bluuebunny/crossref_metadata_2025 huggingface dataset:
Big Dividends from Little Interviews
Authors: Fred Weaver J.
Published: October 2020

There is no “Get-Rich-Quick” scheme for improving the effectiveness of arithmetic instruction, nor will there ever be such a scheme. There are available, however, sound low-cost investments which often yield substantial dividends at high rates of compound interest.
Casting Out Nines: Our Decimal Number System
Authors: Ulrich Louis E.
Published: October 2020

We Americans Hate Despots—those who want us to obey, not to think. Or do we? Do those of us who turn the knob on our TV know why it works? Are despots always human? May we become slaves to mechanical devices without realizing it? What is the price we pay for the privilege of getting results without the toil of thought.
Developing Understanding Through Counting
Authors: Blom E. C.
Published: October 2020

Because A Learner's First Impression tends to be permanent, some apparently elementary conventions are actually very important. Many factors affect the learning of mathematical concepts. It is easy to make the mistake of assuming that beginners learn easily and quickly the many meanings of terms, symbols, and procedures, and their respective uses that have become automatic for an adult. We should, therefore, place great emphasis upon arithmetic instruction in the early school years.
Labeling Answers to Arithmetic Problems
Authors: Ullrich Anna
Published: October 2020

A MUCH DISPUTED QUESTION which frequently confronts the elementary school teacher in marking answers to problems in arithmetic is: “If the answer has no label but is otherwise correct, should it be marked right or wrong?” In the hope that certain guiding principles in t he matter of labeling answers might be formulated, the writer made a questionnaire investigation which involved approximately 250 school people ranging from teachers to superintendents in Wisconsin and some 30 authors of books, tests, and articles in periodicals outside the state. The Wisconsin group also included instructors in normal schools, colleges, and universities.
Supervision in mathematics
Authors: Bartel Elaine V.
Published: October 2020

The task of identifying and subsequently refining an instrument to assess the quality of classroom interaction in specific curriculum areas has involved much time and effort on the part of educators in recent years.
The Russian-peasant algorithm: rediscovery and extension
Authors: Boykin Wilfred E.
Published: October 2020

The opening words of the old adage, “Something old, something new … ” often-times sum up the objectives of those of us who subscribe to a heuristic approach to the teaching of mathematics.
Things you can try: A seventh-grade mathematics class tackles the stock market
Authors: Friedmann Esther K.
Published: October 2020

Our seventh-grade mathematics class had had no previous experience in making graphs, and I wanted to find an approach to the topic that would provide a stimulating, enrichment activity for a bright group of youngsters. I also wanted to involve other mathematics skills so there would be maximum benefit from the project. Remembering my own experience with theoretically buying and selling stocks during a college economics course I had once taken, I decided to try the same approach with the seventh grade.
Using Research in Teaching: Fourth-grade division: how much is retained in grade five
Authors: Kurtz Ray
Published: October 2020

Teachers acknowledge that the division process is difficult for children due to its unique nature of involving all basic mathematics operations. Fifth-grade teachers perennially have a difficult time understanding why they must do so much reteaching of division problems that are similar to those that the students studied during the fourth grade. It is also difficult for fourth-grade teachers to understand why the children need the reteaching in the fifth grade when they have observed, at the close of the fourth year, that the students seem to have the mathematical knowledge and skills needed for the next grade.
National Council of Teachers of Mathematics: Nominees for 1974 Election
Authors: Tolson Juanita , Begnaud Lurnice , Brydegaard Marguerite , Ferguson W. Eugene , Greenholz Sarah , Heinke Clarence H. , Hlavaty Julius H. , McNabb William K. , Smith Lehi T.
Published: October 2020

The Nominations Committee needs your help in selecting nominees for the 1974 election. At that time, four persons will be elected to serve on the Board of Directors. Please send your suggestions of NCTM members whose records of service and leadership in the field of mathematics education qualify them for consideration to Mrs. Juanita S. Tolson, 3003 Van Ness Street, NW, Apt. W727, Washington, D.C. 20008.
Mathematics through visual problems
Authors: Eisenberg Theodore A. , Van Beynen John G.
Published: October 2020

Educational researchers have demonstrated that when a concept is introduced inductively it seems to be wise pedagogy to motivate it through manipulative devices (Lucas 1967; Scandura and Wells 1967; Toney 1968).
Ideas
Authors: Immerzeel George , Wiederanders Don
Published: October 2020

Each ideas presents activities that are appropriate for use with students at the various levels within the elementary school. After you have chosen the activities that are most appropriate for your students, remove the sheets and reproduce the copies you need. After you have used an IDEAS activity sheet with your students, add your comments and file the materials for future use.
A device for indirect measurements: An entertaining individual project
Authors: Patterson William
Published: October 2020

