bluuebunny/crossref_metadata_2025 huggingface dataset:
Attitudes toward introduction of modern mathematics program by teachers with large and small number of years' experience
Authors: Huettig Alice , Newell John M.
Published: October 2020

In the last two decades, the teaching of mathematics has been in an active state of transition. Dissatisfaction with the traditional methods of teaching mathematics has led to considerable research and evaluation of new mathematics programs.
Numerals still count
Authors: Enstrom E.A. , Enstrom Doris C.
Published: October 2020

Schools of today are subjected to an evergrowing barrage of criticism in popular magazines because of the indifferent manner in which handwriting has been taught (or ignored) in far too many places during the past two decades. Some of these criticisms lightly poke fun at the shameful situation. Others strike out at learning losses and school time wasted by pupils and at the paper-checking time wasted by teachers because of the slow, miserable scrawls. Still others lament the millions of dollars lost to commerce yearly due to this teaching deficiency. A few warn of the threat to man's very existence because of misread prescriptions and hospital directions [1-11].*
Teaching aids for elementary school arithmetic
Authors: Clary Robert C.
Published: October 2020

The following teaching aids were selected from a list developed by Mr. Clary. Directions are given for constructing different devices to teach beginning number, operations, and measures and measurement in the elementary grades.
An approach to evaluating arithmetic understandings
Authors: Gray Roland F.
Published: October 2020

Current trends in arithmetic instruction lay greater stress on development of understandings of mathematical principles, generalizations, and relationships than previously has been the case. While the mastery of arithmetic facts and computational skills are not neglected, they are now seen more as tools for developing deeper and richer insights into the nature of mathematics than as ends in themselves. More and more elementary pupils are being encouraged to think and act like mathematicians, to discover important mathematical ideas for themselves, or, in current phraseology, to have some experience in practicing the modes of inquiry of the mathematician.
Visual aid for geometry
Authors: Hewitt Frances
Published: October 2020

In most modern elementary mathematics texts, the distinction between a simple closed curve, such as a triangle, the interior of the curve, and the exterior of the curve is made.
The evaluation of learning under dissimilar systems of instruction
Authors: Brownell William A.
Published: October 2020

Some of you who are present can recall the time when the possible uses of the silent motion picture for instructional purposes first attracted wide attention. As is regularly true on the appearance of a new educational medium, opinions ranged through the whole gamut from expressions of doubt and opposition to extreme claims, such as that we might soon be able to dispense with much that teachers do in the classroom. Naturally, some brave souls saw in the controversy the need to undertake research in order to evaluate the effectiveness of the silent film in comparison with traditional procedures.
Second-grade children solve problems
Authors: Hess Marvel
Published: October 2020

Number sentences interest and aid second- grade children in solving problems. A sequence of developmental stages enables children to acquire skills in translating problem situations into mathematical language. A brief description of activities in problem-solving follows.
From the editor's desk
Authors: Brydegaard Marguerite
Published: October 2020

We dedicate this issue of The Arithmetic Teacher to our first two editors, Ben A. Sueltz and E. Glenadine Gibb, for their excellent contribution to mathematics education. The editorial staffs and many contributors and readers wish to express sincere appreciation and gratitude for the creation and development of The Arithmetic Teacher, which provides a major source of guidance and challenge to its ever-increasing audience. Through the well-directed, discerning, scholarly work of Ben Sueltz and Glenadine Gibb, The Arithmetic Teacher has grown from a quarterly journal of 32 pages to a journal with eight issues per year and with approximately three times as many pages per issue. We are proud of the magazine, and we wish to give special recognition to you, Glenadine and Ben.
A letter to parents about the “new mathematics”
Authors: Petronia Sister Mary
Published: October 2020

I understand that you are anxious about your children and about what is going on in mathematics today. You are wondering what this “new math” is all about, whether it is better than the way you learned it, whether it is here to stay, and more. That is precisely why I am writing this letter to you, hoping r will answer some of these questions for you.
Would you like to submit an article?
Authors: Brydegaard Marguerite
Published: October 2020

Readers are encouraged to contribute to The Arithmetic Teacher. Articles with some novelty of content and viewpoint are desired. Both expository articles and reports of research are welcomed.
Mental growth and the art of teaching
Authors: Adler Irving
Published: October 2020

How should teachers teach? Before we can answer this question, we must answer first another question: How do pupils learn? The art of teaching, if it is to be effective, must be based on an adequate theory of learning.
Focus on research: A conference on needed research in mathematical education
Authors: Fred Weaver J.
Published: October 2020

Several months ago in this journal, mention was made of an invitation conference on “Needed Research in Mathematical Education,” conducted under the auspices of the Department of Mathematical Education, Teachers College, Columbia University. A summary report of that conference recently has been released.1
Nominations for the 1967 election
Authors: Peak Philip , Hess Adrien L. , Lowry William C. , Lund Jens L. , Allen Frank B. , Ingraham Mary L. , Beckmann Milton W. , Longshore Blanche , Schult Veryl
Published: October 2020

