bluuebunny/crossref_metadata_2025 huggingface dataset:
Things you can try
Authors: Metzner Seymour , Sharp Richard M
Published: October 2020

Materials for pupil activity-learnmg in all areas, and especially mathematics, are difficult to find even though more educators are advocating this approach to learning. Some teachers have used considerable initiative and ingenuity to develop and adapt inexpensive materials for pupil activity-learning. One of the most inexpensive, easily obtained, and adapta ble items that can be used is an ordinary deck of playing cards.
Things you can try
Authors: Bell William R
Published: October 2020

Mathematical games are a way of relieving the drudgery of practice for some students, and this adaptation of an old and familiar game (which is often played surreptitiously by students) can also be justified as being educational. In the version of Battleship described here, the basic difference is that the intersections of grid lines are named instead of the squares between the grid lines. The game is best introduced after a study of integers and as a prelude to graphing equations of lines.
Of fractions, fractional numerals, and fractional numbers
Authors: Ballew Hunter
Published: October 2020

Some elementary school mathematics textbooks differentiate between fractions and fractional numerals; others differentiate between fractions and fractional numbers. In the former case a fraction is considered a number, and in the latter case a fraction is considered a numeral.
Teaching mathematics to children through cooking
Authors: Smith Rosalind Bingham
Published: October 2020

Cooking is lots of fun for young children. It is also a fine way to teach them mathematical concepts. I was introduced to the use of cooking as a technique to teach arithmetic in far-off Iran by a British Infant School teacher. It worked so well and seemed such a sensible and natural approach that I wondered why it wasn't used in the United States—why didn't we think of it? When l returned to the United States, I was happy to find that some teachers of young children do employ cooking for this purpose. More teachers would make use of this technique, I believe, if they could gain an understanding of its effectiveness and manageability.
Magic triangles—practice in skills and thinking
Authors: Zalewski Donald L.
Published: October 2020

Can you place each of the numbers 1 through 6 in the triangular chain of circles in figure 1 so that each side has the same sum? If you are successful, congratulations, you have just created one example of a magic triangle. These simple figures may not have as many “angles” as the well publicized magic squares, but they possess a few powers that may be interesting to both you and your students. Obviously, important practice in addition skills is built into the puzzle and it is possible that you can at the same time stimulate the formation of problem-solving strategies.
A model for the construction and sequencing of laboratory activities
Authors: Post Thomas R.
Published: October 2020

The mathematics program in too many of today's schools is textbook dominated, con. cemed primarily with the manipulation of symbols, and, all too often, largely removed from the real world of the child. Mathematics enjoys (or suffers from, depending upon one's perspective) a reputation which is clearly less than inspiring. Why are there such large-scale negative attitudes towards mathematics? Endless repetition, meaningless memorization, a never-ending series of worksheets or practice exercises, and a gen. eral lack of interest and understanding are but a few of the reasons that might be listed. One problem with a textbook-dominated approach to teaching and learning is that young people do not exist in a twodimensional world. Children exist in a world that they are very eager to learn about until that eagerness and enthusiasm is dulled by the establishment of numerous artificial situations to which they are required to respond. What is needed is a mathematics program that is very much alive and vibrant, and relevant and meaningful; a program that parallels the way in which young learners are alive and vibrant and continually searching for relevance and meaning as they seek to understand the world around them.
Ideas
Authors: Burns Marilyn
Published: October 2020

There are several overall objectives for this month's IDEAS. Children will have the opportunity to investigate the concept of probability. Computational skills will be reinforced. Simple graphing will be introduced for recording statistics.
Let's Do It!: Using geostrips for arithmetic
Authors: Bruni James V. , Silverman Helene
Published: October 2020

Making geometric shapes can be an enjoyable way to develop arithmetic concepts. In the activities that follow children are involved in making shapes with homemade geostrips and using the operations of addition, subtraction, multiplication, and division. Basic concepts like binary operation, commutativity, associativity, and distributivity are introduced intuitively as the children make the various shapes and answer questions about them.
Ideas
Authors: Burns Marilyn
Published: October 2020

Activities for reinforcement of whole number operations are provided in this month's IDEAS section. The games present strategic situations for children to use their computation skills. Although the games are separated into various levels, let the children's skills and needs, not their ages, be your guide. In addition, once the children know how to play the game described, encourage them to invent variations.
Ideas
Authors: Burns Marilyn
Published: October 2020

February's IDEAS focuses on geometry by presenting various ways to investigate square shapes. With these suggestions as a beginning, see what other ways your class can find to look at this familiar shape in a new light. Also, use these ideas as a springboard for further geometry investigations using other shapes.
Electronic calculators in the classroom
Authors: Stultz Lowell
Published: October 2020

