bluuebunny/crossref_metadata_2025 huggingface dataset:
One Point of View: Avenues to In-service Education
Authors: Knight Genevieve M.
Published: October 2020

Once teachers have been awarded degrees and are certificated to teach, what opportunities are available to ensure that the teacher's knowledge remains current and adequate? The answers are in “in-service” education. The operational definition often used in teacher education to describe inservice education is “any activity teachers engage in to update or enrich their knowledge after certification.”
The Perceiving I
Authors: Burton Grace M.
Published: October 2020

On seeing mathematical truths most people act as if they believe that mathematical truths are “right out there,” and simply need to be observed to be taken into one's own memory banks. Some mathematicians (and for all I know other “pure” scientists) believe that knowledge is solely a product of the creative genius of the human species—that it is independent of all such referents as “real matter.” Speculations on the nature of knowledge might be passed off as amusing entertainments for professors in their ivory towers were it not for the fact that teachers act on their beliefs about knowledge, even though they may never have consciously formulated them.
One Point of View: Problem Solving versus Applied Problem Solving
Authors: Lesh Richard
Published: October 2020

As the director of a current National Science Foundation-funded research project investigating applied mathematical problem-solving processes for middle-school students, I might be expected to applaud the recommendation (NCTM, An Agenda for Action) that the school mathematics curriculum for the 1980s be organized around “problem solving.” If this means emphasizing Polya-style heuristics and word problems of the type currently in most textbooks, I do not.
What's Wrong with Success and Praise?
Authors: Chandler Theodore A.
Published: October 2020

How many times have you been advised by the school psychologist, the principal, or your supervisor to give this or that child a sense of success and to praise the child for that success? Were there times when the “prescription” backfired? The purpose of this article is to help you understand the dynamics of success and praise and to suggest how to avoid the pitfalls.
How Teachers can use the “Arithmetic Teacher”
Authors: Bologna Elaine M.
Published: October 2020

Featuring an article on “how teachers can use the Arithmetic Teacher” might be construed as “bringing coals to Newcastle” because the Arithmetic Teacher is published for teachers. Nonetheless, we would like to offer our readers some suggestions to enhance an already valuable mathematics resource.
Children Can Understand Mathematics
Authors: Madell Robert L.
Published: October 2020

At our school, we begin our indepth work with fract ions in the fourth grade.
Productive Pieces: Exploring Multiplication on the Overhead
Authors: Stuart Maureen , Bestgen Barbara
Published: October 2020

In working with teachers in the primary grades, there are several mathematical topics that are frequently labeled as trouble spots or difficult topics to teach. One of these is multiplication. How can the concept of multiplication be developed meaningfully? How much time should be spent on developmental work before attention shifts to drill of facts? What model for multiplication is most effective? Should more than one model be used with young children? There are no hard and fast answers to these questions, but we have found a series of lessons using an array model to interpret multiplication to be very successful.
Variations in Kindergarten Mathematics Programs and What a teacher can do about it
Authors: Yvon Bernard R. , Spooner Eunice B.
Published: October 2020

Many kindergarten teachers, elementary school administrators, and parents have been concerned with two questions regarding the kindergarten mathematics programs in their schools: Does the program in our school include most of the concepts presented in other kindergarten programs nationwide? What can teachers do to present these mathematics concepts in a manipulative, nonbook manner when funds for instructional materials are very limited?
Problem Solving for the Junior High School
Authors: Maletsky Evan M.
Published: October 2020

Problem solving is solving problems. To develop problem-solving skills, students need to solve many problems on their own. But they also need to see good problem-solving techniques illustrated by you, the teacher. In this article, four specific problems are presented, discussed, and extended to illustrate how diverse instructional strategies, materials, and resources can be used in the junior high school classroom to develop these skills.
Ideas
Authors: Fennell (Francis (Skip) , Houser Larry L. , McPartland Donna , Parker Sandra
Published: October 2020

