bluuebunny/crossref_metadata_2025 huggingface dataset:
A description of a group-learning experience
Authors: Lilge S. A.
Published: October 2020

In the fall of 1970 I was assigned to teach the first course in a sequence of two mathematics courses required of all elementary education students, and I was informed that 120 students would be permitted to enroll in the course.
Banking interest
Authors: Murphy Elizabeth
Published: October 2020

A lmost everything that I had read concerning economically disadvantaged and culturally deprived children proved to be accurate; but I was amazed at the amount of spending money my third-grade pupils possessed. An experienced, wise teacher suggested that the parents were trying to compensate to the children for other materialistic and psychological disadvantages. Nevertheless, the pocket money created problems for the children. When it was not lost or stolen, it was spent on dill pickles and soft drinks for breakfast or, worse yet, on paper tattoos, wax teeth, or some other toy that distracted attention in the classroom.
Teaching about “about”
Authors: Trimble Harold C.
Published: October 2020

To many adults mathematics is a mystery, an occult science beyond their powers of reason. To test this bald statement, talk to boys and girls of high school age and to adults. Listen to what they say. Observe what they do in simple problem situations that involve numbers. Notice how they try to “remember what to do” or begin to perform random calculations. Notice how few people wade into a problem confident of their own good sense.
Things You Can Try: Don't miss the train
Authors: Porlier Corinna
Published: October 2020

In our fast-moving society of schedules, everyone finds a need for telling time, but whose responsibility is it to teach this critical topic? Is it the teacher's? Is it the parent's? Or, is the child left to learn on his own?
Using classroom lights to teach the binary system
Authors: Morgenstern Frances B.
Published: October 2020

On a recent visit to a fourth-grade classroom, I caught part of a discussion on computers. Computers, like rockets, have great appeal for children because of their aura of importa nce and contemporaneousness. In the course of this particular discussion, one child commented that computers “use base two.”
Teaching elementary school mathematics: A simplified model
Authors: Pikaart Len , Travers Kenneth J.
Published: October 2020

Teachers are decision makers. Every day requires decisions about what students should learn and what should be done to teach them. In their planning for daily lessons or for units, teachers develop objectives and activities, and, in so doing, they make decisions. Teachers also judge when their students have attained the desired goals for the lesson or unit. Perhaps more importantly, teachers decide what to do differently to facilitate learning in future lessons. Maybe the lesson does not go well; and, unexpectedly, the children have difficulty in grasping a concept. Sometimes a new and valuable bit of learning is discovered almost by accident. Or again, the criteria for judging the attainment of concepts may have to be changed because of an unanticipated development during the lesson. These and other kinds of decisions are made so frequently that the teacher may not be aware of making many of them. Yet, students are continually affected by such decisions.
Hidden implications for change
Authors: Thompson Madeleine Gardner
Published: October 2020

In connection with a graduate course in educational psychology that I was taking at a university in Washington, D.C., I became involved in an interesting project. I wanted to do something active while I was taking the course, and so I decided to tutor a young child—this would give me experience in explaining my subject and also help me to see how I related to children in a teaching situation.
Practice and discovery: Starting with the hundred board
Authors: Jones Margaret Hervey , Litwiller Bonnie H.
Published: October 2020

Hundred boards are devices that can be used to assist in the learning and reinforcement of such mathematical ideas as multiples, factors, primes, composites, and checks for divisibility. Both the level of the experience and the mathematical generalizations that may be formulated depend on the mathematical maturity of the students. The activities described here have been used in college classes in elementary methods. If prospective teachers can be involved with the types of mathematical experiences that are appropriate in the elementary school, it follows that they will be better able to provide similar types of experiences in their own classroom.
Ideas
Authors: Immerzeel George , Wiederanders Don
Published: October 2020

Each IDEAS presents activities that are appropriate for use with students at the various levels in the elementary school. After you have chosen tire activities that are most appropriate for your students, remove the activity sheets and reproduce the copies you need. After a sheet has been used, add your own comments and file the materials for future use.
Discovery activities with area and perimeter
Authors: Brougher Janet Jean
Published: October 2020

Area and perimeter are taught from elementary school through high school and still many students manage to confuse area with perimeter and perimeter with area. The activities suggested here are discovery activities that introduce or reinforce some important geometric concepts and provide practice in finding area and perimeter of rectangles.
Things You Can Try: Using the compass for outdoor mathematics
Authors: Feifer Jeffrey P.
Published: October 2020

We are all aware of the importance and value of using the child's environment in his mathematics program. One way of accomplishing this is to use a compass. Such an activity is a particularly good experience for intermediate-grade children. It can provide practice in estimation, in linear and angular measurement, in division of rational numbers, and in geometry.
Bilingualism in measurement: the coming of the metric system
Authors: Bright George W.
Published: October 2020