Anyone who has noticed recent newspaper advertisements or attended book and equipment exhibits at teachers' conferences is aware of the exploding market in electronic calculators. The microcircuit technology spin-off from the space industry has given the consumer a handy mathematical tool that will soon become commonplace in the home, office, shop, and classroom, but it is too early to predict the full extent to which the availability of electronic calculators will affect the teaching of mathematics. This article presents some of the uses of calculators in the elementary classroom as well as some of the changes that may become necessary in the subject content itself.
IDEAS
Authors: Burns Marilyn
Published: October 2020

Each IDEAS presents activities that are appropriate for use with students at the various levels in the elementary school. The activity sheets are so arranged that they Catl be easily removed and reproduced for classroom use.
What do you see?–a discovery approach to prime numbers
Authors: Erb Clinton A.
Published: October 2020

The question “What do you see?” can be the springboard to many interesting discussions. The following example has been successful not only with students but also with teachers taking inservice courses.
A working model for rational numbers
Authors: Moulton J. Paul
Published: October 2020

There are many good models for the rational numbers-area models, Cuisenaire rods, lattices, for example. Each has its merits and its limitations, and none is so good that it should be used to the exclusion of all others. Indeed, it is partly through a variety of experiences that a person acquires the ability to relate the abstract concept of a rational number to the properties of the practical world. I should therefore like to suggest still another model, one that has certain advantages of its own.
A crossnumber game with factors
Authors: Unenge Jan
Published: October 2020

Children need a great deal of practice to learn to factor numbers and find divisors. The following game can vary this practice and make it more interesting for children.
Using research in teaching: Notes from National Assessment: Basic concepts of area and volume
Authors: Coburn Terrence G. , Reys Robert E. , Wilson James W.
Published: October 2020

A direct result of the increased attention being focused on the metric system is the reexamination of the entire area of measurement in the curriculum. For many this reex amination has led to the conclusion that the real problem in teaching metric measurement will not be with the metric units but with basic concepts of measurement. This contention is supported by the results of selected measurement exercises from the mathematics assessment of the National Assessment of Educational Progress (NAEP). This article focuses on two of these exercises that tested fun damental area and volume concepts.
So 3 “guzinta” 5 once! So what!!
Authors: Heddens James W. , Lazerick Beth
Published: October 2020

An educator once commented that division of whole numbers is the most difficult process a person can learn except for the process of integration, which is part of calcul us. This fact is probably true, though untested, for how many of us dread fourth-grade arithmetic when the time comes for division of whole numbers?
Your Council at Work: Board of Directors and Executive Committee
Authors: Gibb E. Glenadine
Published: October 2020

We know that the NCTM exists to improve mathematics education from kindergarten through the two-year colleges, but we don't always know just how. What exactly is the NCTM? How does it operate? What does an NCTM committee do all year?
15 Billion Hamburgers is a lot of Multiplication and Division
Authors: Shoecraft Paul
Published: October 2020

There is a fascination in large numbers and their interpretation that escapes few people. Take the number fifteen billion, for example, a 15 followed by nine zeros: 15 000 000 000. This is the number of hamburgers that McDonald's claims on its billboards to have sold over a period of twenty-five years. Now consider what this many hamburgers means.
Some activity approaches to teaching children the concepts of money
Authors: Kindle E. Glenn
Published: October 2020

One of the questions often asked of me as a mathematics methods professor is, Can you suggest some activities for teaching money concepts to elementary school children? Described in the following paragrap hs are two game-like activities that have been used successfully in many classes.
Mathematical road maps: a teaching technique
Authors: Wheatley Grayson H. , Duinen Alanvan
Published: October 2020

Consider a traveler stopping for directions to the Easysleep Motel. He asks someone and hears, “Oh, that's easy to find. Just follow this road about four or five blocks till you come to a red brick building on your right. Turn left, go over the railroad tracks, and angle off to the right. Go three blocks to Center Street, turn right, and it's the third house on your left. You can't miss it.”
Hamann's conjecture
Authors: Frame Maxine R.
Published: October 2020

Everyone familiar with Goldbach's conjecture knows that every even number greater th at two may be expressed as the sum of two primes. For example, 18 = 11 + 7. This is the form presented in the usual j un ior high school mathematics text.
Facing the energy crisis in a mathematics classroom
Authors: Yant Sandra L.
Published: October 2020

Since the energy crisis had been in the news so much and our principal had been insisting that we needed to make practical application of the subjects we teach, I decided to interrupt my regular classroom work to investigate this area.
ONE POINT OF VIEW: National Assessment—food for thought
Authors: Trafton Paul R.
Published: October 2020

With increasing frequency, the public is raising questions about the quality of American education and seeking information about students' performances in specific areas of the curriculum. Various assessment procedures are being used at the local, state, and national levels to provide data. As mathematics educators, we have an important stake in monitoring the quality of such efforts in mathematics. In particular, it is vital to examine closely the results of any assessments, interpreting the results carefully for their curricular implications and preparing ourselves to discuss them intelligently with the public.
Let's Do It!: Introducing consumer education
Authors: Bruni James V. , Silverman Helene
Published: October 2020

