bluuebunny/crossref_metadata_2025 huggingface dataset:
Let's Do It!: Making patterns with a square
Authors: Bruni James V. , Silverman Helene J.
Published: October 2020

In a previous “Let's Do It!” (Arithmetic Teacher, February 1977) ways to use a square to help develop fraction concepts were suggested. This month we will take another look at that square. In fact, we will do more than look at it. We will “slide it,” “turn it,” and “flip it.” and create all so rts of geometric patterns. Beginning with a square partitioned into eight (then later, sixteen) congruent triangles. the activities that follow suggest ways for children to develop some basic ideas about congruence. symmetry, and geometric transformations (translation, rotation, reflection) while they enjoy many mathematical and artistic experiences and develop their problem solving abilities.
The game of Tri
Authors: Haggard Gary , Schonberger Koch
Published: October 2020

Tic-Tac-Toe is a familiar example of a paper-and-pencil strategy game. Such games help students evaluate alternatives and their consequences. These skills are important mathematical skills as well. Another paper-and-pencil strategy game for two players that can be used to develop these skills is the game of “Tri.”
The one-meter dash
Authors: Brooks Mattie J.
Published: October 2020

Once in a very blue moon one chances on something “too good to keep.” Particularly in elementary school mathematics, if the “gem” can further several concepts or understandings, is the compulsion to share irresistible. (Conscience alone would demand broadcast of the phenomenon.)
Report of Study Group D: minimal competencies in mathematics
Authors: Fey James T.
Published: October 2020

One of the most urgent practical problems facing mathematics education today is the challenge to define minimum levels of competence in mathematics and to devise teaching strategies that ensure student achievement of that competence. The phrase “minimum competence” has many meanings. For parents and employers of school graduates, dismayed by an apparent recent decline in student mathematical achievement, “minimum competence” often implies the arithmetic skills essential for survival in daily life and occupation in business or skilled trades. Teachers, confused by urgings of curriculum innovators and the criticism of skeptics. seek the secu rity of widely accepted standards for mathematical performance at various levels of schooling. College and university mathematics faculty also hope to improve the performance of entering students by specifying minimum levels of secondary school preparation.
Let's Do It: The neglected decimeter
Authors: Lindquist Mary Montgomery , Dana Marcia E.
Published: October 2020

“Why teach about decimeters? Nobody ever really uses them. Have you ever heard of a measurement in DECJM ETERS? So why bother—it's just another thing to learn.”
Metrics with marcel and marcette
Authors: Yvon Bernard R.
Published: October 2020

As a novel addition to the tools of metric measurement, try metrics with M a reel and Marcette. More than just stuffed snakes, Marcel and Marcette are metersticks with personalities, and they will charm students in the lower elementary grades. As the children work and play, they will painlessly absorb the meaning of the meter and even the centimeter. If children like stuffed toys, they will enjoy Marcel and Marcette.
By way of introduction: Problem: Solving Problems
Authors: Skypek Dora Helen
Published: October 2020

“I think problem solving is the basic skill in mathematics. By problem solving I mean more than knowing what to do, in the sense of having knowledge.
Let's Do It: Problem Solving With Five Easy Pieces
Authors: Lindquist Mary Montgomery
Published: October 2020

Many of the best problem-solving situations in primary schools come from everyday situations: “How many more chai rs will we need if we are having five visitors and two children are absent?” “How many cookies will we need if everyone has two?” However, these situations do not always arise at the appropriate time, nor do we always have time to take advantage of them when such situations do arise. There is a need for a set of problems that can be used at any time and the problems selected for this article are of this type. They require a minimum amount of computation but. often, a maximum amount of thinking.
Star Patterns
Authors: Bennett Albert B.
Published: October 2020

Making star patterns such as those pictured in figures 1 and 2 is a common mathematical activity for producing colorful and artistic patterns. Often, however, such patterns are constructed with very little use of mathematics beyond counting. The purpose of this article is to show how the concepts of greatest common divisor and least common multiple are related to star patterns.
Sense with Cents
Authors: Ginaitis Stephen J.
Published: October 2020

In response to teacher inquiries about ways to teach change making, coin recognition, and purchasing skills with their students, I have developed an activity based on area that uses a classroom-size hundreds chart as a pattern. Teachers who have tried the device have found it useful, and their pupi ls have enjoyed it as well as learned change making from it.
Banish the Boring Bulletin Board
Authors: Gersting Judith L. , Kuczkowski Joseph E. , Alton Elaine V.
Published: October 2020

How often have you put a lot of time and effort into constructing a bulletin board that turns out to be an attractive display, admired when first put up, and then ignored? With just a bit more effort, a bulletin board can be elevated from a passive role to an active aid in mathematics teaching. A bulletin board can be activity oriented. By an activity-oriented bulletin board, we mean one that encourages student participation. The student max, for instance, be asked to rearrange objects on the board, to select an object and place it in its correct position, to create illustrative models, or to perform some other physical activity, all in response to a requested mental activity. In other words, the student is elevated from a looker and reader to a doer. We are reminded of the Chinese proverb that says, “I hear and I forget, I see and I understand, I do and I remember.” The activity-oriented bulletin board provides opportunities for exactly the kind of concrete activities that are so important in the learning process.
Classroom Diagnosis and Remediation
Authors: Sovchik Robert , Heddens James W.
Published: October 2020

