bluuebunny/crossref_metadata_2025 huggingface dataset:
What's Going On…
Authors: Haynes Harriet
Published: October 2020

Microcomputer workshop for middle school teachers. A National Science Foundation (NSF) program at Eastern Montana College will assist middle school teachers who want training in how to use microcomputers as effective teaching/learning tools. Many schools that have purchased microcomputers do not have teachers who know how to use them. Teachers who participate in the NSF workshop are expected to conduct workshops and train their colleagues. In this way the program multiplies its effectiveness. For more information contact William A. Stannard, Mathematics Department, Eastern Montana College, Billings, MT 59101
Are We Introducing Mathematical Symbols Too Soon?
Authors: Hamrick Kathy B.
Published: October 2020

Some of the errors children make in elementary mathematics are a result of confusion associated with the written symbolization of mathematics. Try an experiment with your first, second, or even third grade class. First, cover four counters with a piece of paper and place three counters next to the paper. Say, “I have seven counters in all; you can see three. How many do I have hidden?
Remedial Mathematics Program Considerations
Authors: Richbart Lynn A.
Published: October 2020

With the ever increasing emphasis on competency testing, a commensurate emphasis is being placed on developing remedial programs. What makes one remedial program succeed and another one fail? Is there a best method or material? What are the basic considerations to be reviewed?
Some Reflections on Teaching Mathematics for Elementary School Teachers
Authors: Leake Lowell
Published: October 2020

Virtually every college or university training elementary school teachers offers a course in mathematics content with a title similar to “Mathematics for the Elementary School Teacher”, the title we use at the University of Cincinnati. The course is usually a year long and in most states it is a certification requirement for grades kindergarten through eight; it evolved from the recommendations of the Committee on the Undergraduate Program in Mathematics (CUPM) of the Mathematical Association of America in the early 1960s. Little, however, has appeared in journals such as the Arithmetic Teacher about the experiences various universities or instructors have had with this course. This paper describes some aspects of such a course at the University of Cincinnati, and I have had two major purposes in mind in writing it. One is to communicate some successful ideas to others who teach similar courses, and the other is to encourage others to submit their ideas, experiences, and suggestions so that all of us can share and profit from each other's successes and failures. A third possibility is to generate some comments from teachers in elementary and middle schools who once took such a course and now, in retrospect, have suggestions to make to those of us who teach it.
Calculators in the Classroom: A Proposal for Curricular Change
Authors: Wheatley Grayson H.
Published: October 2020

A careful study of the history of mathematics education will reveal that in this country computation has always been the focus of the elementary school mathematics curriculum. In the eighteenth century children were taught ciphering, rote computation with no attempt to develop an understanding of the process. During the nineteenth century there were a few persons like Warren Coburn calling for attention to meaning, but the curriculum remained computational. During the 1930s there was a movement toward social utility and developing meaning in mathematics. Then in the period from 1958 to 1971 there was an emphasis on teaching the structure of mathematics. Viewed from the perspective of today, there was one unfortunate aspect of the so called “modern mathematics” movement—much attention was given to rationalizing algorithms. The division algorithm, for example, was taught in great detail using a subtracting approach so that students would understand why the algorithm worked.
The Division Algorithm: Using an Alternative Approach
Authors: Irons Calvin J.
Published: October 2020

Few topics in the elementary school cause more difficulty for students and teachers alike than the algorithm for long division. Teachers are frustrated by the many things that must be taken into consideration when the algorithm is introduced. Students, on the other hand, find the number of steps, which seemingly must be memorized, difficult to link together and, in general, see little relationship between those steps.
OVERVIEW: Providing for Mathematically Able Students
Authors: Trafton Paul
Published: October 2020

Education of the gifted has rapidly become a major movement with strong educational and popular support for programs for a wide range of capable students. Mathematics, in particular, is the center of much parental interest.
The Mathematics Curriculum for Talented Students
Authors: Payne Joseph
Published: October 2020

The design of a curriculum that allows students talented in mathematics to develop their potential and explore new domains of knowledge is a high priority in many school systems. Such a curriculum should be based on the nature of mathematics itself and on the characteristics of students that are especially important in the learning of mathematics.
PROGRAMS FOR ABLE STUDENTS: District or Regional Alternatives
Authors: House Peggy
Published: October 2020

The current resurgence of concern for gifted and talented students has resulted in an increase in the number of special programs implemented at a variety of levels, from the individual classroom or school to the district, state, or nation. This article reviews some of the alternatives typical of the district or regional programs.
An Enrichment System for any Classroom
Authors: Parkhurst Ralph E.
Published: October 2020

As a neophyte, traditional teacher, one of the first deficiencies I noticed was the need for an enrichment program for gifted students in the classroom. The system developed would have to be usable in any type of teaching environment since I was not sure I would always use a traditional approach. As a busy new teacher, I also looked for a program that would be little additional burden.
One point of view: Stop the Bandwagon I Want Off
Authors: Kilpatrick Jeremy
Published: October 2020