The following persons have been nominated for the indicated offices in the National Council of Teachers of Mathematics by the Nominations and Elections Committee. The committee's report was accepted by the Executive Committee at its October 1966 meeting in Chicago, Illinois. Biographical material and photographs of these nominees will be published in the January 1967 issues of The Arithmetic Teacher and The Mathematics Teacher.
What is mathematics curriculum research?
Authors: DeVault M. Vere
Published: October 2020

Definitions of mathematics curriculum research range from general positions to rather specific ones. Mathematics curriculum research (MCR) could be described simply as those research activities that are engaged in by persons who identify themselves as mathematics curriculum researchers. On the other hand, a specific definition of MCR can be derived out of some understanding of the three ideas represented by the terms “mathematics,” “curriculum,” and “research.”
Commentary upon Suppes-Binford report of teaching mathematical logic to fifth- and sixth-grade pupils
Authors: Smith Gary R.
Published: October 2020

In the March 1965 issue of The Arithmetic Teacher, Suppes and Binford described their efforts to teach mathematical logic to fifth- and sixth-grade pupils. [1]*
On the teaching of decimal fractions
Authors: Geyser G. W. P.
Published: October 2020

At school the whole numbers are usually taught first, followed at a later stage by the vulgar fractions, and still later by the decimal fractions. These decimal fractions are then very often taught as another kind of (vulgar) fraction. It will be the purpose of this article to show that this procedure leads to confusion on the part of the pupils, with the result that they never really understand decimal fractions for what they are, and consequently never become thoroughly efficient in the use of these fractions when calculating. And in modern calculations proficiency in the use of decimal fractions is an absolute and indisputable necessity.
Fractions for low achievers
Authors: Braunfeld Peter , Wolfe Martin
Published: October 2020

This strange-sounding classroom dialogue exhibits some of the new vocabulary which the UICSM hopes will make the study of fractions interesting and understandable to culturally disadvantaged seventh graders.
Fractional numbers with a sum of 1
Authors: Morton Robert L.
Published: October 2020

In exploring fractional numbers, particularly unit fractions, pupils may discover that 1/2 + 1/3 + 1/6 = 1. Search for another set of unit fractions possessing th is characteristic may, for a time, be fru itless. Pupils soon discover that the least common denominator for such a set of unit fractions cannot be a prime number.
Congruence and measurement
Authors: Jackson Stanley B.
Published: October 2020

The elementary ideas in mathematics are abstractions drawn from the experiences an individual has with his physical environment. These experiences are prima rily of two kinds. There are, first, those experiences that arc associated with counting. They arise naturally in dea ling with collections of discrete objects and lead ultim ately to the abstract notion of the counting numbers and the operations on the counting numbers. That is, the experiences of this type a re those that induce us to in vent the counting numbers a nd the usual arithmetic of this system and its extensions. The second category of experiences includes those of a spatial nature. They are related to our perceptions of size, shape, and form. The child discovers that this pencil is too long to fit in that box; that this peg will just fit in that hole; that the faces of two of his blocks fit exactly on each other, and so on. These are the experiences that motivate us to identify and discuss various figures and to give names to the common ones like line segment, line, ray, plane, triangle, circle, and sphere. Thus the developing space percept ion of the individual leads to the creation of the mathematical ideas normally associated with the word “geometry.”
A beginning for student teachers
Authors: Jenkins Frances L.
Published: October 2020

With the increased popularity of, and emphasis on, science and mathematics fairs, I found myself faced three years ago with a unique situation. I had been teaching honors mathematics classes at all levels, and it seemed appropriate to enrich this curriculum with projects for the regional science fair. After our school produced two regional winners—students under other teachers—I found that great interest had developed in having all honors students participate. Not wishing to promote projects just for the sake of entering a science fair, with the only goal being that of winning, I looked for additional ways to interest my students and to enrich their mathematics background. Three kinds of projects looked promising as paths the students might take for their independent study.
Some thoughts about problem solving
Authors: Cohen Louis S. , Johnson David C.
Published: October 2020

The following two articles, “Open Sentences—The Most Useful Tool in Problem Solving” and 'Unusual Problem Solving,” take a look at what has traditionally been considered problem solving by the elementary school teacher and what is currently being considered as an essential addition to the teaching of problem solving in the elementary school.
Open sentences—the most useful tool in problem solving
Authors: Cohen Louis S.
Published: October 2020