Young children are intrigued by money. They sense the importance that adults altach to money and observe it being used as they accompany their parents to the store. Money sometimes represents a gift or reward and can mean the power to purchase something desired. Emptying a piggy bank is a joy—all those coins are something to behold. Thoughts of large numbers come to mind—a hundred, a thousand, a million— in any case, a lot of money.
1776
Authors: Cunningham Helen
Published: October 2020

One of the most important years in the history of the United States, 1776, is being celebrated in numerous and unusual ways. There are many interesting mathematical activities that can bring the bicentennial celebration into your classroom.
Mathematics—for whom?
Authors: Rappaport David
Published: October 2020

If one accepts the year 1957 as the beginning of the “modern mathematics” era for the elementary school and high school mathematics programs, then we are now more than half way through the second decade of the “revolution” in mathematics education. In 1967 a number of speakers at meetings of the National Council of Teachers of Mathematics expressed the view that the first decade of the mathematics curriculum reform movement was devoted to developing worthwhile mathematics content, and since that phase of curriculum reform had been accomplished with great success, the second decade should be devoted to the pedagogical issues of how this content can be taught successfully to children. Although many mathematics educators may be satisfied with the mathematics content of the present programs, an increasing number of educators are raising serious questions about these mathematics curriculums.
Let's play mod 7
Authors: Niemann Christopher E.
Published: October 2020

Choosing a title for this article was a natural because “Let's play mod 7” has been a familiar request in our house. My own children were in the fourth, second, and first grades respectively when they learned to “play mod 7.” It all started some months ago with the familiar “clock arithmetic” of the mod 7 system, {0, 1, 2, 3, 4, 5, 6}. I am partial to this system since 7 is the largest single-digit prime number system one can construct using the decimal digits, and it also corresponds to days of the week.
Hints for mathematics tutors
Authors: Melton Joseph
Published: October 2020

Hooray, he's beginning to enjoy math now!” For the student teacher who made it, after tutoring a child for three months, this comment was like gold at the end of the rainbow. The student teacher's remark was not unusual. Several of my other students have said more or less the same thing. So that they can know firsthand the problems, difficulties, frustrations, and (I hope) the joys that underachievers experience in mathematics, I have members of my mathematics methods classes tutor individual students. Each works with a pupil on a one-toone basis for approximately an hour a week for twelve weeks.
Number patterns and the addition operation
Authors: Granito Dolores
Published: October 2020

Display the following table, then ask a student to pick out one number from each of the four columns.
Egyptian Geometry in the Elementary Classroom
Authors: Hamilton Martha
Published: October 2020

Brian was overheard asking Jeff, “Is this real geometry, or is it just Egyptian geometry?” The setting was a Montessori school in Richmond, Virginia. The junior class of twenty-three children (ages eight and one-half to twelve and one-half) were involved in a historical study of architecture, with Egypt as the focus. Based on the belief that children learn more naturally if sharp distinctions are not drawn between subject areas, the curriculum was developed in an integrated fashion as much as possible.
Your Council at work: President's Report: The Spirit Of '76
Authors: Gibb E. Glenadine
Published: October 2020

The Spirit of '76—a familiar expression this year as the United States celebrates 200 years as a nation. During these 200 years, Americans, from diverse backgrounds and experiences, have had the opportunity to fashion their own lives and the life of their society. Their Bicentennial is a recognition of two centuries of a new nation among nations-a nation described by some as one that has sought to weave a tapestry of different colors, beliefs, and ideas that is both resilient and brilliant. As with any weaving, flaws and mistakes are to be expected. Through these mistakes, Americans have learned the value and importance of debate, discussion, interaction, and involvement. During this Bicentennial year, individuals with common interests in civic, industrial, business, religious, and educational or other professional endeavors are taking advantage of the opportunity to renew their commitments and revitalize their efforts. For each of us, it is a time of reflection as well as rededication.
Calculators in elementary schools? Some tentative guidelines and questions based on classroom experience
Authors: Bell Max S.
Published: October 2020

It seems certain that electronic calculators will cause something of a revolution in the availability and use of calculating power in the world outside of schools. This special issue of the Arithmetic Teacher indicates that there is considerable agreement that they should also play an important role in school instruction. But viable school roles will not be established without finding solutions to many problems: problems of philosophy, problems of curriculum and methodology, problems of design, and school management of the calculators themselves. In the belief that solutions to many of these problems should be worked out in actual classrooms, a small band of local teachers and myself began several years ago to explore classroom uses of calculators. This article reports some of our tentative conclusions and our questions resu lting from these explorations.
Calculators and the mathematics curriculum
Authors: Gawronski Jane Donnelly , Coblentz Dwight
Published: October 2020