Ideas for this month emphasizes fractions, decimals, and percent. The activities presented all focus on a sports-orie nted theme, and present computation and problem-solving examples.
Scope and Sequence for a Problem-Solving Curriculum
Authors: Tobin Alexander
Published: October 2020

“The development of problem-solving ability should direct the efforts of mathematics educators through the next decade. Performance in problem solving will measure the effectiveness of our personal and national possession of mathematical competency… The mathematics curriculum should be organized around problem solving.” (NCTM, An Agenda for Action) It was with these things in mind that the School District of Philadelphia and its Division of Mathematics Education took on as one of its major priorities the creation of a scope and sequence outline for problem solving. We also recognized, from the very inception of this project, that teachers would need activities, direction, guidance, and materials to effectively implement the program.
Let's Do It: Looking at Facts
Authors: O'Neil David R. , Jensen Rosalie
Published: October 2020

The teaching of concepts of statistics and probability in the elementary school offers many opportunities to use “real” data, as well as to provide practice in fundamental operations with numbers. It is important that children begin early in their study of mathematics to develop the techniques of collecting, organizing, and analyzing data. These skills should lead naturally to the making of predictions and, thus, to the study of probability.
Dear Kathy's Teacher
Authors: Moser James M.
Published: October 2020

This is a true story. I do have a daughter named Kathy who is in sixth grade attending a local school here in my hometown of Madison. The school is using one of the recent textbook series that emphasizes the “basics.” Kathy first learned division in fourth grade, spent a great deal of time last year in trying to master the skill of long division, and is at it again this year. The following letter to Kathy's teacher is essentially what I wrote a few evenings ago. After thinking about it a bit, I have added a bit to this more formal rendition. But basically it went something like this.
The Shear Joy of Area
Authors: Spitler Gail
Published: October 2020

The geoboard is an excellent vehicle for developing intuitive understandings of various topics in transformational geometry. In particular, the geoboard can be used most effectively in studying the area of various polygonal regions and what happens to the area of the region as its shape is changed. In the activities described in this article, students discover the fact that when a triangle or parallelogram is subjected to a transformation called a shear, its area is not changed.
Let's Teach Mental Algorithms for Addition and Subtraction
Authors: Musser Gary L.
Published: October 2020

Much of the traditional mathematics curriculum at the elementary school level has been devoted to teaching computational algorithms (methods) that are most effective when using paper and pencil. The familiar terms associated with these addition and subtraction algorithms are “carrying” and “borrowing” respectively.
Training Metric Leaders
Authors: Yvon Bernard R. , Butzow John W. , Marshall Gregory W.
Published: October 2020

The process by which the SI metric system supplants the customary system of measurement is a complex one, affected by a range of political, economic, and social factors. As metric educators, we believe one critical factor leading to the metrication of individual life styles is the infusion into local communities of a group of people who have significant metric knowledge, a positive metric attitude, and an expressed commitment to metric advocacy. We call people who possess these qualities “metric leaders.” Over a six-month period we trained over two hundred such leaders who live in communities throughout the state of Maine. Already these metric leaders have had an impact on the metrication process at all levels, from that of changing individual life styles to that of influencing national metric policy decisions.
Readers' Dialogue
Authors: Meserve Bruce E. , Risher Dennis H. , Economopoulos Majorie P. , Stevenson Robert J.
Published: October 2020

The currency of letters to the editor of a journal like the Arithmetic Teacher is always a problem. At the very best, four month will have elapsed between the time when an article 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 appear before the following fall. The publication schedule alone dictates such a spread of time. and other factors can intervene to further delay publication of a letter.
Fun with Logical Reasoning
Authors: Warman Michele
Published: October 2020

The ability to see patterns and relationships is essential for academic success. Students must be able to sort the barrage of material they are exposed to into manageable sequences they can deal with. Patterns can be mathematical as well as verbal, visual as well as written. Organizing information, evaluating it, and recognizing its interrelationships will help students deal with a future world that promises to be significantly more complex than our world today.
An Ounce of Prevention
Authors: Swenson Esther J.
Published: October 2020

