bluuebunny/crossref_metadata_2025 huggingface dataset:
Mathematics throughout the curriculum
Authors: Frye Helen B.
Published: October 2020

If “Take a Mathematical Holiday,” which appeared in the November 1968 issue of The Arithmetic Teacher, stimulated as much thought in other teachers' minds as it did in mine, many mental wheels have been turning.
Editorial comment: As we read
Authors: Inskeep James E.
Published: October 2020

As you read this month's issue of the journal, note the fine representation that we have from classroom teachers. The key to quality mathematics education is the teacher and the approaches he uses to reach his children. One of these approaches is the use of the mathematics laboratory. Sometimes referred to as an activitycentered approach, the mathematics laboratory has taken on increased importance in the curriculum. This theme in our first month's issue of the Golden Jubilee Year of the National Council will be welcomed by all whose interest is the teaching of mathematics to children.
Trial and experiment
Authors: Biggs Edith
Published: October 2020

Many variations have been tried in the pattern and timing of mathematics workshops in England to encourage more teachers to provide their pupils with opportunities to learn mathematics actively. At initial workshops, which may be of three to five days duration, one important part of the program is the preparation of topics to try out in the classroom. For this, teachers of pupils of age range five to sixteen years work together, and each group chooses a topic.
Polygonal numbers: a study of patterns
Authors: Hervey Margaret A. , Litwiller Bonnie H.
Published: October 2020

Number patterns have interested mathematicians from the time of the ancient Greeks. Some of this interest centered around the relations between number expressed geometrically and algebraically. This idea is basic to the study of polygonal numbers. Polygonal numbers, which are sometimes called figurate numbers, include triangular numbers, square numbers. pentagonal numbers, hexagonal numbers, and so on. For example, if a number of objects can be arranged in the form of a regular triangle, that number is considered to be a triangular number. Figure I shows a geometrical pattern for the first five triangular numbers.
A divisibility test for amateur discoverers
Authors: Berenson Lewis
Published: October 2020

The following is a description of an elementary divisibility test appropriate for students in grades 7 and 8 as an enrichment unit. It offers the average student a golden opportunity to join the ranks of the mathematical discoverers. The brighter student will enjoy refining the process and exploring the many open-ended learning opportunities that the test provides. The simplicity of this very general test as well as the ease with which its underlying principle can be grasped further enhance its attractiveness. The use of divisibility by nine and eleven in checks of computations is an added reason for introducing students to a test of divisibility. As illustrations, we shall consider divisibility by six and by eleven. The procedure may be applied in like manner to any divisibility problem.
Editorial comment: As we read
Authors: Inskeep James E.
Published: October 2020

In the first surge of the mathematics content reform, many new topics were considered and incorporated into the elementary school curriculum. Algebraic ideas and the structure of the number system were given considerable emphasis. In the process, the elder brother of these topics, geometry, was often shelved or merely passed over. Today there is renewed interest in the teaching of geometry in the elementary grades. This concern has been adequately reflected in recent issues of The Arithmetic Teacher. (See the October 1966, February and October 1967, December 1968, and October 1969 issues.)
Kaleidoscopic geometry
Authors: Ann Alspaugh Carol
Published: October 2020

Kaleidoscopic geometry is an interesting type of mirror geometry that could be utilized to introduce geometrical topics such as regular polygons, coordinates of points in a plane, reflections, and symmetry. Most children enjoy the possible explorations offered by this geometry, which would make it useful to the teacher desiring to develop interest and motivation when introducing new materials.
An experimental approach to the Pythagorean theorem
Authors: Buchman Aaron L.
Published: October 2020

Modern mathematics programs for the elementary school stress the involvement of a greater amount of geometry. Among the geometric relations that can acquire meaning in the elementary grades is the Pythagorean relation: In a right triangle, the area of the square on the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
Forum on teacher preparation: Topics in geometry for teachers—a new experience in mathematics education
Authors: Kipps Carol H.
Published: October 2020

Can teachers capture by themselves the excited enthusiasm shown by children in classes sponsored by such curriculum groups as the Madison Project or Nuffield Project? Can a teacher reared on lecturedrill-homework classes feel and show the drama inherent in “I do and I understand” activities, in peer-group discussions, and in concepts such as the concrete-ikonic foundation of abstraction? A new course at UCLA is focusing on these dynamic factors on that teachers will know their value from their own personal experiences and feelings.
National Council of Teachers of Mathematics: Solicitation of Nominees
Authors: Meserve Bruce E. , Ellis Wade , Glenadine Gibb E. , Johnson Donovan A. , Karnes Houston T. , Keiffer Mildred , Magers Dexter A. , Skeen Kenneth C. , Sobel Max A.
Published: October 2020

Your suggestions for members of the NCTM Board of Directors and the next President-elect are the Council's best insurance against a too-narrow base for the selection of leadership. The usefulness of your suggestions will depend in part upon the thoroughness with which you document the recommended person's qualifications.
Mathematics through cardboard carpentry (a unit for low achievers)
Authors: Tinti Robert
Published: October 2020