Indirect measurement is often studied in geometry courses. Usually textbook examples and exercises involving the measurement of the heights of objects are presented. Very seldom, though, do students actually make indirect measurements. The purpose of this article is to outline the construction and use of a device to measure the heights of objects. The device will enable students to actually make indirect measurements and thus appreciate the fact that there are applications of the mathematics they study in class.
Probability on the geoboard
Authors: Niman John , Postman Robert D.
Published: October 2020

The geoboard can be used not only to investigate the properties of two-dimensional figures, but also to study probability. Probability and statistics play a leading role in explaining physical phenomena, and they are also becoming an integral part of the elementary school curriculum. In situations where a probability model is applied, there is a common property of uncertainty. It can never be absolutely determined whether an event will or will not happen; rather, a numerical estimate of the likelihood, or relative frequency, of the event's occurrence is calculated.
Introducing the binary system in grades four to six
Authors: Unenge Jan
Published: October 2020

The teaching of place value is one of the most important—and possibly the most interesting—parts of the elementary mathematics program. You can show the children how you get another name for the number seven if you count in fives. And children will better understand what happens when you go from nine to ten and from ninetynine to one hundred in the decimal system if you discuss different bases with them. I have used the following technique for teaching the binary system in grades four to six.
What am I ever going to use that for?
Authors: Tucker Benny F.
Published: October 2020

What am I ever going to use that for?” is an often-heard complaint in the mathematics classroom. One of the topics about which such a complaint is voiced is that of nondecimal bases. And, perhaps, such a complaint is not unreasonable, for the only answer that most teachers seem to have is some vague comment that the study of nondecimal numeration will help the student better understand the decimal numeration system.
Things you can try: Television games adapted for use in junior high mathematics classes
Authors: Homan Doris
Published: October 2020

Today, as in the past, the use of mathematical games is an effective way to provide meaningful, interesting drill for junior high students. Highly competitive by nature, students at the junior high level respond with enthusiasm to activities of this kind. When these games can be associated with familiar, pleasant experiences, there is an added motivational factor. Why not, then, relate mathematics to the most familiar activity of all—viewing television. Three games that have been adapted from television shows are described here.
Using research in teaching: How thirty measuring sticks, twenty-nine kids, and I started using research in the classroom
Authors: Higgins Jon L.
Published: October 2020

Poily, there's a big box marked ‘measuring sticks’ in the office with your name on it. What are you and all those first graders up to now?”
The metric system: past, present—future?
Authors: Hallerberg Arthur E.
Published: October 2020

The wife's query in an old cartoon gets right to the point: “Well, why on earth don't we adopt the metric system if it's so much better?” The husband's response is equally direct: “Why, just because we never did, my dear!”
Things You Can Try: Diagonally magic square arrays
Authors: Trigg Charles W.
Published: October 2020

Here is a simple procedure that gives mystifying, magic results, that have a very elementary explanation.
The metric system—let's emphasize its use in mathematics
Authors: Alexander F. D.
Published: October 2020

As these words are being written, it is apparent that the metric system is being adopted almost universally; the United States is the only major industrial nation that has not made the transition. With accumulating evidence pointing to metrication, it is essential that our education institutions not delay the process of teaching every student the metric system of measurement.
Metric is here; so let's get on with it
Authors: Fisher Ron
Published: October 2020

In the last 200 years, Congress has often considered adopting the metric system as the basic language of measurement in the United States. Action was always postponed; usually because the metric system was not in use by major trading partners of the United States. This obstacle is now removed; every major nation—except the United States—has converted to metric or is committed to conversion.
Strategies for teaching elementary school mathematics
Authors: Troutman Andria Price
Published: October 2020

Today, the selecting of mathematical curriculum for children is somewhat similar to discriminating fact from fiction found in neatly packaged television commercials.
The content of the elementary school geometry program
Authors: Vance Irvin E.
Published: October 2020

What geometry should we teach in the elementary school? is a very important and frequently asked question.
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. A (ter 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.
Fun with geometry through straw construction
Authors: French James Elbert , Rea Robert E.
Published: October 2020

Straw construction makes geometry an exciting experience for the student as well as the teacher. What makes this learning activity particularly valuable for the teacher is the number and variety of mathematical concepts that arise during a “fun” activity. Concepts such as congruence, measurement, comparison, imagery, unit of measure, equilateral and isosceles triangles, triangular prism, pentagon, vertex, acute and obtuse angles, and counting are involved. This project has been used in fifthand sixth-grade classes in Hazelwood, Missouri, schools and by a teacher-training class at the University of Missouri-St. Louis with quite similar results in terms of interest, ideas generated, and problems encountered.
Teaching tens to Timmy, or a caution in teaching with physical models
Authors: Steinberg Esther R. , Anderson Bonnie C.
Published: October 2020

