bluuebunny/crossref_metadata_2025 huggingface dataset:
Measurement or partition division for introducing study of the division operation
Authors: Spitzer Herbert F.
Published: October 2020

The teaching of the division operation, like many other aspects of elementary school mathematics, is undergoing some profound changes. These changes are due primarily to the new mathematics movement which now dominates the preparation of instructional materials in elementary school mathematics. One of these changes is the seeming shift in beginning instruction from emphasis on the relationship between division and subtraction to emphasis on the relationship between division and multiplication. In the pre-new mathematics, most methods books for elementary school teaching recommended1 that division study be introduced with a measurement division situation. It was argued that measurement situations were better for introducing study because repeated subtraction, drawings, and number lines could logically be used in finding the answer to the division question presented. Most recently published methods books and books designed to give teachers a mathematical foundation for teaching division emphasize that the division operation is the inverse of multiplication. This emphasis is clearly shown in the descriptions of the division operation which are found in these books. The following is representative: “Division is the operation of finding a missing factor when the product and one factor are known.”2
Geometry for primary children: Considerations
Authors: Vigilante Nicholas J.
Published: October 2020

Curious circumstances trigger trains of thought. Glancing across a library table recently, I saw this title appearing in The Arithmetic Teacher: “Geometry for the Primary Grades.” The student reading the article was evidently intrigued by the title, for he seemed to return to the title page on a number of occasions. This caused me to wonder what such notables as Euclid, Poincare, Euler, Gauss, Moebius, Bolyai, Lobachevski, Riemann, and all of the other great minds, both past and present, would have written under the same title. I began to wonder what would emerge if these immortals were to coauthor this topic with another group that included Piaget, Montessori, Bruner, Suppes, Hawley and others. What unified, harmonious medley of understanding would emerge? This surely had all the overtones of a setting of individuals bent on a course that might bring together the necessary components for a panacean program of geometry in the primary grades—a program that would be organized on a logical and psychological basis that takes into consideration the age of the child. This is the context in which present-day geometry for primary-grade children is being explored— the child, the topic, and the environmental influence of both.
Research on mathematics education, grades K-8, for 1966
Authors: Weaver J. Fred
Published: October 2020

Ten years ago there appeared in The Arithmetic Teacher my summary, “Six Years of Research on Arithmetic Instruction: 1951–56,”1 which then was continued on an annual basis.2
Physical representations for signed-number operations
Authors: Ashlock Robert B. , West Tommie A.
Published: October 2020

Are you teaching signed numbers in the elementary school? Many teachers find the study of signed numbers and operations on signed numbers to be an exciting extension of their basic instruction. Other educators, such as those participating in the Cambridge conference, feel that a very early introduction of signed numbers is an essential part of helping children gain insight into the real-number system and its properties [2]*. Whatever your reason for introducing signed numbers, useful physical representations are needed. This article has been written to help you find appropriate representations for your instruction.
The distributive property
Authors: Boyer Lee E.
Published: October 2020

In this period of emphasis on teaching the structure of mathematical systems, the distributive property is indeed basic. Yet, surprisingly, there is a fundamental weakness in the presentations of this property in the textbooks. This is particularly disturbing to prospective elementary teachers who arc now studying more and more of the basic concepts of elementary mathematics.
Discover and learn
Authors: Maroun Sister Mary Basil
Published: October 2020

Are the elementary school teachers in this day and age of mathematics spoonfeeding their pupils? With the advancements mathematics has made in the past decade can we, who are called teachers, be assured that our pupils will be able to do what is expected of them in the years ahead: that is, think creatively and discover the beauties of mathematics?
Discovering the mathematics of a slide rule
Authors: Martin J. Gregory
Published: October 2020

Like mathematics teachers in most junior and senior high schools, I find myself looking for ways to refresh my own enthusiasm as well as new ways to channel the enthusiasm of my students. One method I find to be effective is to introduce a topic that is not in the text, and at the same time is a topic I have not presented before.
New English for the new math
Authors: Reed V. B.
Published: October 2020

The first few years' experience with the new elementary mathematics curricula suggests that something should really be done about the words “commutative,” “associative,” and “distributive” used as names of the fundamental laws of arithmetic. They have done excellent service in their time, but the truth is that they have become a hindrance to traffic in mathematical education.
From the editor's desk
Authors: Brydegaard Marguerite
Published: October 2020

Members of the editorial staff of The Arithmetic Teacher are grateful to the NCTM members who participate in our activities either by writing to us about their reaction to articles printed in the journal or by giving us their own points of view on the teaching of mathematics at the elementary school level, whether in letters or in articles submitted for publication.
A report of the NCTM committee on the low achiever
Authors: Travers Kenneth J. , Jorgensen Paul S.
Published: October 2020