Electronic calculator are small, practically silent, accurate, ea y to use, and very fast. In addition, they have become virtually ubiquitous. Shoppers in supermarkets. adult balancing checkbook, and student in the classroom have all been seen using calculators to help solve a problem. Calculators may even replace the transistor radio as a status symbol.
Just pushing buttons or learning?—a case for minicalculators
Authors: Schnur James O. , Lang Jerry W.
Published: October 2020

The minicalculator has captured the imagination and approval of some educators while receiving the disapproval of others. It has already captured the attention of people in many walks of life.
Let's Do It!: Developing intuitive ideas
Authors: Bruni James V. , Silverman Helene J.
Published: October 2020

Is today yesterday yet? Is it soon now? are questions asked by a young child as he grapples with our extensive vocabulary for the passage and order of events. Rooted in a mental set that is present oriented, a child attem pts to relate all events to his present state. Too often we ignore the intuitive ideas a bout time as we rush children into learning to read a clock dial.
Droopy, the Number Line, & Multiplication of Integers
Authors: Kindle E. Glenn
Published: October 2020

Droopy, that ubiquitous mascot of the Arithmetic Teacher whose wagging tail and bright eyes alert readers to the coming attractions in the journal, can help pupils learn to multiply with signed numbers. Many models have been devised to help students comprehend operations with the integers, but animals and cartoon characters have a strong appeal to students of all ages and backgrounds. Droopy is used in this article in the design of a high-interest model for integer multiplication.
A fun way to introduce probability
Authors: Billstein Rick
Published: October 2020

The typical introduction to probability usually involves tossing a single coin. The students and teacher will soon agree that this is a trivial activity. The possible outcomes of the experiment are a hea,. H, or a tail, T. The outcome set could simply be listed as {H, T}. If the coin were tossed a large number of times, the proportion of heads appearing should approach 1/2. For this reason we assign to each outcome the probability 1/2. We also say that the two outcomes are equally likely and the coin is fair. Figure I illustrates another way of describing one toss of a fair coin. This description will hereafter be referred to as a tree diagram. Each branch corresponds to an element in the outcome set with its appropriate probability labeled on the branch. Also notice that the sum of the probabilities of all the outcomes in the set is equal to I.
Individualized teacher preparation programs for students and faculty through a CBTE model
Authors: Underhill Robert G.
Published: October 2020

A program of competency-based education was begun in the mathematics component of the elementary education program at the University of Houston in 1971.
Your Council at Work: Auditor's report
Authors: McGivern Raymond H.
Published: October 2020

We have examined the accompanying Balance Sheet of Funds of The National Council of Teachers of Mathematics as of 31 May 1976 and the related Statements of Revenues, Expenses, and Fund Balances prepared for the fiscal year then ended. The Council, with Board approval and on a progressive basis, commenced the conversion of its accounting system from the cash to the accrual basis effective for the fiscal year ended 31 May 1976. Accordingly, except for the recognition of Memberships, Subscriptions, and Accrued Annual Leave, which are planned for accrual basis recognition in the fiscal year commencing 1 June 1977, the statements examined and submitted were prepared on this basis. Our examination was made in accordance with
Tricks of the trade with cards
Authors: Lund Charles H.
Published: October 2020

For several years I have maintained in my cabinet a file entitled “Cards Activities.” It contains a collection of miscellaneous ideas, games, and exercises that can be used with children in a mathematics classroom and all use an ordinary deck of playing cards as a learning aid.
Multiplying by eleven—a place–value exploration
Authors: Spitler Gail
Published: October 2020

An examination of shortcuts or tricks for multiplying by eleven can be a very productive activity for older elementary school students. Such an investigation can reinforce many place-value concepts. Additionally, and perhaps more importantly, such an investigation can stimulate a great deal of conjecturing, testing of the conjectures. and refining conjectures.
A glance at the power of patterns
Authors: Thornton Carol A.
Published: October 2020

Recent work in the psychology of perception (Rock 1974) indicates that recognition of patterns plays an important role in daily living and constitutes a large part of the way we organize and understand our world.
Metric measurement: important curricular considerations
Authors: Cathcart W. George
Published: October 2020

A change to the metric system of measurement is now almost a “given.” On the basis of this premise, writers and publishers are burning the midnight oil in an attempt to build metric measurement into their elementary school mathematics programs. Such activity is to be commended.
Your Council at Work: Publications Committee
Authors: Cathcart W. George
Published: October 2020

Except for the official journals, the Publications Committee (PC) is responsible for the NCTM publications program. Although all decisions are made by the whole committee, two internal subcommittees have been formed to focus on different facets of the publications program. One deals with supplementary publications and classics and the other with journals, yearbooks, and professional references.
Investigating symmetry in the primary grades
Authors: Morris Janet P.
Published: October 2020

The children were thoroughly engrossed in investigating the symmetry of the letter S.
Euclidean transformations: elementary school spaceometry
Authors: Richard Kidder F.
Published: October 2020