NO ONE WHO IS INTERESTED in our elementary schools could possibly have missed the continuing controversy as to whether or not Johnny can read and also why or why not. What has happened in the way of public criticism of the teaching of reading may also happen with respect to the teaching of arithmetic. In fact, we occasionally do have rumblings of discontent. During World War II we were told by some that the young men in the armed forces would have been more competent if they had only had more drill. Of course, if the public had only known it, they had probably had too much of the wrong kind of drill. Whether the end result of these public criticisms is favorable or unfavorable to t he schools will depend in large part on how school people meet them.
Report of the Nominating Committee
Authors: Hartung M. L. , Beckmann Milton , Bell Clifford , Bernhard Ida Mae , Lankford F. G. , Mayor John , Smith Rolland R. , Sueltz Ben A. , Wren F. Lynwood
Published: October 2020

The Committee on Nominations and Elections presents below the names of persons nominated for offices to be filled in the election of 1956. The term of office for the President and the Vice-Presidents is two years. Three directors are to be elected for terms of three years.
The Hundred Board
Authors: Osborn Jesse
Published: October 2020

Masteiw of the whole numbers to 100 is basic to everything that follows in arithmetic, and in most other mathematics. The chart shown here is adapted from a board that has helped many pupils toward such mastery.
The Intangibles of Arithmetic Learning
Authors: Clark John R.
Published: October 2020

Before undertaking a discussion of the intangibles of arithmetic learning, we should comment upon the tangibles. These include (1) ideas (meanings or concepts), (2) skills (computational techniques), and (3) reasoning or problem solving. We always recognize these tangibles in our thinking about the objectives of arithmetic learning.
Mathematical Background for Teachers of Arithmetic
Authors: Snader Daniel
Published: October 2020

All of us have heard such expressions as “you cannot teach what you do not know”; or such vague expressions as “we teach children, not subject matter.” These are typical of two opposing views regarding the professional preparation of teachers of arithmetic. The one view holds that methods and devices should be emphasized; the other puts a premium on the mastery of subject matter. The more modern view regards neither of these as wholly satisfactory … and places its hope for improved teaching of arithmetic on the development of a new generation of teachers who know both what to teach and how to teach it. The trend to ward closer cooperation between mathematicians and educationists in a united attack on this problem is very encouraging.
Constructing Tests of Mathematical Concepts for Young Children
Authors: Wrightstone J. Wayne
Published: October 2020

About ten years ago, the Mathematics Program in the elementary schools of New York City was modified so as to place an increasing emphasis on the a bility of young children to do mathematical thinking. It was assumed that children can learn to think in the abstract terms of mathematics only if they learn meaningful concepts of arithmetic, or mathematics. The mathematics to be learned must not be too difficult for pupil understanding and must not be too easy to preclude a challenge to thinking.
Inconsistencies in the Teaching of Arithmetic: Part II
Authors: Dwight Leslie A.
Published: October 2020

In the march issue, thirty test items were offered and the reader was challenged not only to give the correct answer but also to give a rational explanation Which children could understand.
A Fraction Circle
Authors: Lyvers Donald B.
Published: October 2020

Of all the topics presented in the 7th and 8th grade mathematics courses, those dealing with fractions, decimals, and percentage seem to be the most troublesome and the least understood by the student. Often meaningless rules have been committed to memory by the student, but little comprehension has taken place. Occasionally there are students in a class who may add denominators, or insist that 1 /4 times 1/2 does not give the same result as 1/ 2 times 1/4, or become confused that 1/4 divided by 1/8 is 2. Some students do not know or are not sure that 1/3 is larger than 1/4. These are just a few examples of problems common to many classrooms.
Arithmetic—An Old Subject in New Apparel
Authors: Ford Marie S.
Published: October 2020

This is an S.O.S. to all teachers and would-be teachers of arithmetic. Your help is needed. May we enlist you as a recruit? The purpose of this distress call is to save our youth from being exposed to the limitations and barriers set up because of our own experiences with the study of arithmetic.
Developing Facility in Solving Verbal Problems
Authors: Spitzer Herbert F. , Flournoy Frances
Published: October 2020