In teaching certain skills and concepts in arithmetic, the mathematics teachers of the Bellport Middle School decided to develop high-interest activities that would be meaningful to students. We used a weatherproof triple-wall cardboard as the vehicle for these activities.1
A discovery approach to the introduction of flow-charting in the elementary grades
Authors: Kessler Bernard M.
Published: October 2020

Flow-charting comes from the computer industry. It is the technique that programmers use in the logical in truction of the computer
Volume and surface area of rectangular prisms: a maximum-minimum problem for the grades
Authors: Mann Nathaniel , Philippi Dale
Published: October 2020

To emphasize the distinction between perimeter and area, a useful lesson is one in which pupils use graph paper to draw many different rectangles of a given perimeter and then notice that these rectangles all have different areas. Since a lesson like this can be presented even in primarylevel classes, this discussion is limited for implicity's sake to integral values for the dimensions. For instance, rectangles of perimeter 16 could be 1 × 7, 2 × 6, 3 × 5, and 4 × 4. Students doing several such sets of rectangles with a given perimeter will discover the pattern: For a given perimeter, the square or the rectangle with length and width most nearly equal has the greatest area.
GJY insert: Women of Mathematics
Authors: Jacobacci Rora
Published: October 2020

In this day of female emancipation, it is not unusual for women to be engaged in studies of the exact sciences. It was not very long ago, however, that popular opinion opposed such pursuits, and opportunities for such studies were virtually nonexistent for most women. This is reflected in the annals of the history of mathematics where, between Hypatia of ancient times and Emmy Noether of our own, very few names of distinguished female mathematicians are recorded. In this paper, we shall consider briefly the life and scientific work of five extraordinary women, who did achieve mathematical distinction. They are Hypatia, Maria Agnesi, Sophie Germain, Sonja Kovalevsky, and Emmy Noether.
Creative mathematics at Nueva
Authors: Laycock Mary
Published: October 2020

That's the most beautiful description of infinity I have ever thought about,” exclaimed deep-thinking Benjie. For a nineyear-old to consider infinity and express his appreciation was a real mountaintop. With a box of base-three blocks before him, he had seen that three units make a long, three longs a flat, and three flats a block; then, in the same way, three blocks would make a long block, three long blocks a flat block, and three flat blocks a block block. The last question on the activity card was, “Does this process ever end?” At that point Benjie nudged me to say, “If I had all the wood in the world, it would not be enough to finish the process, and that is why it describes infinity.”
Focus on research: A comparison of two techniques for using visual-tactual devices to teach exponents and nondecimal bases in elementary school mathematics
Authors: Trueblood Cecil R.
Published: October 2020

An experiment was conducted to provide evidence on whether pupils, ages 9-1 I, would achieve and retain more by (1) manipulating visual-tactual aids or (2) observing and te!Jing the teacher how to manipulate such devices. Piaget's stages of intellectual development were used to hypothesize th at Method l would be superior to Method 2.
Early Mayan mathematics
Authors: Byrkit Donald R.
Published: October 2020

During the period 500 B.C. to 600 A.D., at a time when the rest of the world was, arithmetically speaking, in the dark ages, the Mayas of Central America built many buildings, temples, and courts that required considerable knowledge of mathematics. They developed a vigesimal system (base 20) of numbers with positional notation and a special symbol for zero. They wrote and used numbers as great as 12,489,781 and developed an intricate calendar that ran, never missing a day, for 2,148 years.
Graphs in the primary grades
Authors: Pincus Morris , Morgenstern Frances
Published: October 2020

Many topics that were formerly introduced in the upper grades are now being introduced successfully in the lower grades, some as early as kindergarten. The construction and reading of graphs is one of these topics.
Multiplication mastery via the tape recorder
Authors: Shafer Dale M.
Published: October 2020

Most instructors who have had the responsibility of teaching children the multiplication facts will readily admit that at several intervals preceding student mastery a certain amount of drill is necessary. The word drill should suggest nineteenth-century pedagogy only to those individuals who do not know how this teaching technique is being imaginatively employed in elementary classrooms today.
Better perception of geometric figures through folding and cutting
Authors: Ibe Milagros D.
Published: October 2020

Folding and cutting are very popular activities in the elementary school because children love to cut and create things. A book by Johnson1 has clearly shown how paper folding can be used as a concrete approach for understanding geometric concepts, line and angle relationships, symmetry, and circle relationships among other things. For children, however, these relationships can be made more concrete through folding and cutting activities.
Useless knowledge and how to produce it
Authors: Steinen Ramon F.
Published: October 2020