Spaceometry—the study of simple relationships of three-dimensional space; an intuitive exploration of location (whereness), direction, size, and distance. Docs this sound familiar? Of course, its an apt description of informal geometry, kindergarten through grade eight. (Brydegaard 1972). And nowhere is the term spaceometry more appropriate than in describing the study of Euclidean transformations in the elementary and middle school. Yet, is consideration being given to the interrelatedness of elementary geometry and children's spatial ability? Are we. as teachers, aware of the different levels of spatial conceptualization and the difficulties encountered by young children in their attempts to internalize spatial concepts and subject them to mental operations? And, what has research to tell us concerning the child's ability to learn transformational concepts at the different spatial levels?
Playing store for real
Authors: Dahlquist Joyce
Published: October 2020

Fifth-grade students at Western Elementary School are now active merchants and consumers.
Fractions, decimals, and their futures
Authors: Firl Donald H.
Published: October 2020

Forces are at work that suggest that those who teach mathematics and those who design mathematics programs should evaluate the position of fractions and decimals in elementary and junior high courses of study. More and different emphasis on decimals and less and different emphasis on fractions may be reasonable considerations.
Your Council at Work: Nominations And Elections Committee
Authors: Schaaf Oscar
Published: October 2020

The charge of the Nominations and Elections Committee is to select the nominees who will be on the annual ballot for the elected NCTM offices that become vacant as a result of expiring terms. The Committee has been given considerable freedom in determining the slate of candidates but is bound by the by-laws, which require that there must be at least one member on the NCTM Board of Directors from each of seven geographical areas (West, Southwest, Canada, North Central, Central, Northeast, and Southeast) and one from each of five levels of instruction (elementary, junior high, high school, two-year college, and college). This restriction means that on certain occasions the ballot must be planned so that the Board will be properly representative. When such planning is done the electorate is notified through the official NCTM journals.
What's Going On
Authors: Gawronski Jane Donnelly
Published: October 2020

Learning disabilities in mathematics: A Curriculum Design for Upper Grades is the subject of a U.S. Office of Education (Handicapped) Grant at the University of Connecticut. The focus is on children at the middle school/junior high level or those grade equivalents, starting at approximately the sixth grade, but exclus ive of that content formally associated with first year algebra. For additional information, contact John F. Cawley, Box U-7, School of Education, University of Connecticut, Storrs, CT 06268.
Number concept for school beginners. Is it possible?
Authors: Nicholas Susan
Published: October 2020

The setting is a classroom, grade one, with pupils between six and seven years of age. The time is the ten o'clock break.
The young child as a problem solver
Authors: Liedtke Werner
Published: October 2020

In mathematics, there are problems—like trisecting an angle with a straightedge and a compass—and theorems—Fermat's last theorem—that do not have a solution or for whrch a proof has not been found. Some riddles or problems do not have an answer.
Let's Do It!: More indoor games to motivate computational skills
Authors: Bruni James V. , Silverman Helene J.
Published: October 2020

How difficult it is to get children to practice computational skills! Most of us are conti nuously seeking techniques to motivate children to invest their time in learning number recognition, basic facts, and operations on whole numbers and fractions. Dominoes, dice, and cards are three inexpensive materials that can be used to generate teaching games that children are willing to play. Each of these materials is explored here for the possibility of teaching and motivating the development of computational skills. Although several vari ations of each game are suggested, it is hoped that individual teachers will be encouraged to devise still other games that are appropriate to the concepts and skills needed by the children in their own classes.
What's Going On…
Authors: Gawronski Jane Donnelly
Published: October 2020

Fractions in the mathematics curriculum is the subject of a position paper developed by a group of mathematics educators in Minnesota. Because of poor results in the topic of fractions on assessment programs, the participants recommended, among other things, that the teaching of the algorithms of operations with fractions be postponed until grades 7 and 8. They also emphasize the use of manipulatives in the development of concepts dealing with fractions. The paper was the result of a weekend conference cosponsored by the Minnesota Council of Teachers of Mathematics and the Minnesota State Department of Education. For additional information, contact Helen Kock, MCTM Executive Secretary, MECC, 2520 Broadway Drive, St. Paul, MN 55113.
One point of view: stop! look! think!
Authors: Reys Robert E.
Published: October 2020

All across the country—in local districts and on state levels, in meetings after school or in a workshop day—parents, administrators, and laymen are meeting together to identify and list basic skills in mathematics. The resulting record of basic skills then serves as a beacon to guide the development of a “test of minimal competency,” which is supposed to separate the wheat from the chaff and insure that all students master “the basic skills in mathematics that are necessary to survive in today's society.” The skills-assessment bandwagon is rolling—hop on quick!
Teaching Basic Concepts with Slides
Authors: Gibson Stephanie Salem
Published: October 2020