THE IMPROVEMENT OF pupil achievement in verbal problem solving is an important objective of most upper grade arithmetic teachers. That this objective is not often reached with any degree of satisfaction is evident to all students of arithmetic teaching. It is also quite evident to students of arithmetic teaching that, although there are many problemsolving improvement procedures in usc, the most widely used procedure is that of just having pupils work problems without specific direction or suggestions. The other problem-solving improvement procedures practically all suggest specific steps for pupils to engage in. There arc, then, two broad classes of procedures, the one general (that of just working problems) and the other characterized by use of specific exercises.
Teaching: Using the Bulletin Board to Teach
Authors: Alton Elaine V.
Published: October 2020

Bulletin boards can be used to make classrooms attractive or to display students' work. They can also be used to convey information. The content of a bulletin board can provide review, reinforcement of topics currently being studied, introduction to new ideas, and enrichment.
Creating Problem-Solving Experiences with Ordinary Arithmetic Processes
Authors: Bernard John
Published: October 2020

For teachers of arithmetic who are seeking new and interesting ways to provide students with needed computational practice or review, here is a way to cast such practice in a problem-solving context without moving into “word problems.” To illustrate by way of an example, suppose you start with the number 99; are allowed only two kinds of legal moves, adding eleven or subtracting seven (you can switch back and forth or repeat such moves as often as you like); and you are to hit 100. Try this before reading on.
One Point of View: Mathematics and the Environment
Authors: Cooney Thomas J.
Published: October 2020

There is a story I sometimes tell my preservice elementary school teachers.
Teaching: Using a Textbook Effectively
Authors: West Tommie A.
Published: October 2020

Every profession has its tools: plumbers have wrenches, carpenters have hammers, doctors have stethoscopes, and teachers have textbooks. Teachers also have other tools, but a study of factors affecting student achievement has found that the textbook was the one variable that seemed to determine what was learned (Begle 1973). lf a topic was not in the textbook, it was not likely to be learned.
Ideas
Authors: Tucker Benny F. , Bazik Edna F.
Published: October 2020

Ideas for this month focus on the topic of numeration using whole numbers, fractions, mixed numbers, decimals, and percents. Concepts and skills of numeration are important to the development of mathematics. Teachers need to help children communicate about quantities. These activities can help students to think about ways of representing and naming quantities.
One Point of View: Alternatives to Social Promotion
Authors: Taylor Harold D.
Published: October 2020

One of the most pressing concerns in education today is the teaching of mathematics to public school students. The decline in the mathematical ability of entering college freshmen and the resulting decrease in the number of students who elect majors in science represents a crisis in American public education. There is a comparable decline in the mathematical ability of high school students, a decline that can be traced through all levels of schooling from the first grade.
The “Steps” of Metric Conversion
Authors: Tolman Marvin N.
Published: October 2020

In working with students in the elementary school and with prospective teachers of those students, I find that one of the common difficulties in using metric measurement is in changing from smaller to larger or from larger to smaller units within a given basic unit of measure. For instance, in converting 36.2 decimeters to kilometers, the students have difficulty remembe ring how many decimeters in a kilometer. And deciding what to do about it, after the “how many” question is answered, is sometime perplexing. Although multiplying and dividing by powers of ten are relatively simple processes, problems with the application of these processes seem to occur as students struggle with the newly-acquired vocabulary and with their efforts to remember how many of what are in what, all the time trying to keep the prefixes in true perspective.
Ideas
Authors: Bazik Edna F. , Tucker Benny F.
Published: October 2020

Ideas for this month consists of two posters that provide motivational problem-solving activities with money. Suggested uses of the posters provide experiences related to making change.
Backward Mathematics for Enrichment
Authors: Westcott Alvin M. , Shuler Nancy L.
Published: October 2020

