bluuebunny/crossref_metadata_2025 huggingface dataset:
National Council of Teachers of Mathematics: 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 1973, the related Statements of General Fund Revenues and Expenses and the Statements of Fund Balances. 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.
Catherine's discovery
Authors: Mitchelmore Michael C.
Published: October 2020

My daughter Catherine, aged 5, recently surprised the family at breakfast by announcing, “Mummy, the 4-times table is in the 2-times table.”
Mathematics games in the classroom
Authors: Kerr Donald R.
Published: October 2020

Games are fun, and it is important to have fun. Mathematical games in school are good because, in playing them, children have fun associated with a topic that in not always considered to be enjoyable. It is neither possible nor desirable to organize the bulk of mathematics instruction around games, but it is sometimes possible to develop games in such a way that they complement the regular mathematics instruction and thereby justify more classroom time. This article chronicles one classroom experience of the author in which a simple game was introduced to a fifth-grade class on a Friday afternoon.
Magic while they are young
Authors: Cox Anne Mae
Published: October 2020

To effect optimal learning for second graders it is essential that many forms of drill in the abstract basic processes of addition and subtraction be provided. The activities that have proved most successful arc those where a stratagem is used to motivate the children to do enormous quantities of practice. A number design, which the children choose to call “magic,” can provide such motivation and practice.
The case of the missing digit
Authors: Litwiller Bonnie H. , Duncan David R.
Published: October 2020

One problem often encountered by prospective elementary and junior high school teachers is that they learn involved, complicated mathematics without seeing applications or uses for this material.
Geoboard mathematics
Authors: Liedtke W.
Published: October 2020

Various reasons can be given for the universal success of the geoboard. Probably the main reason is that the geoboard is complex, yet patterned.
Things You can Try: Fracto
Authors: Molinoski Marie
Published: October 2020

Upper elementary and junior high mathematics teachers are always searching for ways of teaching or reviewing the relationships between decimals, percents, and fractions. Fracto is a card game designed to make the review a little more fun.
A simplified presentation for finding the LCM and the GCF
Authors: Sherzer Laurence
Published: October 2020

Given the prime factors of two positive integers, the least common multiple (LCM) of these two numbers is the product of the union of these prime factors, and the greatest common factor (GCF) is the product of the intersection of these prime factors. If we could just state this fact to our students and be understood, our job of teaching them to find the LCM or the GCF of two numbers would be greatly simplified. Unfortunately, as in most teaching, simple verbal statements do not suffice.
Things you can try
Authors: Crouse Richard , Shuttleworth Jan
Published: October 2020

Most mathematics educators would probably agree that the ability to motivate students is an essential condition for successful teaching. Some teachers seem to possess this ability innately and in abundance, while most of us have to work hard at trying to motivate students. Therefore, it would seem logical that if certain devices, problems, or techniques can be found that will help in this respect, then we should use them in our classes when appropriate. The problem described here is one that the authors have found to be extremely effective in motivating students in the area of computational skills.
Magic squares: would you believe…?
Authors: Pagni David L.
Published: October 2020

A magic square of nth order is a square array of n rows and n columns whose components are n^2 distinct integers. Furthermore, the sum of the numbers in any row, column, or main diagonal must always equal a constant—the “magic constant.– The array in figure I, then, is a magic square of 3rd order whose magic constant is the number 15.
Let's Do It!: Developing the concept of grouping
Authors: Bruni James V. , Silverman Helene
Published: October 2020

After a child has learned to count, the next important process for him to master is grouping. This implies considering objects as sets as well as individual entities. Most children find it difficult to conceive of objects as separate entities and as members of a set at the same time. Although teachers commonly use materials for counting, the use of materials for grouping is less frequent Manipulating objects to form new wholes is important to understanding grouping. Here are some techniques for developing an understanding of grouping.
A mathematics fair in the lower grades
Authors: Freeman William W. K. , Kroll Diana Lambdin
Published: October 2020

Athough mathematics fairs have sometimes included exhibits by children as young as sixth graders, we arc not aware of any fair that has had a demonstration like “Bransfield's Supermarket” in grade 2, in which small-fry bought groceries and took turn as check-out clerk. Even grade 1 took part in the mathematics fa ir at the Tower School. It was an “all-hands operation,” by groups in grades 1 through 4A, and 72 exhibits in grades 4B through 9.
Let's Do It!: Using cubes
Authors: Bruni James V. , Silverman Helene
Published: October 2020

Those wooden or plastic cubes often found in primary-grade classrooms can be a wonderful vehicle for learning some basic mathematical concepts. Children like to use the cubes for building all kinds of structures and teachers like to use them as concrete material for teaching addition and subtraction facts. But there is so much more that can be done with those beautiful cubes.
Tiger-bite cards and blank arrays
Authors: Smith C. Winston
Published: October 2020