Open number sentences are useful in finding solutions of verbal problems. To write open sentences for problems, one must be able to translate verbal phrases and sentences into mathematical language. Mathematical sentences, much like English sentences, are made up of phrases and verbs. It is the combination of these phrases and verbs that will make the mathematical sentence complete.
Mathematics in the kindergarten?
Authors: Schlinsog George W.
Published: October 2020

Can kindergarten children be introduced to real mathematics, or is one merely being pompous in using such a word to describe the number experiences appropriate for this level?
Experiences with approximation and estimation
Authors: Schmid John A.
Published: October 2020

The uses of approximation and estimation arc strongly indicated where the elementa ry school mathematics program is designed to help the child to learn to operate effectively in his cultural pattern. Approximation and estimation are processes which can play important roles in helping develop children's attitudes, interests, and skills in mathematics to the ends now deemed desirable in any program at any level.
Creatamath, or—Geometric ideas inspire young writers
Authors: Junge Charlotte W. , Carrol Emma C.
Published: October 2020

It happened because of Flat Stanley, Jeff Brown's delightful, two-dimensional boy, who became so when a falling bulletin board flattened him out!1 My fourth graders couldn't resist this fellow whose accident cost him a dimension and gained him some adventures. Slithering under doors was fun. Being flown like a kite was even better! Fun ended, though, when the boy-kite became entangled in the treetop! Brother Arthur and his bicycle pump accomplished the feat of returning Stanley's lost dimension and making him a creature of this world once more!
Classification and mathematical learning
Authors: Weaver J. Fred
Published: October 2020

The ability to classify or to categorize things is an essential aspect of mathematical learning. This is true both for the development of geometric ideas and for the development of number ideas.
Geometry readiness in the primary grades
Authors: Gibney Thomas C. , Houle William W.
Published: October 2020

Geometry is an area of mathematics that has received much attention and space in contempora ry mathematics textbooks, but geometry readiness is a topic that appears to have been slighted.
Editorial comment: As we read
Authors: Inskeep James E.
Published: October 2020

The modern elementary school teacher deals easily with number sentences, inequalities, and other basic ideas for expressing the characteristics of number relationships. Such an expression as 4 + □ = 7 is common in most primary-grade classrooms. Ideas of negative integers are not unfamiliar to the elementary school pupil. Solution sets cover many a junior high school mathematics class chalkboard. These ideas are not difficult and seem quite natural in the context of the elementary- junior high school curriculum. But, when I went to school, we called it algebra! And we called it algebra in the first year of high school! No sooner.
A number pencil
Authors: Clarkson David M.
Published: October 2020

So much use is being made of number lines these days that it may not occur to elementary teachers to represent numbers in other ways. There are, in fact, many ways to picture whole numbers geometrically as arrays of squares or triangles or other shapes. Often, important insights into, for example, oddness and evenness can be gained by such representations. The following account of a sixth-grade class discussion of fractions shows how a “number pencil” can be constructed to represent all the positive rational numbers, and, by a similar method, also the negative rationals. An extension of this could even be made to obtain a number pencil picturing certain irrational numbers.
Manipulating points and figures in space
Authors: Overholt Elbert D.
Published: October 2020

This article is intended as a follow-up to my previous one in The Arithmetic Teacher, “From Number Lines to 2–D Space Concepts” (February 1966). That article mentioned the possible use of number-line rules in the elementary classroom. By substituting various values in the frames of selected number-line rules, a variety of thought-provoking exercises can be developed, giving the elementary school child much needed practice in quantitative manipulation. By introducing the second number line and jumping from one number line to the second, one method of showing the relationship between quantity and space was introduced.
Discovery approach—polar coordinates in grade seven?
Authors: Needleman Joan R.
Published: October 2020

Are we going to learn about polar coordinates this year?” asked one of my able seventh-grade students on this particular morning. From past experience, I answered in the negative, at the same time assuring him I would provide him with material on the subject if he were interested.
Where do I start teaching numerals?
Authors: Muente Grace
Published: October 2020

In teaching arithmetic to beginning children. a teacher needs a focal point at which to begin. I have found combining color words and numerals to be helpful in teaching number meanings to my first grade.
Teaching geometry through creative movement
Authors: Marie Complo Sister Jannita
Published: October 2020

Last year I taught Creative Movement to forty first graders in a very enjoyable and meaningful manner. Creative Movement is the child's creative interpretation of thoughts and feelings through the use of his body. Children discover movement experiences through shape, space, rhythm, music, percussion instruments, locomotor activities, and ideas. For some children, this is a way of expression. Some children express themselves very readily in conversation; others in writing; but many find movement an opportunity to be responsive.
Save those egg cartons!
Authors: Hyde David , Nelson Marvin N.
Published: October 2020

As the child begins to understand the frustrating subject called mathematics, he soon comes to the point of working with fractional numbers. He also learns quickly that solving the problem isn't as difficult as trying to figure out what he has done.
Reflections on the courtship of mathematics and science
Authors: D'Augustine Charles H.
Published: October 2020