Timmy, a second grader, was having difficulty with an arithmetic problem involving addition of tens in picture form. Just start him out, “ten, twenty …,” and he could easily continue counting correctly by tens and arrive at the answer. Was it just a matter of pointing out to him that he could count by tens as a shortcut, or was Timmy's problem more basic? Did Timmy understand why he was counting this way? Did he know that two tens and twenty are different names for the same number? Did he even know what we mean when we talk about a ten?
Developing the subtraction algorithm
Authors: Cleminson Robert A.
Published: October 2020

Have you ever taken a moment to reflect upon what you are asking children to do when you have them do subtraction problems? Have you considered the knowledge that each student has had to acquire in order to perform successfully in subtracting? Take a moment to think about these things. A review of the totality of learning involved in the subtraction operation will greatly enhance your ability to assist those children who may experience difficulty in this area.
Integrating geometry and arithmetic
Authors: Perry E. L.
Published: October 2020

Although the arithmetic texts that are currently in use in the first six grades include some sections on geometry, the texts that will appear in the next few yea rs will have more emphasis on geometry and on the interrelationships between geometry and arithmetic. The trend today is to teach more arithmetic than can be readily applied to everyday problems, as opposed to teaching more theoretica l mathematics. Geometry lends itself very well to this situation. Many professional people, such as architects, draftsmen, astronauts, carpenters, engineers, and navigators, use geometry daily in their work. There is an abundance of applied problems available on all competence levels in geometry.
Polygons on a lattice
Authors: Sullivan John J.
Published: October 2020

The set of points in a plane, each with two integral coordinates, is one example of a lattice. Geoboards, of course, are useful models of lattices. Current enthusiasm for geoboard work calls to mind an elegant lattice theorem discovered by G. Pick (Coxeter 1961). In the following statement of Pick's theorem, b represents the number of lattice points on the sides of a polygon, and i the number of interior points, respectively.
A critical assessment of published tests for elementary school mathematics
Authors: Carry L. Ray
Published: October 2020

This paper is intended as an aid to the elementary school mathematics teacher who uses published tests for evaluating student achievement in e lementary school mathematics. (“Published tests” jn this paper refers to standardized tests and to published criterion-referenced tests.) Often teachers must administer to their students tests that do not directly assess the teacher's objectives. The almost certain outcome of such a procedure is that average student achievement is revealed to be unexpectedly low. Such an outcome may result in pressure to modify the instructional objectives so that instruction becomes consistent with the behaviors assessed by the achievement tests. Over a period of years this process could lead to a situation where mathematics course objectives are in effect determined by test content. Stated tritely perhaps, but accurately, we could end up “with the cart before the horse.”
What the tests don't tell
Authors: Peck Donald M. , Jencks Stanley M.
Published: October 2020

Paper and pencil tests, as commonly used for evaluating progress and for diagnosing the difficulties children have with subject matter, are so often misinterpreted that they need to be supplemented with other means of evaluation. This is particularly true for students who get high scores because one cannot infer understanding from tests which, at best, measure manipulative skill.1 Teachers are fooled into thinking that because high-scoring students have done so many problems correctly they must understand the subject matter.
Generalizing a property of prime numbers
Authors: Dubisch Roy
Published: October 2020

It is common practice to define a prime number as a number with exactly two divisors. A very natural question which can be (and has been) raised by children meeting this definition is, Are there any numbers with exactly three divisors? This question can lead to a very nice discovery experience in which all children can participate to some extent, but which can also challenge the most talented.
Some geometry experiences for elementary school children
Authors: Moulton J. Paul
Published: October 2020

Geometry in the elementary school has been plagued with three pervasive emphases: (1) false utilitarianism, (2) superficial attention to form, and (3) sterile Euclidean formalism.
Things you can try: Holiday plot-dots
Authors: Deatsman Gary A.
Published: October 2020

Here is an activity that will interest and challenge third graders and advanced second graders. By carefully following written directions, each child plots ordered pairs of natural numbers to get points on a coordinate system. Each point is labeled with a number and when the plotting is done the child has constructed a follow-the-dots puzzle which he can then complete. Directions for three of these “plot-dots” are given here. The first turns out to be a Halloween pumpkin and the second a Christmas tree. The third, which is shown in figure 1, is a Valentine heart.
Pascal's triangle
Authors: Hoffman Nathan
Published: October 2020

Number patterns in arrays of numbers can be a source of great interest to students. They can also provide highly motivated practice in fundamental operations. One of the most interesting arrays is known as Pascal's triangle. As the name suggests, this is a triangular array of numbers. Parts of Pascal's triangle are shown in figure 1 in three different forms.
A new look for the hundreds chart
Authors: Randolph Winifred , Jeffers Verne G.
Published: October 2020