A student in Ms. Smith's second-grade class was having difficulty with addition examples involving regrouping from ones place to tens place.
Guidelines for Evaluation of Published Metric Materials
Authors: Trueblood Cecil , Szabo Michael
Published: October 2020

The metric system has been adopted in the United States, and classroom teachers are being urged to teach metric measurement. Consequently, school districts are looking for quality instructional materials, curriculum guides, and other metric resources to assist teachers in the conversion to the International System (SI). Commercial publishing companies have anticipated the demand for new instructional materials by producing a plethora of metric handbooks, workbooks, worksheets, filmstrips, and metric-measurement instruments of varying quality. Experience in foreign countries (Chalupsky, Crawford, and Carr 1974; Chalupsky et al. 1975) shows that publishers rush in to fill the gap in commercial materials created by legislation. In the haste to publish, the materials that are developed often are inappropriate and even incorrect.
Track Cards: A Different Activity for Primary Grades
Authors: Walle John A. Van de
Published: October 2020

Do the child ren in your class talk with their friends about mathematical ideas? Are they given the opportunity to plan, to try, to discover, and to create? The development of both the mental capability and the enthusiasm for creative expression and discovery must be nurtured at all age levels and all ability levels.
Be a Super Shopper!
Authors: Burzler Donald R.
Published: October 2020

Resources for individualized. relevant mathematics activities lie no farther away from us than our wastebaskets. All we have to do is dig in, clean up, and organize the endless variety of containers that we acquire from the local supermarket. Add to this some simple activity cards, duplicated standardized worksheets, and a record-keeping grid, and presto, we have a teacher-made mathematics kit that will handily use the operations of addition, subtraction, multiplication, and division in a relevant meaningful way.
A Pocket Multiplier
Authors: Grove Julia
Published: October 2020

Coordinating rectangular arrays, repeated addition, skip counting. and multiplication can be confusing tasks for teachers, not to mention for children. Here is a simple, child-made device which can establish a basis for understanding the relationships involved and which. at the same time. can help to fix multiplication facts in mind.
Michelle's Multiplying Monsters
Authors: Deatsman Gary A.
Published: October 2020

On a recent examination in a mathematics conten t course for teachers, I asked students to give an example showing that multiplication of counting numbers is associative. One student, Michelle Henry, devised a very original variation of an example she had seen in class. Her example was so obviously appealing to children that we felt it should be shared.
Orienteering: New Ideas for Outdoor Mathematics
Authors: Arnsdorf Edward
Published: October 2020

Outdoor activities are often used to achieve goals of mathematics instruction. Taking instruction outdoors provides teachers with opportunities to show applications, to promote student appreciation. and to present enjoyable learning experiences. Including orienteering in outdoor mathematics can help in leading to the successful accomplishment of all of these goals. Moreover. orienteering includes active learning experiences. which certainly are desirable for most students in their study of mathematics.
Problem Solving with Calculators
Authors: Morris Janet Parker
Published: October 2020

Any teacher who has experienced the excitement and complete concentration of a group of children working with calculator knows that the question is no longer whether calculators should be used in elementary schools, but how they should be used. Ways to use calculators with existing texts and mathematics programs are being sought by teachers at all grade levels. Calculator activities that require problem-solving skills, that use the calculator as a tool to avoid “getting bogged down” in tedious computations, and that stimulate the imagination and interest of students, are valuable and compatible with existing programs.
Living In a World of Transformations
Authors: Sanok Gloria
Published: October 2020

We live in a world of transformations. Some transformations change the size or shape of an object or figure (Swadcner 1974). Some transformations change neither. Transformations that change neither the size nor shape are translations (slides), rotations (turns), and reflections in a line (flip). A dilation is a transformation that changes the size of an object, but does not change its shape. Congruency and similarity, which are often studied initially in the context of triangles, may be learned more intuitively through transformations.
Helping Parents Help Their Preschool Children
Authors: Burton Grace M.
Published: October 2020

Parents can provide experiences for their children that will make those first crucial school years a happier time for everyone. As a professional concerned with the cognitive growth of young children, you, the nursery-school teacher, can do much to sensitize parents to the ways they can help foster their children's cognitive growth in the years preceding format school instruction.
A Mathematics Laboratory, Alive and Well
Authors: Yares Schussheim Joan
Published: October 2020