The 1980s, so we are told, are to be the decade of “problem solving.” Ready or not, we are apparently destined to have problem solving as the “focus” of school mathematics for the next ten years or so. Toward this goal, the NCTM's An Agenda for Action recommends the organization of the mathematics curriculum around problem solving. How can one argue with such a sensible agenda?
One point of view: Imminent Instructional Implications for Teachers
Authors: Frye Shirley M.
Published: October 2020

The actions listed in An Agenda for Action infer that teachers will shoulder a great deal of the responsibility for the implementation of the recommendations for the mathematics curriculum of the 1980s. It is, therefore, imperative that teachers participate in the determination of how to achieve the goals that have been set forth.
Functioning with a Sticky Model
Authors: Reys Robert E.
Published: October 2020

Searching for patterns is an integral part of mathematics, and arithmetic provides excellent opportunities for students to look for patterns, make conjectures to continue a pattern, and then to check these predictions. The early study of functions is a natural place to reinforce basic computational skills as well as develop some pattern-finding techniques.
The Current Status of Preservice Elementary Teacher-Education Programs
Authors: Dossey John A.
Published: October 2020

In the October 1979 Arithmetic Teacher, James Fey (1979) reported on the current status of elementary school mathematics teaching as viewed through the results of a set of studies funded by the National Science Foundation (NSF).
The Critical Role of Elementary School Mathematics in Equalizing Opportunity
Authors: Sells Lucy W.
Published: October 2020

In many school districts across the country, students' assignment to mathematics courses in the seventh, eighth, and ninth grades is based on scores on proficiency tests given in the sixth grade. Students who are seriously below grade level on these tests get assigned to remedial courses so that they have the opportunity to catch up. Students who do not master the basic skills needed to catch up will never make it through the algebra and geometry courses required for admission to many colleges, and increasingly required for advancement in technical fields that do not require a college degree. Thus, failure to achieve mastery of arithmetic skills at grade level presents a serious barrier to job opportunities for students.
President's Report: Recipe for Revival: Recommendations for the Twenty-first Century
Authors: Sobel Max A.
Published: October 2020

I would like the reader to pretend with me that we are able to tum the clock ahead. So let us spin the dial and watch the years go by throughout the 1980s and the 1990s until we arrive in the twenty-frrst century, all of us at the Annual Meeting of the National Council of Teachers of Mathematics held once again in St. Louis, Missouri. The guest speaker at the 80th Annual Meeting, held in this year, 2001, is Max A. Sobel, a Past President of NCTM.
How the Media Specialist can use the Arithmetic Teacher
Authors: Meyer Deanna M.
Published: October 2020

What can a media specialist do to promote the wealth of material available in the Arithmetic Teacher? And, should that be part of the service that the media specialist provides for the staff? The answers: a multitude of things and yes.
Using Arrays for Teaching Multiplication
Authors: Hall William D.
Published: October 2020

For the elementary school teacher, multiplication is a topic that is constantly recurring. Multiplication includes two different phases. One is the concept. Two is the ensuing algorithms that are taught in order to facilitate the process of arriving at a product.
Using a Calculator to Develop Mathematical Understanding
Authors: Wiebe James H.
Published: October 2020

Calculators are slowly making their way into the elementary school mathematics classroom. Many teachers are beginning to realize their value for checking answers, exploring number patterns, problem solving, and largenumber computations. Calculators can also be very useful in developing understanding of mathematical concepts and operations.
The Learning Machines
Authors: Martin Kathleen
Published: October 2020

The microcomputers are here, and their influence will be felt significantly within the lives of our children. Presently, the educational impact of microcomputer technology is focused primarily on the upper and middle grades. However, it is in the elementary grades, perhaps even among preschoolers, that microcomputers may ultimately challenge and radically alter traditional instructional modes. Attention to the pictures accompanying this article provides a subtle insight into the potential of this technology. The expressions are those of a group of preschoolers intent upon their first encounter with a microcomputer. The children are “doodling” within the parameters of a preprogrammed videographics module. All of the faces reflect deep concentration, yet the variety of moods—surprise, curiosity, intensity, frustration, tentativeness—dispel any notions of singularity of experience. It is within this diversity of individual moments that we must come to recognize and to understand the work of the microcomputer.
The Stored-Ten Method of Subtraction
Authors: Ferguson Audrey
Published: October 2020

Have you ever met a subtractionresistant student? Have you asked yourself that agelong question, How do I help students develop the skill to perform subtraction problems at a rate that allows them to keep pace with their regular class?
Detective Stories
Authors: Woodward Ernest , Schroeder Linda
Published: October 2020