At such time as the metric system is adopted as the measurement system in the United States, every American will develop some degree of bilingualism in the English and metric languages of measurement. The burden of encouraging this development will fall to a large extent on elementary school teachers, for they will have to confront the confusion of young children. But there are advantages that will accrue for those who learn to use the metric system. As teachers recognize these advantages and begin to exploit them, acceptance of the metric system will increase.
A geometry course for elementary teachers
Authors: Zweng Marilyn J.
Published: October 2020

Mathematics educators generally agree that elementary school teachers should know “something” about geometry. There is little agreement, though, about what that “something” ought to be. If one were to use the textbooks which claim to provide a course in “Geometry for Elementary Teachers” as a guide, we might conclude that the course should be a rehash of the synthetic Euclidean plane geometry of the high school with one chapter on the geometry of the coordinate plane tossed in for flavoring. There arc a couple of notable exceptions to this generalization, but these exceptions, which are in fact quite different from the course described above, do not have an apparent underlying scheme or intent.
Things you can try: Integer “football”
Authors: Demchik Virginia C.
Published: October 2020

Generally, students in the upper elementary and junior high grades are interested in sports. The card game “lnteger Football” uses that enthusiasm for sports as motivation for practice with directed numbers. The game is designed for use with an entire class or with a small group of students.
Reading and mathematics
Authors: Feeman George F.
Published: October 2020

Teachers of mathematics have long realized that many of the difficulties encountered by students in the learning of mathematics are reading difficulties related to the subject area rather than intrinsic mathematical difficulties.
Things you can try: from second base to third base
Authors: Alfonso Michael , Balzer Richard , Hartung Paul
Published: October 2020

You may have seen the game consisting of four cards–call them A, B, C, and D, for convenience—on which sets of eight numbers are written. (See fig. 1.) Using these four cards, Mr. Rhee asks a student to pick a number from one to fifteen and to tell him which cards the number appears on-whereupon Mr. Rhee quickly announces the number to the amazed student.
Things you can try: Another “sieve” for prime numbers
Authors: Rockwell Charles H.
Published: October 2020

Over the past several years I have enjoyed the articles in the arithmetic teacher relating to primes and to various uses and forms of prime number sieves. For use in our classes, we have developed a way of sorting out prime numbers that seems to have more uses and to provide more information than the usual sieve.
Practical paper models for number concepts
Authors: Fisher Nancy Capozzolo
Published: October 2020

The use of models in teaching elementary school mathematics has been extensively researched and recommended. Since number concepts and basic operations constitute a major part of the elementary mathema tics curriculum, a variety of models—extending on a continuum from Cuisenaire rods; Dienes blocks; and objects like sticks, straws, and buttons; to representations such as drawings and number sentences—have been recommended. The remainder of this paper is devoted to several uses of paperand-pencil models which are simple enough for children to construct. The descriptions of the models indicate the level of suggested use.
Ideas
Authors: Immerzeel George , Wiederanders Don
Published: October 2020

Each IDEAS presents activities that are appropriate for use with students at the various levels in the elementary school. After you have chosen the activities that are most appropriate for your students, remove the activity sheets and reproduce the copies you need. After a sheet has been used, add your own comments and file the materials for future use.
Repeating decimals
Authors: Winzenread Marvin R.
Published: October 2020

As we move away from the English system of measurement to the metric, more emphasis should be placed on decimal algorithms and less on algorithms using fractions or mixed expressions. Measurements in the metric system are given in terminating decimals instead of the mixed expressions used in the Engljsh system. For example, a common measurement using the English system might be 3% inches; in the metric it would be 9.2 centimeters.
The ubiquitous square
Authors: Granito Dolores
Published: October 2020

The teacher enters the classroom and asks the class to think of a square. A conditioned class would immediately envision a closed figure with four right angles and four equal sides. Fine, but what if it's not a geometry class. How about a history class, an English vocabulary class, an arithmetic class, or an algebra class?
Word problems—a mirror of society
Authors: Burton Grace M.
Published: October 2020

A popular word in the lexicon of educationists today is “relevance.” Though this word has not always been in vogue, there has never been a time when word problems were not couched in terms that had meaning for their readers. In 1871, travel problems were stated in terms of railroad trains and horse-drawn carriages. In 1971, problems dealt with jet plane schedules and automobiles. Each setting, however, was relevant to its own time. Each, in fact, is a mirror of aspects of the culture of that time.
Ideas
Authors: Immerzeel George , Wiederanders Don
Published: October 2020

Each ideas presents activities that are appropriate for use with students at the various levels in the elementary school. After you have chosen the activities that are most appropriate for your students, remove the activity sheets and reproduce the copies you need. After a sheet has been used, add your own comments and file the materials for future use.
Dramatizing division
Authors: Maxfield Margaret W.
Published: October 2020