One committee of the NCTM-the Committee on Mathematics for the NonCollege- Bound (MNCB)-devotes its time to the problems of students at all grade levels who are having difficulty in learning mathematics. A predominant point of view of the committee was summed up in one of its annual reports to the NCTM Board of Directors. In that report it was recognized that the problem of the low-achieving student is an extremely complex one whose solution calls on the creative talents not only of teachers but also of mathematicians, psychologists, sociologists, guidance counselors, and other specialists concerned with mathematics education.
An inverse square relationship in science
Authors: Norris Theodore R.
Published: October 2020

Great discoveries and achievements in science have nearly always been associated with mathematics, the language of science. There are many types of scientific activities that can be used to challenge elementary-level children to discover for themselves quantitative relationships existing in the physical world. One such discovery that proved to be a challenging and rewarding experience for an accelerated Grade 6 class is the inverse square law.1
Computers and the use of base two in the memory unit
Authors: Thompson Gerald A.
Published: October 2020

When my sixth-grade class was involved in the study of base systems, many questions were raised concerning computers and the base systems they employ. To answer their questions, I decided to develop a lesson encompassing these objectives: (1) to familiarize the students with the various components of a computer system, (2) to demonstrate how some of these components function, and (3) to develop an understanding of the use of base two in the memory unit of a computer system.
Developing geometric concepts in the kindergarten
Authors: Heard Ida Mae
Published: October 2020

At the moment there is a great discussion going on in Texas about making the kindergarten a part of our public school system. Bringing these five-year-olds into the public school poses problems of finance, curriculum, housing, and most important, the education of qualified teachers for these young learners.
As we read
Authors: Inskeep James E.
Published: October 2020

The ancient Greeks sought and observed patterns in the world about them. The world seemed to be naturally arranged in a particular, predictable fashion. It is not strange that the earliest of the Greek mathematicians would also see patterns in the common counting numbers. Many of us have neglected these strong ideas of pattern and prediction in our presentation of number work to children. As you read this month's journal, you will surely be encouraged to try new methods in the teaching of whole numbers. The theme of whole numbers, operations, and ideas inherent in the system will be refreshing.
Introduction to the numeration of two-place numbers
Authors: Ikeda Hitoshi , Ando Masue
Published: October 2020

The primary teacher has one of the most important tasks in the teaching of arithmetic—that of introducing and instilling in the minds of children a firm founda tion of the concept of place value. Much of the success children will have in working with the operations of addition, subtraction, multiplication, and division depends on their concept of place value. With admirable patience and stamina, the primary grade teacher has circul ated amid the bundles of counters, popsicle sticks, tongue depressors, and what-have-you to help children gain this concept. This is well and good.
Familiarity breeds understanding
Authors: Braun Charles
Published: October 2020

A few years ago I was assigned to a class of ungraded youngsters in a metropolitan area that today would be called the inner city.
Napier's rods: practice with multiplication
Authors: Traub Raymond G.
Published: October 2020

Many teachers in Grades 3 through 8 are constantly searching for new approaches to motivate practice in multiplication. Students, as well as teachers, often become bored with the laborious struggle of learning to multiply. Teachers have been overheard saying, “Something different and active is needed to keep the students turned on.” Like “The Poor Scholar's Soliloquy,” this might well be entitled “The Poor Math Teacher's Lament.”
A second example of informal geometry: milk cartons
Authors: Walter Marion
Published: October 2020

This article describes some work that children can do with milk cartons. You will need paper milk cartons and construction paper. Cut the top off the milk cartons so that the height is equal to the width. Rule the construction paper with two-inch squares.
Play shuffleboard with negative numbers
Authors: Frank Charlotte
Published: October 2020

Shuffleboard, anyone?” Can you imagine how a student-filled math classroom would I respond to that invitation? Compare that with the reaction to a teacher announcing, “Students, today we are going to learn the four fundamental operations of the set of integers.” By the time the teacher had finished saying the word “fundamental” his pupils would have tuned out both him and his lesson. Negative Shuffleboard can be used to introduce the four basic operations of negative integers to the elementary school youngster in a fun setting.
In the classroom: Hide-a-region—N≥2 can play
Authors: Overholser Jean S.
Published: October 2020

Hide-a-Region is a game that can be played by two or more persons, from the first to the twelfth grade. Its purpose is to give practice in locating points on a grid, and in the concept of the area of a region.
Computation: low achievers' stumbling block or stepping stone?
Authors: Travers Kenneth J.
Published: October 2020

Legend has it that inscribed over Plato's porch were the words, “Let no one ignorant of geometry enter here!” I suspect that as mathematics teachers most of us have shared a measure of this fervor, and in our imaginations have chiseled over the doors of our classrooms mere mortal inscriptions like, “Let no one ignorant of computation pass through these portals!” For it seems that large proportions of students are blocked from appreciable progress in mathematics because of their inability to compute.
Forum on teacher preparation: The prospective elementary school teacher and mathematics methodology
Authors: Arnold William R.
Published: October 2020