The teacher held a manila folder in front of her as she looked out at her third-grade class. “Boys and girls,” she began, “today we were going to work with arrays, but on my way to school an accident occurred which makes that impossible.” A murmur arose from the class as all eyes focused on the teacher.
These three: minus, negative, opposite
Authors: Hall Wayne H.
Published: October 2020

Many confusions that exist in the minds of students arise primarily because of inconsistencies in the language used by their teachers. For example, many of the difficulties faced by the student just beginning work with negative numbers could be eliminated if teachers were more careful in their use of mathematical terms. Mathematical terms should be used consistently and inconsistencies that occur should be clarified.
A new algorithm for subtraction?
Authors: Ikeda Hitoshi , Ando Masue
Published: October 2020

To suggest a new algorithm in place of one that has had popular use over many decades can be very upsetting to many teachers. Such was the case when the subtractive algo rithm for division appeared. The new algorithm, however, gained popularity over the conventional division algorithm as it contributed to easier rationalization, especially in the early stages of learning long division. Such a painless transition makes one bold enough to suggest another change. This article proposes that a new algorithm replace the more commonly used forms in the subtraction of whole numbers.
Three observations of mathematics instruction in inner-city elementary schools: some issues for thought
Authors: Taback Stanley F.
Published: October 2020

During the academic year 1972–73, I had the opportunity to observe mathematics classes in a large number of “inner-city” elementary schools in New York City. All of the schools were located in extremely poor neighborhoods and served black and Puerto Rican children, for the most part. In this article I would like to describe three observations, each of which suggests a number of interesting questions and issues that the elementary school teacher may wish to consider. Not only will no attempt be made to offer prescriptive solutions to the problems delineated, but, as will become evident shortly, the author has no simple solutions to offer.
Deci-deck
Authors: Fisher John W.
Published: October 2020

Cards appear to have a universal fascination among children. Many important mathematical concepts (ordering, counting, and equality, for example) can be learned from traditional card games played with a standard deck. New decks based on equivalent suits of fractions or decimals can also be created and adapted to any card game the students may wish to play. A deci-deck is an example.
Choice + math = pleasure
Authors: Hodges Ethel , Downs Lavinia D. , Schwartz Herbert S.
Published: October 2020

Enthusiasm for learning is a major goal at the American School in Japan, but several years ago we became painfully aware that as far as mathematics was concerned, the children were far from enthusiastic. Our students, mostly American businessmen's children, usually did pretty well according to national test scores in the United States, but boredom, lack-luster mathematics classes, and tension were too common.
Six is a fascinating number
Authors: Hohlfeld Joe , Schwandt Lynn
Published: October 2020

This article is a sequel to “What You Always Wanted to Know about Six but Have Been Afraid to Ask” by Alan R. Hoffer in the March 1973 issue of the Arithmetic Teacher. The realization that other six addicts exist was a source of encouragement. Perhaps the observations about six noted below have been observed by other six fans, but sixy readers never tire of six!
Initiating task card activities with teachers
Authors: White Philip , Brownstein Bonnie , Wagner Victor
Published: October 2020

The Workshop Center for Open Education1 is a place where school personnel and members of the community may investigate their own interests and where they may participate in scheduled working sessions in an environment that supports the development and extension of learning.
Money on the number line
Authors: Sharkey Verena
Published: October 2020

Everyone wants money! Everyone needs money! Everyone uses money! Since these are all true statements teachers often relate other mathematical concepts to money as a means to foster the understanding of number value.
Guided discovery with magic squares
Authors: Atkinson Thomas P.
Published: October 2020

Magic squares have attracted considerable attention among elementary school teachers in recent years, as indicated by the appearance of several articles in the Arithmetic Teacher and other educational publications.
Let's Do It!: Graphing as a communication skill
Authors: Bruni James V. , Silverman Helene
Published: October 2020

Many children seem to have difficulty communicating mathematical relationships. As teachers, we often move too rapidly from concrete manipulation to the world of symbolic representation, without providing children with the tools necessary for the communication of mathematical ideas.
Think metric about weather
Authors: Freeman William W. K.
Published: October 2020

To use a language with facility, a person must think in that language. An English-speaking person can use French with facility only if he thinks in French; he is less fluent if he thinks in English and has to translate. In the same way, to use metric easily one must THINK METRIC.
Experiences with blocks in kindergarten
Authors: Liedtke W.
Published: October 2020