The only “property” you need for this play is some fake money, in decimal units: ones, tens, hundreds, thousands, perhaps ten-thousands. Slips of color-coded construction paper will do, or game chips, but imagination in assembling props will pay big dividends in student interest, so consider such possibilities as painted rocks (perhaps prepared by primary grades during their crafts periods), small shells from a collection, bubble-gum trading cards, trading stamps, macaroni bows or shells (may be spray-painted silver or gold), various lengths of drinking straws, buttons (political campaign buttons).
Alan's geo-igloo
Authors: Burrows Darryl B.
Published: October 2020

Knowing my reluctance to throw away anything that might at sometime come in handy in our classroom, the children arc always turning up with odd bits and pieces. Parents say apologetically, “He would bring it. I kept saying it was broken and of no use, but he said you'd want it.” I am embarrassed sometimes as I explain that I really do like getting broken clocks, plastic bottles, bits of motorcycles, and wheels off prams. Our school is quite well off for storage space and we manage to find a usc for most things sooner or later.
Reducing fractions can be easy, maybe even fun
Authors: Wassmansdorf M.
Published: October 2020

Reducing a fraction or finding a fraction equal to a given fraction can be quite a task for the slow learner. By the time he lists all the factors of the numerator and all the factors of the denominator, finds the greatest common factor (GCF), and divides the GCF into the nume rator and the denominator, so much time has elapsed that the student is quite often tired and frustrated. A “fraction machine,” which the student himself can construct, may eliminate some of his frustration and give him a feeling of confidence. He is also able to keep up with the class when they begin adding and subtracting fractions.
A simple proof for a fun problem
Authors: Jansson Lars C.
Published: October 2020

Pick any four one-digit numbers (just so no three digits are the same) and write them down as one four-digit number. Even better, have your fifth- or sixth-grade pupiJs choose the numbers. Now take this number and rearrange the four digits so that they are ordered high to low as you read from left to right. Next, off to the side, again rearrange the digits, this time ordering low to high, and then drop the highest digit so that you have a three-digit number. Now go back and subtract this three-digit number from the high-to-lowordered four-digit number. For example, if you had chosen 3781 your subtraction problem would be 8731 − 137 =?.
Things you can try: Making drill more interesting
Authors: Patterson W. H.
Published: October 2020

Looking for ways to make drill more interesting, entertaining, and even fun? Isn't everyone? I have developed a little device that may help you provide more interesting drill sessions for your students. I call it a drill wheel.
Times without tears
Authors: Fishbach Sylvia
Published: October 2020

It wasn't until I was in my first year of teaching, struggling with both the “why” and “how” of multiplication and batting practically zero both ways that I made a startling discovery. Quite by accident, I heard a child reciting in singsong fashion as she jumped rope, “2, 4, 6, 8, 10.” I translated the chant from a game on the playground to a game in the classroom. Applying the song to the numerals from one to ten, the children and I constructed the matrix shown in figure 1 on the blackboard.
Ideas
Authors: Immerzeel George , Wiederanders Don
Published: October 2020

Each ideas presents activities that are appropriate for use witf. students at the various levels in the elementary school. After you have chosen the activities that are most appropriate for your students, remove the activity sheets and reproduce the copies you need. A fter a sheet has been used, add your own comments and file the materials for future use.
Developing a “competency–based” teacher education program: a report on a project
Authors: Brown O. Robert , Morrison R. Ruel , Byrne Mary Ann , Cooney Thomas J. , Davis Edward J. , Mahaffey Michael L. , McKillip William D. , Wilson James W. Wilson
Published: October 2020

Interest in competency-based instruction has been evident at all levels of education. The Georgia Elementary Mathematics Teacher Education Project (GEMTEP) was designed to develop a “competencybased” training program in mathematics for inservice and preservice elementary teachers.
Some difficulty in the language of sets
Authors: Schoen Harold L.
Published: October 2020

A set is a well-defined collection of objects. The objects in the set, called elements, can be almost anything-people, chairs, numbers. On the surface, this is a very simple idea that is basic to all mathematics. As long as sets of physical objects are observed and manipulated, the concept remains a simple one. Difficulties begin when symbols are adopted to communicate the idea of sets and their elements. If any mathematics is to be learned from the use of sets, however, a meaningful language is necessary.
An observation on patterns
Authors: Johnson Martin L.
Published: October 2020

Patterns abound in mathematics. It is generally believed that the recognition of patterns in numbers facilitates the learning of mathematics. However, a recent experience of mine showed quite clearly that children will sometimes “discover” patterns that result in the attainment of incorrect answers.
Mathematical aspects of the attribute games
Authors: Coltharp Forrest L.
Published: October 2020