It has been said that mathematics is the queen of the sciences. However, if one wants a truly dynamic elementary school mathematics program, then one must promote the marriage of mathematics and science curriculums. We have only to study the current elementary school science and mathematics programs in order to realize that not only are mathematics and science unmarried, but neither curriculum reflects a very serious awareness of the other's existence.
Sunpaths that lead to understanding
Authors: Smith Bernice
Published: October 2020

Having taught self-contained grades and most recently being a social studies teacher, I strongly feel that the most significant learning occurs when content areas are closely related and if possible never separated. For elementary children to relate the history, economics, geography, and sociology of the world they must understand the changes in seasons and the climatic factors produced by the apparent movement of the sun in the sky. A student who has the understanding necessary to draw “pictures” or representations of sunpaths can use mathematics in a meaningful way.
Readiness for mathematics learning
Authors: Paschal Billy J.
Published: October 2020

In this space age of Telstar, Lunar Orbiter, Apollo, nuclear reactors, automation, cybernetics, and inventions, the chief reason why children are still experiencing difficulty with modern mathematics is that far too many elementary teachers fear that its logic will not lead children to the “right concl usion.” The several new mathema tics programs have made the typical teacher extremely defensive. Thus, teachers are still conce rned more with product readiness than with process readiness. They are more concerned with the correctness of inferences than with increasing children's willingness to experiment with data and at the same time increasing their ability to make inferences from the data. It is not ncces ary to evaluate everything children do in mathematics. Teachers should encourage children to take a calculated risk every now and then; they should give children time to sit back and do absolutely nothing but think about different solutions to the problems; they should respect the efforts of children and show them that their efforts are of value even if they are rough or unfinished; they should not criticize prematurely but should give children a chance to make their own mistakes and to learn from them.
Mathematics for four-year-olds
Authors: Oberlin Lynn , Oberlin Mary Jean
Published: October 2020

School-oriented mathematics instruction can start at the time a child begins attending school. The procedures described in this article have been used with nursery school groups of four-year-olds. As at any age level, there are great differences among students. Some of the children in these nursery school groups responded to all learning situations, while others entered into only part of the activities. No child was fo rced or pushed beyond his ability or interest.
Arithmetic skills begin at home
Authors: Norwood John K.
Published: October 2020

I never could do fractions in school, so I don't imagine that my Mary will be able to do them either.”
The kindergarten child measures up
Authors: Mcclintic Joan
Published: October 2020

Delighted, the kindergarten child launches another imaginary rocket ship: five … four … three … two … one … zero … SHWHOOOOOOSH! Child and teacher meet in enthusiasm to investigate some ideas in the measurement of height.
Math for the low, slow, and fidgety
Authors: Stenzel Jane G.
Published: October 2020

One characteristic that distinguishes American teachers from many of our counterparts abroad is our attidute that children should enjoy learning, and that it is our obligation to help them to enjoy it. Furthermore, we feel that it is our duty to teach all children; that if the child does not learn, it is less his fault than ours.
The performance of four- and five-year-old children in Operation Head Start on selected arithmetic abilities
Authors: Lehew Charmon
Published: October 2020

When a child participating in the Operation Head Start program puts his hand into the teacher's and says, “How come you always say, ‘Now it's time to…'?” or “Goody, today is tomorrow so now we can go on the ferryboat trip,” language development becomes mathematical development. One of the basic aims of Operation Head Start is to enhance the language growth of the preschool chi ld. Mathematics as a language art must be an integral part of the development of sufficient language skill for each child.
New mathematics for Ethiopian elementary schools
Authors: Dutton Wilbur H.
Published: October 2020

Modern education in Ethiopia is very young, a phenomenon of this century. In Jess than sixty years a primary school system embracing 1,600 schools, 380,000 pupils, and over 9,000 teachers has been established.
An open letter to mathematics teachers
Authors: Petronia Sister Mary
Published: October 2020

I have always thought that teachers form one of the groups most dedicated to their profession. This is still my belief. Consequently, it seems strange to me to learn that some teachers are saying, “I learned my mathematics the old way. That was good e nough for me. Why isn't it good enough for those I teach?” I find this difficult to understand and begin to wonder about it.
Some comments on developing proper instrumentation for research studies in mathematics
Authors: Riedesel C. Alan
Published: October 2020

In previous issues of The Arithmetic Teacher, the need for appropriate research topics and good research design was explored. There are many other important considerations in improving research in elementary school mathematics. One of the most pressing is the topic for this month's column—the use of tests and other instruments to measure the outcomes of the research treatments. The goal of the material that follows is to suggest several key considerations in developing, using, and reading studies that utilize research instruments.
Now try this—division of fractions
Authors: Junge Charlotte W.
Published: October 2020