As an undergraduate I had a library card whose number was 1066. There was one librarian who was often at the checkout desk, and for three years, each time she checked out books for me, she cried, “1066—Battle of Hastings!” This fact, which has been indelibly imprinted on my mind, is a good illustration of what I choose to call “useless knowledge.” The reason I feel it is cless is that I have no idea where Hastings is or who fought the battle, no idea why the battle was fought or who won. (And I have no wish to learn, since that would spoil this illustration!) Unfortunately, this is the kind of “knowledge” that many students acquire in their mathematics classes.
Making a game of it–responsive teaching
Authors: Crowhurst Norman H.
Published: October 2020

A conference for mathematics teachers in Brookings, Oregon, scheduled a panel discussion titled “Making a Game of It.” Because of a heavy and unexpected snowstorm, panel members did not arrive and this part of the program was canceled. To help allay the disappointment of those who were interested in the topic, the author offered to moderate a group discussion. It is outlined here to show how, by responsive teaching, you can make a game of ordinary topics in arithmetic.
Things you can try: Dominoes in the mathematics classroom
Authors: Junge Charlotte W. , Massey Tom E.
Published: October 2020

During a summer mathematics program for ninth-grade students at the P. K. Yonge Laboratory School of the University of Florida, the mathematics staff found a traditional game to be a very popular and effective learning aid. The game of dominoes was enjoyed and played frequently by students of all levels of ability.
Understanding through Involvement
Authors: Bartel Elaine V.
Published: October 2020

Educators have known for a long time that maximum learning occurs when children become actively involved in the learning process. Principals, classroom teachers, and those involved in teacher training have long proclaimed the desirability of such active involvement on the part of the learner; yet observations of classrooms in action often do not give evidence of anything beyond lip service to this fundamental principle.
The Computer Motivates Improvement in Computational Skills
Authors: Pagni David L.
Published: October 2020

Like most of us, children are aware of the proliferating use of computers. Television has portrayed the computer as an “electronic brain” capable of solving any problem; the space program stressed two computer-monitored Apollo missions; and a Disney movie featured a computer as a costar. The very word computer carries with it an aura of magic and mystifying omnipotence because of its far-reaching applications.
Things You Can Try: Confirming The Pythagorean Theorem
Authors: Sullivan John J.
Published: October 2020

The following remarks may be considered an appendix to Aaron Buchman's article, “An Experimental Approach to the Pythagorean Theorem,” in the February 1970 issue of The Arithmetic Teacher. Their major objective is to provide an intuitive demonstration of the Pythagorean theorem while reinforcing notions of area measure of tri angles and squares.
Things You Can Try: Make a Whole-a Game Using Simple Fractions
Authors: Rode Joann
Published: October 2020

The game called “Make a Whole” helps develop the concept of fractional numbers by using concrete examples; it gives reinforcing experience with the use of fractions and their equivalents. It is suggested for use at third-grade level and above, depending on the achievement of the students.
ONE POINT OF VIEW: One Teacher's Point of View
Authors: Hight Donald W.
Published: October 2020

In the past decade the NCTM has become outstanding in encouraging and sponsoring meeting at which can exchange ideas, examine new materials, and learn of new procedures, research, and innovation. Furthermore. from the NCTM, excellent publications providing imilar information have become quite numerous, varying in size and price. Recently movies have been produced that teach and inform me of new materials and concepts. Indeed, the NCTM has excelled in peaking to me and providing information and encouragement to me.
One eagle is worth ten dollars
Authors: Watman Michael X.
Published: October 2020

Charity book sales often deliver to the casual peruser some gems of antiquity for little mo re than pocket change. Between the covers of stacks of faded-yellow National Geograplric magazines, within the countless mystery yarns of yesterday, and among last year's best sellers lie insights unimagined by their authors. No type of book is ric her in its commentary than the outdated mathematics textbook! Before your burgeoning disbelief causes you to flip the page, let me cite two examples from my collection of attic-library rejects
If I could only make a decree
Authors: Johnson David R.
Published: October 2020

President of state mathematics council cannot make decrees, and that is a good thing! I am pleased that I do not have that power- and yet, if I did, I would make but one decree. This dec ree would affect all mathematics educators in the nationelementary, junior high, econdary, and college teachers! That's the way decrees hould be made. They should affect the total population.
Children's errors in telling time and a recommended teaching sequence
Authors: Reisman Fredricka K.
Published: October 2020

The basic units of time are natural ones: the year, the period of recurrence of the easons; the day, the period of recu rrence of daylight and darkness. The first recorded descriptions of man-made divisions of the year and the day were given by the Sumerians about 3500 B.c.
Improving mathematics verbal problem-solving ability through reading instruction
Authors: Henney Maribeth
Published: October 2020

One area that elementary school children find difficult is solving verbal problems in mathematics.
IDEAS
Authors: Immerzeel George , Wiederanders Don
Published: October 2020

Ideas is presented to provide you with an easy way to try out some ideas that we have found interesting in our classroom. In each issue we plan to present several worksheets. One of these worksheets will be appropriate for your students.
Paper folding and cutting a set of tangram pieces
Authors: Dickoff Steven S.
Published: October 2020