One of the most exciting approaches to the study of elementary school mathematics is the mathematics laboratory. Herein “children work in an informal manner, move around, discuss, choose their materials and methods, and generally make and discover mathematics for themselves” (Ewbank 1971). By “acting and experiencing math” (Matthews and Comber 1971) children actually “can learn mathematicalideas”(Yanceand Kieren 1971). Labs are “activity centered” (Barson 1971) highly motivating places resulting, quite often, in “more efficient education” (Biggs and MacLean 1971).
Individualized Arithmetic Instruction for Fifth and Sixth Grades
Authors: Cunningham Betty
Published: October 2020

The problem of how to meet the needs of individual learners in heterogeneously grouped classes has been a matter of educational concern for many years. The phrase “individualized instruction” embodies our present efforts to make learning more effective for all learners.
National council of teachers of mathematics: Annual Financial Report
Authors: Wells David W. , Kriegsman Helen , Devlin John , Stipanowich Joseph , Egbers Elden , Gates James D. , Tewell James R.
Published: October 2020

Each year prior to the April Board of Directors Meeting, the Financial Policies Committee (FPC) prepares and recommends to the Board a budget for the next fiscal year.
President's Report: Problems of the Teacher of Mathematics and Some Solutions
Authors: Egsgard John C.
Published: October 2020

One of the greatest joys in doing mathematics is finding the solution to a problem. The problem does not need to be difficult, Even discovering the answer to a simple problem can bring happiness. All of us know the excitement that comes with suddenly finding the key to the solution of a problem on which we have been working for a long time. One of the great things about mathematics is the fact that it is relatively easy to state a problem even if great difficulty exists in finding the solution of it. In addition, it is usually quite clear when the solution to a problem is found. Problem solving is one of the challenges and joys of mathematics— somuch so, that many of us teach mathematics so that we can share in the delight of our students as they joyously show us that they have solved a problem whose solution has been evading them.
Task Cards
Authors: Barson Alan
Published: October 2020

A task card describes an activity or a job or “task” for a student or students. Task cards can be important tools for learning. They are not just busy work for students who get their assignments finished quickly.
Minimal Competencies: a Position Paper
Authors: Smith William D.
Published: October 2020

One of the major trends in elementary and secondary education in America today is the back-to-basics movement. Many advocates of back-to-basics argue for more emphasis on the three Rs, less emphasis on the socializing functions of the school, fewer child-centered curricula, and less social promotion. Accountability is usually closely associated with this movement. Thus, it is natural to find the notion of minimal competency surfacing as an important issue in mathematics education. After all, mathematics is one of the three Rs; and accountability suggests that tudents be able to perform at some minimal level of competency as measured by a proficiency instrument.
ALL-Star GCF
Authors: Scheuer Donald W.
Published: October 2020

It was fourth down and Leah had a decision to make. Should she try for a gain of at least 3 yards or punt the ball to put her opponent in a less desirable field position? Leah's marker was on the 37-yard line. After a few seconds' thought, he chose to punt, tating that 37 is a prime number and she couldn't gain 3 yards. She rolled the dice, producing a 4 and a 10, and the ball was punted 20 yards downfield.
Understanding the Check of Nines
Authors: Johnson Phillip E.
Published: October 2020

The check of nines for the four arithmetic operations is a useful device not only for the check that it gives, but also for the extra computational practice (without calling it that) that it furnishes. Students generally react much more favorably to this kind of drill than to straight adding, subtracting, multiplying, and dividing.
Let's Do It: Gad Zucchs! Zucchini in Your Math Class?
Authors: Lindquist Mary Montgomery , Dana Marcia E.
Published: October 2020

Did you ever consider using zucchini in your math class? Don't squash the idea until you've tried it. Seriously, zucchini have many properties that make them quite appropriate for young children (kindergarten and primary grades) to examine and measure.
More Problems, Please
Authors: Masse Marie
Published: October 2020

Did you ever imagine that your class would actually request more problemsolving activities? They will when the problems are short on computation and long on logical thinking.
Let's Metricate Parents, Too!
Authors: Threadgill Judith
Published: October 2020

Metrication is a word that frightens many people. It implies change—breaking old habits and forming new ones. When Timmy arrives home from school and joyfully announces that he now weighs 27 kilograms, he is more likely to be greeted with confusion than shared joy. As teachers, we admit that much of our learning of the metric system takes place during classroom hours when we, along with our students, are actively involved in measuring activities. But what is true for teachers can also be true for parents. One of the most painless ways for parents to adapt to the metric system is to learn it along with their children.
Calculators: What Difference Will They Make?
Authors: Schmalz Rosemary
Published: October 2020

In any discussion of calculators, we must begin by agreeing that calculators are in and that they are never going to be out. They may change form, but they will not go a way. They are not a fad that will disappear after a certain number of years due to boredom on the part of the A111erican consumer.
A Model for Evaluating Individualized Mathematics Learning Systems
Authors: Houser Larry L. , Heimer Ralph T.
Published: October 2020