For many years the hundreds chart has been used in a variety of ways to help develop mathematical ideas with children—it is quite possible that many children formulate their initial ideas about number through experiences with the chart. The typical hundreds chart, however, shows numerals going downward as they go “up” in number value. This causes a directional conflict in the minds of some children; it would seem that a different arrangement of the chart could help overcome this conflict. Rather than starting in the upper left hand corner and progressing to the lower right, the chart could originate in the lower left hand corner and terminate in the upper right as illustrated in figure 1. In this arrangement, number values increase as we progress “upward” through the chart.
They all add up
Authors: Heckman M. Jane
Published: October 2020

The games described here have provided practice in addition for many children in numerous classes. The games are easy to play and the needed materials can be readily prepared by a classroom teacher for a small price. They all add up to addition'n fun.
Things You can Try: Geo-gin
Authors: Berman Janis A.
Published: October 2020

Most students in the upper elementary grades have played and enjoyed card games. Geo-gin is a card game that makes use of some important geometric concepts such as spatial perception, identification, and discrimination. It is designed for groups of two to four students.
Procedures for designing your own metric games for pupil involvement
Authors: Trueblood Cecil R. , Szabo Michael
Published: October 2020

Although much has been written on the values of mathematical games in the elementary grades and many game books have been published, little has been written that would help classroom teachers design, produce, and evaluate games for use in their classroom. The focus of this article is to present a set of seven criteria that were developed in a summer workshop for inservice elementary teachers who decided that they wanted to be able to produce metric games and related activities that would fit into their “metrication” program.
Things you can try
Authors: Turek Stephen , Kaiser Karen
Published: October 2020

The game “Tic Tac Toe” can be used for reviewing a variety of mathematical concepts, and the needed materials are inexpensive and easily provided.
Things you can try
Authors: Temple Richard J
Published: October 2020

Mathematical games and puzzles have gained tremendous popularity and support in today's “hands-on” approach to classroom instruction. Manipulatives can be useful both as learning devices and as a means to drill. However, many middle school students feel the need for written drill work. The trend is to let the student do drill work on his own. Too often, such drill is never checked or perhaps never even done.
Training elementary mathematics teachers in a one-semester course
Authors: Crittenden William B.
Published: October 2020

When the writer joined the faculty of Houston Baptist University in 1968, he was given the assignment of prescribing the mathematics education training experiences for prospective elementary teachers. Since the college is primarily for the liberal arts and the curriculum includes a large number of required cources, there was only one three-semester-hour course available in which elementary teachers could be prepared in mathematics.
Development of a mathematics laboratory
Authors: Schnell Jacqueline H. , Klein Lane Krasno
Published: October 2020

In the following pages, we shall describe the development of a mathematics laboratory that has become an integral part of our school mathematics program, serving several functions in the total mathematics curriculum.
Readers' Dialogue
Authors: Olson Alton T. , Izzi John , Zaslavsky Claudia , Madell Robert , Weiland Linnea , Allan Robert N.
Published: October 2020

Recently, in a mathematics curriculum class of mine, we had an opportunity to critically evaluate an article by Harold M. Ness, Jr., entitled “Another Look at Fractions” (January 1973). It was the general consensus of the class that the pedagogical ideas put forth in the article deserved a written reaction. Specific criticisms follow.
A project for the low-budget mathematics laboratory: the game of kalah
Authors: Brill Randall L.
Published: October 2020

Teachers often see a kit or game that they feel would be ideal for use in the mathematics-laboratory activities of their classrooms but find it financially out of reach. By using a little imagination, they very often can make similar kits or games and at a much lower cost.
Metrication of the American family
Authors: Lampman Donna
Published: October 2020

Since I am interested in mathematics and science, I have watched with much interest as the United States Congress has deliberated on conversion to the metric system of measurement. Because conversion was anticipated and because I have enough science background to be familiar and comfortable with metric terms, I eagerly taught my fifth graders to use metric measurements. We had several lively and thought-provoking discussions concerning the relative ease of using metric measures versus using traditional measures, economic factors in conversion, and simple Amcricanistic pride. Even my most stubborn fifth-grade traditionalist came to agree, after working comparable problems and calculations in each system, that the metric system is more logical and metric measures are easier to work with.
Using research in teaching: Diagnosing and remediating systematic errors in addition and subtraction computations
Authors: Cox L. S.
Published: October 2020

What can classroom teachers do to help children who have difficulty with computational skills? Some people may argue that teachers need not worry about computational skills because of the increasing availability of miniaturized calculators. Such an argument assumes that an individual will (1) know what operation should be used; (2) have the financial resources to buy hand calculators; (3) have a hand calculator at his fingertips every time he needs to add, subtract, multiply, or divide; and (4) be able to determine the reasonableness of an answer once it has been derived. These assumptions are difficult to satisfy. The development of basic computational skills clearly should not be neglected; it remains one of the objectives of elementary school mathematics programs.
Let's Do It!: Making and using board games
Authors: Bruni James V. , Silverman Helene
Published: October 2020