Steve Allen, while host of the “Tonight Show,” popularized a comedy construct he titled “The Question Man.” Allen felt the United States frantically pursues answers to questions with such verve that its people are obsessed with the value of answers. The result is an over-supply of answers and a shortage of good, creative questions. “The Question Man” specialized in posing unusual if not unpredictable and funny questions.
One Point of View: Perspective on Mathematics Education Today
Authors: Carl Iris M.
Published: October 2020

Not since Sputnik has the United States of America been faced with an educational crisis of such magnitude. At issue are the appalling shortage of qualified teachers of mathematics, weakened academic standards, and decreased student achievement.
Teaching: Ways to “Change Gears”
Authors: Bologna Elaine M.
Published: October 2020

Does your teaching sometimes seem to be on “automatic”? As you carefully follow your textbook and curriculum guide, and your mathematics class moves along smoothly, albeit monotonously, do you somehow feel a need to change pace—to give your students a lift, some enthusiasm, some enjoyment? Then it's time to “change gears.”
Life with an Exciting Nine-Year-Old
Authors: Olson Melfried
Published: October 2020

I share the same concern as Moser (1982) who, in his article “Dear Kathy's Teacher,” indicated he was as concerned about the whys in mathematics as about the hows. My daughter does well in the mechanics of mathematics; she feels that is what must be important because that is what the teacher demands. After years of being accused of being crazy by this child who, through reluctant patience, has managed to put up with my attempts to encourage her to become “friendly with numbers” rather than to do just computation, I received an unexpected reward.
Ideas
Authors: Bazik Edna F. , Tucker Benny F.
Published: October 2020

Ideas for this month focuses on the topic of symmetry. The activity sheets are planned to help children develop a concept of and kills related to symmetry.
Slam Dunks, Free Throws, and Problem Solving
Authors: Jamski William D.
Published: October 2020

What makes a problem interesting for a tudent? The presentation of a mind-catching situation set within an interesting general topic appear to be of paramount importance. Some logical rules for proceeding, a reasonable chance for success, and a stimulating challenge are also necessary.
One Point of View: Let Kids Write Programs
Authors: Shumway Richard J.
Published: October 2020

Teacher often ask me if I think computers are just another fad and will go the way of other “innovations” such as programmed learning, television. or behavioral objectives. My an wer has been, yes, if we use commercial software and use the computer to tell kids what to do. In my view. the principal value of computer rest in allowing students to write programs. There are some reasonable questions to ask, however.
Let's Do It: Dice Have Many Uses
Authors: Horak Virginia M. , Horak Willis J.
Published: October 2020

Dice are often available in elementary school classrooms. Although they generally are found in commercial games and arc used simply to generate move in game situations, their implicity and versatility allow them to be used in many other ways, too, In this article we describe some educational uses for dice and various activities appropriate for children in the primary grades.
Guidelines for Introducing Microcomputers in the Schools
Authors: Filliman Paula K.
Published: October 2020

Members of a school district's computer advisory committee come together for their first meeting. In brain-storming fashion, they enthusiastically generate a list of questions, concerns, and needs.
Teaching Mathematics with Microcomputers: Junior High School
Authors: Hatfield Larry L.
Published: October 2020

The ubiquitous computer! Do you realize that there may be a great variety of uses of a microcomputer in your classroom? Indeed. if we view the computer a a tool, or as a context for many differing activities, then we must learn how to choose our uses of it. This will require that we know the possible option, and have some rationales for our choices.
A Second-Grade Probability and Graphing Lesson
Authors: Woodward Ernest
Published: October 2020

Prior to the lesson, Ms. Cooper had made an 11-by-10 grid and a 6-by-6 grid on opposite sides of a piece of posrer board. The first part of the lesson was init iated with an examination of the six sides of a par ticular white die. Then Ms. Cooper produced a similar red die and indicated that the students would be tossing the pair of dice, and they would be concerned with the sum of the numbers of dots on the two dice. She rolled the dice several times, each time indicating the number of dots on the red die, the number on the white die, and asking the children what the sum was.
Ideas
Authors: Bazik Edna F. , Tucker Benny F.
Published: October 2020