There may be elementary classroom teachers who have had no contact with the attribute games or activities, but the purpose of this article is not to introduce teachers to the fun and accomplishments that can be experienced through the use of the various attribute games. Primarily, the author would like to direct attention to some of the mathematical aspects of the “games that we play,” to suggest a few games, and to indicate some sets of objects that can be used successfully for attribute games.
Using research in teaching: Solution methods used in solving addition and subtraction open sentences
Authors: Grouws Douglas A.
Published: October 2020

Open sentences arc an in tegral part of the mathematics curriculum in contemporary elementary schools. The level of children's performance in solving simple addition and subtraction sentences at different grade levels has been studied and reported in several places, including this journal.
Discovery on a geoboard
Authors: Aman George
Published: October 2020

The geoboa rd is one of the more versatile teaching aids that has been used successfully in the elementary classroom. In Syracuse we have made our own geoboards from 9″-by-9″ squares of plywood. On each board we have made five rows and five columns of nails (1″, round-beaded). If the distance from the outer nails to the edge of the board is half the distance between two nails, then several geoboards can be used together to make a larger geoboard. Given a handful of rubber bands (preferably multicolored) a student (or teacher) is ready to explore and discover.
Nebuchadnezzar, seller of newspapers: an introduction to some applied mathematics
Authors: Papy Frédérique
Published: October 2020

The lessons related here were taught with a class in the fourth year primary (age 9) in the Normal School Berkendael in Belgium by Mme Frederique Papy. The children in the class had been for three years in a modern program that used the Minicomputer and Papy's graphing method. The account that follows has been taken from the fourth volume of Children and Mathematics, which is to be published by Didier.
The numerical coding of information
Authors: Swerdlin Richard
Published: October 2020

The notation “6-4-3” can make one person literally jump for joy, while it activates the ulcer of another. Why? It conveniently summarizes baseball action: the ball was fielded by the shortstop, who threw to the second baseman, who threw to first to complete a “double play.” The notation reflects a numerical code.
Using uniform structures to ease learning
Authors: Berenson Lewis
Published: October 2020

The more things change, the more they are the same.” I recalled this maxim one day when my students were struggling to understand the subtraction of signed numbers.
Ideas
Authors: lmmerzeel George , Wiederanders Don
Published: October 2020

Each ideas presents activities that are appropriate for use with students at the various levels in the elementary school. After you have chosen the activities that are most appropriate for your students, remove the activity sheets and reproduce the copies you need. After a sheet has been used, add your own comments and file the materials for future use.
Hindu-bobtailed multiplication: An efficient mathematical algorithm
Authors: Ercolano Joseph
Published: October 2020

In the mathematics of finance, as well as in numerous engineering calculations, it often happens that one is required to perform the multiplication of two numbers, each of which contains a considerable number of digits to the right of the decimal point, and round off the product to a desired number of places (considerably fewer relative to the places appearing in the original numbers).
Preservice laboratory experiences for mathematics methods courses
Authors: D'augustine Charles H.
Published: October 2020

A criticism made frequently by students in colleges of education is that their methods classes are not sufficiently related to work with children.
Efficiency problems
Authors: Willcutt Bob
Published: October 2020

Multibase arithmetic blocks lend themselves to many fundamental mathematical concepts and skills. An activity that has been highly successful for me in working with students involves a sequence of efficiency problems. These problems are full of patterns, generalizations of basic algebraic and geometric relationships, and excitement for students.
IDEAS
Authors: Burns Marilyn
Published: October 2020

Measurement is the theme to start this school year's IDEAS. The activities here are designed to give the children measurement experiences that are truly personal, encouraging them to learn more about themselves and their classmates in a mathematical way. These activities also provide experiences with ratio and proportion, graphing, and estimation.
Let's Do It!: Developing the concept of linear measurement
Authors: Bruni James V. , Silverman Helene
Published: October 2020

Many children find it difficult to use measuring instruments for linear measurement. One of the problems seems to be the child's lack of the realization that linear measurement is continuous. Another problem seems to be the repeated use of a unit of measure in the same way each time. Children also need to develop an appreciation of the approximate nature of measurement.
Patterns from a birthdate chart
Authors: Bernstein Robert , Barson Alan
Published: October 2020

A chart like the one shown in figure 1 was developed to give children an opportunity to discover prime and composite numbers. The chart was displayed and the children were asked what they observed in the chart. They noted that each of the first three symbols was a different shape. And they saw that the representation for 4 was made up of 2 with 2. They spotted that the symbol for 5 was unique, but 6 was made up of 2 with 3. Some children stated that the symbol for 4 was made up of 2 and 2. Others said it was “built with two 2s.” It appeared that some students relied on addition while others referred to multiplication.
A simple balance beam: construction and uses
Authors: Yvon Bernard R.
Published: October 2020

The following is an illustration of how a simple, inexpensive, homemade device can be developed and used as an effective teaching aid. Several different commercial models of simple balance beams are available, but they can also be made by teachers, and sometimes even by students, at a small cost.
IDEAS
Authors: Burns Marilyn
Published: October 2020