The availability of a great variety of manipulative materials in kindergartens today makes it relatively easy to capitalize on a young child's eagerness to explore and interpret the world around him. A set of blocks is just one such manipulative aid which is well suited for the provision of preschool experiences in mathematics. A variety of experiences based on the use of blocks are explored in the following paragraphs by presenting some sample problems. These problems could be posed to individuals or to small groups of children as they are engaged in free play. Some of the problems may also be suitable for large group presentations and discussions.
If you don't know how children think, how can you help them?
Authors: Pincus Morris , Coonan Margaret , Glasser Harold , Levy Lillian , Morgenstern Frances , Shapiro Herbert
Published: October 2020

Why do so many children have trouble computing in mathematics? There are undoubtedly many reasons; some simple, some complex. It seemed to us that one important aspect of a teacher's job is to determine how a child goes about getting the wrong answer. Careful examination of the kinds of errors made may reveal patterns that are quite logical to a child, if not to us.
Using research in teaching: Notes from National Assessment: perimeter and area
Authors: Carpenter Thomas P. , Coburn Terrence G. , Reys Robert E. , Wilson James W.
Published: October 2020

This is the second article based on the results of the National Assessment of Educational Progress (NAEP) to consider the process of measurement. In the October issue two NAEP exercises dealing with the primary concept of partitioning regions and sol ids into units of measure were examined. The resu lts of these exercises and the other research reviewed indicated that many younger students do not have any understanding of this fundamental concept that underlies area and volume measurement, and some misconceptions persist with many older students.
A human maze
Authors: Ring Art
Published: October 2020

A maze is usually designed for use with mice or rats. This activity turns things around. Students are required to find their way through a maze blindfolded. In doing so they not only learn for themselves something about mazes; they also have experiences in collecting, recording, and analyzing data.
Your Council at Work: Annual Financial Report
Authors: John Lenore S. , Smart James R. , Wells David W. , Kriegsman Helen , Devlin John , Gates James D. , Tewell James R.
Published: October 2020

The National Council of Teachers of Mathematics was able to live within its income during 1974–75, in spite of increased costs for most of our activities. In the Publications account, however. expenditures were again greater th an receipts: and it was deemed necessary to increase the prices of our publications.
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 1975, and the rela ted Statements of Revenues, Expenses, and Fund Balances. 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.
An attitudinal device for primary children
Authors: Dunlap William P.
Published: October 2020

Teachers are concerned about the atti tudes of children toward mathematics because there is a high positive correlation between achievement and attitudes. Many attitude sca les that will alert teachers to the feelings of children toward mathematics exist, but they require that children read several words or sen tences prior to making a response that indicates some attitude toward mathematics. Teachers of children in the primary grades or with reading difficulties need an instrument that does not involve readin g and will provide an indication of the children's attitudes toward mathematics. A simple device that meets these needs can be readily constru cted; it makes use of happy, neutral, and sad faces. Children look at a mathen1atical exercise and then color with a crayon the face that best matches their feelings toward that particular exercise. For example, in figure I the child looks at the exercise 2 + □ = 5, decides how he feels toward the exercise, and colors the -appropriate face.
JIGSAW MATHEMATICS
Authors: Martin Dennis S.
Published: October 2020

As a confirmed jigsaw puzzle addict and a teacher of mathematics, I have always been interested in how much work is left to be done after the easy edge of the puzzle is completed. I have noted that most standard puzzles are in a rectangular array and therefore, the percentage of edge pieces is easy to calculate.
The Möbius strip: an elementary exercise providing hypotheses formation and perceptual proof
Authors: Richardson Lloyd I.
Published: October 2020

An invitation to speak before the fourth-grade class of one of my former students had been accepted. As an enrichment lesson, I had decided to use the Möbius strip and to relate William H. Upson's story (Fadiman 1962), “Paul Bunyan versus the Conveyor Belt,” to the class. Beyond telling the story, any attempts toward hypothesis testing or looking for patterns would depend on class reactions.
Using research in teaching: Notes from National Assessment: addition and multiplication with fractions
Authors: Carpenter Thomas P. , Coburn Terrence G. , Reys Robert E. , Wilson James W.
Published: October 2020

Development of computational skills with fractions has long been a part of the upper elementary and junior high school mathematics program. Current movements toward metrication have led some individuals to suggest that decimals will receive more attention in the mathematics curriculum with a corresponding de-emphasis on fractions. The suggestion may find an increased number of supporters, as recurring evidence indicates that pupil performance with fractions is discouragingly low. An alternative point of view is that although metrication may somewhat alter work with fractions, their importance within the structure of mathematics and to applications justifies their continued emphasis in the curriculum.
ONE POINT OF VIEW: Let's put it all together
Authors: Trafton Paul
Published: October 2020

A new school year has begun. By now many or the initial activities and adjustments accompanying the opening of school are concluded and the program is almost in “full swing.” Although this is a busy period for first-year and returning teachers alike, it is a time to give careful thought to directions. goals. and approaches in curriculum areas.
Criteria for concrete models
Authors: Sowder Larry
Published: October 2020

