”), eidos (“form”), and skopeo (“I see”)—he named his invention kaleidoscope.
The board stretcher: A model to introduce factors, primes, composites, and multiplication by a fraction
Authors: Cohen Louis S.
Published: October 2020

Most children are aware that some numbers are even and the rest are odd, but they know little else about our number system. The “board-stretcher” model provides a means to discovering the idea of factors and obtaining a feeling for prime and composite numbers. It portrays the inverse relation between multiplication and division and, as a finale, it can be used to introduce the concept of multiplication by a fraction. This model suggests the notion that the sum of the prime factors of a number (except for four) is always less than the product of the factors. The Fundamental Theorem of Arithmetic (or Unique Factorization Theorem) is understood by youngsters when they see that every composite number can be expressed as a product of prime factors that is unique except for the order of the factors.
Hand-held calculators: help or hindrance?
Authors: Hawthorne Frank S.
Published: October 2020

For more than a decade mathematics educators have been on notice that the day is approaching when everyone will have ready access to sophisticated electronic computers. Recent advances in the development of small, inexpensive calculators provide impressive support for the prediction.
Things you can try: Multi-bet
Authors: Miki Arthur K.
Published: October 2020

The game “Multi-Bet” provides practice with the more difficult multiplication combinations and has proved to be one of the most popular games in the fou rth grade.
Things you can try: Two mathematical games with dice
Authors: Good Ronald G.
Published: October 2020

Each of the games described here uses a pair of dice. The two dice must be distinguishable by color, one die of one color and the other of a different color. The variations in color can be in the dice or in the spots on the dice. Such dice can be purchased commercially or they can be produced by making wooden cubes and then using magic markers to make the required spots on the faces of the cube. Only two colors are needed and it might be a valuable activity to allow students to make their own dice before learning how to play the games.
National Council of Teachers of Mathematics: Annual Financial Report
Authors: Begle Edward G. , Egsgard John C. , John Lenore S. , Smart James R. , Wells David , Gates James D. , Tewell James R.
Published: October 2020

Fiscal 1972–73 was financially sound for the National Council of Tea chers of Mathematics; and we were able to exceed our budget in some critical revenue areas and operate under budget in some expense areas. The Financia l Policies Committee remains concerned that the publications and convention activities do not result in excessive deficits. These two areas have been financially troublesome; and we will continue to encourage firmer control on the long-term planning of these activities.