Ideas for this month provides experiences for in vestigating whole number patterns. Have you ever played the game of Monopoly? Can you picture the Monopoly board in your head? See where GO is? Remember where the four railroads are? What about Boardwalk and Park Place? How did you learn to visualize the board? The answer probably is that you did it by logging many hours playing the game. Your goal certainly was never to try to carry about a mental image of the Monopoly board; this accomplishment came from lots of experience with the game. And it was an effortless achievement.
A new approach to the Council's yearbooks
Authors: Hatfield Larry L.
Published: October 2020

Members of the NCTM are certainly famili-ar with the excellent volumes produced as the Council's yearbooks. These yearbooks continue to serve as significant references throughout the varied facets of mathematical education. The dedicated leadership of the yearbook editors and the unselfish contributions of many authors have assured the high quality we have come to expect as each of the thirtyseven yearbooks has been released. Long and meticulous planning and production have often resulted in a considerable time lag between the inception of a theme and the presentation to the Council by the editor at an annual meeting. At the same time, the costs of production have increased, driving up the price paid by member. Acting under its charge, the Publications Committee has kept a close watch on these developments.
Active games: an approach to teaching mathematical skills to the educable mentally retarded
Authors: Taylor George R. , Watkins Susan T.
Published: October 2020

Pragmatic experience has shown that curriculum adjustment must be made if schools are to meet the everyday needs of educable mentally retarded children. Many retarded individuals have been unable to cope successfully with the curriculum of the regular grades; they are too different from the average child to adjust to the usual academic demands. For this reason various forms of instructional procedures have evolved. “Active games” are an example.
Addition for the slow learner
Authors: Batarseh Gabriel J.
Published: October 2020

Teaching single-column addition to the slow learner and the educable retarded child is relatively easy. The difficulty arises when you try to teach these students the addition of multiple-digit numbers and the concept of “carrying.” A method that helps to develop the idea of carrying and uses the skills developed in the learning of single-column addition has been developed and used with success at the Coastal Center. An example will serve to explain and illustrate the method.
Annual Financial Report
Authors: Egsgard John C. , John Lenore S. , Smart James R. , Wells David W. , Kreigsman Helen , Gates James D. , Tewell James R.
Published: October 2020

The financial picture for the NCTM is good. Adjustments in membership and subscription fees made during the fiscal year 1973–74 have helped the Council to meet the rising cost of inflation. The Financial Policies Committee believes that the Council can still manage a financially sound operation, provided special attention is paid to balancing the budget in the publications area. The FPC hopes to assist the Publications Commtttee this year to come close to a balanced budget.
Materials, competence, and confidence: products of a district mathematics laboratory
Authors: Bitter Gary G. , Mikesell Jerald L.
Published: October 2020

The Mesa Public Schools in Mesa, Arizona, is a school system with 26,000 students. Improvement in mathematics achievement scores had been a basic goal of the district for several years. Teachers had indicated a willingness to make a concerted effort to improve mathematics instruction, but they felt that the district should provide more than a textbook. Concrete materials, games, puzzles, and equipment for various activities were in limited supply in the school district and, therefore, most inservice work and workshops went for naught insofar as improving the attitude of children and teachers toward mathematics. With this in mind, the district, in cooperation with the staff at Arizona State University, decided that a teacher-involvement program needed to be implemented.
“Think Metric Week” in Minneapolis
Authors: Taylor Ross , Gawronski Jane Donnelly
Published: October 2020

Metric education is a topic of great interest and concern to professional educators and community members, and many groups are looking ahead to metrication. In the Minneapolis public school system a committee of consultants, mathematics and science resource teachers, classroom teachers, and parents met to develop a program of activities for metric education. One idea that met with great enthusiasm was a “Think Metric Week.” Its purpose was to initiate a metric education program in the Minneapolis public schools; activities were planned to involve all elementary, junior high, and senior high schools and to include various subject areas. The idea was proposed to the Board of Education with the result that the week of May 14–18, 1973, was designated as “Think Metric Week” by the Board.
Understanding (in the style of St. Paul, I Corinthians 13)
Authors: Crittenden William B.
Published: October 2020

Though I figure with the skills of men and computers and have not understanding, I am become as a mechanical toy, or a lifeless robot.
Using research in teaching: Low-stress subtraction
Authors: Hutchings Barton
Published: October 2020

The term “low stress” is applied to a set of algorithms that, among other things, allow computation with a minimum of stress. The techniques cover whole-number operations for addition, subtraction, multiplication, and division. The algo rithms were developed by the author, but research on them has involved several colleagues and many students. Reports of the research are being prepared for publication.
The large-blue-triangle: a matter of logic
Authors: Vance James H.
Published: October 2020