Ideas for this month consists of two posters that involve digits and number fun to provide motivational activities for students. The poster can be used to introduce some ideas from elementary number theory.
Initial Decimal Concepts: Are They Really So Easy?
Authors: Zawojewski Judith
Published: October 2020

Decimals have long been considered an important mathematical topic and are even more important today. The increasing availability of calculators and the increasing use of the metric system are giving decimals a more prominent place in the mathematics curriculum than previously.
Teacher Preparation—a Coordinated Approach
Authors: Burger William F. , Jenkins Lee , Moore Margaret L. , Musser Gary L. , Smith Karen Clark
Published: October 2020

In the September 1981 issue, Dossey reported the “somewhat discouraging” comparison of recommended program criteria with the current teaching situation and curricula for grades K-6. We at Oregon State University had had similar concerns, and in the 1981 fall term we implemented a revised, comprehensive mathematics preparation component for the elementary school teacher education program. Based on the Dossey article, this revised program would rank in the top 5 percent of programs in the country, and we believe it contains the elements necessary to produce an exemplary program.
TEACHING: Improve Your Evaluation Techniques
Authors: Norton Mary Ann
Published: October 2020

Are the words evaluation and test synonymous to you and your students? To a child, a test means “What grade will I get?” To the teacher it means “How are my children doing?” and, perhaps, “Am I doing a good job teaching?” Evaluation, however, should represent many dimensions beyond those a test brings to mind. The National Council of Teachers of Mathematics (NCTM) stated in their publication An Agenda for Action (1980) that “the first purpose of meaningful evaluation in school mathematics should be improvement of learning program, teaching, and materials.” (p. 13). This article will focu on what happens before and after the test, on ways to evaluate student progress before the test is given, and to use the information that tests can provide.
Organizing for Mathematics Instruction
Authors: Larson Carol Novillis
Published: October 2020

A plan that incorporates diagnostic teaching, unit planning, and flexible grouping is one viable alternative for organizing the elementary school classroom for mathematic instruction. I used this plan when I taught fifth and sixth grades in New Hampshire, and some Title I third- and fifth-grade teachers in Tucson, Arizona, have used it during the past two years.
President's Report: Courage to Change
Authors: Willoughby Stephen S.
Published: October 2020

I look around me, and all I see is change. Police officers are getting younger. The children whose diapers I used to change have grown up and left home. Such changes are inevitable—have been going on for centuries—and, in one sense, are more a sign of stability than of change.
Research Report: Teaching Effectiveness
Authors: Suydam Marilyn N.
Published: October 2020

Have you ever wondered what teachers do that makes them effective? Suppose effective teachers are those whose students achieve higher test scores. Certain ways in which such teachers manage their classes are different from the ways less effective teachers handle their classes. For instance, effective teachers are much more likely to—
Multiplication Clue: A Game Activity for the Classroom
Authors: Falco Thomas
Published: October 2020

Have you ever experienced the frustration of trying to teach to, or to learn from, another person a totally unfamiliar game? My experience with game has led me to feel that the best and most enjoyable way to learn a game i by first observing other at play. Then, once motivated to try it, the involvement of playing it and the reward of success enhance the learning process.
Teacher Education: Elementary Teacher Education Focus: Problem Solving
Authors: LeBlanc John F.
Published: October 2020

Somebody in a gathering or at a party is often likely to announce to the group, “I've got a problem for someone here to solve! Who would like to hear it?”
Number or Prenumber Foundational Experiences for Young Children: Must We Choose?
Authors: Clements Douglas H. , Callahan Leroy G.
Published: October 2020

Extended discussion can be found in the literature regarding the appropriateness or inappropriateness, of teaching counting and other number kill to pre chool and kindergarten children.
Teacher Education: How Teacher Educators Can Use Manipulative Materials with Preservice Teachers
Authors: Young Sharon L.
Published: October 2020