In a recent teacher-training workshop conducted by the author, a question arose concerning a method for duplicating the seven pieces of the ancient Chinese tangram puzzle without having to trace the pieces of another puzzle. After some thought about the relationships of the pieces in the puzzle to one another, the following paper-folding and cutting method, illustrated diagrammatically, was conceived.
Abstract (verb) versus abstract (adjective)
Authors: Steinen Ramon F.
Published: October 2020

In a previous article it was suggested that a student can best learn to deal with mathematical abstractions by making them.1 This means that a mathematics teacher should think of the word abstract as a transitive verb rather than as an adjective. The aim of this a rtic le is to illustrate this thesis with a few specific examples.
Ideas
Authors: Immerzeel George , Wiederanders Don
Published: October 2020

Ideas gives you an easy way to try a variety of ideas in your classroom. Each month this feature focuses on a key area of mathematics. Several worksheets are provided. At least one of the worksheets will be appropriate for your students.
Teaching one of the differences between rational numbers and whole numbers
Authors: Prielipp Robert W.
Published: October 2020

What are some ways in which rational number (fractions) differ from whole numbers? How can we make these differences evident to elementary school children? We begin by looking at two ways in which rational numbers and whole numbers differ, and then we consider in depth a procedure that can be followed to teach one of these differences.
Elementary school mathematics in the 1970s
Authors: Clark John R.
Published: October 2020

Following the successful launching of Sputnik, Congress created the National Science Foundation with instructions and funds to upgrade the scholarship of teachers of mathematics and science. Prestigious professors of mathematics, in cooperation with committees of the Mathematics Association of America and the National Council of Teachers of Mathematics, set out to produce a modern program of instruction in school mathematics. The then-existing programs were analyzed and found to be seriously inadequate in structure, in definitions and assumptions, in development of properties of operation with their appropriate symbolism, and in precision of vocabulary. During the early 1960s institutes and writing teams were engaged in producing and promoting the so-called new mathematics. The resulting reform movement in mathematics education eclipsed any previous one, both in scope and in speed of implementation.
Ideas
Authors: Immerzeel George , Wiederanders Donald
Published: October 2020

Ideas presents an easy way for you to try out a variety of ideas that have a high level of student interest. Each issue of the Arithmetic Teacher will present several worksheets on a key concept of mathematics. At least one of these worksheets will be appropriate for your students.
Fun with fractions for special education
Authors: Jacobson Ruth S.
Published: October 2020

A device to aid the learning of addition and subtraction of fractional numbers named by like and unlike fractions has been developed in a class for children with special learning disabilities at Boston University School of Education. It is a manipulative device that provides immediate feedback on the correctness of the child's answer to a problem.
One Point Of View: What's the answer?
Authors: Suydam Marilyn N.
Published: October 2020

We hear from all sides: “Schools have problems. We must solve these problems. Here is the way to solve them.”
An elementary theory of equations
Authors: Lay L. Clark
Published: October 2020

Curriculum changes in elementary mathematics during the past fifteen years have featured the introduction of algebraic content at lower grade levels than formerly. For example, there has been a drop from the ninth grade to the first grade for the first mention and use of parentheses and inequalities. But some ideas from beginning algebra have been more resistant to introduction in the primary and middle grades. One such topic that has lacked an elementary introduction is truly fundamental. It is the study of the solutions, and the transformations to equivalent forms, of simple linear equations.
Diagnosing pupil errors: looking for patterns
Authors: West Tommie A.
Published: October 2020

Diagnostic teaching is teaching that looks at the errors children make and subsequently structures the learning experiences so that the errors will be eliminated. There is hardly a skill in the teacher's repertoire that is more important than the ability to identify pupil errors and prescribe appropriate remedial procedures.
Things you can try: A snip of the scissors
Authors: Witt Sarah M.
Published: October 2020

When her class put on a play about Betsy Ros, my daughter played the part of Bchy. According to legend, Betsy fashioned the American flag from thirteen alternating strips of red and white cloth and a patch of blue. She made the stars with just “a snip of the scissors.” My daughter came to me with the problem “How can it be done?”
Things you can try: A model for using diagnosis in individualizing mathematics instruction in the elementary school classroom
Authors: Trueblood Cecil R.
Published: October 2020

A revolution in mathematics instruction has begun and will probably continue through this decade. The revolution consists of a major change in the elementary school teacher's role in the educative process. The teacher of elementary school mathematics is modifying his traditional role as “director” and “lesson planner” for classroom-sized groups and is assuming the role of “instructional programmer” for individual learners. In assuming this role, the elementary mathematics teacher's concern has shifted to exercising more control over the instructional environment by arranging scope, sequence, content, feedback, evaluation, and materials appropriate for individual learners.
Considerations for teachers using manipulative materials
Authors: Reys Robert E.
Published: October 2020