Learning activities that encourage students to think logically and to discover valid modes of reasoning are receiving increased attention in the elementary mathematics curriculum. Several excellent games through which children learn to ask good questions and to make efficient use of available information have been described in the Arithmetic Teacher (Gessel et al. 1972, Aichele 1972). A concrete setting for a variety of experiences for developing principles of logical reasoning is provided by a set of attribute blocks (Dienes and Golding 1966). In this article a guessing-type game based on these materials is described. While the game in its simplest form can be played and enjoyed by children in the primary grades, it can also be used as a point of departure for worthwhile activities for junior and senior high school students.
Let's Do It!:Using geostrips and “angle-fixers” to develop ideas about shapes and angles
Authors: Bruni James V. , Silverman Helene
Published: October 2020

Geometry is an important, excitig part of elementary school mathematics. Children can be involved in relating mathematics to shapes in their environment. The activities described here suggest one way to help children develop some basic ideas about simple closed shapes, angles, and triangles. By constructing models of geometric shapes and physically transforming those models, children can examine the changes that occur with a transformation. This can help organize and synthesize thinking about basic geometric concepts. It can also serve as a foundation and a springboard for activities involving the use of a ruler, compass, or protractor.
The game of “Race To”
Authors: Kurtz Barry L.
Published: October 2020

Race To is a variation of the ancient game of Nim. One player designates an eligible set of whole numbers {1, 2, …, N} and a goal number (usually much larger than N). The other player starts either by calling out an eligible number or by declining to begin. The game sta rts at 0 and the first player selects one eligible number and adds it to 0. Then the second player selects an eligible number and adds it to the previous total. The player to add a number that brings the total to the goal number is the winner. A winning strategy exists for the player who allows his opponent to select the eligible numbers and the goal number.
How to give your class the business (math)
Authors: Shapiro Joseph B.
Published: October 2020

Good morning, students. My name is Mr. Shapiro. I will be your mathematics teacher this year. During the course we will review the basic number facts of addition, subtraction, multiplication, and division of whole numbers. Then we will work on fractions, decimals, and percents. We will also try to ….”
Subtraction: regrouping with flexibility
Authors: Cacha Frances B.
Published: October 2020

Students are often unsuccessful in subtracting multidigit numbers with one or more zeros in the minuend because they are not able to regroup numbers successfully. When students are able to be more flexible in the regrouping there are fewer opportunities for errors.
Let's Do It!: Using a pegboard to develop mathematical concepts
Authors: Bruni James V. , Silverman Helene J.
Published: October 2020

Very often, in planning to teach mathematics, we first decide what concepts and skills we will stress and then choose activities and materials that can be used to help develop those concepts and skills. We might decide to use plastic counters for basic ideas about number, or an abacus for teaching place value, or assorted geometric figures to teach shapes. We recognize the need for the child to develop these ideas through experiences with concrete materials.
A bulletin board idea for your room
Authors: Hutcheson James W.
Published: October 2020

Enterprising teachers seize every opportunity to enrich the learning experie nce of each student. These teachers know that learning is enhanced when the learner is motivated to learn and when the learning environment is conducive to learning. Bulletin boards have traditionally served to motivate interest in a new topic and to create a mathematical environment in the room. Busy teachers need a fresh bulletin board display that is both motivating and attractive while being easy to make.
Mortimer Mathematics
Authors: Yyon Bernard R. , Walo Trudy J.
Published: October 2020

All learning in mathematics can and should be enjoyable. If you, as a teacher, believe in this premise, and act on it, your tudents will more likely enjoy their classroom experiences and acquire knowledge and skills at the same time. Modern methods of teaching mathematics require the use of a wide range of teaching materials. Other things being equal, the greater the use of effective aids, the greater will be the pupils' grasp of abstract ideas and the greater their motivation to learn. With these things in mind, Mortimer Mathematics was devised as a teaching aid for mathematics in a kindergarten classroom.
Computational skills: a point of view
Authors: Trafton Paul R. , Suydam Marilyn N.
Published: October 2020

The question, Why don't children learn to compute better? is being asked frequently by school administra tors, teachers, and parents, which reflects the current concern over this aspect of the curriculum. While the evidence on children's performance today as compared to that of other children in previous times may be mixed, it is clear that performance could be improved and that consideration again needs to be given to improving the learning of number ideas and the acquisition of computational skills.
Let's Do It!: An introduction to fractions
Authors: Bruni James V. , Silverman Helene
Published: October 2020

Very young children have had many experiences involving the concept of a whole and its parts. They have shared food: a beverage poured into glasses; a cake, sandwich, pie, candy bar, pizza, orange, melon, or apple cut into slices or parts. While working on activities in the classroom, they have assembled puzzles, played with geometric shapes, broken up clay, and poured sand and water-additional experiences with whole-part relationships. The common argument between two children over who has the “bigger half,” however, may indicate that although children understand a half as one of two pieces, the concept of equivalent pieces sometimes eludes them. Activities with a set of geometric shapes may help to focus children's attention on the need for equivalent pieces and provide the basis for understanding equivalent fractions.
A new multiplication algorithm: on the complexity of simplicity
Authors: Brown Stephen I.
Published: October 2020