The notion that individuals differ is well documented in literature. Galton, one of the first men to use psychological measurement as we now know it, noted individual differences in his experiments in the 1880s. Most educators now agree that each student learns at his own rate and in his own way. Providing for the needs of individual learners in mathematics has been widely discussed since the turn of the century and, over the years, many schemes for individualizing instruction in mathematics have been tried but subsequently discontinued. These schemes probably were unsuccessful due to a variety of conditions of adequacy that were not met.
Let's Do It: Almanac Facts
Authors: lindquist Mary Montgomery , Dana Marcia E.
Published: October 2020

If you need some fresh ideas for activities and problems that involve estimating, computing, and thinking, try an almanac. Almanacs provide a multitude of interesting facts that can be used in a mathematics class. With these facts, you can quickly devise a variety of real-life problems for almost any grade level; children may even learn more about some aspects of our world while they are solving the problems.
Fractions on Grid Paper
Authors: Brown Christopher N.
Published: October 2020

A lesson on fractions, using colored pencils and grid paper, can be both enjoyable and a good mind-stretcher for students' conceptualization of fractions. You can introduce the lesson with a discussion of checkerboards, flags that have rectangular subdivisions, or tiled floors or walls, asking such questions as What fraction of the checkerboard is red? What fraction of all the tiles are green? or What fraction of the French flag is white?
How I Learned to Do Percents
Authors: Teahan Teresa
Published: October 2020

So, you're teaching percent! Your students have mastered fractions and decimals and the relationships of one to the other. All seems to be going well and you proceed to have your students change readily from the fraction to its decimal equivalent, and then from the decimal to its percent equivalent. Soon you arrive at something like table 1.
What's Going On…
Authors: Donnelly Gawronski Jane
Published: October 2020

Increasing The Participation Of Girls And Women in the study of mathematics is the concern of a new organization. Membership information for the Association for the Promotion of the Mathematics Education of Girls and Women (APMEG&W) is available from APMEG&W, c/o Education Department, George Nason University, 4400 University Drive, Fairfax, VA 22030.
Geometry in the Middle School: Problem Solving with Trapezoids
Authors: Thomas Diane
Published: October 2020

A three-by-five card, a ruler, and a pair of scissors—these are the makings of a problem-solving lesson on area. Ask students to follow these steps.
National council of teachers of mathematics: Annual Financial Report
Authors: Kriegsman Helen , Devlin John , Stipanowich Joseph , Egbers Elden , Choate Stuart , Gates James D. , Tewell James R.
Published: October 2020

Each spring it is the responsibility of the financial policies committee to review the requests of the various components of the national council of teachers of mathematics and to recommend a budget to the board of directors for the next fiscal year.
Let's Do It!: Measurement for the Times
Authors: Lindquist Mary Montgomery , Dana Marcia E.
Published: October 2020

This is an article about measurement and multiplication. We chose this topic for three reasons. First. children need a variety of practice in multiplication. We hope that when children are working with problems in interesting meaningful situations, they will be motivated to do the related computations thoughtfully and accurately. The individual activities do not contain a multitude of multiplication exercises—we are more interested in the quality than in the quant ity of work done. Second, measurement is one of the main ways we use mathematics in everyday life. Thus, at the same time the children are practicing multiplication. they are applying it. Third, mathematical skills often are taught separately and child ren do not see the relationships among them. Here we have provided ways to tie measurement and multiplication together.
Color Their Arithmetic
Authors: Finstein Phyllis
Published: October 2020

Looking for a sure way to drill your students in their multiplication facts? There is no sure way for every child, but I have found a way that has helped me and, more important, it has helped my students.
The Number 6174 An Arithmetical Curiosity
Authors: Alden Loomis
Published: October 2020

Given the number 6174, arrange its digits in descending order of magnitude to form the largest number possible. Also arrange the digits in ascending order to form the smallest number possible. Subtract the smaller from the larger: 7641 minus 1467 equals 6174, the original number!
Metric Dominoes with a Challenge
Authors: Gregory John W.
Published: October 2020

There are literally hundreds of activities on the market today that are designed to help students become familiar with the metric system. Some serve as a true challenge for more able students, but such activities are either costly or hard to find. A game of metric dominoes can be challenging and the materials for the game are easily made.
Let's Do It: Positive Patterning
Authors: Leutzinger Larry , Nelson Glenn
Published: October 2020

Skill in associating numbers with sets of dots is useful as an intermediate step between counting and the development of concepts that are important in learning and understanding addition and subtraction.
Chinese Primary Mathematics Education: A Report of a Study Visit to the People's Republic of China
Authors: Modell Robert L. , Becker Jerry P.
Published: October 2020

On 21 October 1977, an NCTM sponsored group of twenty-three mathematics educators from sixteen different states and the province of Quebec arrived in the People's Republic of China (PRC) to begin a study visit that would last for seventeen days.
Let's Do It: Let's Take a Geometry Walk
Authors: Nelson Glenn , Leutzinger Larry P.
Published: October 2020