Classroom teacher of mathematics are witnessing an unprecedented period of proliferation in manipulative materials. Commerical catalogs list a great variety of available materials; professional journals carry many advertisements claiming that this device or that aid will provide a panacea for learning a certain mathematics topic; and professional meetings are frequently inundated with exhibits displaying new manipulative materials. This influx of newly available materials has precipitated many problems. The wide range of quality found among various materials has made the problem of selection much more difficult. It has made it impossible to list all ava ilable materials and discu s the merit-or lack of merit-of each. It has created doubts in some teachers minds about the educational value of the materials. It has rai cd additional teacher-oriented questions such as “What are some guidelines for selecting manipulative materials?” “What materials should be used?” “What arc some dos and don'ts of using them?”
Ideas
Authors: Immerzeel George , Wiederanders Don
Published: October 2020

Ideas presents an easy way for you to try out a variety of activities that have a high level of student interest. Each issue of the Arithmetic Teacher presents several activity sheets that focus on a key concept of mathematics. At least one of these activity sheets will be appropriate for your students.
A game introduction to the binary numeration system
Authors: Niman John
Published: October 2020

Have you ever encountered a teasing child who would only answer you with yes or no? If you ever do, tell him that you are going to read his mind through his revealing yeses and noes—and all you are going to do is ask him the same question several times! Tell him to choose a number between 1 and 256. Then pose the question “Is the number odd?” If he says yes, tell him to subtract one and divide the remainder by two. If he says no, simply tell him to divide his number by two. Follow this procedure until the question has been asked at most eight times. The game stops when the number one is reached.
Individualized instruction: Sweet in theory, sour in practice
Authors: Henderson George L.
Published: October 2020

According to Western tradition, the two greatest teachers were Socrates and Jesus Christ. Both individualized their teaching. A Socratic technique was to bring the learner to recogni tion of a concept or generalization through teacher-led discussion. Christ communicated in a forceful and lucid way with individuals and with groups of individuals.
Success for all: An adventure in learning
Authors: Rouda Eileen M.
Published: October 2020

Trying to unlock the door of learning to underprivileged children can certainly be an adventure! This has become the recurring theme with the initiation of a systematic skill-development program for the children in an urban second-grade classroom.
Ideas
Authors: Immerzeel George , Wiederanders Don
Published: October 2020

Ideas Presents an easy way for you to try out a variety of activities that have a high level of student interest. Each issue of the Arithmetic Teacher presents several activity sheets that focus on a key concept of mathematics. At least one of these activity sheets will be appropriate for your students.
One point of view: Flight to reality
Authors: Brydegaard Marguerite
Published: October 2020

If we are to teach geometry to young children, we must take flight to reality. We no longer live in an age in which we can be satisfied with merely requiring teachers to take university credits and then implementing their inadequacy with in-service workshops. The new age demands a new revolution—a revolution in which action is taken that produces knowledgeable, enlightened, liberated teachers. Such liberation calls for teachers who (1) understand the concepts and language of the informal geometry that is basic to the elementary school program, and (2) see and master excellent procedures for teaching the subject. Teachers have a tendency to teach in a way similar to that in which they were taught. Teachers should create classroom environments that are innovative, creative, and designed to challenge the scholarly thinking of pupils. The flight to reality must be fashioned in a search for wisdom that extends beyond the acquisition of knowledge.
The sands of time—a sandglass approach to telling time
Authors: Strangman Kathryn Besic
Published: October 2020

Time, like length, area, volume, weight, temperature, and so on, is an entity we measure. But the approach to teaching how to “tell” time is usually different from that used for other types of measurement. In fact, the approach that a teacher uses often varies from one type of measurement to another.
It's moving time
Authors: Swerdlin Richard
Published: October 2020

Wheels turn and turn, and another American family is on the move. With millions of Americans changing their place of residence each year, an increasing number have taken the do-it-yourself approach to moving household goods by using a variety of rented equipment. This trend can be used to advantage in the classroom, for it provides a source of many realistic mathematics problems. One such problem, for instance, is to determine the requirements for moving goods. To do this it is necessary to estimate the space required.
Nominees for 1973 Election
Authors: Johnson Donovan A. , Ellis Wade , Ferguson W. Eugene , Greenholz Sarah , Heinke Clarence H. , Karnes Houston T. , McNabb William K. , Smith Lehi , Tolson Juanita S.
Published: October 2020

The Nominations Committee needs your help in selecting nominees for the 1973 election. At that time, a president-elect and four new members for the Board of Directors will be elected. Board nominees who represent the elementary school level, the junior high school level, the two-year college level, and the North Central region are needed.
The addition table: Experiences in practice-discovery
Authors: Hervey Margaret A. , Litwiller Bonnie H.
Published: October 2020