These division algorisms have been gleaned from my collection of old arithmetic textbooks. (Some were published as early as 1800. Others carry publication dates of the 1850–1870 era.) Some of these algorisms are more easily understood than others, but all of them can be used to extend and enrich sixth-grade children's comprehension in mathematics.
Elementary series and texts for teachers—how well do they agree?
Authors: Hicks Randall C.
Published: October 2020

Lack of mathematical background on the part of the teacher, it is often said, is the most serious deterrent to a modern program in mathematics in the elementary school. To remedy this situation, courses for teachers have been widely instituted at the preservice and in-service levels. Among other resources, there is available a large variety of textbooks written especially for teachers.
The missing factor in division
Authors: Reeve Olive R.
Published: October 2020

Most primary grade teachers will admit that they are concerned about helping young children build concepts which are mathematically correct. It is upon these early concepts that a child builds and broadens his ideas regarding the quantitative aspects of the world around him.
Books and materials
Authors: John Lenore
Published: October 2020

This text is designed for a prescrvice methods course for teachers of Grades K-6. The a uthors have not attempted to cover every topic that might be incorporated in the elementary school. Rather, they present a structured development of ideas they regard as central.
Every teacher is a researcher
Authors: Riedesel C. Alan
Published: October 2020

Research is a high-hat word that scares a lot of people. It needn't. It is rather simple. Essentially, research is nothing but a state of mind—a friendly, welcoming attitude toward change … going out to look for change instead of waiting for it to come. Research, for practical men, is an effort to do things better and not to be caught asleep at lhe switch. … It is the problem-solving mind as contrasted with the let-well-enough-alone mind. … It is the “tomorrow” mind instead of the “yesterday“ mind.—Charles F. Ketiering, 1876-1958.
From the editor's desk
Authors: Brydegaard Marguerite
Published: October 2020

We appreciate the contributions of all persons who submit manuscripts for consideration for publication in The Arithmetic Teacher, and we always welcome additional manuscripts. At present our greatest need is for material for the kindergarten- primary level—material in which ideas regarding classroom situations are developed. We encourage classroom teachers to submit manuscripts. Sometimes a classroom teacher coauthors an article with a school principal, a supervisor, or a college instructor. The production of such articles is usually very rewarding to each of the authors and to readers.
Primary-grade instruction in geometry
Authors: Inskeep James E.
Published: October 2020

Recommendations for teaching geometry to young children run as a thread through much of the recent literature. In the Cambridge Conference Report of 1963, it was recommended that “geometry is to be studied together witb arithmetic and algebra from kindergarten on.”1 The Cambridge Conference Report of 1967, dealing with teacher education, suggested early merging of arithmetic and geometry, instruction in spatial relationships, and the study of standard shapcs.2 It was felt that geometry provided a rich area for an integrated study of abstract mathematics and the environment. In the preparation for statewide adoption of mathematics texts, the State of California recently reaffirmed the need for geometry as an integral part of the primary-grade curriculum.3 Other states and groups have made simil ar recommendations.
Wanted—your comments
Authors: Riedesel C. Alan
Published: October 2020

This month we should like to raise a question concerning the dissemination of research information: How can information concerned with elementary school mathematics instruction be most effectively developed so that classroom teachers and others with limited time and statistical background can make use of research findings on specific topics?
Subtraction steps
Authors: Smith C. Winston
Published: October 2020

While games that provide practice in subtraction are easily located, those that also build an understanding of the inverse relationship between addition and subtraction are not easily found. A few years ago we developed an activity the children called “Subtraction Steps” that seemed to do just that. It was fun. It provided practice and yet strengthened the children's understanding of the inverse operations of addition and subtraction. And, as an added dividend, children soon found they could easily make their own “steps” to contribute to the arithmetic table.
Placo—a number-place game
Authors: Calvo Robert C.
Published: October 2020

This game emphasizes fun and the learning of positional and place-value aspects of our number system. Placo (pronounced play-so) is a number game that boys and girls can play to good advantage in the classroom. The children blindfold each other, one at a time, and then attempt to fit the rings on the highest place-value pole (see diagram). One value of the game is the manipulative aspect. The children enjoy handling the rings, fitting them on the dowels, and then computing to find the amount they “win.”
Editorial comment: As we read
Authors: Inskeep James E.
Published: October 2020

The mathematics laboratory! It has been said that the laboratory is a place for “labor” at the sacrifice of “oratory.” How long has it been since your children were allowed to “do” some mathematics? The doing of mathematics has long been characterized as a man with a pencil and paper writing interesting abstractions in an organized fashion. Perhaps we have too often applied this definition to the learning of mathematics. H paper-and-pencil activity were restricted in an elementary school classroom, how would the teacher teach mathematics? Many of the articles in this issue of The Arithmetic Teacher are devoted to such questions. The mathematics laboratory offers exciting experiences for teacher and student al ike. As you read this issue of the journal you may wish to jot down ideas for the development of your own lea rning laboratory in mathematics.
Mathematical activity
Authors: Clarkson David M.
Published: October 2020