Showing the relevance of a topic in mathematics to life can make the topic more meaningful to students. Noting the topic's existence and use in the world around us can provide motivation for the study of the topic and opportunities for real life applications. The study of geometry is a good example. Enterprising teachers have always used objects in the classroom to illustrate geometric terms and ideas. This a pproach can be extended by taking a geometry walk outside the classroom.
Using Questions to Diagnose and Remendiate
Authors: Mcaloon Ann
Published: October 2020

To diagnose means to determine the nature of a problem or situation. Applied to the (mathematics) classroom, it means to identify weakness or deficiencies that could block a student's progress in learning. Although the process of diagnosis is usually associated with formal testing, the focus of this article will be on diagnosis in a normal classroom setting.
Strategies for Teaching Children Gifted in Elementary Mathematics
Authors: Waters Margaret M.
Published: October 2020

Federal legislation has mandated that a ll children with special education needs should have those specific needs met by the school. Included in this special education group along with the learning disabled, physically handicapped, and mentally reta rded are the gifted and ta lented children. This public mandate and reawakened interest in the early identi fica tion and education of gifted and talented children has brought into sharp focus some serious curriculum problems and interesting challenges to teachers.
What's Going On
Authors: Haynes Harriet
Published: October 2020

NIE and NSF seek proposals for grants involving mathematics and technology. The NIE and the NSF announce a joint program of development and research concerning the use of information generated through technology. The objective is the deve lopment of prototypes of (1) educationally relevant software, (2) instructional courseware, and (3) methods of assessing students' progress. Individua ls requesting information must ident ify the project correctly as the Joint NSF-NIE Mathematics and Technology Program. For information contact the Science Education Directorate, National Science Foundation, Washington, D.C. 20550, telephone (202) 282-7910, or the National Institute of Education, Washington, D. C. 20208, telephone (202) 254-6572.
Primary Coin Card Activities
Authors: Daane C.J.
Published: October 2020

Teachers have been told that they should make mathematics relevant to the lives of their children. One very important aspect of children's lives is mo ney. Children are used to having coins and bills to save and spend.
Readers' Dialogue
Authors: Madell Robert , Attivo Barbara J. , Tweedt Barbara J.
Published: October 2020

I was very much interested in Beattie's report on “Children”s Strategies for Solving Subtraction-Fact Combinations” in the September 1979 issue. I have been observing for quite some time that the third-grade children in my school use methods similar to those that he calls “bridging” when solving subtraction problems that require regrouping.
Let's Do It: Meaningful Measurements
Authors: Leutzinger Larry P. , Nelson Glenn
Published: October 2020

To many elementary school students—and, in fact, to many adults—measurement means one of two things. The first meaning involves using a device (ruler, tape measure, scale, or graph paper, for example) to obtain a “measure” of an object—that is, to obtain a number that characterizes the object in some way. Measurement, then, involves the physical act of using a measuring instrument.
The Calculator in the Classroom
Authors: Zekariya Norma , McClung Margo , Winner Alice-Ann
Published: October 2020

The hand-held calculator was introduced into the mathematics curriculum of the United Nations International School at the upper-elementary level during the 1977–78 school year. The new program was inspired by a summer workshop at T eachers' College, Columbia University. Calculator instruction began on an experimental level in a fifth-grade class in November 1977. This was followed by instruction in a fourth-grade class, and later in a third-grade class.
Analogy and Problem Solving: A Tool for Helping Children to Develop a Better Concept of Capacity
Authors: Szetela Walter
Published: October 2020

When students make comparisons between regions or containers of different shapes, they are often misled by visual deceptions or by application of incorrect mathematical generalizations. For example, in the two triangular regions with congruent bases and altitudes shown in figure 1, when students are asked to select the triangle of larger area, they are more likely to select triangle DEF because it “looks larger.” The longer sides of triangle DEF are a deceptive visual clue typical of misconCeptions held by students without a well-established concept of area.
GE-O-ME-TR-y A Lotto Game
Authors: Morrell Linda Anderson
Published: October 2020

I have been an avid user of the ideas and games section in the Arithmetic Teacher for several years. I firmly believe that games are very useful in motivating students and in helping them maintain positive attitudes toward mathematics. I have had great success using games of the lotto or bingo type to reinforce the basic addition and multiplication facts, and so recently, while teaching a section of geometry on the basic polygonal shapes, I decided to make a game on the idea of bingo to emphasize the geometric material. I have not seen a game like this and want to share it. The game is called GE-0-ME-TR-Y.
Annual Financial Report
Authors: Devlin John F. , Stipanowich Joseph J. , Egbers Elden B. , Choate Stuart A. , Immerzeel George , Gates James D. , Tewell James R.
Published: October 2020

Each year it is the responsibility of the Financial Policies Committee (FPC) to prepare and recommend to the Board of Directors a budget for the next fiscal year. During its April meeting the Board modifies the budget submitted by the FPC, and the adopted budget becomes a plan for the use of revenues for the succeeding year.
Number Bracelets: A Study in Patterns
Authors: Trotter Terrel , Myers Mark D.
Published: October 2020