Mathematics is often referred to as a study of relations and patterns. Many elementary teachers would agree with this idea, but they may have difficulty in finding materials that will provide opportunities for their students to discover patterns. The addition table may be used as an effective vehicle for the discovery of some number patterns. While searching for patterns, the students are engaging in purposeful practice, which results in a “practice-discovery” activity.
Gus's magic numbers: A key to the divisibility test for primes
Authors: Oliver Charlene
Published: October 2020

An of us are familiar with a divisibility test for 3 in which we add the digits of the number being tested. Some of us are familiar with a divisibility test for 7. How many of us, though, are aware that a divisibility test for 7 may also be used for 3?
A different approach to the sieve of Eratosthenes
Authors: Omejc Eve
Published: October 2020

The sieve of Eratosthenes, as a method of determining prime numbers by elimination of all multiples of primes, has been known and used by teachers for many years. The process usually presented becomes tedious as the numbers become larger. For instance, in crossing out all multiples of 29, one must count twenty-nine numbers each time or use multiplication or repeated addition to locate each succeeding multiple.
A fifth grade's revision of our system of number names
Authors: Pincus Morris
Published: October 2020

During a discussion on large numbers in a fifth-grade class, one chi ld said, “I have an uncle who says ‘fivety-five’ instead of ‘fifty-five.’” There was a burst of laughter from the class.
Eight-ring circus: A variation in the teaching of counting and place value
Authors: Rinker Ethel
Published: October 2020

This article describes a technique used by one third-grade teacher to provide enjoyable learning experiences in the study of counting and place value. The technique may be used in other grades with appropriate adjustments for the grade level and the needs of the individual classes.
The Match Game
Authors: Holtkamp Larry
Published: October 2020

After the concept is understood, children need much drill in changing percents to decimals and fractions or changing fractions to decimals and percent. However, needless to say, drill can be very boring unless there is some mean of motivation. To provide such motivation, I developed a game that I call the “Match Game.”
“Fradécent”—a game using equivalent fractions, decimals, and percents
Authors: Armstrong Charles
Published: October 2020

Fradécent is a card game that is useful in helping sixth graders learn equivalent fractions, decimals, and percents as well as aiding them in adding and subtracting fractions. The word fradécent contains parts of the words fraction, decimal, and percent.
Where is Droopy?
Authors: Rainsbury Ron
Published: October 2020

Cartoons and cartoon characters are great favorites among children. Why not use this interest in the classroom! Sixth graders at Washington School in Eugene, Oregon, were introduced to the rectangular coordinate system with a game—and the object of the game was to locate Droopy, a cartoon canine.
Things you can try: A permanent-soap-bubble geometry
Authors: Wahl M. Stoessel
Published: October 2020

For years the study of soap-bubble geometry has been a source of surprise and fascination to individual students. However, it has not been a satisfactory technique for classroom study: just as the teacher holds up a good specimen for the class to admire, the bubble bursts!
Using research in teaching: Piagetian research and the school mathematics program
Authors: Rosskopf Myron F.
Published: October 2020

The tasks Piaget and his co-workers (the “Geneva group”) have devised for their investigations usually have a mathema tics or science basis. For this reason alone, the Piagetian research is of inter est to teachers of mathematics. Another reason for the growth in appeal of the work of the Geneva group is that their descriptions of the development of thinking in children explain so many of the sometimes curious answers children give to a question posed in a classroom. Experienced, observing teachers have often been puzzled by these answers. Piagetian theory helps to make sense out of them. For one of the keen observations of Piaget is that a child's logic is not the same as an adult's logic. The logic a child uses is not an immature form of adult logic. It is his own, and it develops as he acts on objects, explores them, and manipulates them.
A case against teaching mathematical concepts to slow-learning children
Authors: Rebec Linda
Published: October 2020

Concept teaching in mathematics is one of the sacred cows of education that we have revered in the past several decades. We have convinced ourselves that it is wiser and infinitely more modem than teaching mathematical operations by rote. Our concern with teaching the why of numerical operations has taken us to the point of inventing a “new math.” Under the new mathematics, instead of “ teaching” concepts, we have students “discovering” the same. It's merely a new means to an old end—learning accuracy in working with mathematical problems. And it brings with it numerous headaches for teachers, parents, and most unfortunately, the students themselves.
IDEAS
Authors: Immerzeel George , Wiederanders Don
Published: October 2020

Ideas presents an easy way for you to try out a variety of activities that have a high level of student interest. Each issue of the Arithmetic Teacher presents several activity sheets that focus on a key concept of mathematics. At least one of these activity sheets will be appropriate for your students.
Things you can try: “Fraction Rummy”—a game
Authors: Rowland Rowena
Published: October 2020

“Fraction Rummy” is a card game for two to six players. The deck contains fifty cards, thirty-one showing a common fraction and nineteen showing a decimal fraction. Each player is dealt five or seven cards, depending on the number of players. The stack of undealt cards is laid face down, except for the top card, which is turned face up to start the discard pile.
Adapting the area of a circle to the area of a rectangle
Authors: Colter Mary T.
Published: October 2020