It sometimes happens that by looking at the familiar or the dull from a new perspective we open up unusual horizons for ourselves and for our students as well. Though we may agree for a variety of reasons that much of the curriculum is in need of revision, it is shortsighted to conclude for any content area that it ought to be eliminated solely on the grounds that it is intrinsically dull and cannot generate worthwhile mathematical thought. What follows provides an example of how 1l ts poss ible, by examining some old and familiar multiplication facts with a new metaphor in mind, to uncover an entirely new algorithm for multiplication. (See Brown 1974 for additional educational discussion.) The “fallout” along the way also opens up many avenues for exploration that penetrate beyond the algorithm itself. There is much to be said for introducing the hand-held calculator in the elementary grades, but we hope to show why the elimination of a search for algorithms for the standard operations of arithmetic is not one of them.
A diary of remedial instruction in division—grade seven
Authors: Swart William L.
Published: October 2020

The problem was one well-known to upper elementary and junior high school teachers—a student who has been instructed for several years in the rote application of an algorithm, who is generally not successful with it, but whose mental set prevents him from accepting a different approach. Laurie and Patty were perfect examples.
Ideas
Authors: Burns Marilyn
Published: October 2020

“Mathematizing the Alphabet” is the theme for this month's IDEAS section. The activities are presented in a sequence starting with the simpler investigations. Levels are indicated for your general use, but choose the worksheets that best suit your own students.
Let's Do It! An introduction to weight measurement
Authors: Bruni James V. , Silverman Helene
Published: October 2020

In their play, young children generally enjoy trying to balance things—themselves on a balance board, each other on a seesaw, objects on a mobile, and piles of blocks stacked high on each other. These natural tasks from a child's play can be extended to further develop the concept of balance and how scales function to measure weight.
Is immediate reinforcement appropriate?
Authors: Jencks Stanley M. , Peck Donald M.
Published: October 2020

Contrary to popular opinion, it is frequently not wise to immediately reinforce a child's answer with “right” or “wrong.” For example, just a few days ago a boy was trying to rewrite expressions like
Your Council at Work: Meetings Committee
Authors: Cohen Louis S.
Published: October 2020

The Meetings Committee is responsible for all NCTM conventions and conferences not specifically designated as charges of other committees. Their duties include site and time selection, local arrangements, coordination with other major NCTM committees, and program planning, implementation, and evaluation.
Let's Do It!: Organizing a metric center in your classroom
Authors: Bruni James V. , Silverman Helene J.
Published: October 2020

Most teachers will readily agree that the best way for elementary school children to learn metric measurement (or any kind of measurement) is through direct experiences that involve measuring real things in different ways. Convinced of the merit of “active involvement” measurement experiences, we face the difficult problem or how to organize classroom activities so that these experiences can happen
“New math” in the gay nineties
Authors: Deatsman Gary A.
Published: October 2020

I had always assumed that the development of school mathematics curricula since the nineteenth century had been characterized by fairly steady progress accelerated by the “new math” movement of the last decade. Back in the days of horse and buggy, mathematics education was supposedly strictly rote learning of rules and algorithms with little or no understanding. Endless drill was employed to produce the army of accurate human calculators needed before machines were developed to take over this work.
The study of space experiences: a framework for geometry for elementary teachers
Authors: Kerr Donald R.
Published: October 2020

Elementary school teachers, preservice or inservice, are not usually given the background in geometry that they need. Some college courses for elementary teachers contain no study of geometry. Those courses that do contain geometry may be limited to traditional topics in measurement, some terminology, and certain facts concerning familiar geometric shapes; or they may review the definitions, theorems, and proofs that the teacher has already had in high school. Judging on hearsay, experience, and an analysis of current mathematics texts for teachers, few courses are providing the teacher with what is needed.
What we can do with a × b = c
Authors: Erckmann Ruth
Published: October 2020

Our students are constantly asking for mathematics that is relevant to the needs of today's world. One way we can show relevance is by considering a mathematical model and then pointing out practical applications that use this model. We may also start with the word problem (the application) and then write the mathematical sentence (the model) that expresses the action of the problem. Consider the sentence a × b = c, the very simplest example of a multiplicative or divisive situation depending on which of a, b, or c happens to be the unknown. For the elementary school, we can limit our use to only the natural and the rational numbers.
Introducing decimal fractions with the meterstick
Authors: Ashlock Robert B.
Published: October 2020