If you are interested in a novel approach to number patterns, an experience in following an algorithmic procedure different from the usual one, some practice in systematic search techniques, and something that provides students with significant amounts of practice with the basic facts—all this in one activity—we would urge you to consider number bracelets.
Miscellany: What's in a Number-Name?
Authors: Schlesinger Beth M.
Published: October 2020

Introductory comment: Too often arithmetic is taught as a series of unrelated topics. This idea may help to bring it all together.
Wrap It, Laminate It, and the Game Begins
Authors: Smith Weinstein Pauline
Published: October 2020

Arithmetic gameboards can be very practical instructional materials. Teachers can use them to reinforce the numerous but varied concepts and skills taught during any given year.
National council of teachars of mathematics: President's Address 58th Annual Meeting
Authors: Hill Shirley A.
Published: October 2020

I count myself as very fortunate tonight. I am accorded the opportunity to be a spokesperson for a remarkable collective of highly professional members of that most important occupation, teaching. On your behalf, I will be presenting to the educational world, to policy makers in education, and to the public a document that can be a catalyst and force for positive change.
Let's Do It: Fractions with Counters
Authors: de Walle John Van , Thompson Charles S.
Published: October 2020

The wrong kind at the wrong time may be an apt description of the instruction with fractions usually provided children in the upper grades, a period in which fraction skills and concepts seem to be developed all at once.
One Point Of View: Four Essential Forward Steps
Authors: Shulte Albert P.
Published: October 2020

Computational facility is commonly perceived to be the learning of basic number facts and the acquisition of speed and accuracy in using penciland- paper algorithms. As we move into the 1980s, computational facility must be viewed as a broad set of skills. Knowledge of number facts will still be important— no one can compute rapidly without them— and people will continue to use pencil-and-paper algorithms in many situations, but to stress extended calculation involving multidigit numbers on pencil and paper ignores the availability of electronic calculating aids.
Polyhedron Candles: Mathematics and Craft
Authors: John Laffan Anthony
Published: October 2020

Very often the best ideas in teaching come about purely by accident. This certainly applied when we made some very attractive and unusual candles in my class.
Concepts of the Fundamental Operations: Results and Implications from National Assessment
Authors: Rathmell Edward C.
Published: October 2020

Several items on the second NAER Mathematics Assessment focused on the concepts of the fundamental operations. Specifically, children of ages 9 and 13 were asked to relate models for the operations to number sentences involving basic facts. An analysis of the results on these items is presented here, followed by a discussion of the results and implications for instruction.
Dangers of Formalism
Authors: Noddings Nel
Published: October 2020

In the February 1978 issue of the Arithmetic Teacher, Lichtenberg invited mathematics educators to engage in dialogue on the topic of mathematical symbolism. It is vital that we do so. Lichtenberg's suggestions belong to a doctrine of pedagogical formalism laid out in the sixties, one that has natural appeal for mature students of mathematics. But formalistic methods may not be effective with mathematically immature students. Indeed, it is likely that formalistic methods sacrifice the very goal they purportedly seek, achievement of meaning.
A New Look at an Old Weight Problem
Authors: Adkins Bryce E.
Published: October 2020

An increase in the incidence of use of balance-pan scales in the elementary school classroom has accompanied the increase in instruction in metric measurement. The resulting experience of pupils in using balance-pan scales gives renewed appropriateness to an ancient mathematical recreation named, “Sachet's Weight Problem.” (Bachet, Claude-Gasper, published in 1612, Problemes plaisans et delectables, qui se font par les nombres, which David E. Smith states is, “The first noteworthy collection of recreative problems to appear in print. … ”) As originally stated, Sachet's weight problem asks the student to determine the least number and the size of weights necessary to weigh every integral number of pounds from one to forty. It should be noted that the scales available at that time were of the balancepan type. In the modern setting, using metric terms, the problem could be restated to ask the number and size of weights necessary to weigh every whole number of grams (or kilograms) from one through forty
Readers' Dialogue
Authors: Liedtke Werner , Rausch Patricia
Published: October 2020

The currency of letters to the editor of a journal like the Arithmetic Teacher is always a problem. At the very best, four months will have elapsed between the time when an article is published and the time when a letter commenting on that article can appear in the Journal. Sometimes the m1nimum time is even greater. For example. letters about an article that appears in a January issue will almost never appear before the following fall. The publication schedule alone dictates such a spread of lime. and other factors can intervene to further delay publication of a lener.
One Point Of View: Early-Teaching for Effective Numeracy
Authors: Bell Max S.
Published: October 2020