Mathematicians are constantly warning the public that mathematics is not a spectator sport—that you must get in there with pencil and paper and fight if you are to profit from its study. But even penciland-paper work may be essentially passive. For example, many teachers today make use of the technique of programming instruction, yet little research is available to predict the effect on children of an extensive amount of this kind of teaching. There is something narrow, perhaps even crippling, about a long string of questions like “A triangle has____sides.”
“Stock-market” unit
Authors: Thomashow Beatrice E.
Published: October 2020

Wouldn't teaching and learning any concepts and skills be more enjoyable if we could do it by being able to utilize all the above techniques and goals? Is not our most important mission as teachers to be able to instill in our children a “joy in learning”?
Discovering centigrade and Fahrenheit relationships
Authors: Schall William E.
Published: October 2020

The following approach has been used successfully with elementary school children in developing an understanding of centigrade and Fahrenheit thermometers.
Preparing prospective teachers of elementary school mathematics
Authors: Robert Houston W.
Published: October 2020

During the past decade, major changes have occurred in mathematics in the elementary school, both in content and approach. Indeed, “modern mathematics” has become a household term epitomizing the radical changes in today's curriculum which separate the younger generation from their parents. Parents complain they can no longer understand, much less help their children with mathematics. Innovations in experimental programs, technical advancements, and new insights into human learning promise even greater changes in the future.
Grids, tiles, and area
Authors: Besic Strangman Kathryn
Published: October 2020

The purpose of this article is to report a method for introducing area to fifth-grade pupils which is mathematically sound and readily teachable.1 Some programs begin their approach to area indirectly by making direct linear measurements and computing the area obtained from these. Some methods define the area of a rectangle as the product of the length and the width of the rectangle and then proceed to discover relationships between the areas of a rectangle and other polygons and, later on, other types of regions.
The address of a point
Authors: Vigilante Nicholas J.
Published: October 2020

The number line has many uses in developing mathematical concepts at the elementary school level. In the recent past, applications of the number line have covered a vast range, from the basic mathematical notions of counting to more extensive abstract representations, such as the development of linear equations. This discussion outlines some of the possible applications that can be considered for a sequential development of the integral number line, from the theoretical representation of any integer1 by a point on a line using zero as a reference point. to the development of the concept as a point representing the intersection of lines whose address or names are pairs of numbers found in the rectangular coordinate system. This sequential experience was employed with a group of fourth-grade children early in the school year.
Problem solving using the sphere
Authors: Sullivan John J.
Published: October 2020

A critical topic in the elementary school is map reading. Naturally, we hope that the skills and concepts developed in the mathematics program will be extremely helpful in map reading. A stress on ratio, for example, is necessary for an understanding of map scales. The study of coordinates will assist in learning about latitude and longitude.
Divisibility rule for seven
Authors: Rogers Frank
Published: October 2020

None of the usual simple rules for divisibility apply to the prime number seven. Below is a little-known rule, which is fairly practical, and its explanation gives one more good excuse to use the distributive property, which is, after place value, the most important concept of elementary mathematics.
Secret number sentence
Authors: Swart William L.
Published: October 2020

Here is a game for primary arithmetic, providing stimulating drill on mathematical sentences and on addition, subtraction, multiplication, and division combinations.
A deck of cards, a bunch of kids, and thou
Authors: Gurau Peter K.
Published: October 2020

One of the more frustrating problems faced by the kindergarten and first-grade classroom teacher is the problem of providing for individual differences.
Stand for something or you'll fall for anything
Authors: Phillips Jo Mckeeby
Published: October 2020

A few years ago, for a reason I find hard to fathom even in terms of random sampling, I was asked to participate in a consumer survey involving two brands of laundry detergent. Two boxes arrived, one labeled “A,” and the other labeled “B.” The contents, as far as I could tell, were identical. I agreed to try each of the detergents and then fill out a questionnaire — check boxes on the paper to indicate which of their prefabricated descriptions I subscribed to. Which brand do you like better? Why? Under “Why,” one of the responses available for checking was “more modern.” That really stumped me. What is it that makes a detergent modern? What makes a detergent old-fashioned, or traditional, or conventional, or decadent, or whatever the antonym for “modern” is? Suppose one detergent is modern and the other is not. Is the one which is modern better? It's a curious thing, this word “modern.” If it is followed by “strawberry jam” or “apple pie,” most people turn up their noses at the product being described. If it is followed by “airplane” or “fabric” or “diet” or “mathematics,” most people think that what is being described is a consummation devoutly to be wished. What is a modern detergent? Whatever it is, if I am a housewife, I want it. (I'll keep a bar of Grandma's lye soap on hand for the shirt collars.) What is a modern mathematics? Whatever it is, if I'm a parent, I want my children to have it.
Time utilization in arithmetic teaching
Authors: Milgram Joel
Published: October 2020