One of the most difficult problems for a student studying the areas of regions bounded by geometric figures, regardless of whether he is in the fifth or ninth level in mathematics, is the area of a circular region. The student may memorize the formula, know where to plug in the values, consistently arrive at the correct answer, but never comprehend and master completely the problem. The teacher assumes Johnnie knows what the area of a circular region means by hearing him repeat some “fed facts.”
What's Your Position On Behavioral Objectives?: Behavioral objectives, a cause célèbre
Authors: Walbesser Henry H.
Published: October 2020

Although I view with great alarm the growing number of negative effects on mathematics education that are being generated by the application of behavioral objectives, I remain a behaviorist. This paper is written with two objectives in mind: (1) to expose the educationally damaging consequences of adopting behaviorism and (2) to attempt to reestablish the credibility of behavioral objectives as a significant educational strategy.
Ideas
Authors: lmmerzeel George , Wiederanders Don
Published: October 2020

Each IDEAS presents activities that are appropriate for use with students at various levels in grades K-8. Whett you have chosen the activities that are most appropriate for your students, remove the sheets and reproduce the copies that you need. After a sheet has been used, add your own comments and file the materials for future use.
Using research in teaching: Another look at “A change in focus”
Authors: Reys Robert E.
Published: October 2020

The Arithmetic Teacher bas published more research studies in mathematics education than any other journal. This is quite an accomplishment: it becomes even more significant when you realize that the Arithmetic Teacher is not yet twenty years old! During this period, the type of research article published in the Arithmetic Teacher has undergone a complete metamorphosis. In addition to an improvement in the quality of articles, there has been a considerable change in manuscript style and format.
Five “nontrivial” number games
Authors: Trotter Terrel
Published: October 2020

Number games can provide elementary students with a good opportunity to test their observation skills for problem solving, and at the same time they will be practicing such drill skills as adding and subtracting. Here are five trivial number games guaranteed to provide hours of fascination and lots of hidden drill. The word trivial is used here with two meanings in mind. The games are trivial in the usual mathematical sense—namely, once the secret is known to both players, the game's winner is predetermined, based on the starting number and who begins play. The games arc nontrivial from the point of view that they are valuable teaching aids for motivating student thinking.
Reading big numbers
Authors: Morgenstern Frances B. , Pincus Morris
Published: October 2020

On several occasions the writers of this article have noted the difficulties that children encounter in reading large numbers. When confronted with a number beyond the order of magnitude of thousands, children begin to produce such strange combinations as thousand hundreds, ten hundred thousands, and even million hundreds; thereby revealing the lack of any organizing principle. For many children, there seems to be no recognition that there is a pattern within large numbers that provides a key to understanding and reading the numbers.
If the hands can do it the head can follow
Authors: Jacobs Israel
Published: October 2020

Maureen looked down at the egg cartons. Tentatively she separated the singles, then she took the three sets of four out of the group and put them aside. Hesitatingly she continued the process of separating the cartons until the whole set of egg cartons was apart. She pursed her lips and stared down at the disassembled cartons. A pencil and paper lay nearby to record comments.
One point of view: The next decade
Authors: Engen Henry Van
Published: October 2020

In the past decade, great progress has been made in improving the mathematics found in elementary school textbooks. True, it is still possible to find, here and there, some rather horrible examples of mathematical ineptitude, but by and large the situation is much better than it was ten or fifteen years ago.
Method or justification?
Authors: Quast W. G.
Published: October 2020

Many of the recent elementary school textbook series and other programs utilize a variety of procedures in presenting the algorithms for work with whole numbers. The purpose of this multiprocedure approach is to seek to develop within the students some degree of understanding of computation rather than to rely on rote, mechanical, step-by-step directions. Unfortunately, the use of a variety of procedures raises some problems with regard to intent and implementation on the part of the teacher. In particular, teachers frequently become confused as to whether or not a given procedure is a method (an algorithm) or a justification for an a lgorithm.
The fourth operation is not fundamental
Authors: Zweng Marilyn J.
Published: October 2020

It is becoming increasingly more popular to define mathematics programs in terms of behavioral objectives. Statements of behavioral objectives serve to highlight the significant aspects of a lesson, or a set of lessons, and as such are helpful in planning for teaching and learning. However, there is cause for concern. All too frequently, behavioral objectives are short range and piecemeal, and little distinction is made between intermediate goals and broad objectives. This is particularly true with respect to the teaching of computational skills. A reading of most lists of behavioral objectives for elementary school mathematics programs leaves the impression that being able to add, subtract, multiply, and divide are ends in themselves. They are not. Being able to compute is of very little use unless it can be appropriately applied to problem solving.
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 from your arithmetic teacher and reproduce the copies you need. After you have used an activity sheet with your students, add your comments and file the materials for future use.
Perspective in the Field of Arithmetic
Authors: Buckingham B. R.
Published: October 2020