The Comprehensive School Mathematics Program (CSMP) has developed a series of lessons based on what they call detective stories. These lessons all follow the same basic format. A first clue is given, which is appropriate to the selection of a subset of the whole numbers. This is followed by a sequence of further clues, each of which narrows down the choices untill, eventually, a single number is selected. We have observed several of the problem-solving lessons being taught by CSMP teachers in the Clarksv ill e-Montgomery County School System (Tennessee) and found that students reacted enthusiastically to this approach. These lessons were all done with large-group format and were teacher directed. Unfortunately, it is quite difficult to adapt the lessons for use in standard classrooms, since the CSMP lessons make rather extensive use of clues involving the mini-computer and most elementary school students are not familiar with this device. As a result, we decided to write our own detective stories for a third grade class. Our format was different in that we used a learning-center approach and our subject matter was geometry. The remainder of this paper is devoted to a description and evaluation of our detective stories.
Project CAL—Take 1
Authors: Shanahan Dolores
Published: October 2020

Stephen, a young, gifted kindergarten student sits on his mother's lap. His eyes gleam with excitement. His legs swing freely as he runs a computer program that most adults could only master by using paper and pencil.
Guiding Young Children in Successful Problem Solving
Authors: Lee Kil S.
Published: October 2020

In the past twenty years, problem solving has received much attention from mathematics educators. Inclusion of imaginative problems in school mathematics curricula was recommended in the 1963 Cambridge Conference report. Problem solving was the first of the ten basic mathematical skills identified by the National Council of Supervisors of Mathematics in 1976 and the position of the NCSM was endorsed by the National Council of Teachers of Mathematics in 1978. “That problem solving be the focus of school mathematics in the 1980s” is the first of eight recommendations expressed in An Agenda for Action: Recommendations for School Mathematics of the 1980s published by the NCTM.
Teaching Problem Solving to Preservice Teachers
Authors: Krulik Stephen , Rudnick Jesse A.
Published: October 2020

Problem solving! Problem solving! Problem solving! Wherever mathematics teachers turn today, they are confronted by these two words, whether it be when reading NCTM's An Agenda for Action, current educational sections of their newspapers, professional journals, or when attending a mathematics education conference. In fact, at the annual NCTM meeting in St. Louis approximately 20 percent of the sections had problem solving in either the description or the title of the talk.
Teaching Textbook Story Problems
Authors: LeBlanc John F.
Published: October 2020

Jane and Ruth have the same hobby, raising guppies. One day Jane told Ruth she had 38 guppies. Ruth said, “I have 53!” How many more guppies does Ruth have than Jane?
Let's Do It: That's Eggzactly Right!
Authors: Jensen Rosalie , O'Neil David R.
Published: October 2020

Have you been saving styrofoam egg cartons? Do you have empty hosiery containers or some of the brightly colored plastic eggs that are available at this time of year for filling with goodies? Have you wondered how you could use these abundant and inexpensive items to enhance your mathematics teaching? If your answers are yes, read further and discover how to develop a variety of concepts and skills in your classroom.
Brian's Question
Authors: Goodman Terry A.
Published: October 2020

It has been my observation that children are not only good problem solvers, but also good problem posers. The following episode is a good example.
A Computer-Literacy Module for the Junior High School
Authors: Gress Eileen K.
Published: October 2020

The most significant technological achievement presently affecting the quality of life in our society is the computer. Despite its rapid invasion into the marketplace, the computer is often personified with adjectives such as controlling, impersonal, and intimidating. Yet we cannot deny that the computer is imbedded in every aspect of our society. Technological advancements are developing at such a pace that it is difficult to keep abreast of the field. The personal computer now offers the promise of being available to all United States citizens within the next three to five years (Braun 1977, p. 3).
A Closer Look at Standardized Tests
Authors: Freeman Donald J. , Kuhs Therese M. , Knappen Lucy B. , Porter Andrew C.
Published: October 2020

It is commonly argued that teachers should use scores from standardized tests to facilitate instruction. Specifically, teachers are encouraged to use standardized test results to evaluate student achievement on both a group and individual level, to identify students with learning problems, and to assess the effectiveness of instructional strategies that have been used. The use of standardized tests for any of these functions, however, must be tempered by the teacher's knowledge of the extent to which the content of the test parallels the content of instruction.
Bowl-a-Fact: A Numbers Fact Game
Authors: Shoecraft Paul
Published: October 2020

When it comes to having children master the number facts, nothing surpasses having them use the facts over and over again. And when it comes to motivating children to use the facts over and over again, nothing surpasses a game. So how about having your students play “Bowl-a-Fact”!
Let's Do It: Informal Geometry Through Geometric Blocks
Authors: Jensen Rosalie , O'Neil David R.
Published: October 2020