The elementary classroom teacher must make day-to-day decisions about the emphasis to be placed on various kinds of reaching activity. Developmental lessons are important; drill and practice also are important. Whatever each daily lesson theme might be, every teaching procedure must be used in the best interests of the children.
Graphs tell a story
Authors: Coppola Jean N.
Published: October 2020

I am certain that you who teach fifthgrade students know that they like to watch progress being made.
Teaching division by two-digit numbers
Authors: Dilley Clyde A. , Rucker Walter E.
Published: October 2020

Let's watch an elementary school student who is doing (with help from his teacher of course) his first long-division problem with a two-digit divisor.
Charged particles: a model for teaching operations with directed numbers
Authors: Cotter Stanley
Published: October 2020

In preparing to teach mathematical concepts, a good deal of a teacher's time is spent in finding suitable models for the concrete stage of learning. In no other area of elementary mathematics is this more critical than in the presentation of operations with directed numbers. Whether the topic is presented for the first time in the sixth grade or occurs in a remedial course in algebra at the college level, there is always a need for some students to relate directed number operations with a physical interpretation. Many such models have been devised, and the literature abounds with helpful suggestions in this area.1 The usefulness of any particular model is directly related to the success of the student in conjuring a vision of the model when it is needed. It is also helpful to the teacher when he can evoke the image of the model with a simple verbal reminder.
Zero, the troublemaker
Authors: Henry Boyd
Published: October 2020

Every elementary school teacher will agree that the concept of zero is difficult for mimy children to grasp. In fact, many teachers themselves are uncomfortable when they must work with numbers involving zero. One veteran fifth-grade teacher was observed drilling her students to repeat that 6 × 0 = 0, but that 0 × 6 = 6. Apparently she didn't really believe the commutative law which she had previously “taught” her students. Moreover, the role of zero in the structure of the number system was at best vague and certainly confusing to her. We will never know how many hundreds of students she had confused about zero over the long years of her teaching career. The fault does not lie entirely with the teacher alone, of course. At least one textbook she had used in years past made quite a point of stating that zero is not a number. Such mjsinformation as this could only confuse both teacher and students. After all, she might reason, if zero is not a number, it is not obliged to follow the laws of numbers such as the commutative Jaw for multiplication.
Disguised practice for multiplication and addition of directed numbers
Authors: Milne Esther
Published: October 2020

Practiciog computation can be drudgery. But practicing computation with integers is necessary. Games aren't drudgery. Let's combine games with practice. Then students can have fun as they improve the accuracy of their computation.
Estimating quotients for the new long division algorithm
Authors: Mclean Robert C.
Published: October 2020

The new algorithm for division of whole numbers reduces the dependence upon correctly estimating quotients because it compensates for estimates that would have been too small in the old algorithm. But without any techniques of estimating quotients, a child can spend hours doing only a few examples.
Editorial comment: As we read
Authors: Inskeep James E.
Published: October 2020

Euclid is dead. Long live geometry! This is the age when slogans and protests are a matter of record, and the miJitant attracts considerable attention. In somewhat similar fashion the teaching of geometry in the elementary school needs our attention. Geometry is probably the oldest of the mathematical disciplines and has undergone little change in the curriculum. There is a message for educators in this month's issue of The Arithmetic Teacher. This message is that geometry should become an important part of early mathematics instruction. As you read you will find more than slogans however. There are many suggestions for the classroom teacher and descriptions of activities that will make geometry Jive.
Geometry all around us—K–12
Authors: Egsgard John C.
Published: October 2020

There is growing evidence among mathematics educators that geometry should be experienced in each year of schooling from kindergarten through grade 12. Geometry is the study of spatial relationships of all kinds, relationships that can be found in the 3-dimensional space we live in and on any 2-dimensional surface in this 3-dimensional space. These relationships can be discovered all around us. Observe the many different shapes in your environment. This is geometry. Listen to the description of the path of the latest space rocket. This is geometry. Compare the photograph taken with a polaroid camera to the object that it pictures. This is geometry. Notice the symmetry to be found in a spherical or cubical shape and the lack of symmetry in some modern works of sculpture. This is geometry. AU of these involve spatial relationships. Children are aware of spatial relationships from their earliest days. Introducing them to the idea of geometry as being concerned with shape and size in the material world will help them to realize and appreciate that mathematics is something that plays an important role in the world in which we live.
Geometry: an artistic approach
Authors: Ogletree Earl
Published: October 2020