One of my colleagues at Ohio State University, although he taught courses in the field of elementary education, used to dismiss arithmetic with the remark—often repeated during the twenties—that the subject had come to a standstill, that there was little more to be learned about it, and that those who concerned themselves with it as a field of inquiry were dealing with trivialities. We knew all we needed to know, said he, about arithmetic and all of any consequence that we were ever likely to want to know.
An Experimental Approach to the Division Idea
Authors: Dawson Dan T. , Ruddell Arden K.
Published: October 2020

There are but few serious questions today about the theoretical value of meaning theory in teaching arithmetic. A previous article in THE ARITHMETIC TEACHER1 clearly states the case for meaning in arithmetic. However, previously reported research deals primarily with transfer of learning, retroactive inhibition, and drill. Relatively few leads have been provided for teachers interested in specifics such as, “What methods do I use in presenting division?” or “Just how does one use manipulative materials?”
Concept of Money via Experience
Authors: Smith Linda C.
Published: October 2020

The difficulty which children encounter in the reading and interpretation of problems is a concern of every teacher of arithmetic.
The Function of Charts in the Arithmetic Program
Authors: Williams Catherine M.
Published: October 2020

Many teachers do an effective job of using concrete manipulative materials to help children with initial stages of the formation of arithmetic concepts. All too frequently, however, the teachers shift so rapidly from these concrete, visual experiences to abstract verbal symbols that children are unable to breach the gap. Children need intermediary helps paced to their emerging insights. Charts are one type of visual aid which can be developed to help children along the road from need for concrete materials to ability to operate with abstractions.
=, Equal or Equals?
Authors: Boyer Lee Emerson
Published: October 2020

Some Time Ago a group of our students were planning an arithmetic television program. They raised the question whether 3+2=5 should be read “Three plus two equals five” or “Three plus two equal five.” Also, they asked, “Does it make any difference if we speak about concrete objects?” For example, should we say, “Three bears plus two bears equals five bears” or “Three bears plus two bears equal five bears?”
The Abacus as an Arithmetic Teaching Device
Authors: Flewelling Robert W.
Published: October 2020

The Instructions that you are about to read should help you to understand arithmetic better by showing you, step by step, how different kinds of problems can be done on the oldest kind of adding machine in the world. Because each step will be harder than the one before it, you should work each problem with pencil and paper to help you understand as you go. It would also be a good idea to make up some extra problems to check your understanding. If you have trouble anywhere, you will probably find that you have not understood something in an earlier step.
An Experiment with Hand-Tally Counters
Authors: Hooper Barbara
Published: October 2020

WHO EVER HEARD OF GIVING twenty-seven children in first grade their very own calculators with which to work and to learn? It was done, and resulted in a basic concept in place value, a beginning knowledge in the use of such accurate machines, a way to see the processes of various number problems, and we played at numbers with the excitement and pleasure and downright good time of a rousing game of Red Rover!
I Went to an Arithmetic Workshop
Authors: Taffs Annie A.
Published: October 2020

In Summarizing My Reactions to the arithmetic workshop I would begin by saying that I was getting a new point of view, a changed outlook on the whole field of arithmetic. I would go on to explain that this had involved first of all a sort of “re-view” or backward glance at my past experiences with this subject; then a kind of bird's-eye view of the area of mathematics, followed by something like a 3-D view of the meaning of arithmetic as it confronts the child at school, and a preview of the possibilities regarding my future work in the classroom.
The Scarbacus or Scarsdale Abacus
Authors: Mayer Louise A.
Published: October 2020

The “Scarbacus” a project of a seventh grade group in Scarsdale, New York, grew out of a class discussion about types of counting devices. I said that I thought a counting device like an abacus should be one of the open end variety in order to give children a correct impression of number combinations. Young children in particular get a wrong impression from a counting frame that permits counting only to ten.
A model for teaching multiplication of fractional numbers
Authors: Green George F.
Published: October 2020

Mature students of mathematics can readily cope with new and abstract terms if precise definitions of the terms are provided. For such students, neither the new term nor its definition needs to have any obvious connection with the real world. Most young children, on the other hand, require relatively clear associations between abstract terms and physical reality. Making these associations is the role of pedagogical models. The word model has many meanings in mathematics and elsewhere, but it is used here simply to mean an assignment of meaning to an abstraction, in familiar—frequently physical—terms. The child's model, then, is somewhat analogous to the mathematician's definition.
Things you can try: Jupiter horse race
Authors: Writt Elinor J.
Published: October 2020

Eighth graders at our school recently had a great deal of fun trying to solve a problem in logical reasoning that was invented by one of their classmates. Perhaps your students will enjoy solving such a puzzle, and they might possibly be motivated to create similar ones. The problem is presented here as it was submitted by the student.