There is little doubt that today the “discovery approach” is the preferred method for teaching mathematics. Implicit in this method is the notion that children should discover mathematical concepts, that the Ieamer engage in some form of inquiry, and that the ongoing process of learning is of prime importance. All this is reflected in the recent emphasis in mathematics education upon discovery, inquiry, and process.
Editorial comment: As we read
Authors: Inskeep James E.
Published: October 2020

Work with number has a strange fascination for many people. In man's invention of number, the aesthetic aspects of abstraction and the down-to-earth appeal of practicality are joined. Notwithstanding the distinction between number and numeral, the numerals we “manipulate” often become objects of interest in themselves. It is a stimulating experience to discover a pattern in a set of numerals. To some, these patterns border on the occult. To others, they are mute evidence to the power of abstraction in mathematics. Do you like to work number puzzles? Are your children intrigued by interesting combinations in the multiplication table? You will find this issue of The Arithmetic Teacher a source of worthwhile ideas. For others, the potential for acquainting children with number combinations will be a practical reason for reading. There is something for each level from primary through junior high school, and those whose interests fall elsewhere will find many of the suggestions personally appealing.
In the classroom: Live models in arithmetic?
Authors: Livingstone Isobel L.
Published: October 2020

Want to bring new life—and new learning—to your arithmetic class? Try this interest-catching technique. Simply ask twelve students to come to the front of the room. These are your live models who will demonstrate all kinds of arithmetic concepts. First of all, ask them to arrange themselves in any way they wish. Then call on a child from the group at their scats to supply the mathematical sentence that describes the situation they are seeing. It might be 8 + 4 = 12, or 4 + 8 = 12, or 12 − 4 = 8, or 12 − 8 = 4. At this point, ask the models to rearange themselve, and again ask the rest of the class to make a true statement about what they sec.
1970 Elections: Report of the committee on nominations
Authors: Trimble Harold C. , Glenadine Gibb E. , Keiffer Mildred , Magers Dexter A. , Meserve Bruce E. , Rickey Agnes Y. , Steffens Herbert R. , Sobel Max , Wooten William
Published: October 2020

The Committee on Nominations presents its nominations for the offices to be filled in the 1970 elections. These nominations and the election are the first to conform to the bylaw changes enacted at the Annual Busines's Meeting, April 1969. in Minneapolis
Focus on research: The mathematical understandings of preservice and in-service teachers
Authors: Riedesel C Alan , Pikaart Len , Gibney Thomas C. , Ginther John L. , Pigge Fred L.
Published: October 2020

The mathematics education of preservice and in-service elementary teachers has been the topic of several previous articles in the ARITHMETIC TEACHER.
Editorial comment: As we read
Authors: Inskeep James E.
Published: October 2020

The child with special learnjng problems is not new to the schools. From Socrates to Sputnik, these children's needs have demanded talent from teachers and have tested the pedagogy of experts. Today with many sophisticated technical achievements, we still face the child who does not learn quickly. Or, we locate the child who is creative and then provide little outlet for his energies. Even gifted children with special talents are largely left to their own devices. This issue of the arithmetic teacher is devoted to these problems of special education in mathematics.
Forum on teacher preparation: Comments of some problems of teacher education in mathematics
Authors: Mueller Francis J. , Dienes Z. P.
Published: October 2020

Practically the whole world seems to be engaged in some form of revision of mathematics curricula as well as mathematics teaching methods. Why this is so or if it is a good thing or a bad thing is not the concern of this article. It is assumed that it is historically an inevitable process, and the remarks made in this article are aimed at clearing up some of the difficulties that have been encountered in trying to train teachers to teach different kinds of mathematics and to teach mathematics differently
Kindergarten mathematics laboratory–nineteenth-century fashion
Authors: Leeb-Lundberg Kristina
Published: October 2020

A small boy of five came into the kindergarten one morning with radiant face and sparkling eyes, crying out in joyful tones: “I have something for you l It's hard and long and has four edges and two ends!” The precious object was held behind him, while he danced around in fond anticipation of the pleasure he was about to give his teacher, of whom he was very food.
Some observations of children's reactions to computer-assisted instruction
Authors: Rothbart Andrea , Steinberg Esther
Published: October 2020

In January of 1969 twelve terminal for computer-assisted instruction (CAI), each consisting of a key set and a television display (fig. 1), were installed in a small room in Washington Elementary School, Champaign, Illinois, as part of the Programmed Logic for Automatic Teaching Operation (PLATO) project at the University of lllinoi, Urbana. We wi hed to learn how the computer could but be used to supplement the arithmetic classroom. Therefore, we experimented widely in the types of lesson we wrote. Moreover, we involved children of all age and ability group available in the K-6 school, including the educable mentally handicapped (EMH).
A graphical representation of multiples of the whole numbers
Authors: Hervey Margaret A. , Litwiller Bonnie H.
Published: October 2020