Children are naturally interested in drawing, coloring, painting, and other artistic activities. And geometry, if examined from the standpoint of nature, has an inherent beauty, harmony, and artistic form. Geometric beauty permeates every shape we perceive, from the tiniest snowflake to the greatest star in the cosmos, from the humble spider's web to the glorious blossom of the flower. These are all exquisite lessons in the artistic beauty of geometry.
In the classroom: Editorial feedback
Authors: Faulkner William R.
Published: October 2020

I delighted in Sally Mathison's article, “Mathematicalosterms,” in the January 1969 issue of The Arithmetic Teacher. Consequently, I introduced it to my seventh-grade class as an enrichment and funfilled diversion. The response was both instantaneous and positive as they began their search. Faced with this enthusiasm, I replaced their scheduled assignment with the direction that they locate as many mathematical words as possible within the allotted forty-five minute study period. In the next class, the eleven boys discovered that a total of eighty-one words could be verified, but this was just the beginning of my story.
Patterns for multiplication
Authors: Herold Joan
Published: October 2020

Some readers of The Arithmetic Teacher may be interested in patterns for multiplication tables that, I have found, delight many children.
A three-by-five card plus an opaque projector plus an ice pick
Authors: Schiele Gerald D.
Published: October 2020

Three-by-five cards, an opaque projector, and an ice pick can be used to develop a workable technique for giving tests, grading them, and storing test questions for future use. These three elements also permitted the summer school students of two remedial mathematics classes to progress at their own rate without the assignment of a specific text.
Drawing conclusions from samples (An activity for the low achiever)
Authors: Burt Bruce C.
Published: October 2020

The 1963 Cambridge Report1 suggests that more applications of mathematics will be possible in the upper elementary grades due to the amount of science that has been and probably will continue to be introduced into primary school. Some of the most important applications involve probability and statistics, which should be considered purely empirical subjects at this level.
In the classroom: Fun can be mathematics
Authors: Junge Charlotte W. , Kopp Audrey , Hamada Robert
Published: October 2020

Every mathematics classroom can be a laboratory where students experiment with numerical ideas. Two-way communication between teacher and class by means of games can foster an atmosphere of eager participation in mathematical activities. The games suggested below have characteristics that can stimulate the student's mathematical thinking by the use of number ideas and number sequences and patterns. Some of the exercises call for use of paper and pencil by students and either the chalkboard or the overhead projector for the teacher to show collection of data. Often each child may be asked for an oral response, thus allowing all to participate, as well as permitting the teacher to check if each student understands the rules of the game.
A romantic excursion into the multiplication table
Authors: Callahan Leroy C.
Published: October 2020

Whitehead in his Aims of Education1 states an educational “truism”—that different subjects and modes of study should be undertaken by pupils at fitting times when they have reached the proper stage of mental development. In relation to intellectual progress he discusses three stages: the stage of romance, the stage of precision, and the stage of generalization.
Research findings applicable in the classroom
Authors: Suydam Marilyn N. , Alan Riedesel C.
Published: October 2020

Teachers, administrators, textbook authors, and textbook editors often discuss the role of research in elementary mathematics instruction. Usually one of two dichotomous views is brought forth. Either they express the view that there has been little or no valid and important researchor they state that the findings of research are being used daily in their work. Probably the actual status of the use of research in the teaching of elementary school mathematics is somewhere between these poles.
Editorial feedback
Authors: Jeffers Verne G.
Published: October 2020

I noted with interest the article entitled “Mathematicalosterms” by Sally Mathison in the January 1969 issue of The Arithmetic Teacher.
Forum on teacher preparation: A mathematics laboratory for prospective teachers
Authors: Clarkson David M.
Published: October 2020

The Report of the Cambridge Conference on the Correlation of Science and Mathematics in the Schools recommends that schools of education plan programs of “apprentice teaching in the schools, including work with materials of the sort being developed in new curriculum projects.”1 A group of mathematics educators in England has urged the use of courses emphasizing problem solving: “It is the exploration of these more open problems which we feel to be the essential characteristic of real mathematical activity.”2 A loud chorus of opinion suggests that courses in methodology should be jointly planned and executed by both mathematicians and educators and that they should involve practical work with children. When the opportunity to design an experimental elementary mathematics methods course was offered the writer, he decided to emphasize the mathematics laboratory approach which gives an important role to problem solving. Conferences with members of the mathematics and education departments, as well as with school officials, paved the way for the experiment; the sympathetic support of the chairman of the division of education at the college made it possible financially.
In the classroom: A game with fraction numbers
Authors: Thomas Zytkowski Richard
Published: October 2020

The game described below is a unique way to provide practice in the addition, subtraction, multiplication, and division of fractions. The game can also be used to teach ratios as well as the sequence of numbers