Teaching grades one through three in a Title I mathematics laboratory sett ing posed problems and situations that I had not encountered in my previous teaching experience. Specifically, I found that I was unable to teach my first graders some of the most basic concepts, even though I had access to a multitude of manipulative materials and teaching aids. It was immediately evident that a nontextbook approach was required and that certain prenumber concepts had to be mastered before I could expect my students to recognize numerals and count rationally.
Teacher Extraordinary
Authors: Bobo Annie R.
Published: October 2020

Who would think of trying to teach mathematics to a two-year-old? Why he would, of course. And I became the interested spectator and sometimes ally.
Let's Do It: Recycle Your Math With Magazines
Authors: Lindquist Mary Montgomery , Dana Marcia
Published: October 2020

Magazines have great potential for helping teach mathematics. Their use is directly related to some of the concerns in teaching mathematics today. For one thing, magazines are readily available and inexpensive—if you or the children collect used ones. Another “plus” is the fact that the ads, the articles, and the pictures are chock-full of “real-life problems.” There are consumer problems of all sorts. Also. there are many magazines that focus on things that are interesting to children. Different children will enjoy sports, movie. racing, news. or other types of magazines. Thus. magazines can assist in individualizing instruction as you tap the interestf of the children.
Mail-Order Math
Authors: Bensman Katherine H.
Published: October 2020

Motivating students during the preholiday weeks of december is a particularly difficult job. Children are under the same pressures as everyone else at this time of year. Their out-of-school activities are distracting—their homes are full of unusual and exciting plans. To compete for children's attention we must resort to special motivational tactics.
A Look at a Million
Authors: Makurat Phillip A.
Published: October 2020

Nearly every item in the federal budget is listed in the millions of dollars. The populations of states and larger metropolitan areas are often greater than a million. In the future, almost everyone will be exposed to figures that are larger than a million. People will encounter them in magazines. newspapers, and over radio and television. Besides these, many individuals in the science fields will work with figures in the millions.
Mr. Ten, You're Too Tall!
Authors: Brennan Alison D. House
Published: October 2020

Teachers are often confronted with children who are unable to make the transition from the conceptual stage of mathematical thought to the computational stage in base-ten operations. One of the major areas of difficulty occurs when the children begin working with place value. They are unable to conceptualize and therein comprehend the base-ten place-value system. With most children, paper-and-pencil activities are not enough to lead them to successful independent computation. One way to overcome this difficulty is to demonstrate visually the processes of addition, subtraction, regrouping, and so on.
Ideas
Authors: Ockenga Earl , Duea Joan
Published: October 2020

The IDEA this month is to use an overhead projector to provide practice with fractions.
Nominees for 1979 Election
Authors: Hill Thomas J. , Elliott Mabel M. , Forbes Jack E. , Geppert William J. , Glatzer David J. , Kent David , Price Jack , Smith Eugene P. , Smith Louise
Published: October 2020

The Nominations Committee needs your help! In the 1979 NCTM election a president and four new members of the Board of Directors will be elected. We need suggestions for NCTM members whose records of service and leadership qualify them for consideration.
Let's Do It: Thinking Up Your Own Practice Games
Authors: Dana Marcia , Lindquist Mary Montgomery
Published: October 2020

Have you been wanting to use more games to practice mathematics but have been unable to find games that practice what your children need or that fit your children's ages and interests? Perhaps you have found games that you like, but they have come in expensive kits or needed special materials. Would you like to make up your own games—games that do not take long to think up, are easy to prepare and play, and provide just the practice some or all of yo ur children need?
Snipshots
Authors: Ranucci Ernest R.
Published: October 2020

The snip in the title is no error of the printer. It refers to the snip of a pair of scissors. The materials needed for the lesson I am about to describe are simple: a pair of scissors, some sheets of paper, and a blackboard. (I know. You call it a chalkboard and it's sometimes green—so what else is new!)
Black Jack
Authors: Molinoski Marie
Published: October 2020

Everyone enjoys games, and games can be an enjoyable and meaningful way to reinforce basic concepts or provide drill in a way that is not boring. During the past few years I have used games with seventh- and eighth-grade students and have been pleased with the results. The successful use of the games and the enthusiasm of the students have enco uraged me to make up mathematics card games of my own. “Black Jack,” which is one of mine, provides practice with positive and negative numbers. It is based on the actual card game and is easy to learn.
Another Look at Least Common Multiple and Greatest Common Factor
Authors: Henry Loren L.
Published: October 2020

Most contemporary middle school mathematics programs use the notion of prime factorization to obtain the least common multiple and the greatest common factor of a pair of natural or whole numbers. Success in determining the least common multiple or greatest common factor for a pair of numbers then depends on the ability to obtain the prime factorization for any given number. The main disadvantage of this approach arises when either of the pair of numbers is quite large. For example, determining the least common multiple of 2464 and 7469 by prime factorization involves knowledge of divisibility tests for primes and of the primes themselves. The purpose of this paper is to examine another method for obtaining the least common multiple and greatest common factor of a pair of numbers without using prime factorization. These methods provide opportunities for students to make and test conjectures about the possible generalizations of the results to more than two numbers. Such conjecturing should aid students in developing problem-solving skills.
A Calculator Activity That Teaches Mathematics
Authors: Lappan Glenda , Winter Mary Jean
Published: October 2020