Geometric concepts and skills that are appropriate for elementary school pupils include comparing figures with respect to likenesses and differences, comparing and seriating figures with respect to size, classifying figures, making measurements, and performing informal activities related to congruence and line symmetry. AJI of these concepts and skills can be developed through the use of geometric blocks. A large set, which can serve to develop many ideas presented in the elementary school grades, is shown in figure 1. Various subgroups of these shapes can be used as the basis of structuring appropriate activities on different levels.
Ideas
Authors: Fennell Francis (Skip) , Houser Larry L. , McPartland Donna , Parker Sandra
Published: October 2020

Ideas for this month presents two posters that emphasize probability and statistics in a school fair setting. The posters involve determining the likelihood of events, actual recording of results, and analysis of data.
Results of General Mathematics Tests
Authors: Nelson Theodora
Published: October 2020

What conclusions can be drawn from the analysis of the results of timed, competitive, objective-type, achievement tests in general mathemat ics on interhigh school contests? Although the immediate objective of the test has been to rank the contestants and to determine the winner, I believe that a study of the types of problems that were missed or omitted could yield something of significance to those of us interested in the teaching of general mathemat ics and arithmetic.
Division for First Graders?
Authors: Ambrosius Dorothy S.
Published: October 2020

In our first grade we take advantage of every possible arithmetic experience that presents itself in class. Very early in the year the children discovered why they counted; to find out “how many.” As simple as that. And they have gleefully counted everything ever since. Then came groupings, and again we used the many materials available in every classroom, including ourselves. The children particularly loved to work with some cork discs that I retrieved from a small manufacturer just before he threw them in the scrap barrel. These are light weight and don't clatter if they fall to the floor.
Testing the Attainment of the Broader Objectives of Arithmetic
Authors: Moyer Haverly O.
Published: October 2020

Teachers have always given tests for one reason or another. Many times these tests have been homemade; sometimes they have been standardized. Both kinds have a place in the evaluation of any arithmetic program. However, if these tests measure only the ability to compute and to solve abstract problems then they can be criticized more for what they have not mea-Sured than for what they have, to some degree, measured.
Inconsistencies in the Teaching of Arithmetic in the Elementary Grades
Authors: Dwight Leslie A.
Published: October 2020

In order to introduce the subject matter in this article the following truefalse test is given for the reader. It is suggested the reader take this test and attempt to rationalize each answer in Ianguage suitable for elementary grade pupils. Preserve your test answers and compare them and your discussions of the items with those of the author which will be printed in the next issue.
Multiplying Fractions
Authors: Hibbard Wilbur
Published: October 2020

Do you have difficulty showing that 2/3 of 3/4 is 1/2? Try this simple device. In the presentation of multiplication of fractions, pupils are usually confused because they are told to multiply numerators and denominators separately for their answers.
Minutes of the Annual Business Session
Authors: Karnes Houston T.
Published: October 2020

Mrs. Marie S. Wilcox, President, called the meeting to order at 4:30 P.M.
Definitions in Arithmetic
Authors: Brumfiel Charles
Published: October 2020

TEACHERS OF MATHEMATICS know how difficult it is to teach students to use definitions skillfully. Perhaps one explanation of the difficulty which even the better students seem to have in using definitions properly lies in the fact that in early arithmetic experiences they did not often work consciously with definitions. The writer feels that t here are many rich opportunities in the early arithmetic years to allow youngsters to share in the construction of definitions. Moreover, in many arithmetic situations opportunities for critical examination of definitions arise naturally.
Whither in Arithmetic Teaching? A Perceptive Perspective View
Authors: Osborn Jesse
Published: October 2020

Are we making progress in the teaching of arithmetic? Yes, but … Looking back over the past thirty, or so, years, I become discouraged at the confusion and lack of direction. Two professional educators (invented by me) will give a somewhat exaggerated view of what I have in mind.
Ideas
Authors: Bazik Edna F. , Tucker Benny F.
Published: October 2020

Ideas for this month focuses on basic number work—recognizing numerals, practice with basic facts, and computational work with whole numbers and decimals. Practice activities presented in a motivational format are more interesting for students than pages of exercises from a textbook. The activities presented here may, in turn, help teachers generate other similar activities.
Missing Addends: A Case of Reading Comprehension
Authors: King Julia A.
Published: October 2020

Missing addends cause much grief to both teachers and children. Teachers throw up their hands in frustration when children respond with a cheerful 11 to 4 + □ = 7. Children. even those who have done well in mastering addition and ubtraction facts, are disappointed and confused to learn that this answer is wrong. Since missing addends appear early in the curriculum, this experience may be the first blow to a child's self-confidence in mathematics.
Primary Matholympics
Authors: Johnson Gayle S. , Sheets Betsy Mickley
Published: October 2020

All work and no play makes mathematics a dull subject. This may sound like a bit of a cliche, but research has shown that children form attitudes toward mathematic and numbers in general very early in their development (Aiken 1970). Feeling that mathematics is dull. boring, and cary have been reflected in those attitudes (Aiken 1972).
Graphing for Any Grade
Authors: Nibbelink William
Published: October 2020