Both we and the children we now teach must come to terms over the next few decades with inventions that have potential for great progress or great harm. Everyone must live with these dilemmas but we in mathematics education are thrust to the forefront of them by four additional circumstances. First, technological advances require that at least a few tens of thousands of people be very well educated in mathematics. (Here and elsewhere I intend “mathematics” to include “statistics and computers.”) Second, middle-level mathematical capabilities are needed in the everyday occupations of millions more people now than would have been the case only a few decades ago. Third, much of the information served up by our modern world can only be properly examined by people with sound numerical intuition—comfort with things mathematical has become a condition of intelligent citizenship for millions of people. Fourth, universal availability in developed countries of very cheap calculators has suddenly and fundamentally altered what might be meant by numeracy, since essentially no one outside of school now chooses to use the calculation procedures which dominate elementary school mathematics instruction.
Calendar Fun for the 1980s
Authors: Barson Alan
Published: October 2020

The calendar chart in figure 1 and the day Line in figure 2 can be used to find out on what day of the week a certain date will fall during the 1980s. The chart is set for 1980 or 1985. To find information for the other years in the decade, the “day line” strip is placed, with the proper year at the top of the chart, on the center day Line of the chart.
Games for the Primary Grades
Authors: Liedtke Werner
Published: October 2020

The statements “Let's play a game” or “We will play a game” are sure to generate some excitement in any classroom. There is something intrinsically motivating about a game. The majority of young children enjoy playing games, which alone could justify their occasional use. However, many other worthwhile reasons for the use of games as part of the instructional setting or learning process in the mathematics classroom can be given.
Minutes of the Annual Business Meeting
Authors: Gates James D.
Published: October 2020

President-elect Max A. Sobel called the Annual Business Meeting to order at 2:55 p.m. It was announced that Past President E. Glenadine Gibb would serve as parliamentarian.
The Mathematical Game Contest
Authors: Cruikshank Douglas E. , Martin John A.
Published: October 2020

Instructional games are one means for helping children learn new concepts, reinforce certain skills, and memorize basic arithmetic facts. A game may be noncompetitive in the sense that a child wins or loses because of chance—the luck of the draw. Or games may be competitive; speed or a superior memory are required.
MISCELLANY: Stephen's Game
Authors: Tugwell Claudia
Published: October 2020

One of my eighth-grade students bas invented a game. I have shared it with grades four and five, where it has been received enthusiastically. Grades six, seven, and eight have also found it fun.
MATHEMATICALLY ABLE GIRLS: A Special Challenge
Authors: Fox Lynn
Published: October 2020

Susan and Ted were identified as mathematically talented when they were in the seventh grade. Ted began to accelerate his educational progress and completed a four-year high school program in three years. At age seventeen he entered a university with sophomore standing. He had acquired a year's worth of college credits by taking the Advanced Placement program's examinations in several subjects and college courses on a part-time basis while in high school. He is planning a career in electrical engineering. Susan, on the other hand, did not accelerate her progress in school and did not elect a physics or calculus course in her junior or senior years of high school. Her career plans are vague and she is not excited about going to college.
Units of Measure: Results and Implications from National Assessment
Authors: Hiebert James
Published: October 2020

Measurement skills provide children with a powerful link between the abstract world of numbers and the concrete world of physical objects. Before young children learn to measure, they can only describe objects or quantities with relatively vague, uninformative terms such as “big” or “many.” As they learn to measure, children acquire the skills to describe quantities in more precise and more useful terms. They can now talk about the size of quantities as the number of units measured.
CLASSROOM ACTIVITIES FOR ABLE STUDENTS: In Kindergarten, First and Second Grades
Authors: Rathmell Edward C. , Leutzinger Larry P.
Published: October 2020

A major part of the instructional time devoted to mathematics in the primary grades involves helping children learn to count, read and write numerals, memorize basic addition and subtraction facts, add and subtract twodigit numbers, tell time, count money, and solve word problems. Since many able students already know or quickly learn these topics, primary teachers are faced with the problem of providing appropriate learning experiences for these children while the remainder of the class is learning them.
CLASSROOM ACTIVITIES FOR ABLE STUDENTS: In Third and Fourth Grades
Authors: Schulman Linda
Published: October 2020

A major goal of the mathematics curriculum for third- and fourth-grade students is the development of numeration and computation skills. These skills are frequently maintained through routine drill. Most gifted students have a strong dislike for drill, preferring activities that require the use of higher cognitive processes. One way of providing for these students is to present them with problems related to the basic content that also enhance their problem-solving abilities.
Too Many Blanks! What Workbooks Don't Teach
Authors: Touger Hallie Ephron
Published: October 2020

Recently I observed a student teacher giving a group of third graders a mathematics quiz. He passed out plain paper and began to read off some addition examples for the children to copy. The children were panic stricken. Aghast! Write mathematics? No one had ever asked them to write mathematics. They had been cast adrift from their comfortable worksheets and workbooks and left to flounder about on a sheet of white paper. The results were illuminating. Fewer than half of the children could consistently and correctly reproduce a correct vertical algorithm. They did not know how to line up the numbers according to place value.
One Point of View: Beyond the Textbook
Authors: Greenes Carole E.
Published: October 2020