The purpose of this article is to present a “calculator activity” that has many variations and affords many opportunities for the teaching of mathematics to children in the upper-elementary grades. It has been received with enthusiasm by children in grades three through five.
A Visual Approach To Decimals
Authors: Schmalz Rosemary
Published: October 2020

Many manipulative materials are used in the primary grades to teach place value. However, when this concept is extended beyond whole numbers to decimal fractions, manipulatives are noticeably absent. In most books, explanation of decimals is entirely dependent on knowledge of common fractions
Using Tables to Solve Some Geometry Problems
Authors: Bright George W.
Published: October 2020

Organization of data in tables is a technique that can be used to solve counting problems in geometry. The purpose of this paper is to illustrate the use of this technique in the solution of five problems
Auditor's Report
Authors: McGivern Raymond H.
Published: October 2020

We have examined the accompanying Balance Sheet of Funds of The National Council of Teachers of Mathematics as of 31 May 1977 and the related Statements of Revenues and Expenses and Statement of Changes in the Fund Balances prepared for the fiscal year then ended. Our examination was made in accordance with generally accepted auditing standards and accordingly included such tests of the accounting records and such other auditing procedures as we considered necessary in the circumstances.
What's Going On
Authors: Donnelly Gawronski Jane
Published: October 2020

Alaska Instructional Diagnostic System (AIDS) provides testing and instructional support in four parts: a comprehensive set of mathematics objectives, instructional resources to identify promising instructional materials or practices, a communications network to make the system accessible in remote areas of Alaska, and provisions for staff development. For additional information contact Allen Barnes, Director, Southeast Region Resource Center, 127 S. Franklin Street, Juneau, AK 99801.
Meet the Zorkies: A New Attribute Material
Authors: Massaro Lettieri Frances
Published: October 2020

Attribute materials are valuable instructional devices. Their structure and use help develop a better understanding of mathematics. There is a continuing need for varied types of attribute materials that teachers can easily reproduce and adapt for classroom use. For these reasons, the author has developed a set of attribute pieces called the “Zorkies.” To accompany the Zorkie pieces, a sequential series of activities has been designed to develop fundamental skills essential to understanding the concept ofnumber.
Variations on Rummy
Authors: Nelson Rebecca S.
Published: October 2020

Rummy is a sufficiently interesting card game for even adults to spend leisure time in its pursuit. Because of this high interest in the game, variations on rummy can provide many hours of excellent practice for related mathematical concepts at both the pictorial and abstract levels. This practice can be offered without requiring any paper grading by the teacher and, since only three to five players are needed to play rummy, the wise teacher may provide for individual differences by careful assignment of students to the appropriate game.
Access to Multiplication Facts
Authors: Vigilante Nicholas J.
Published: October 2020

“Memorize your multiplication facts” is a phrase that rings through the homes and schools of this land. “Nobody knows their times tables” implies a conspiracy provoked by children to heighten the level of anxiety of adultsor so it seems. I am confident, however, that all children would be delighted to satisfy us all and would be able to do so if they were provided with the appro-priate “access” to the multiplication facts.
Let's Do It: Let Squares Do Their Share
Authors: Dana Marcia E. , Montgomery Lindquist Mary
Published: October 2020

Harnessing square power could save teachers a lot of energy. We all know squares are aesthetic creatures full of symmetries, congruence. similarities.
Teaching Measurement in an African Village
Authors: Ryan W. J.
Published: October 2020

Several years ago, while undertaking a research project in Africa. I had the good fortune to meet a bright young teacher with a particular interest in mathematics. Mr. Gaspar Duri was born in the lnyanga Mountains on the border of Mozambique and Rhodesia.
Rational Counting
Authors: Liedtke W.
Published: October 2020

Most children of four to five years of age know the difference between cats and dogs, or cats and chickens. Even when two very different types of dogs or pictures of dogs—a dachshund and a Saint Bernard, for example-are presented to young children, most children will call both animals “dog,” although these dogs are obviously very different in size, shape, and color. As a result of a variety of past experiences, the class, dog, has been well established in the minds of the children.
My Favorite Lesson: Mrs. Weill's Hill: A Successful Subtraction Method for Use with the Learning-Disabled Child
Authors: Weill Bernice F.
Published: October 2020

Subtraction can prove to be a frustrating problem for many children, especially the learning-disabled child. With the use of “Mrs. Weill's hill,” many children have learned to compute correctly the answers to otherwise difficult subtraction examples.
Constructing Magic Square Number Games
Authors: Bernard John E.
Published: October 2020