Metersticks are appearing in classrooms throughout the United States as the more familiar yardstick is assigned a position of somewhat lesser importance. When children begin to use these metersticks they soon are talking of centimeters and millimeters, often with greater ease than their teachers. As we, together with the children, learn to “think metric,” we do well to consider the potential of a specific instructional use of a meterstick, that is, the use of a meterstick to introduce decimal fractions.
Using creativity in elementary school mathematics
Authors: Jensen Linda R.
Published: October 2020

When creativity is mentioned, a person often thinks of art or music and neglects the idea that someone can also be very creative in mathematics, science, or any of the other “academic” subjects. In order to cope with the future, children need experience in formulating their own problems and developing their own solutions rather than memorizing facts from a textbook.
Using research in teaching: Notes from National Assessment: processes used on computational exercises
Authors: Carpenter Thomas P. , Coburn Terrence G. , Reys Robert E. , Wilson James W.
Published: October 2020

Most assessment and evaluation measures check only for the result or answer obtained in a computation or in solving a problem. This note examines exercises from the Mathematics Assessment of the National Assessment of Educational Progress designed to examine some of the processes students use in doing computations, along with measuring their computation performance.
Your Council at work: Instructional Affairs Committee
Authors: Mcintosh Jerry
Published: October 2020

The Instructional Affairs Committee (IAC) is made up of ten members– the chairman, a representative of the Board of Directors, an NCTM staff member, and seven others. Each member except the NCTM staff member serves a three-year term. IAC meets twice yearly in various geographic locations. In recent years the committee has made a special effort to thoughtfully communicate with, and listen to, the ideas of local leaders in mathematics education. This exchange of ideas is designed to maximize the participation of NCTM members in IAC activities and to strengthen IAC contributions to the profession.
Behavioral objectives—are they restricting?
Authors: Mckeen Ronald L.
Published: October 2020

Are behavioral objectives that are relatively easy to come by worthwhile? Do they have value? Do they restrict the learner to achievement of predetermined cognitive goals? Does achievement of these cognitive goals have future payoff? The answers to these questions are relative. They must be framed with respect to a position on the role of “knowledge” in the curriculum. For Skinner (cited by Milhollan & Forisha, 1972) past “knowledge” is to be recapitulated through the curriculum and serve as a basis on which to build new knowledge. For Bruner (1963) “knowledge” is not the end product, but the means by which the learner becomes proficient at “getting knowledge.” For Bruner, then, the process of getting knowledge is paramount. From the first position it could be argued that “knowledge” as described by behavioral objectives should reflect quality and be judged worthwhile as an end product against some acceptable standard. From the second position it could be argued that the worth of a behavioral objective is the degree to which its acquisition promotes and develops certain knowledge getting processes.
The development of a modern mathematics curriculum in Africa
Authors: Alele Williams Grace A.
Published: October 2020

The introduction of modern mathematics into the mathematics curriculum of African nations had its beginning in 1960 in conferences and discussions between African and American educators. A consensus of these meetings was that a more lasting type of aid to Africa might take the form of assistance in educational institutions and programs. Thinking along such lines led to the creation of the African Mathematics Programme (AMP), which was based at the Educational Development Center (EDC) of Newton, Massachusetts.
IDEAS
Authors: Burns Marilyn
Published: October 2020

Investigating some of the mathematics of what we eat is the unifying theme for this month's IDEAS. The foods that are part of children's lives provide a way to deal with mathematics in several areas. Use these ideas as springboards. As you munch your meals and snacks, look for other mathematical possibilities
Your Council at work: Commission For The Education Of Teachers Of Mathematics
Authors: Hoffer Alan
Published: October 2020

The National Council of Teachers of Mathematics (NCTM) has been successful, through its publications and meetings, in helping to improve mathematics education. The Council has also worked actively to improve the education of mathematics teachers and to give teachers more control over their own profession.
A concrete approach to integer addition and subtraction
Authors: Bennett Albert B. , Musser Gary L.
Published: October 2020

A survey of modern elementary textbooks reveals that the concept of integer subtraction is usually introduced by using integer addition.
Ideas
Authors: Burns Marilyn
Published: October 2020

Telephones are tools in our daily lives. Most children in our schools have seen telephones all of their lives. The activities in this month's IDEAS use both the telephone and telephone directory to spark some mathematical investigations. It will be necessary to have at least six telephone directories for your telephone area.
Getting a good start in teaching metric measurement meaningfully
Authors: Doherty Joan
Published: October 2020

Studies of mathematics needed by people in all walks of life clearly reveal that some facility with measurement is needed by everyone. In the course of our lifetime, all of us will need to learn to measure many aspects of our envi ronment. The problems of teaching the measurement process will be compounded as the United States moves to an expanded use of the metric system. Articles in past issues of the Arithmetic Teacher have presented ideas on the history of our progress toward metrication, advantages of the metric system, metric measurement terms, materials available, pilot programs for developing plans for teaching the metric system in schools, and some ideas for classroom activities.