For the past five years, we educators have been bombarded with data indicating that our students cannot solve problems. Results of the second evaluation of student abilities in mathematics by the National Assessment of Educational Progress not only demonstrated that students' problem-solving ability was poor, but also that this ability has declined in recent years. This is not surprising considering the emphasis placed on computation since the beginning of the “back-to-basics” movement more than seven years ago.
Meaning Metrics: Measure, Mix, Manipulate, and Mold
Authors: Shaw Jean M.
Published: October 2020

Are you looking for ways to make metric measurements meaningful to children? Cooking play dough, then using the play dough for more mathematical explorations offers this opportunity. Play dough is an appropriate learning material for young children, but even intermediate-grade youngsters can learn from preparing dough and using it as a manipulative material in specific measurement explorations.
Let's Do It: A Single-Handed Approach to Telling Time
Authors: Thompson Charles S. , de Walle John Van
Published: October 2020

Many school children have difficulty learning to tell time via traditional teaching methods because some clock times are read “after the hour” whereas others are read “before the hour.” Some children also have trouble telling time because minute numbers are not written on their clocks. Still other children learn to tell time, but do not have good concepts of the duration of time. They keep wanting to know, for example, when five minutes will elapse before they go to recess.
Give and Take: Getting Ready to Regroup
Authors: Tucker Benny F.
Published: October 2020

Regrouping (or borrowing and carrying, if you prefer) consistently seems to be one of the hard spots for children. Most teachers who have taught elementary school mathematics have seen children do surprising things when faced with computational examples that require them to regroup. The following are examples of what might be seen.
Summer Laboratory Experience for Children: Professional Growth for Teachers
Authors: Feinstein Irwin K. , Levin Alan J.
Published: October 2020

The problems involved in planning and running a successful summer school program are compounded by limited funds. As state funding in Illinois was eliminated, the most extensive summer school programs, those which featured a combination of remediation and enrichment, began to disappear. Without state funding, local school districts saw their per pupil costs soar to prohibitive levels and school districts began to question what should constitute a viable summer experience.
Putting an Old Puzzle to Work
Authors: Donegan Joseph P. , Pricken John D.
Published: October 2020

Many teachers are familiar with the mathematical puzzle that consists of cutting apart an 8-by-8 square piece of paper and rearranging the pieces into another rectangular shape that has a different area. This puzzle is demonstrated in figure l. It seems the area of the square is 64 square units while the area of the rectangle is 65 square units. The question is, Where does this extra square unit come from?
Readers' Dialogue
Authors: Rappaport David , Stibal Willard , Franson Joseph P. , Austin Virginia Allen , Brekke Gail , Young Jerry L. , Stettner Christine , Porter Fay A. , Tunis Harry B.
Published: October 2020

The currency of letters to the editor of a journal lilte the Arithmetic teacher is always a problem. At the very best. four months will have elapsed between the time when an article is published and the time when a letter commenting on that article can appear in the journal. Sometimes the minimum time is even greater. For example, letters about an article that appears in a January issue will almost never appear before the following fall. The publication schedule alone dictates such a spread of time, and other factors can intervene to further delay publication of a letter.
Second Graders Can Be Problem Solvers!
Authors: Spencer Patricia J. , Lester Frank K.
Published: October 2020

Much has been written in recent years about the importance of problem solving in school mathematics at every level. Most of the discussion of elementary- school problem solving, however, has focused on the intermediate grades. This article describes an attempt to make problem solving a real part of the mathematics program in a second-grade classroom.
Let's Do It: We've Got You Pegged!
Authors: Jensen Rosalie , O'Neil David R.
Published: October 2020

Preschool and elementary-school teachers are always searching for inexpensive, versatile manipulative teaching aids. Ordinary pegboard, used with such common items as pegs or golf tees, can be such an aid. Pegboards of several types and wooden golf tees will be used in illustrations throughout this article. Golf tees were selected because they are colorful and easy for children to handle.
Fractions vs. Decimals—the Wrong Issue
Authors: Swart William L.
Published: October 2020

Since the move to the metric system was accelerated in this country a few years ago, there has been considerable comment about the importance of common fractions in the elementary school. Some of what has been said is nonsense, but some perfectly sensible comments about the need for emphasis on decimals have led some people to the erroneous conclusion that fractions are going to be out of date. It is true that in the metric system most measurements are expressed in decimal notation. That is also true of our monetary system. But the notion that fractions are any less important because of the use of decimal notation in the metric system is based on a superficial view of fraction concepts and the mistaking of certain manipulations of fractions for the substance of fractional operations.
Take the Metric System Personally—Play “Merrily Metric”
Authors: Sherman Helene J.
Published: October 2020

“Merrily Metric” is an appealing, useful metric activity suitable for players from age nine to ninety. The game provides practice in estimating lengths as well as in actual linear measurement. Conversion among prefixes within the system can also be included at a pictorial level. The great popularity of the game is its application to each individual playing and, thus, its wide variability. It is also a game that can be played with an entire class.