Have you ever considered a graphical representation of multiples of whole numbers? Could such a representation be used to reinforce and extend the ideas of prime numbers and composite numbers? These questions were posed in our elementary methods classes. In considering these questions the students constructed graphs. As the students constructed their graphs they discovered that they had a representation that summarized many ideas of arithmetic.
Investigation of line crossing in a circle
Authors: Vaughn Ruth K.
Published: October 2020

One of the prime aim of education should be to help children learn how to solve problems. Mathematics is a field that provides the teacher with endless opportunities to help the child learn methods of attacking and solving problems. The following problem demonstrates how, when one approach fail, we should restudy the problem and perhap try a completely different approach.
IDEAS
Authors: Immerzeel George , Wiederanders Don
Published: October 2020

Ideas is presented to provide you with an easy way to try out some ideas that we have found interesting in our classroom. We plan to present several worksheets in each issue. One of these worksheets will be appropriate for your students.
Kindergarten in the “Arithmetic Teacher”: A decade of growth
Authors: Norman Laurel
Published: October 2020

In this annotated bibliography an attempt has been made to include every article appearing in the Arithmetic Teacher during the sixties which had relevance to kindergarten teaching, even if an entire article was not about kindergarten. These articles constitute a good collection of readings for teaching mathematics at the kindergarten level. The January 1968 issue is particularly notable, containing five relevant articles.
“The Experts and the Simpleton”—A fable
Authors: Schwartz Herbert
Published: October 2020

Onee there was a child in school who was simple—the kind of boy who, when he hears someone say, “She's so dumb that she thinks a football coach has four wheels,” laughs genially and then asks, “By the way, how many wheels has it?” (You know the kind of boy.)
Division isn't that hard
Authors: Spigno Joseph Di
Published: October 2020

Learning to work division problems is probably the most difficult arithmetic task for Jementary school child ren to handle. When they master the mechanics of division, they lay have little or no understanding of the division process.
Geometry through inductive exercises for elementary teachers
Authors: Wong Ruth E. M.
Published: October 2020

Geometry frequently suggests only a sequence of definitions, postulates, theorems, and proofs. While this is part of geometry, it represents the finished product—a systematic, well-organized body of knowledge about plane and space figures. Preceding this formal organization into a deductive structure are a number of processes. These include: searching for patterns, recognizing patterns, making guesses, observing similarities and differences, assembling data, generalizing from specific instances, checking conjectures, expressing ideas accurately, and recognizing concepts in concrete situa tions (Hawaii Curriculum Conference 1966).
“Activity board”— the board of many uses
Authors: Swadener Marc
Published: October 2020

Teachers in the elementary grades are continually searching for ideas that will stimulate learning in the student. Such ideas frequently involve manipu lative materials; and this is consistent with the current trend toward laboratory activities in mathematics instruction, the objective of these being to actively involve the students in the learning process.
Things you can try: Arithmetic games
Authors: Dilley Clyde A. , Rucker Walter E.
Published: October 2020

Often there is little variation in the setting in which children practice arithmetic skills (basic combinations and algorithms). In many cases the practice is unchallenging and unrewarding. An appropriate game can provide children with both a challenging and rewarding experience and an opportunity to discover mathematical concepts. Some games that have been used successfully with children at all levels are described below.
One point of view: A call for a commission on elementary school mathematics
Authors: Payne Joseph N.
Published: October 2020

It is time for the formation of a National Commission on Elementary School Mathematics.
The concept of the shifting unit
Authors: Ellison Alfred
Published: October 2020

The word unit has a built-in potential for confusing teachers as well as students. As a collective noun it may refer to a single thing or to a group of things. Yet, the word itself so clearly means one, and it has so often been used mathematically to refer to ones, that not seeing the unit in varying ways as required by some mathematical problems may lead to unnecessary difficulties and confusions.
Intellectual growth and understanding mathematics: implications for teaching
Authors: Lovell Kenneth R.
Published: October 2020

The thirty-second yearbook of the NCTM (Jones 1970) deals with the history of mathematics education in the United States and Canada. Scattered throughout the book are references to psychological and educational theories and their impact on mathematics education. The name of Piaget occurs on seven pages, and some of his books are named; but the volume does not spell out the precise ways in which Piaget's work is of value to the mathematics educator. Personally, I have been greatly influenced by his work, details of which have been published in a vast array of books and papers over almost fifty years, although it would be true to say that it is only in the last ten years that there has developed a widespread interest in his work in the United States. I believe that his position regarding the acquisition of certain kinds necesof new knowledge is of more value to the mathematics teacher than any other position at the moment, although I affirm with equal conviction that his theory does not cover a11 the facts and that one day it will be replaced or subsumed by a more allembracing one. Some of the strengths and inadequacies of his theory in relation to mathematics learning have been given by Lovell ([a] 1966) and Beilin (1971). Although it would be wrong for me to outline Piaget's cognitive-development system here, I must make six points that are the assumptions, so to speak, on which the remainder of my paper rests.
Minutes of the Annual Business Meeting
Authors: Gates James D.
Published: October 2020