Board games can be recreational and fun to play. They can also provide many opportunities for developing number concepts, drilling in basic skills and number facts, and teaching movement along the number line. If children are taught to make their own games, additional skills of planning, ordering, and making and testing rules can be developed. The actual games may reftect content studied in other curriculum areas, hobbies, stories, contemporary problems, and individual interests.
Measuring, discovering, and estimating the metric way
Authors: Pottinger Barbara
Published: October 2020

Mirror, mirror on the wall, what about metric should I teach to them all?’ Faced with this dilemma, I charged ahead with many ideas but with few materials at my disposal. Most of the metric materials I had seen were far too advanced for my third-grade class.
Preparing teachers for individualized teaching of mathematics
Authors: Chinn Phyllis Zweig
Published: October 2020

Lrecent years many people have recognized the value of Jetting children learn by doing. Issues of the Arithmetic Teacher have been devoted to mathematics laboratories and individualized teaching. Several books make eloquent pleas for using a child's natural curiosity and innate learning skills to allow him to continue to grow in all learning, including mathematics. Crisis in the Classroom, Freedom to Learn, and What Do I Do Monday, provide detailed statements of the weaknesses of some traditional approaches to teaching and the exciting possibilities inherent in some alternatives.
Parents make a difference in teaching in urban schools
Authors: Lincoln Eugene A. , Briscoe Lloyd W. , Williams Dorothy K.
Published: October 2020

Many attempts to find solutions to the incredibly complex problems facing urban schools have not been highly successful. A “jungle” of myths may have been created in the process. For example, there are those who would say that a large number of pupils in urban schools are innately inferior intellectually to pupils of other schools. Others would take the position that the home environment of a vast majority of the pupils is not conducive to formal learning. Still others would argue that very few parents in urban centers support education.
Reviewing and Viewing: Etcetera
Authors: Denman Theresa I.
Published: October 2020

Dictionary definitions or etcetera usually include a phrase about “a number of other things or persons unspecified.” Without a doubt, “unspecified” is the proper word to apply to the wide variety and vast number of manipulative kits, games, and audiovisual aids that have been produced for classroom use. Multisensory might apply in many cases, but the basic appeal of some aids is to a single sense mode. So …, etcetera seems the logical name for a column whose purpose is to report on everything that does not fit the categories or any other review section.
Decoding student names, or if Alan is 42, then Robyn must be 82
Authors: Bernstein Robert , Barson Alan
Published: October 2020

The activity described below was used as a motivational device to reinforce addition facts, geometric definitions, and statistics. The object was to have the students decode the letter construction of their names according to the “key” (fig. 1) and then compute its value. Following that, the class compiled group statistics including the measures of central tendency and the range.
Let's Do It!: Making the holidays a “solid” success
Authors: Bruni James V. , Silverman Helene J.
Published: October 2020

Children rarely have the opportunity to make and to explore three-dimensional shapes in most elementary school mathematics programs. Although the exploration of properties of different three-dimensional shapes is an important part of preschool and kindergarten experiences (especially through play with blocks), when shapes are studied in elementary school programs the focus is usually on two-dimensional shapes. Children often “meet” three-dimensional shapes again when they see twodimensional representati ons of these shapes in their mathematics books. We sometimes assume that children need no further concrete experiences. that they can explore ideas a bout three-dimensional figures based on these diagrams. When c hil dren are not successful, we may guess they are not “ready” for work with threedimensional shapes.
Geoboard activities for primary grades
Authors: Kratzer Richard O. , Allen Bruce A.
Published: October 2020

The geoboard is a popular device for developing a variety of geometric and arithmetic patterns in mathematics. It frees the child from the static pictures and diagrams of the traditional paper-and-pencil activities. When children are able to “stretch” a rectangle, form squares of many different sizes, and transform one shape into another, they have a feeling of creating their own geometry. With an aroused interest children are more apt to sense patterns and shapes that occur in their own explorations.
A method of subtraction
Authors: Schwartzman Steven
Published: October 2020

The method of subtraction described here can be used either for youngsters who have never been able to master the conventional subtraction algorithm, or as enrichment for students who already know how to subtract and have a knowledge of negative numbers. The system is more process-oriented than st ructureoriented. at least on the surface. The result is that poor students who learn the process will come up with right answers fairly consistently, no matter how large the numbers involved, while better students may discover the structure that underlies the process.
Money talks
Authors: Becker Stanley
Published: October 2020

Money is the root of all … not evil, in this case, but motivation for an interesting mathematics game. Using the format of lotto (cover every space on the board) money can be useful in reinforcing a child's knowledge of the multiplication “tables.”
Your Council at Work: Committee on Affiliated Groups
Authors: Fisher Lyle
Published: October 2020