Not long ago I wa ob erving Martha Peterson, a preservice teacher from my methods course, as she was teaching the subtraction algorithm to some third grader. Martha was using base-ten blocks to show how the physical exchange of a “long” for ten “unit,” in relation to a written step in the algorithm, when Johnny exclaimed, “so that' why you cross out the tens!” As we left the classroom, Martha was elated and said. “Did you hear Johnny? The base-ten block really helped him understand. l didn't think manipulative material would really work but now I do”
How Can 425 Students Learn to Use 1 Microcomputer? A Success Story
Authors: Hart Lynn C.
Published: October 2020

The K-7 public school where I am a full-time teacher of seventh-grade mathematics and science has had a microcomputer for one year. The school system had provided one computer for every elementary school in the district, with two conditions. first, one teacher from each school must participate in a graduate course in BASIC programming and computer literacy that carries. five quarter-hours of credit. second, the school must offer minicourses on the computer to Its sixth-and seventh-grade students After completing the five-hour course during the summer and receiving the title “computer teacher-in-residence,” I arranged for the delivery of the microcomputer to our school. That was one year ago.
Research Report: Manipulative Materials
Authors: Suydam Marilyn N.
Published: October 2020

In responses to questionnaires. most teachers indicate that they believe that manipulative materials (chips, blocks, fraction pieces, etc.) should be used for mathematics instruction. Children should be involved in the process of doing mathematics, and the use of concrete materials is integrally related to the development of meaning. As children work with objects and talk about what they're doing, they begin to see relationships— to learn mathematics.
Iggies Come to Kindergarten
Authors: Yvon Bernard R. , Dallinger Dopheide Jane
Published: October 2020

An Iggie has many “people” char-acteristics—arms, legs, ears, and so on—but it also has its own unique features, such as being yellow and always wearing both a hat and a smile. The Iggie was born in a kindergarten classroom in Winterport, Maine. The teacher created the character while she was exploring early mathematics
Diagnosis and Remediation of Sentence–solving Error Patterns
Authors: Sadowski Barbara R. , Houston Mcllveen Delayne
Published: October 2020

When you grade a set of arithmetic test papers, how often do you notice that you seem to be marking the same items incorrect on one test paper after another? You know the feeling; as your pencil moves down the set of answers—right, right, right, wrong, right, wrong, right, … —you know that you've graded two or three other papers with exactly the same incorrect items. You might even make a mental note of the students' names, trying to find a reason why they all missed those particular items. And if all these students happen to have mastered basic arithmetic skills, you might check to see if they were all out of class for some reason (such as a meeting or chorus practice), or you check over the test items to see if they are misleading or poorly reproduced on their test papers. There is a nagging feeling that something is causing all those good students to miss the same items. Yet since they all passed with 80s or better, the feeling goes away until next year when that topic is encountered and you promise yourself that when you have time you'll take a closer look.
Alternatives for Teaching Multiplication Facts
Authors: Lessen Elliott I. , Cumblad Carla L.
Published: October 2020

Teachers have searched for successful ways to teach multiplication. Vigilante (1978) and Bolduc (1980) discussed ways to “access” multiplication facts.
Teaching Rational Numbers—Primary Grades
Authors: “Mickey” Hollis L. Y.
Published: October 2020

The first question that ought to be asked about the teaching of rational numbers in the primary grades is. “Should fractions be taught in the primary grades?” The answers to this question differ. Leutzinger and Nelson (1980) state.
Teaching Rational Numbers—Intermediate Grades
Authors: Hall Jacobson Marilyn
Published: October 2020

The introduction of decimals is an important rational-number activity in the middle grades.
One Point of View: Making Room
Authors: Swafford Jane
Published: October 2020

Computers and calculator are here to stay. The challenge facing us, as stated in An Agenda for Action, is to “take full advantage of the power of calculator and computer at all grade levels.” Much has been written and said about how this goal might be accomplished, about what we should add to the curriculum or how we can enhance the existing curriculum. But where will we find the room?
Eekorian Encounter—a Measurement Mystery
Authors: Krustchinsky Rick
Published: October 2020