President H. Vernon Price called the Annual Business Meeting to order at 9:05 A.M.
Mental imagery in mathematics
Authors: Jencks Stanley M. , Peck Donald M.
Published: October 2020

At the elementary school level, teachers need to help each child form a basis for trusting his own thinking. For example, the authors recently asked numerous sixthgrade children for the sum of ½ + ⅓. Many of the children, even those from “culturally advantaged” schools, were unable to find a correct answer or even to attack the problem with understanding. Furthermore, many of those producing correct answers were unable to relate the process to anything very meaningful. What is worse, the children had no place to go to construct a sensible answer for themselves. They were completely dependent on their teachers to remind them about common denominators before they could proceed. If a major objective of education is, in fact, “to enable a child to get along without his teacher,” then there is still much work to be done.
Addition, Subtraction, and the Number Base
Authors: Bell Clifford
Published: October 2020

When the ten one-digit NUMBERS are added two at a time in all possible ways, we obtain the 100 addition facts as shown in the following table.
Implementing a Mathematics Program
Authors: Hughson Arthur
Published: October 2020

No Program Of Education can be more effective than the means, methods and personnel selected to perform the implementation. Despite all claims to the contrary, teachers still find it easier to teach as they were taught than to teach the way they were (are) taught to teach. The old program in any area of the curriculum must first be held up for inspection before the eyes of those who do the teaching and supervising, its problems must be analyzed and pointed up, and the need for change indicated and emphasized through precept and example. The job of the researcher and administrator becomes that of selling the new because it holds more values than the old in child understandings, learnings and skills and makes possible easier assimilation by pupils. Once teachers and supervisors can see these values, the new program is launched.
Take the Folly Out of Fractions
Authors: Latino Joseph J.
Published: October 2020

One Of The Obvious Tenets of modern arithmetic teaching is that we must not encourage children to repeat rote style a manipulative process without meaning and understanding. At least the pupil ought to be able to explain in a reasonable manner whatever processes he performs with numbers. While there are other facets in the meaning theory of arithmetic instruction, many people are spending time attempting to lend at least some reason to the mechanical processes every child seems to learn.
The Fracto-Percenter
Authors: Roys William B.
Published: October 2020

This Device Can Be Made On heavy paper or “oak tag” and then pasted to a rigid background such as plywood or compoboard. The edges can be bound with masking tape. For classroom use it is suggested that the outer circle be twelve or sixteen inches in diameter. The twenty sections of the circles can be made by use of a protractor: Each section being 18 degrees wide. It is suggested that the percents be lettered in blue and the fractions in red. When all the design work has been done, the surface should be shellacked so that it is more permanent and will soil less readily.
Egg cartons again?!
Authors: Sherrill James M.
Published: October 2020

In the November 1967 issue of the arithmetic teacher, there was a very useful article entitled “Save Those Egg Cartons!” At the time that I read the article, I was not particularly concerned with the practicality of making use of inexpensive materials. However, the intent of that article has remained with me. I would now like to share a few other uses that an elementary school teacher can make of egg cartons.
Understanding the Russian peasant
Authors: Reardin C. Richard
Published: October 2020

From time to time, elementary teachers have encountered, used, or taught the Russian-peasant method of multiplication of two natural numbers and are curious about the rationale behind the process. It is an intriguing method because it involves a very simple set of facts and operations: multiplying by 2, dividing by 2, and addition. In some instances this method is called the doubling and halving technique. By whatever name it is known, any explanation as to why the method works usually is omitted from the discussion, or else there is a nebulous reference to the binary system as an explanation for it, leaving the user to ponder unsuccessfully the meaning of the reference.
Things you can try: Creative drill with pictures
Authors: Crouse Richard , Rinehart Elizabeth
Published: October 2020

The word drill has some bad connotations for many mathematics educators—probably generated by the recollections of gross misuses of drill in the past. However, many educators believe that drill as meaningful practice bas a definite place in the sequence of teaching activities, and they accept axiomatically that drill should occur after students understand a concept or skill.
Mastering the basic facts with dice
Authors: Gosman Howard Y.
Published: October 2020

The dice are “loaded” with activities to help children master basic number facts and enjoy the experience. “Double Trouble” is a good example of an activity that can be used in any grade. This game helps children master the basic facts in addition, subtraction, multiplication, and division. The game can be used in any classroom, and the teacher may modify it to suit his own classroom needs.
The factor game
Authors: Harkin J. B. , Martin D. S.
Published: October 2020