The purpose of the National Council of Teachers of Mathematics (NCTM), as stated in its charter, is to assist in promoting the interest of mathematics in America — and to vitalize and coordinate the work of local organizations of teachers of mathematics. Thus, NCTM is an organizat ion of persons in terested in mathematics, the teaching of mathematics, and concerns related to mathematics education.
“Life,” a fascinating game
Authors: Meneghan Lauren L.
Published: October 2020

John Conway's game of “life” provides a delightful and fascinating game for students of junior high school. (The introduction to Mr. Conway's game can be found in an article by Martin Gardner in the October 1970 issue of Scientific American.) Mr. Conway intended that the game be played by one person, but it can easily be adapted so that two or three students can play the game at one time.
Using research in teaching: Notes from National Assessment: Recognizing and naming solids
Authors: Carpenter Thomas P. , Coburn Terrence G. , Reys Robert E. , Wilson James W.
Published: October 2020

Little attention was given to the study of geometry in the elementary school until the curriculum changes instituted during the 1960s. The goals for geometry in the modern programs varied from visualizing and describing spatial concepts and relationships to developing aesthetic abilities and critical thinking skills. In addition to the importance of developing spatial concepts, some mathematics educators feel that geometric ideas are helpful in developing certain measurement and number ideas. Thus geometry has several basic ro les to play in the elementary school mathematics curriculum and its inclusion is well justified.
IDEAS
Authors: Burns Marilyn
Published: October 2020

This month's IDEAS section presents several measurement activities. It is important for your students to become familiar with the metric system. Learning by doing is most effective; ideally students learn by using metric measurements to solve real problems in their lives. The activities included here aim at providing activities for getting students using some of the units. The emphasis is on exploring a problem, with the side benefit of the experience of using metric units.
Your Council at Work: Nominees for the 1977 Election
Authors: Schaaf Oscar , Edwards Edgar L. , Elliott Mabel M. , Hardgrove Clarence E. , Hill Thomas J. , Howitz Thomas A. , Price Jack , Clair Irene St. , Ross Taylor B.
Published: October 2020

The Nominations Committee needs your help in selecting nominees for the 1977 election. At that time a president for NCTM and four new members for the Board of Directors will be elected.
Let's Do It!: Using indoor games to motivate mathematics learning
Authors: Bruni James V. , Silverman Helene J.
Published: October 2020

Most teachers recognize the motivational value of games and the tremendous opportunities they afford for using numbers in meaningful ways. Familiar or traditional games can be modified to use with children of different age groups or developmental levels and to include different aspects of the mathematics curriculum that need to be developed. Jacks, pick-up sticks, and tiddly-winks are examples.
IDEAS
Authors: Burns Marilyn
Published: October 2020

The IDEAS this month are for investigating multiplication facts and multiples in some different ways. The activities presented do not guarantee that all students will have their multiplication tables committed to memory, but they are an attempt to provide a variety of experiences in which children have the opportunity to learn the facts through repeated exposure and use. Other activities that will help to fill your classroom with the mysteries of multiplication appear in the following IDEAS sections in the Arithmetic Teacher: November. 1974. pp. 608-9, and April. 1975. pp. 301-2.
ONE POINT OF VIEW: The hand-held calculator
Authors: Immerzeel George
Published: October 2020

One out of ten people in the United States has a minicalculator. When you walk through the grocery store you see shoppers, with calculators in hand, making decisions about the best buys. Your banker may use a minicalculator to answer some of your questions. At the calculator counter in your favorite department store, you see clusters of customers examining calculators to buy for themselves or their friends. There is no question that more and more people are using a calculator. It is time for each teacher of mathematics to have a minicalculator and it is time that we, as teachers of mathematics, find ways to use these amazing little devices to teach mathematics.
The basic fact “bug”
Authors: Dillard Rogers Barbara
Published: October 2020

Are basic racts bugging your kids? Then try the “basic fact bug,” a vehicle that runs on addition or multiplication. Get more mileage out of drill and practice on basic facts.
Skittlefact
Authors: Carlisle Earnest
Published: October 2020

The “skittle” games are very popular with today's youth. It is a simple task to transfer the idea to mathematics and create a game to challenge children and give them a solid drill activity at the same time. We named our game “skittlefact.”
Magic triangles and a teacher's discovery
Authors: Yates Daniel S.
Published: October 2020

I had a very interesting experience recently with a number puzzle that I would like to share with others. At a mathematics convention, I saw a friend, Evelyn Graham of Chesapeake, Virginia, who thrust nine little cardboard squares, each containing one of the digits, I through 9, into my hand and challenged me to … well, due to convention noise and the fact that when Mrs. Graham is enthusiastic and excited about something, she tends to talk faster than I can listen, I came away with two ideas. First, the digits had to be arranged in the shape of a triangle, and second, it had to be magic (meaning that each row should add up to the same number).
Spiral mathematics
Authors: Stewart Margaret
Published: October 2020