This article suggests some criteria to keep in mind when using a pictorial or a concrete representation to support the treatment of a mathematical concept or sentence. The healthy trend toward such representations at all grade levels, not just the primary grades, must not develop into a blind stampede that uncritically equates concrete with good.
ONE POINT OF VIEW: It's in your hands
Authors: bnmerzeel George
Published: October 2020

As you can tell as you read the articles in this issue, things are happening in many classrooms with the amazing device called the hand-held calculator. The seventy or so million already out are only the beginning; and the few hundred classrooms that are now using calculators may well be the forerunners of a substantial change in the way mathematics is taught.
Using hand-held calculators in sixth-grade classes
Authors: Sullivan John J.
Published: October 2020

During the 1973-74 school year. two sixth-grade classes in New York conducted classroom tri als of hand-held calculators. Each child in these classes had a Bowmar “Brain” hand-held calculator for his usc during mathematics lessons each day. The project was organized by the Bureau of Mathematics Education, New York State Education Department. The calculators were provided free of charge by Bowmar/ALl, Inc., and supervision was provided by the principals of the project schools.
Why not have a calculator tournament?
Authors: Guthrie Larry F. , Wiles Clyde A.
Published: October 2020

Why not have a calculator tournament? We did and in a matter of a few weeks had 128 participants from 28 schools registered for the Saturday morning competition.
Christmas and the Canender
Authors: Jamski William D.
Published: October 2020

How many days are there in a week? How many in a year? If your students can answer these questions, then they “qualify” to take a look at an interesting phenomenon—the calendar. That's right, the calendar.
The calculator a calendar?
Authors: Kahn Henry F.
Published: October 2020

Without a doubt, there are free calendars available from many quarters, and even the perpetual calendars can be obtained free or for modest sums. Thus, the electronic calculator is neither the cheapest nor necessarily the most efficient calendar. However. using it as a calendar will demonstrate some important mathematical concepts that are usually taught in the abstract.
A modest proposal concerning the use of hand calculators in schools
Authors: Hopkins Edwin E.
Published: October 2020

Educators and laymen alike have shown a great resistance to the use of hand calculators in schools, particularly in the lower grades. Educators have been willing to admit—or to consider the admittance of—hand calculators only in a case where the calculator adds a “new dimension” of learning to the experience of the child; only in a case where a calculator allows a child to do something, or learn something, that he could not before. I submit that this resistance to the use of hand calculators is irrational and I propose that we make fullest possible use of calculators in all grades of our schools.
Out of balance
Authors: Tredway Dan
Published: October 2020

The balance beam is an old, simple, easily constructed device that should be reexamined by most elementary teachers. This device, whether commercially manufactured or homemade, has been typically consigned to either the storage cabinet or kindergarten and first grade where its use is in assisting pupils in developing the concept of equalities and inequalities.
Compound subtraction—an easier way
Authors: Wenner William J.
Published: October 2020

In order to perform compound sub-traction, pupils are generally taught to use one of three methods, the decomposition, the equal-addition, or the additive.
M & M's candy: a statistical approach
Authors: Hyatt Donald W.
Published: October 2020

Surely you have wondered which colms are most predominant in a package of M & M's candy. Well, why not use a statbtical approach in your classroom to research this topic.
Bingo & The Law Of Equal Ignorance
Authors: Lai Theodore
Published: October 2020

Bingo, like other games of chance, can be used in teaching ideas of probability. An introduction to probability may begin with simple experiments using the “law of equal ignorance,” which is the basis of the theory of probability. In a fair experiment, each possible outcome has the same chances to occur. That is each outcome is as “ignorant” as the other. In an unfair experiment, an outcome is favored to occur over the other possible outcomes; the favored outcome is not as “ignorant” as the other.
Build a better geoboard…
Authors: Klein Judith S.
Published: October 2020

In these days when the necessity for economy sometimes pinches good intentions, many teachers are being forced to make do with old instructional materials, to improvise replacements, or to teach without the benefits that manipulative materials bring to the classroom. Although teachers are increasingly aware of the many fine materials that a re available to assist in elementary mathematics instruction, many of the commercially produced aids are frequently too expensive to be considered seriously in class quantity. The geoboard is an example.
Geometry with a Mira
Authors: Woodward Ernest
Published: October 2020

Are you looking for a device that will help you teach the ideas of symmetry, congruence, and reflections; a device that will make the construction of parallels, perpendiculars, and bisectors easy and intuitive? If your answer is yes, you should consider the possibility of using a Mira.
What’s Going On…
Authors: Gawronski Jane Donnelly
Published: October 2020