In a systems approach to teaching, particularly in the individualization of activities, manipulatives and other media hardware play an essential role. An activity package in the delivery system is a sequence of multigroup activities developed for a content unit. A variety of media hardware (a term that embraces everything from a geoboard, a projector, or a video set to a piece of chalk) can be exploited in the activity package. This includes a computer, when it is available to a school.
The division algorithm
Authors: Tucker Benny F.
Published: October 2020

A situation problem is an excellent way to get into the development of the division algorithm.
Things you can try: Keith's secret discovery of the sieve of Eratosthenes
Authors: Bradford Cheryl L.
Published: October 2020

Keith enjoyed working projects, especially mathematics projects, more than anything else that he was assigned at school. It was obvious from the intricate details he included in his creations that he spent long, intense hours on them.
“Pick-a-word”—a base-26 generalization of “Pica-Centro”
Authors: Charmonman Srisakdi (Sak) , Reed Deborah K.
Published: October 2020

The games of Pico-Fumi (Gessel et al. 1972) and Pica-Centro (Aichele 1972) a re number games in the decimal number system. The objective of the games is to logically deduce an n-digit number where n equals two in Pico-Fumi and three in Pica-Centro. An extension to larger numbers of digits was suggested in Douglas Aichele's article, but a more challenging and useful generalization will be proposed here.
Things you can try
Authors: Ristor Celli T
Published: October 2020

This game can be played by two, three, four, or more players using an ordinary deck of cards. Six cards are dealt to each player and the remaining cards, placed face down, form a drawing pile. The idea is for each player to try to rid himself of aU his cards before any of the competing players by playing his cards one at a time consistent with the rules of the game.
Learning through doing in teacher education: a proposal
Authors: Bausell Barker , Moody William B.
Published: October 2020

The rationale for teaching mathematics to prospective elementary school teachers is quite straightforward. A teacher must obviously have some knowledge of the discipline's subject matter in order to insure adequate learning on the part of instructed students. This is normally accomplished by requiring the elementary education major to take a prescribed number of courses dealing with concepts deemed relevant to the elementary mathematics curriculum. The problem with this procedure is that the college textbook writer must himself arbitrarily decide which concepts are relevant and which are not. The purpose of the present article is to propose a procedure for teaching mathematics to propective teachers that avoids much of this arbitrariness.
“Math football” is fun
Authors: Maynard Malinda
Published: October 2020

Football is a popular game in the fall and early winter and the classroom game described here, which we call “Math Football,” has proven to be very popular in my classes. The students look forward to it and eagerly participate.
Metricating—painlessly, cheaply, cooperatively
Authors: Peavler Cathy Seeley
Published: October 2020

With all the present commotion over the coming of the metric system to the United States, teachers need as many practical ideas as possible. I have included here some suggestions for use in the classroom, for finding materials, and for involving the community in your metrication program.
The fourth operation is not fundamental—fractional numbers and problem solving
Authors: Zweng Marilyn J.
Published: October 2020

Few topics in the elementary school mathematics curriculum are a greater waste of time than division of fractional numbers. It is seldom used to solve problems, and those problems which children are taught to solve by division of fractional numbers are dealt with just as adequately by resorting to multiplication.
The energy crisis: an opportunity for meaningful arithmetical excursions
Authors: Post Thomas R.
Published: October 2020

The energy crisis, expected by at least some segments of our society for several years, has arrived. Its precise causes are unclear and perhaps always will remain so, but it is likely to have profound effects on many aspects of our economy as well as on our environment. Some of these effects may be positive in nature. For example, expanded use of smaller, more economical automobiles; renewed efforts to locate and develop additional sources of energy; and the evolvement of a more energy-conscious citizenry are likely to result.
1 + 2 + 3 + 4 + …: a geometric pattern?
Authors: Pereira-Mendoza Lionel
Published: October 2020

Elementary school students often see the mathematics curriculum as containing distinct components; one is arithmetic, which deals with numbers and their operations, and another is geometry, which deals with shape, Jines, and planes. The following series of mathematical investigations show how number patterns, part of the arithmetic component of the elementary mathematics curriculum, are related to the solution of geometry problems. Hence these investigations provide a link between arithmetic and geometry.
Don't just think metric—live metric
Authors: Shumway Richard J. , Sachs Larry
Published: October 2020

The range of reactions that parents have to the introduction of metric measures in the classroom can be illustrated by two quotations.
Warmer-uppers and azmuds
Authors: Posner S. Jay
Published: October 2020

My experience has been that many students, especially the quiet and reserved ones, will rarely volunteer and, unless called on, they do not actively participate in much of the classwork. Brief exercises that require simple computations can provide practice and involve all members of the class in an active way.
On creating creativity in sixth-grade mathematics
Authors: Kennedy Jean W.
Published: October 2020