This article reports an instructional sequence for teaching graphing that has been extensively field tested in each of grades kindergarten through six. What is outlined in this article need not be used as a “graphing unit” in the usual sense. Graphing is better treated as an ongoing activity. Too often it is treated in a “crash course” manner just before standardized test time.
Readers' Dialogue
Authors: Abramsky Suzanne , Schielack Janie , Jensen Rosalie , Baratta Louise , Modell Lance , Dye David L.
Published: October 2020

The currency of letters to the edttor of a journal like the Arithmetic Teacher is always a problem. At the very best, four months will have elapsed between the time when an artiicle is published and the time when a letter commenting on that article can appear in the journal. Sometimes the minimum time is even greater. For example. letters about an article that appears in a January issue will almost never appears before the folloing fall The publication schedule alone dictates such a spread of time, and other factors, can intervene to further delay publication of a letter
Let's Do It: Developing Mathematical Understandings with Bead Strings
Authors: Horak Virginia M. , Horak Willis J.
Published: October 2020

Children in the primary grades need diverse concrete models to adequately develop basic number concepts. Various manipulatives such as bean sticks, bundles of counting sticks, paper dot plates (Thompson and Van de Walle 1980) and Cuisennaire rods have been discussed over the years. Bead strings are another alternative. They are an inexpensive teacher-made manipulative that can be used over and over again. This article deals with ways in which bead strings can be used for reinforcement and concept development.
Individual Differences in Problem Solving
Authors: Moses Barbara
Published: October 2020

You've decided to teach a unit on problem solving. You've compiled a list of illustrative problems and are prepared with suggestive hints for each problem. You're armed with patience for Johnny's “I don't understand” comments. And Monday it begins.
Ideas
Authors: Tucker Benny F. , Bazik Edna F.
Published: October 2020

Ideas for this month gives students practice in rounding numbers to the nearest ten and estimating sums, products, or quotients, which they then check with a calculator. Estimating answers to check on the reasonableness of the results of calculations is an important skill. The ability to estimate quantities will help students deal with many everyday problem situations when they are adults.
Sneaking in Basic Drill with Sneaky Squares
Authors: Kuczkowski Joseph E.
Published: October 2020

“Sneaky Squares” are versions of a type of magic square introduced in an article by Martin Gardner many years ago (Scientific American, January 1957, pp. 138–42). His main example was that of a square using whole numbers under addition. As Gardner indicated, it is possible to construct such squares using addition or multiplication and to involve whole numbers, integers, rational numbers, or decimals. With a little variation, subtraction and division can also be involved. Thus Sneaky Squares can be conveniently used for a variety of basic drill work at all grade levels.
TEACHING: Evaluation and Problem Solving
Authors: Charles Randall I.
Published: October 2020

As problem-solving experiences begin to play a more significant role in the mathematics program, the evaluation of these experiences will become of greater interest to parents. administrators, and even students. The purpose of this anicle is to share two ways that have been used successfully to evaluate problem-Solving performance in the classroom.
The Use of Strategies in Estimating Measurements
Authors: Hildreth David J.
Published: October 2020

One of the recommendation in An Agenda for Action (NCTM 1980) was that estimation of measure be given increased emphasis in school mathematics. Estimation was also listed as a basic skill by the National Council of Supervisors of Mathematics (1978).
Let's Do It: Take a Chance
Authors: Horak Virginia M. , Horak Willis J.
Published: October 2020

What are the chances that it will rain today? Do you think five children will be wearing blue today? What are the chances your birthday will be on a Saturday? Do you think you have a good chance to win a free soft drink at the restaurant? Questions such as these illustrate that mathematics is a part of everyone's daily experiences. Even children in the lower elementary grades can work with ideas such as an unlikely event, a sure thing, and an even chance.
Decimal Notation: An Important Research Finding
Authors: Grossman Anne S.
Published: October 2020

Ordering a set of decimals is a type of question that is used often to test basic understanding of decimal notation. While students rarely have difficulty learning to order whole numbers, their performance on tests indicates that there is much misunderstanding concerning decimals and how to order them correctly. “Decimals: Results and Implications from National Assessment” (Carpenter et al. 1981) indicated that students “lack a firm understanding of the place-value interpretation of decimals” and, furthermore, that “many areas of difficulty for 13-year-olds were still problem areas for the 17-year-olds.” It should come a no surprise then that many students, because of the lack of initial understanding of the notation and the short time devoted to teaching decimal notation concepts, carry confused and fuzzy notions about decimals with them through adulthood.
Let's Do It: A-Plus for Counters
Authors: Shaw Jean M.
Published: October 2020