Events for the third annual mathematics field day, on 23 April 1977, of the Pomona (California) Unified School District will include Strategy Games, Leap Frog Relay, Math Bowl, and Terminology Tournament.
Discoveries in geometry by folding and cutting
Authors: Edwards Ronald R.
Published: October 2020

Most elementary students have had some experiences in paper folding—either with origami or such simple activities as folding a sheet of paper in quarters or constructing a paper airplane. Also, by cutting and folding, students may have constructed cubes, open boxes, snowflakes, or chains for Christmas trees. Students show interest in such activities and the following series of simple folding and constructing activities may prove both pleasurable and mathematically rewarding. Through these activities, relationships of geometric shapes and regions may be examined; definitions in geometry, reviewed; statements of geometric theorems, visualized; and students' creative talents, exercised.
Behold! A magic square
Authors: Lott Johnny W.
Published: October 2020

Many mathematical activities have been generated through the use of magic squares in ways described in articles of the Aritlunetic Teacher. Recently, while trying to master a card trick, I found an unexpected magic square that elementary students could discover for themselves.
Magic in the mathematics classroom
Authors: Mohr Dean J. , Leutzinger Larry P.
Published: October 2020

Imagine if you will, seventy hushed sixth graders straining to hear every word and stretching to see every movement, their faces masks of concentration and awe. They watch as a hand reaches into a pile of still-smoldering ashes and slowly withdraws the remains of their papers, which only moments before contained numbers they had written. Slowly the handful of ashes is rubbed across the magician's hand and to the utter amazement of the students. the number that was written on each of their papers is formed on the magician's arm. Does this hocus-pocus have any value fo r the mathematics classroom, or is it just a fun way to spend the hour? We feel it has real value both mathematically and motivationally. Mathematics in and of itself is a fascinating field of study, but often the way it is presented hides the marvelous mystery that is mathematics. We have prepared, from many sources, a traveling road show of mathematics magic that can be adapted for any grade level. While the road show may be best for junior high and above, we have shown it to over 2000 students in grades kindergarten through six with remarkable success, despite the fact that the magic did not always work due to the ineptness of the magicians. Some of the best “tricks” we have tried are described in the remainder of this article.
Four television games for your classroom
Authors: Vrbka Maxine M.
Published: October 2020

Mathcmatics games patterned after television quiz shows can review and reinforce concepts previously learned. They provide practice in mental arithmetic and quick recall of facts and processes. I have used all the games described here in my Title I remedial mathematics classes and the ch ildren prefer them to the commercial games. Questions can be geared to the area on which you are working. By keeping the number of participants small, the games move quickly, provide a great deal of practice, and hold interest. The games are most suitable for grades five through eight.
Elementary Mathematics Resource Teacher Program
Authors: Tobin Alexander , Bonner James
Published: October 2020

Standardized test results over the years have shown that children in Philadelphia's inner-city public schools have been doing poorly in mathematics. In fact, the alarming statistics indicate that as the number of years a child spends in school increases, the child's success in achieving grade-level standards decreases.
Another use for the pegboard
Authors: Jeffers Verne G.
Published: October 2020

For several years I have been presenting to my classes an aid to teaching basic facts of addition that is based on the “make a ten” method described by May (1974). In the process of trying out the various ideas suggested by Bruni and Silverman (1975), I came up with an idea that I would like to share. This is another example that shows that the pegboard is a good manipulative device for relating sets to the counting numbers and reenforcing the grouping process in place value.
Update on sex-role stereotyping in elementary mathematics textbooks
Authors: Kuhnke Helen Fuesy
Published: October 2020

The awareness of sexism in the curriculum (Frazier 1973) and the numerous articles on sex-role stereotyping in elementary textbooks prompted me to take a close look at some elementary mathematics series myself. Since I had immediate access to them, I examined two sets of elementary mathematics texts, kindergarten through grade six, both with 1974 copyrights. I am pleased to report that my examination of these books indicates that apparently an all-out effort has been made to eliminate the sexist bias and offensive sexrole stereotyping.
What's Going On…
Authors: Gawronski Jane Donnelly
Published: October 2020

The new mexico state university elementary teachers math project provides inservice train ing for area teachers. Thirty-five teachers of grades four through six are enrolled in one class every semester during the 1977–78 academic year.
Metric Measurement and Instructional Television
Authors: Meiring Steven P.
Published: October 2020

“McasurcMctric”—an admonishment to use the world's official measurement system? Possibly. But it is also the title of a new series designed to teach metric measurement to eleven- to thirteen-year-olds.*
On The Uniqueness of Problems In Mathematics
Authors: Robinson Edith
Published: October 2020

Facility in problem solving is an acknowledged aim of any mathematics program. But ability to solve problems is also considered to be a goal of science instruction, and a social science program may be built around a “problems approach.” Thus the topic of problem solving is not the exclusive property of mathematics. The purpose of this article is to explore differences other than content between problems in mathematics and problems in other subject matter areas.
One Point of View: Labels, Labels, Labels
Authors: Frye Shirley M.
Published: October 2020