OK, let's sec all the ways that we know to check to see if fractions arc equivalent.”
Children as teachers—some fundamental operations
Authors: Clarkson David M.
Published: October 2020

As part of a research project at Exeter University in which the use children made of language in “talking mathematics” was studied, I had occasion to ask several nine-year-olds to teach some of their classmates how to subtract. The results of their efforts recapitulated many common teaching problems so well that it seemed worthwhile to examine the results in some detail.
Make Up Your Own Mazes
Authors: Ordman Edward T.
Published: October 2020

A few years ago I showed a class of prospective elementary teachers a theorem that I had always assumed to be part of the folklore of topology. Apparently, however, it is little used today, either by teachers or by mathematical researchers. It was so well received by the class of prospective teachers that I then showed it to inservice teachers, and finally I visited a few elementary classes to try it on the pupils firsthand. It was regularly a success—in one instance pupils were so excited they showed it to fri ends during lunch and disrupted school for much of the afternoon. Even at the third-grade level, some pupils were able to follow the reasoning well enough to convince another classroom teacher (who had not seen the material in advance) of the truth o f the theorem. At higher grade levels, the theorem continues to be appropria te for any pupils who have not yet had exposure to the “theorem-proof” arguments of the sort common in Euclidean geometry.
Your Council at Work: EDITORIAL PANEL OF THE ARITHMETIC TEACHER
Authors: Zweng Marilyn J.
Published: October 2020

The Editorial Panel of the Arithmetic Teacher sets standards for the content of the journal and specifies the procedure for the refereeing and acceptance of manuscripts. The Panel determines the general format of the journal and defines the content and balance of materials in individual issues. They decide on the departments of the journal and appoint the appropriate editors for specified terms. The Panel meets three times a year. Between meetings they are involved in the final selection of manuscripts for publication, based on the evaluations of the referees.
Arithmetic: must it be mechanical monotony and individualized boredom?
Authors: Moody William B.
Published: October 2020

The recent movement in the direction of individualization of elementary school a rithmetic curricula may well be leading many youngsters down a dull, seemingly endless road paved with computation problem after computation problem. Ever since the introduction of programs such as the Individualized Prescribed Instructional materi als produced by the Learning, Research, and Development Center at the University of Pittsburg (along with other commercial and teacher-made versions of a student tailored curriculum), school personnel have been attempting to individualize their programs in arithmetic. It is time to take a close look at what is happening in the classrooms because, from what I have observed, the situation may be turning off more children than we realize.
Arithmetic education in Tokyo primary schools
Authors: Dutton Wilbur H.
Published: October 2020

The need for continuously analyzing and consciously shaping curricula for young children's schooling has been noted by two international curriculum leaders, Goodlad (1973) and Joyce (1969). Worth (1972) suggests that the time is ripe for international exchange of ideas concerning curriculum problems as well as for studying persistent problems a rising in regions or in countries throughout the world.
Management by Learning Activities: An Alternative to Objectives
Authors: Arnold William R.
Published: October 2020

This article is both theoretical and practical. The theoretical part relates to a description of an alternative basis for mathematics programs. In suggesting an alternative, I criticize the present, major basis for programs. Whether the suggested alternative is generally viable would have to be determined by research. The practical part of the article defines four categories of learning activities, with examples, that could be helpful to creative teachers. Such teachers could use the examples and definitions for development of varied activities for their pupils.
Teacher-made Aids for Teaching Place Value and Estimation
Authors: Easterday Kenneth E.
Published: October 2020

The teaching of place value and estimation continues to chal lenge teachers. Two simple devices and some related activities that will facilitate the teaching of these concepts are described here.
Teaching the concept of ½ in the Primary Grades
Authors: Miller Ann
Published: October 2020

A fundamental concept introduced in the primary grades is the number one-half. It is of particular importance for two major reasons. First, it is the student's first experience with a fractional number, and hence a thorough understanding of this concept will facilitate the introduction of other rational numbers. Secondly, most children entering school have some preconception of one-half and often these basic notions are imprecise. if not erroneous. This is evidenced by the all too frequent use of such phrases as “the bigger hair” and “the smaller half.” Thus it is important that the student clarifies the concept of one-half in the primary grades and possesses a clear and correct understanding of this idea. The following are suggested approaches and activities designed for the primary grades to introduce and reinforce this concept.
Kindergarten Mathematics—a Survey
Authors: Ray Kurtz V.
Published: October 2020

It is relatively easy to identify the mathematical concepts that first-grade and older children should master. It is much more difficult to identify with any degree of certainty the mathematical concepts that are to be mastered by kindergarten children.
Mathematics and the Active Learning Approach
Authors: Masalski William J.
Published: October 2020