Children can learn a great deal from manipulating counters—small objects that can be grouped, arranged, and counted. Because they can illustrate mathematical concepts in meaningful ways and because they are convenient and versatile, counters can really help students learn mathematics.
“Stamp Collector's Nightmare,” Phase Two
Authors: Willcutt Bob
Published: October 2020

Problems that span the simple to the complex and that can therefore be used with many different groups of students, problems that have a strong motivational thrust, and problems that are full of many different kinds of mathematics are very special problems. When I discover such a problem, I like to share it with others in the hope that the challenges, frustrations, and satisfactions that go with it will be shared also. One such problem is the old problem of placing stamps on a grid. Ernest Ranucci (1968) deserves the credit for the basic version of this problem, which he entitled “The Stamp Collector's Nightmare.”
Teaching Games: More than Practice
Authors: Nelson Rebecca S. , Whitaker Donald R.
Published: October 2020

Children like to play games. For this reason, many elementary school teachers have used games as a way to practice basic facts and computational skills. To make the most effective use of games, however, teachers should discriminate carefully between maintenance games, in which the child must already know the fact or kill, and teaching game which are designed to help the child learn the fact or skill involved. Let's consider two examples to illustrate the difference.
Cardboard, Rubber Bands, and Polyhedron Models
Authors: Campbell Patricia F.
Published: October 2020

Young children's pre chool years are filled with three-dimensional objects as the children come to understand spatial and topological idea. These idea, such a nearness order or enclosure are based on the child's experiences and sensory impressions of shape and solids. However. too often early school experience with geometric concepts are limited to plane figure. This is because solid are difficult to represent on paper or the blackboard and young children have difficulty constructing model of three-dimensional figure with cardboard and paste. The “cut and paste” method of constructsion also produces permanent figures that are difficult to store.
The Mathematics Education of Primary–Grade Teachers
Authors: Isenberg Joan P. , Altizer-Tuning Carol J.
Published: October 2020

Mathematics is often viewed as difficult subject matter by students preparing to be primary-grade teachers (kindergarten through grade 2). Many of them need to develop competence and confidence in mathematics in order to teach it in a meaningful and appropriate way. Providing for the preservice mathematics education of primary-grade teachers must be the joint responsibility of both the mathematics educator and the teacher educator.
Teaching Rational Numbers—Junior High School
Authors: Prevost Fernand J.
Published: October 2020

Whole numbers are used to count sets, report measures, and order a set. You can report the sum and difference of two counts, report the product of twice a measure, and divide two whole numbers to determine how many subsets of a given size are contained in a larger set or find how many objects will be in each subset if you divide the given set into a specified number of parts.
Problem Solving: Some Thoughts and Activities
Authors: Slesnick Twila
Published: October 2020

Since the beginning of our system of formal education, the major focus of the mathematics curriculum has been on computation, not on problem solving. Technology, however, has progressed to the point that computation alone is not a salable skill. Machines can handle computation easily and efficiently, but problem solving is still a capability of the human mind. The recent National Assessment of Educational Progress confirms that, in general, although the public can compute, its problem-solving skills are poor.
Teacher Education: Mathematics Educators: Establishing Working Relationships with Schools
Authors: Trafton Paul R.
Published: October 2020

Mathematics education is a broad. diverse field. At the college level, mathematic educators engage in many professional activities. including instructing preservice and in-service teachers, conducting research, and addressing various problems and issues.
Research Report: Compensatory Education
Authors: Suydam Marilyn N.
Published: October 2020

Are compensatory education programs effective? Such programs try to offset any negative effects on achievement caused by students' disadvantaged backgrounds. Mullin and Summers (1983) reviewed forty-seven studies of compensatory education programs, most of which included work in mathematics.
Fractions Revisited
Authors: Chiosi Lou
Published: October 2020

Students must understand the concept of a fraction before they can be expected to learn the various operations dealing with fractions.
Computer Corner: News from the Classroom
Authors: Beckwith Melinda F.
Published: October 2020

Would you believe these are typical comments made by fifth– and sixthgrade students who can't seem to get enough of school since computers have become part of our classroom?
Teacher Education: Helping Preservice Teachers Develop an Awareness of Curricular Issues
Authors: O'Daffer Phares G.
Published: October 2020

A teacher refuses to allow calculators in the classroom because “the children won't learn their facts and computational skills.” Another teacher elects not to read anything about computers, since “we don't have one in our classroom anyway.” A third teacher skips the text's chapters on geometry, since “I don't see any real use for it.” A fourth teacher “doesn't see why people think problem solving is so important” and calls it a passing fad. Another teacher wants a book that doesn't teach fract ions because “we are in a metric age, and decimals are all that are needed.” At the same time, another teacher wants a book that teaches only the customary units of measurement, since “the metric system didn't catch on.”
Research Report: Problem Solving
Authors: Suydam Marilyn N.
Published: October 2020