In the last decade the number of labels assigned to students has increased phenomenally. The amount of assistance and funding provided for children with learning problems has been both amazing and effective in helping them overcome and compensate for their difficulties, differences, or disabilities. But there is indeed a concern that many students are being labeled, grouped, and isolated because of their deviations, however slight, from the “norm.” In many cases the “norm” is being determined subjectively by those who believe that any behavior not conforming to their standards is deviant.
Test-Item Tendencies: Curiosity and Caution
Authors: Callahan Leroy G.
Published: October 2020

Standardized achievement tests have attracted the favor, or flak, of citizens in our society for many years. Educators have used information from them for both summative and formative eva luation purposes. Summatively, standardizedtest results may be used to judge the degree to which a student, class, or school system has achieved desired learnings in a particular area of study. The objectivity of standardized tests fu rther allows com pari ons with other students, classes, or school systems. Today, millions of dollars are dispensed annually by governmental agencies based on standardized-test performance of students. Formatively. these test res ults may be used by teachers or cu rriculum workers in determining program directions and emphases. Whether for formative or summative purposes. caut ion has always been urged in interpreting standardized-test perform ance of students. These urgings are not always heeded.
Reducing Practice Time without Reducing the Value of the Practice
Authors: Barr David C.
Published: October 2020

Several years ago, Lord (1971 [a) and [b]) was interested in the problem of reducing the amount of time children spend doing tests. His nexilevel test was an outcome of the research into tailored test ing that became necessa ry with the increasing usc of individualized mathematics programs. Most tailored testing techniques have involved the use of a computer (Linn, Rock, and Cleary 1969), but Lord's flexilevel test overcomes this problem, possibly at some cost to the precision of the procedure.
Marshmallows Toothpicks and Geodesic Domes
Authors: Wahl M. Stoessel
Published: October 2020

Young children grow up in and Patterns for Domes adapt to a world of three-dimensional objects. Solids. however, are difficult to show on textbook pages and in chalkboard drawings, with the result that there is a tendency to limit early school geometric experiences to recognition of plane figures.
Problem Solving: Some Considerations
Authors: Krulik Stephen
Published: October 2020

A major difficulty in discussing problem solving is the lack of a clear-cut definition of what con titutes a problem.
Introducing Place Value
Authors: Ronshausen Nina L.
Published: October 2020

The purpose of place-value learning activities in the first grade is to associate sets grouped by tens and ones with two-digit numerals. The activities described in the following paragraphs for numerals 10 through 99 can be repeated in second grade for numerals 100 through 999. Then the concept of exchange can be introduced.
Ideas
Authors: Bright George W.
Published: October 2020

Ideas for February are on two posters you can display on a bulletin board or in a mathematics center. Both posters emphasize pattern recognition and problem solving; they also provide opportunities for practicing addition of two-digit numbers, ordering numbers, and, in the second IDEAS, finding factors of numbers. The activities on these posters will require several days to complete if students work on them o utside the regular mathematics period.
How High Is a Flagpole?
Authors: Hunt John D.
Published: October 2020

Alexander Graham Bell said th at if you leave the beaten track occasionally and drive into the woods you will be sure to find something you have never seen before. This may be said in a different way. Leave the classroom occasionally and go outside to the school yard to measure buildings, trees, or a flagpole. How can these items be measured? All of these structures can be measu red by using indirect measurement techniques. The equipment needed is inexpensive.
Let's Do It: Strip Tease
Authors: Lindquist Mary Montgomery , Dana Marcia E.
Published: October 2020

What can be done in a mathematics class with strips of paper? Let this article tease your mind with ideas of how to use paper strips to make geometric figures. to practice measu ring, to investigate patterns. to practice addition facts and reading numbers. and to explore other mathematical ideas.
Ideas
Authors: Bright George W.
Published: October 2020

Ideas for April is a set of games that reinforces concepts of ordering and place value. Each game can be played by a small group, two to four players, with players alternating turns, or as a solitaire game with the object being to achieve as high a score as possible. Each game calls for the use of a single die. A spinner or number cards drawn out of a box or bag would work equally well.
Introducing Additional Concrete Models of Operations: A Discovery Approach
Authors: Vest Floyd
Published: October 2020

Most mathematics educators agree that children should have a broad view of the operations on whole numbers (Ashlock 1971. Reys 1972). Children. in other words. should not be limited to a single interpretation or model of an operation. There are several advantages to giving children experience with more than one interpretation of an operation. including the belief that children will become better problem, solvers when they have a broader view of the operations.
A Model for Understanding Understanding in Mathematics
Authors: Davis Edward J.
Published: October 2020