The active learning approach to exploring mathematics shifts the emphasis from a teacher-dominated classroom to a student-centered classroom. It capitalizes on the experiences of children and their interaction with the world around them rather than relying primarily on the basal textbook as the source of the curriculum. The active learning approach takes advantage of children's natural curiosity to motivate learning, provides for a wide variety of interesting experiences by using physical materials and the environment, and individualizes learning whenever appropriate to do so.
Magic Squares: Concrete to Pictorial to Abstract
Authors: Robold Alice I.
Published: October 2020

Magic squares can be intriguing to students of all ages. However, the usual method of constructing magic squares does not allow children to be successful if they are unable to work efficiently at a very abstract level of performance. The usual approach has the student write numerals in a square array so that sums indicated by each row, column, and diagonal are equal. If the student is not very skilled in addition, the activity is frustrating. If the student has learned most of the addition facts reasonably well, but occasionally needs a concrete or pictorial reference, the activity does not meet that student's needs.
Some Dos and Don'ts for Teaching the Metric System
Authors: Zalewski Donald
Published: October 2020

Professional journals and commercial publications have helped to acquaint the people of the United States with the metric system. In their enthusiastic support, however, they have bombarded teachers with numerous lists of metric objectives for the curriculum and countless activities that might be used to achieve those objectives. A group of teachers attending a workshop on measurement and metrics decided that a set of simple directives might help teachers to make a wise selection of objectives and methods for teaching the metric system. The teachers suggested the following list of dos and don'ts.
Ideas
Authors: Bright George W.
Published: October 2020

Ideas for this month provides activities to build the concept of area measure. Considerable experience with the idea of comparing and measuring areas seems to be needed for students to understand area measure fully. The introduction of units of area measure, non tandard or standard, should be delayed until students are able to compare regions directly (first IDEAS activity this month) and to put such regions together to cover a larger region (second IDEAS activity). Only then will the repeated use of a single unit (third IDEAS activity) be meaningful. Finally, a standard unit and formulas for area can be used (fourth IDEAS activity).
A Successful Strategy for Teaching Missing Addends
Authors: Thompson Charles , Babcock Judith
Published: October 2020

First-grade teachers frequently state that teaching students how to solve missing addend problems, like 3 + □ = 5 is one of their most difficult teaching tasks. The teachers feel that first-graders are not developmentally ready to work such problems; they think that the missing addend concept is too abstract for first-year students and should be postponed until a later grade.
LCM and GCF in the Hundred Chart
Authors: Roy Sneh P.
Published: October 2020

The hundred chart is a useful and inexpensive tool in the hands of an elementary school teacher. It is used to give practice in counting and to establish concepts of betweenness, greater than, less than, place value, skip counting. and number patterns. It is also useful in teaching multiplication facts and the four fundamental operations. In this article, an effort is made to show how the hundred chart can be used effectively in teaching the concepts of the least common multiple (LCM) and greatest common factor (GCF).
Odds and Evens
Authors: Huff Sara C.
Published: October 2020

I named the colorful pieces of cardboard “Odds and Evens,” but the children in my second-grade class called them “magic counters.”
Linear Clocks
Authors: Schultz Klaus
Published: October 2020

Nearly all children, sooner or later, come to have an adequate operational understanding of clock time, which is surprising since the formal teaching of the subject is normally brief and perfunctory, and the skills involved are difficult. The list of composite skills is imposing: understanding of angular motion, the coordination of two related motions (of the hands), interpolation, counting by fives, coordination of “before the hour” and timetable notation, and even modular arithmetic. The almost universal mastery of these skills tells us something about the role of motivation in learning. Dealing with time is one of the most important and useful survival skills for children as well as for adults.
Using the Digital Clock to Teach the Telling of Time
Authors: Jeffers Verne
Published: October 2020

Telling time is one of the most difficult measurement skills for children to learn. yet can be one of the most enjoyable and rewarding topics to teach. Until recently the literature touched only lightly, if at all, on the methodology of developing concepts of time and how to teach the use of the clock. Peterson (1973) and Reisman (1972) are two methods books that treat the topic in enough depth to provide teachers with some rather specific ways to approach the topic.
Hovv to Use, Not Abuse, Those Practice Exercises
Authors: McKillip William D. , Aviv Cherie Adler
Published: October 2020

We are, as teachers, under considerable pressure, from society in general and from within our profession, to pay close attention to the development of computational skills. The sources of this pressure are clear to those who are involved: School boards are considering or have adopted tests for promotion from grade to grade or for high school graduation; articles on declining test scores appear regularly in the press; the “back-to-basics” movement is highly popular with the general public; checklists of computational skills are used to insure that no student slips through unskilled; and so on. In response to this, textbooks are becoming longer and they contain increasingly longer sets of exercises. It is the purpose of this note to suggest an approach to the use of sets of practice exercises that is more like the actual use of computation by adults and may be more effective in attaining accuracy and, ultimately, speed.