In An Agenda for Action, the NCTM (1980) recommends that problem solving in mathematics should include a broad range of strategies, processes, and modes of presentation.
Research Report: Learning the Basic Facts
Authors: Suydam Marilyn N.
Published: October 2020

What can help children to learn the basic facts for whole numbers? Research has indicated that helping them to develop thinking strategies is an important step between the development of concepts with manipulative materials and pictures and the mastery of the facts with drill-and-practice activities.
Exploring Geometry with Logo
Authors: Thomas Eleanor M. , Thomas Rex A.
Published: October 2020

Providing appropriate and meaningful problem-olving experience for each student within the classroom setting is a difficult task. A problem that is too challenging for one student is too simple for another. A problem that captivates one student will bore the next. Differences among students in ability, interest, motivation, and experience create the need for a different problem-solving environment for nearly every student in the class.
Understanding Multiplication of Fractions
Authors: Sweetland Robert D.
Published: October 2020

You “multiply the top times the top and put it over the bottom times the bottom.” This is certainly a dandy verse for remembering the computational rule for multiplying two fractions, but it doesn't help tudents understand multiplication of fractions or encourage them to think about what is happening when fractions are multiplied.
Ideas
Authors: Shaw Jean M.
Published: October 2020

The IDEAS section for this month includes activities to give children practice in working with sets and basic facts. The activities should be useful as reinforcement after topics are first introduced or can offer variety when the topics are reviewed or re-taught. The activities capitalize on young children's love of manipulatives and older children's fascination with puzzles.
Training Elementary School Teachers to Use Computers—with Emphasis on Logo
Authors: Davis Edward J. , Helms Jim , Norman F. A. , Ponte Joao
Published: October 2020

For the past two summers we have taught a two-week “computer camp” for teachers of grades one through seven. The teachers, who were paired by grade level (one pair at each computer), spent approximately three hour each day in “class” at an Apple II+ microcomputer and averaged another two hours a day in individual practice. Participant were selected on a first-come, first-served basis in response to announcements sent to area schools. The most recent camp session included eleven elementary and four middle school teacher and was taught by a university faculty member and four graduate assistants in the mathematics education department.
Uncovering the Algorithms
Authors: Young Jerry L.
Published: October 2020

Some students don't seem to be able to apply the standard procedures (algorithms) for addition. subtraction, multiplication, and division. The purpose of this article is to present a method for diagnosing and correcting errors that your students might make in applying algorithms.
Mainstreaming and the Mathematics Classroom
Authors: Fennell Francis (Skip)
Published: October 2020

Federal legislation known as Public Law 94-142, the Education for All Handicapped Children Act, was passed in November 1975. This legislation determines regulations and requires actions by school districts and teachers relative to exceptional children. Many have interpreted state legislat ion and PL 94-142 as legislative remedies for some of the schools' past failures to provide an appropriate education for handicapped students. The law's programmatic and budgetary requirements became enforceable in October 1977. Public Law 94-142 mandates that free public education for handicapped students between the age of three and twenty-one begin no later than September 1980. Some exceptions to the mandate do occur, but the implication is that public schools may no longer refuse to admit handicapped students into educational programs.
Let's Do It: Fractions with Fraction Strips
Authors: Van de Walle John , Thompson Charles S.
Published: October 2020

In the elementary school classroom, activities with fractions seem to move much too quickly to the symbolic level of working with pencil and paper. Methods for finding common denominators, “reducing” fractions to lowest terms, cross multiplying, and so on, come in an endless string of rules and procedures. For children with only weak grasps of these concepts—and there are far too many such children around—the rules become mysterious, confusing, and frustrating.
Searching for Patterns of Divisors
Authors: Brown G. W.
Published: October 2020

The need to encourage students to look deeply into the nature and workings of the number system has been proclaimed ever since William A. Brownell's research (1935) established that achievement improves with understanding. A useful approach for developing insights and discovering patterns is to examine numbers in relation to the number of their divisors. The following teaching procedure has been tried in this regard.
One Point of View: Looking Back, I Think I See the Future …
Authors: Kansky Bob
Published: October 2020

In an earlier life, 1 was a “new math” addict. Ten years of my misspent youth were invested in writing and disseminating all manner of wondrous classroom materials; 1 also helped prepare a generation of teachers of that “mathematical writ.” Both the new-math materials and its teacherpreparation programs expressed a belief that the true attraction of mathematics was to be found in the examination of its axiomatic details (e.g., the commutative property of “this here,” the associative property for “that there,” and the distributive property for “something over or under whatever”). It was an exciting time (for me). It made some im portant contributions. It passed.
The Role of Questioning
Authors: Burns Marilyn
Published: October 2020