Teacher today are continuously faced with the problem of motivating students. especially the slowlearning junior high student. Mathematics teachers ure no exception. Teachers try every “trick in the book.” and make up a few on the side. in their efforts to get and keep the interst of students.
A bonanza of card games
Authors: Reagan Brenda Sue
Published: October 2020

This bonanza of card games is three games—Primo, Exponential Express, and Primo Express—in one. Each of the games is played by three or four players.
“Chek-Math”—a new old game
Authors: Rasimas Joseph A.
Published: October 2020

The game “chek-math” is a post-instructional, drill activity based on the game of checkers. The object of the game, naturally, is to win at checkers, but to do this one must be more competent than one's opponent in the mathematics areas coordinated with the activity. The necessary materials are readily available to most teachers and students or can easily be constructed. Two individuals can play the game, or small teams can play.
Your council at work: Research Advisory Committee
Authors: Dessart Donald J.
Published: October 2020

One of the major task facing the Research Advisory Committee (RAC) is to serve the needs of two groups: researchers in mathematics education, who are primarily concerned with understanding the learning process: and practitioners (teachers, supervisors. principals), who are mainly concerned with finding more effective ways to teach children. Researchers, guided by their intuitions, study problems and often obtain results that are not directly applicable to the classroom situation: practitioners, on the other hand. actively pursue better ways to educate children in the classroom. To insist that researchers should address themselves only to the immediate problems of the classroom seems to be an unwise course of action, since the history of science includes many discoveries that had useful applications years, or even centuries, after their di scovery. Yet for researchers to ignore the need of the classroom may lead to sterile research results that only collect dust in the darkened corners of a library.
Let's Do It!: The multiplication facts: once more, with understanding
Authors: Bruni James V. , Silverman Helene J.
Published: October 2020

Knowledge of basic multiplication facts is part of the basic competency that most educators expect from all students in the study of mathematics—few educators deny the importance of children knowing the multiplication “facts” through 9 × 9. It is an important objective of every elementary school mathematics program. Many teachers spend a great deal of time helping children “learn their facts,” and often these experiences are frustrating for both the children and their teachers. One day a child seems to know the facts, and a week or month later many facts are forgotten. Often children will remember familiar products like 36, 54, or 72, but be willing to assign those numbers to any pair of factors, indiscriminately.
The Missing Link
Authors: Harring Ruth
Published: October 2020

Have you ever done any “chaining”? Here's the chain to conquer all chains! It began quietly and innocently when Larry saw a bin full of rectangular paper strips tucked away in a dark storage shelf in the art area. It was almost as if the paper st rips were waiting to be discovered. It wasn't unusual that Larry, of all people, would discover them. Larry is the type of child who sees and touches everything.
Addition practice through partitioning of sets of numbers
Authors: Murray Peter J.
Published: October 2020

Tommy has 5 sacks of marbles. Each sack is labeled with the number of marbles it contains. (Fig. 1) He wants to give all of these marbles to his two friends, Joe and Billy. How can he give each of them the same number of marbles without opening any of the sacks?
Will tokens and trophies teach mathematics?
Authors: Sternberg Betty J.
Published: October 2020

As usual, Rodney met me at the car as I arrived at school. While helping me unload my car of mathematics equipment he said, “You always bring all that stuff. Why don't you give up and just give us our awards?”
Flower power, inc.: a lesson in economic growth
Authors: Ross Beverly B.
Published: October 2020

As an experiment in making economics a “thriving” course of study, fifth-grade students at Cedar Lane Elementary, a Fairfax County public school in Vienna, Virginia, undertook a th ree-month, full-scale managerial project. They established a classroom corporation.
Coding for fun and mathematics
Authors: Chinn Phyllis Zweig
Published: October 2020

Using various types of coding can provide pleasurable practice in mathematical skills at many levels of sophistication. This article provides many examples of poss ible ways to combine mathematics and coding, giving a wide variety of applications.
String sculpture in the mathematics laboratory
Authors: Perl Teri
Published: October 2020

Early last school year. during a parent's work night, a group of parents made a dozen 36- and 37-nail circular geoboards for our mathematics laboratory. This was the beginning of one of the most popular and successful activities in our mathematics laboratory that year—string sculpture.
Energetic lessons on energy
Authors: Solana Terry
Published: October 2020

Amid complaints about being too hot or too cold, not being able to take weekend trips, having to drive too slowly, and myriads of other such complaints, the creative mathematics teacher has once again risen to the forefront. What seems to be a very trying experience for everyone can be transformed into a very meaningful unit of instruction in the truest tradition of Nuffield.
GCF and LCM on a geoboard
Authors: Jeffrey Neil J.
Published: October 2020