Teachers strive to help students understand their subject. But what does it mean to understand something?
Some Mathematical Hard Spots
Authors: West Tommie A.
Published: October 2020

“There is no royal road to geometry,” Menaechmus told his young student, Alexander. The statement is true of the rest of mathematics as well. Indeed, the journey to mathematical prowess is beset with hard spots, points where learners frequently stumble along their way to attainment of mathematical skills. Yet the path over many hard spots may be smoothed by teachers who know the road and who anticipate the difficulties. Identifying some hard spots and considering ways to minimize them will be useful.
Renaming with a Money Model
Authors: Logan Henrietta L.
Published: October 2020

Running his fingers sullenly along the edge of the book, Vic attempted yet another subtraction problem with little hope of success. Through his behavior, he expressed the view of many children of elementary school age; he's tried subtraction with borrowing many times. Once he even cared, but somehow the subtraction never came out right for him.
Using a Calculator to Do Arithmetic in Bases other than Ten
Authors: Schultz James E.
Published: October 2020

The method described here for doing arithmetic in bases other than ten on an ordinary calculator is of interest not only because of its direct application to computation, but also, perhaps more so, because of the example it provides of the folly of jumping to conclusions too quickly. In the hands of an effective teacher, this method can be used both to foster a better understanding of place value and to illustrate the danger of blind dependence on the calculator.
Let's Do It: Let's Try Triangles
Authors: Dana Marcia E. , Montgomery Lindquist Mary
Published: October 2020

Skill in problem solving is a primary goal of mathematics instruction. The purpose of this article is to help you build a collection of problems that can be posed to children of varying ages or abilities. These particular problems require searching for different possibilities that fit a given condition. The number of solutions that are found and how they are found will vary with the groups of children involved. In fact, for some children you may want to use these searches as class activities rather than as projects for individual students.
Operations from Number Sequences
Authors: Sawada Daiyo
Published: October 2020

The idea of a number sequence is rarely regarded as a basic concept in elementary school mathematics. When we do study number sequences we do so (1) indirectly, as when we speak of the “whole number sequence,” wherein the idea of a sequence appears only in a manner of speaking—we really are much more interested in the whole numbers per se: or (2) as a topic in enrichment, as when we study the triangle number sequence (1, 3, 6, 10, …) or some other sequence from number theory. But even in the enrichment setting, we are more interested in the numbers themselves than in the fact that they form a sequence.
Let's Do It: From Halves to Hundredths
Authors: Dana Marcia E. , Lindquist Mary Montgomery
Published: October 2020

Today there seems to be an urgency to teach decimals at an earlier age. Occasionally one hears that the common fraction should be abandoned.
“Digits”—a Game of Strategy for All Ages
Authors: Flener Frederick
Published: October 2020

Teachers often use games to break the normal classroom routine. The games may be group games, games of chance, or games of strategy. “Digits” is a game of strategy for two players, a simple adaptation of Mastermind to a pencil-and-paper game. The rules for Digits can be modified to fit the players.
So Your Students Know about Area?
Authors: Jamski William D.
Published: October 2020

When evaluating junior high school students' mastery of the area concept, the tendency is to measure their achievement with only superficial recall testing.
Teaching Division of Fractions with Understanding
Authors: Charles Thompson
Published: October 2020

How did you learn to solve 3/4 + 1/6 = □? Like me. you probably learned the clever rule, invert the second fraction and multiply it by the first fraction. Specifically, 3/4 ÷ 1/6 = 3/4 × 6/1. A logical question arises: Why does that procedure, which seems extremely arbitrary to children, yield the correct answer?
The Case for a Comprehensive Mathematics Curriculum
Authors: Suydam Marilyn N.
Published: October 2020

All across this country, children are being cheated. They are being deprived of mathematical experiences which they should have in order to live effectively in their world.
A Case for Geometry: Geometry Is Important, It Is There, Teach It
Authors: Kerr Donald R.
Published: October 2020

Stop and think how you use geometry in your life.
Ideas
Authors: Bright George W.
Published: October 2020

Ideas for April is a set of graphing activities. Graphs are useful for organizing information in order to search for patterns. Some students who do not like arithmetic may enjoy graphing very much.
Children's Strategies for Solving Subtraction-Fact Combinations
Authors: Beattie Ian D.
Published: October 2020

Many teachers at the intermediate grade level are constantly frustrated in their teaching of arithmetic by pupils who have not mastered their basic facts. Such mastery is important, Research in the area of computational errors has consistently shown that many errors are due to lack of mastery of basic facts. Teachers justifiably set mastery of basic facts as an important goal for the year. Each September they optimistically set out to accomplish what the previous year's teachers failed to do—to have all children in their classes master their basic facts. They provide drill, extra practice, and motivating games. Each June they concede defeat. The same children who did not know the facts in September are still making mistakes. This situation is common, but knowledge of what causes these basic-fact errors may prevent it from being inevitable.
Teaching estimation and reasonableness of results
Authors: Johnson David C.
Published: October 2020