A third-grade teacher was beginning a class lesson in which the children were to work in pairs. When assembling the supplies for each pair of children. the teacher raised the question “How many pair of children will we have?” None of the students had a ready answer, nor did they seem to know immediately a way to proceed to get an answer. The teacher asked anot her question, “What do you need to know to figure this out?” One student suggeted that they needed to know how many students there were. The teacher questioned further, “How can we find this out?” The children suggeted different ways-having the students count off, counting by rows, or having each student in the class stand or sit down when counted.
Instructional Computing
Authors: Hatfield Larry L.
Published: October 2020

One of the most important goals of mathematics education is the development of students' abilities to think and reason in numerical and spatial situations. How might we use computers as tools for stimulating and guiding the construction of the child's mathematical thinking? The approaches taken by two elementary school teacher are briefly described. Although the uses of the computer by the teacher differ, both adopt a problematic approach to teaching to emphasize the child's mathematical thinking.
Estimation
Authors: Reys Robert E.
Published: October 2020

Estimation and mathematical thinking go hand i n hand. Both are multifaceted, and each involves many different processes. I feel that instruction in estimation provides a natural context not only to develop but also to practice many important thinking skills.
Projective Geometry in the Elementary School
Authors: Mansfield Helen
Published: October 2020

Simple ideas in projective geometry are rarely taught in element ary school. This article suggests some reason why such idea should have a place in the curriculum and describes some lesson on projective geometry that were taught to a class of ten-year-olds.
Children's Natural Processes
Authors: Madell Rob
Published: October 2020

From time to time the Arithmetic Teacher has published articles and letters in which the authors describe the thinking processes that children use to solve computational problems.
One Point of View: Improving Performance
Authors: Braswell James
Published: October 2020

For the past fifteen years, I have been involved in the development of mathematics examinations for College Board programs. At present, my primary area of responsibility is the development of the mathematical sections of the Scholastic Aptitude Test (SAT), a test taken each year by over 1 million college-bound high school students. During my years at Educational Testing Service, much of what national test results have indicated about the general state of education has been negative, reflecting a decline in achievement throughout the elementary and secondary school years. In regard to mathematics, I would like to discuss some of the factors that may affect this situation.
Mathletes, One and All
Authors: Yannone Denise Stamp
Published: October 2020

Ready, set, go! Hush, everyone. We are conducting our daily mathematics competition.
Ideas
Authors: Shaw Jean M.
Published: October 2020

Thi month's IDEAS features two map posters. The map for younger children feature a neighborhood and problems about getting around town. For adventurous older students—and most of them are—the second map show a wilderness area with options for canoeing, portaging, and hiking. Students can work the problem included on each poster, but they hould also be encouraged to make and solve their own problems using the maps as a basis.
One Point of View: Geometry—More Than a Holiday Prelude
Authors: Kennedy Leonard M.
Published: October 2020

Pressures to raise children's scores on mandated tests cause many teachers to adhere to a mathematics program that emphasizes computation and routine word problems. Daily instruction and drill on computational skills and frequent practice with routine story problems are the norm in many classrooms. Such a narrowly focused program contains little variety, denies children chances to develop mathematical backgrounds that give them confidence in the knowledge and skills they need to cope with unsolved (and unknown) problems, and offers us little hope for their futures.
And the Last One Loses!
Authors: Barson Alan
Published: October 2020

The origin of the word NIM has never been truly explained, but one of my students once observed that if you write the word NIM on a piece of paper and turn the word upside down, it spells the word WIN. It may be that WIN reflects the true meaning of these infectious strategy games.
How to Make a Million
Authors: Harrison William B.
Published: October 2020

Every teacher at some time has heard a child use the words million, billion, and trillion to describe large numbers. Some rather enterprising students of mine who were bored with such “piddling” numbers as these came up with a vigintillion. (Have you heard of it? I hadn't!) A vigintillion is 1063 in the United States and France and 10120 in Germany and Great Britain.
Coordinate Geometry—Art and Mathematics
Authors: Terc Michael
Published: October 2020

Our sutudents cry for self-expression, for a chance to see mathematics in action. Frequently, however, the structure of mathematics does not lend itself to individual style or variation. Problem solving can tend to be dull and monotonous rather than exciting and stimulating.
Research Report: Forming Geometric Concepts
Authors: Suydam Marilyn N.
Published: October 2020

Geometric idea are vital: we live in a three-dimensional world. Yet, for many children, in truction in geometry in the elementary school revolves around only two points: recognition of hape and development of vocabulary. Re earch provide some evidence on how these points are taught but also indicate other ideas that can be developed.
Dot Method for Renaming Fractions
Authors: Beede Rudy B.
Published: October 2020

If renaming fractions is difficult for your students, try using the dot method. Renaming fractions by the dot method has been used successfully with students from grade 3 through grade 12. The method requires no prior knowledge of multiplication facts, common factors, or greatest common factors. It can be used to introduce renaming at the manipulative level in a meaningful way prior to moving to a more abstract level where prime factorization will be involved.