The theme that physical devices illustrating mathematical concepts enhance children's understanding of those concepts is an old one. A Atempting to integrate various branches of mathematics is a current trend in mathematics education. For these reasons, I was particularly interested in the somewhat unexpected appearance on my geoboard of the greatest common factor (GCF) of the two numbers with which I was working.
Hot & cold cubes
Authors: Jencks Stanley M. , Peck Doald M.
Published: October 2020

A simple model that portrays both addition and subtraction of positive and negative numbers is hard to find. A few years ago the authors ran across one that has been so successful it must be passed on for other teachers to use. This model lies in the realm of fanta sy yet provides an easily imaginable and crystal-clear picture of how positive and negative numbers behave when they are added or subtracted.
Sometimes material leads to discovery
Authors: Morgenstern Frances B. , Pincus Morris
Published: October 2020

The use of manipulative materials for the exploration and discovery of mathema tical ideas or relationships, and for making symbols and operations meaningful, is considered an important feature of mathematics programs today. However, sometimes ma terials are used in too casual or transitory a manner. The fact that the material lends itself to discovery and to understanding does not automatically insure that discovery or understanding will occur.
An easy way to change repeating decimals to fractions—Nick's method
Authors: Robidoux Dennis , Montefusco Nicholas
Published: October 2020

During a pre-algebra class on changing repeating decimals to fractions, Nick noted a relationship between the original problem and the answer and proposed a method for finding the fraction. After checking this method through various types of problems, it appears that the method is feasible.
Your Council at Work: The Editorial Panel Of The Mathematics Teacher
Authors: Nichols Eugene
Published: October 2020

The Mathematics Teacher's Editorial Panel is responsible for creating the overall policy regarding the reviewing of manuscripts. It is also responsible for balancing the journal's content and for creating special se.ctions. Their goal is to produce a journal that serves the interests of mathematics teachers in grades seven through fou rteen.
Measuring, science, and history
Authors: Webb Leland F.
Published: October 2020

The time-line problem that is described here is an activity that requires the use of the metric system and develops a moderate amount of integration of science and mathematics, with a little history added. Since a “group” effort may be required to deal with some of the mathematics concepts involved, it is best to work in teams (two or three students to a team). Each team will need the following materials (1) a narrow strip of paper about 5 meters long (adding machine tape is ideal), and (2) a meterstick (one per team).
Blueprint for ratio and scale
Authors: Coppel Arlene Cohen
Published: October 2020

My mathematics class was a high ability, sixth-grade group who understood ratio and scale, but, at the start of the project described here, needed practical exercises in using these skills. The need for practice in applying the concepts of ratio and scale suggested the use of architectural floor plans.
A model for a remedial mathematics program
Authors: Trembley Phil , Luke Hope
Published: October 2020

Children manifesting arithmetic learning problems have traditionally received patchwork help on a given assignment or on the lesson the class was currently tackling.
Even Peanuts can do it
Authors: Catanzano Robert , Welker Debra J.
Published: October 2020

Johnny was a child who had always failed mathematics. His first-, second-, and third-grade teachers passed him conditionally. His fourth-grade teacher recommended that Johnny obtain special help in reading and mathematics before he should enter the fifth grade. We found Johnny to be a happy, well-mannered len-year-old who indicated strongly that he hated mathematics.
Pentommoes for fun and learning
Authors: Cowan Richard A.
Published: October 2020

A pentomino is a plane figure that is formed by grouping five congruent, square shapes together so that every square has at least one of its sides in common with at least one other square. Two simple pentominoes are shown in figure 1. Before reading further, how many different pentominoes can you construct? Two In figure 2, for example, a, b, c, and d are the same pentomino.
Unexpected classroom episodes can teach mathematics
Authors: Meyer Rochelle Wilson
Published: October 2020

Courses in mathematics content are standard fare for prospective and practicing teachers. Most of these courses are necessarily taught without an integrated component of classroom experience. Although the primary focus of a content course is mathematics not methodology, the content course is a proper forum to demonstrate an interplay between the mathematics understood by the teacher and the teaching methods used by that teacher. For example, a teacher who is insecure in his knowledge of an area is often very rigid in his presentation of that area and does not recognize or follow interesting student ideas. Having students play the role of classroom teacher is a technique that has helped students in my classes to see the interplay between understanding content and teaching it and to examine their depth of understanding in a particular area. I call it the “episode technique.”
The “new math”
Authors: Edwin Hirschi L.
Published: October 2020

There are critics of the “new math” and defenders of the critics of “new math,” and much has been written and said by both. While I respect the rights of these people to propound their views, I should like to present my own observations, supported by such evidence as seems appropriate and available.