How often have you seen children fill page after page with tic-tac-toe games and hoped for a way to direct their energy and enthusiasm into the learning of mathematics? This article describes how magic squares can be used to generate an assortment of number games that are “the same as” tic-tac-toe. Perhaps these games will be prized not only for their educational value, but also because they provide tic-tac-toe with stiff competition in the “interest- getting department.”
Exploring the Multiplication Table and Beyond
Authors: Cacha Frances B.
Published: October 2020

An exploration of the multiplication table for patterns and relationships provides students with an opportunity to increase their understanding of mathematics. In the process, they are reinforcing their knowledge of number facts and practicing their computational skills. But perhaps more important, in their search lor patterns and relationships children are not only learning to verbalize their discoveries and to make generalizations about their findings, but also they are developing critical and creative thinking skills.
Measuring Attitudes Toward Mathematics? Some Questions to Consider
Authors: Michaels Linda A. , Forsyth Robert A.
Published: October 2020

In the last decade or two educators have become more and more concerned with the affective outcomes of educational programs. The development of a positive attitude toward the subject being studied is probably one of today's most prevalent educational goals. Many teachers believe that a student's attitudes toward a school subject will affect that student's achievement in the subject.
Math in the Shade
Authors: Beede Rudy B.
Published: October 2020

What do word-search puzzles and flashing scoreboards have in common? They inspired the shading puzzle described here. Maybe this little idea will help to motivate your students to some more computation practice.
One Approach to the Problem of Mastery
Authors: Adams Sam , Schilling Guy
Published: October 2020

Mastery of computation facts is a major task confronting elementary school arithmetic students. For example, there are one hundred basic facts in multiplication, and students are crippled in their efforts in other aspects of this operation until they have mastered the basic facts.
Consider Your Alternatives
Authors: Spitler Gail
Published: October 2020

There are numerous procedures for performing addition, subtraction, multiplication, and division. For example, some people would write the subtraction 452-276 as shown in figure la. rather than as in lb. These are examples of using different algorithms to subtract. An algorithm is simply the step-by-step procedure for completing a mathematical process or computation.
Let's Do It: Wallpaper Caper
Authors: Lindquist Mary Montgomery , Dana Marcia E.
Published: October 2020

Get a sample wallpaper book or some old pieces of wallpaper and come wallpaper capering! Wallpaper is a fantastic source for many problems involving geometry, statistics. measurement, and estimation. The capers we have suggested involve these types of problems, but you may think of capers that involve computation, probability, or other topics in a comprehensive mathematics program.
Graphing in the Primary Grades: Our Pets
Authors: Jacobson Marilyn
Published: October 2020

There are two types of graphing skills that children need to acquire: (1) the ability to collect, organize, and display information, and (2) the ability to interpret information presented by a graph. These skills are developed through experiences with graphs. Incorporating graphing activities into an elementary classroom program is often possible, but neglected. “Our Pets” is an example of the steps that can be followed to provide a classroom graphing experience. Mrs. Quinn's class was a combination first and second grade.
Ideas
Authors: Bright George W.
Published: October 2020

Ideas for this month is a series of puzzles that give students opportunities to use logical reasoning with a variety of concepts.
Probability in the Intermedicate Grades
Authors: Enman Virginia
Published: October 2020

Because probabilistic events saturate our conversations and daily lives, I planned a series of experiences in evaluating and understanding chance for my fourth grade. Although many of my students had an intuitive understanding of chance events before we studied probability, many also employed a hitor-miss approach and jumped to conclusions without evaluating the evidence. As a result of their study of probability, the children developed more systematic thinking and understanding of basic probability ideas.
A Case and Techniques for Computers: Using Computers in Middle School Mathematics
Authors: Hatfield Larry L.
Published: October 2020

Computers are rapidly becoming accessible to everyone. The costs of purchase have continued to decrease, with the recent mini processors and microprocessors representing pricing breakthroughs, and inexpensive microcomputers being promoted as persona l, home computers. Though much of their suggested usages to date relate to family leisure or home management, some vendors offer packages for computer-based games and drills involving mathematical ideas. Instructional programs will become increasingly available as the marketplace develops. Today's middle school students are growing up in a computerized society. Students probably feel more comfortable (often excited and curious) with the prospects of “everyman” routinely using computers than do many adults, who still view computers as complex and futuristic.
Critique on the Chisanbop Finger Calculating Method
Authors: Greenwood Jay
Published: October 2020

During the early part of 1978, the Chisanbop Finger Calculating Method was featured on the Johnny Carson Show. The demonstration of Chisanbop on this show generated tremendous interest in and curiosity about the method. The Curriculum Department of Multnomah County Education Service District alone received n umerous requests for information, materials, and inservice workshops on Chisan bop from teachers, administrators, and even parents.