The National Council of Supervisors of Mathematics' Position Statement on Basic Mathematical Skills (1977) speaks to the importance of the two key ideas, “Alertness to the Reasonableness of Results” and “Etimation and Approximation.” In particular, the paper notes that these skills, although always important, have become even more critical in a world of calculators and computers. It is often necessary to assess a machine-produced result in terms of the reasonableness of the result when one considers the numbers involved or physical reality
Let's Do It: Counting with a Purpose
Authors: Leutzinger Larry P. , Nelson Glenn
Published: October 2020

Counting by ones from one is a skill that children develop early and use in many situations. Primary-grade teachers encourage their students to count to find out how many objects are in a set. Such counting is helpful in determining answers to introductory addition and subtraction examples. After an understanding of these two operations has been developed and the basic addition and subtraction facts have been introduced, however, the “counting by ones from one” skill that children have can become a liability. Many students 6 use the method, since it almost guarantees a correct answer, but such counting is very inefficient if students use this method to find every answer.
My Favorite Lesson: Mathematics on Tour
Authors: Scalzitti Joyce
Published: October 2020

One of the goals of an effective mathematics curriculum should be that your students take their knowledge of mathematics everywhere they go. Competency in mathematics is not only important in the classroom but also in its applications in their daily lives. When I say mathematics should go everywhere with students, I mean everywhere, including being packed in their suitcases when they go on vacation.
National council of teachers of mathematics: Minutes of the Annual Business Meeting
Authors: Gates James D.
Published: October 2020

A very timely yearbook … because of the renewed emphasis on basic skills and the public concern for the achievement of computational skills.
Hand Calculators What's Happening in Schools Today?
Authors: Reys Robert E. , Bestgen Barbara J. , Rybolt James F. , Wyatt J. Wendell
Published: October 2020

What's happening with calculators in school's today? Are they being used? If so, by what students? How do teachers feel about using calculators in the mathematics program? Should calculators be used on standardized tests? Should use of calculators be integrated into basal mathematics textbooks? Accurate answers to such questions are essential in assessing the current status of calculator use in schools today and more importantly, preparing for calculator usage in the mathematics curriculum during the 1980s.
Prime Factorization
Authors: Lappan Glenda , Winter Mary Jean
Published: October 2020

For children to understand prime factorizations they must be comfortable with products of varying lengths, and products that do not immediately suggest basic multiplication facts. The authors have used the following sequence of activities to present the basic relationships among factorizations, factoring, multiplication, and division. The activities begin with “hands-on” experience with rectorizations of a large number—1350—and build up to the idea of prime factorization, which is then used as a problem-solving strategy. The children we worked with had calculators at their disposal.
Making Sense Out of Dollars and Cents
Authors: Bradford John W.
Published: October 2020

One of the difficulties associated with learning about coins and calculating their numerical values is that coins do not have any obvious systematic physical relationship to each other. That is, five pennies cannot be placed together somehow to make something that looks Like a nickel, two nickels cannot be melted together to make a dime, and so on. Another difficulty is that the use of actual coins for classroom teaching poses many problems because of the monetary value of the coins. Thus, instructional efforts on this to pic are limited by constraints that make meaningful learning difficult to accomplish.
Bilingual Education: What Role for Mathematics Teaching?
Authors: Lovett C. James
Published: October 2020

The first bilingual schools in the United States were established prior to 1850 (Andersson and Boyer 1970) and bilingual education has existed in some form since that time. In recent years the field has expanded greatly and the literature on bilingual education has increased correspondingly, most of it focusing on general issues of language development and on the specific areas of language arts, reading, and social studies. Very little has been written specifically on the role of mathematics in bilingual classrooms. Not only must interested teachers search for isolated bits and pieces of information, but they also frequently discover that mathematics educators in many cases have been left out of the planning and implementation of bilingual programs.
Using Geoboards in the Primary Grades
Authors: Holcomb Joan
Published: October 2020

At the kindergarten and first grade levels, children love to explore and do things with their hands. What better way than on a geoboard! Children can make designs, three-sided figures, foursided figures, “look-alikes,” and even practice letters of the alphabet. (Fig. 1) They can decide which letters are “closed” and which are “open.” (Fig. 2) They may make the smallest letters possible on their geoboards and then the largest letters possible. They may investigate to see how many As or how many Xs can be made on one geoboard.
Building a Metric City or Town
Authors: Alec Rudi
Published: October 2020

There are four basic competencies in linear measurement that students need to acquire in using metric measurement.