This story of the Eekorian encounter is the basis for an exciting activity that enables student to find various metric measureme nts within their own classroom. The only materials needed are metersticks and the story itself. Blank space in the story are provided next to each object to be measured. For example, after measuring the first object. the students record their measurement beside the number I, the second measurement will be placed next to the number 2, and so on. Students may want to create similar stories of their own or have a contest to draw the Eekorians.
One Point of View: Guiding the Elementary School Curriculum
Authors: Schultz James E.
Published: October 2020

An Agenda for Action (NCTM 1980) certainly provides a framework to guide school mathematics in the 1980s and beyond. Although it is a major step in the right direction, this relatively brief document does not spell out many of the specific steps needed to direct mathematics instruction for millions of students in this decade.
One Point of View: Crisis in Arithmetic Teaching—the Future Is Here
Authors: Altizer-Tuning Carol
Published: October 2020

New gadgets beckon to the imagination, and robots work in our factories and homes. We are facing a society that is increasingly automated, one that is going to change fundamentally the nature of the work expected of human beings. Such a change has occurred once before in history. During the Industrial Revolution, steam engines and other devices began to do the physical work of human beings. Today, computerization is changing familiar work patterns. Computers are taking over much of the mental labor we do routinely and repetitively. They free our minds to engage in more creative endeavors. People must be equipped for such changes. They must be prepared for the nonroutine, the unforeseen, the unfamiliar, and the uncertain. The standards of the past are inadequate for the present and future. It is important to recognize that not only do problems change over time but also do the methods, the tools, and the knowledge required for their solutions.
Added Dimensions to Literacy
Authors: Scalzitti Joyce
Published: October 2020

The question for the 1980s may well be “What is computer literacy?” More interpretations of computer literacy exist than do types of microcomputers. But, regardless of how you define it, additional dimensions need to be considered.
Readers' Dialogue
Authors: Matthews Warren N. , Buess Larry D. , Keeley Robert J. , Gilbert Robert K.
Published: October 2020

We just finished a unit on the division and multiplication of fraction, and a “dicovery” by one of my eighth-grade students fits in very nicely with your February 1984 issue and its focus. on rational numbers.
From the File
Authors: Azzolino Agnes , Ruemmler Ronald E.
Published: October 2020

You are to plan a route through a dungeon for Indiana Jones, who wants to search for a hidden treasure. This route must cover all rooms to make sure that the treasure is found, and it must contain a minimal number of turns to allow for a rapid search.
Readers' Dialogue
Authors: Kohn Aaron , English Lyn , Jenkins Lee , Woodcock Gary , Spieler Robert
Published: October 2020

I read with interest Judy Crawford's method of teaching subtraction of fractions with borrowing (“From the File.” January 1984). Students enrolled in the Queensland Primary Correspondence School have been using this method successfully for a number of years. We have found that our students a re able to cope easily with this approach, as it is a natural extension of their subtraction acti vities with whole numbers.
Ideas
Authors: Shaw Jean M.
Published: October 2020

Practice in measuring skil ls is necessary if students are to become compete nt at using mea uring tools and understanding the process of measurement. The “Metric Me” exercises presented this month offer many opportunities for measurement and comparison of measurements. Since the measurements are made of the students themselves, the activities are highly motivating and relevant.
Research Report: Questions?
Authors: Suydam Marilyn N.
Published: October 2020

You'd be an unusual teacher if you didn't ask questions. But what kind of questions do you ask?
Ideas
Authors: Shaw Jean M.
Published: October 2020

This month's lDEAS features acti vities in which students use the newspaper to find information and use it in problem solving. Newspaper activities are appealing because they allow students to use a real and up-to-date medium as they practice skills.
The Role of Problem Solving
Authors: Charles Randall I.
Published: October 2020

The importance of problem solving in mathematics has been attested to by many individuals and groups (e.g., Snowmass 1973; NCSM 1977; CBMS 1982). Furthermore, the belief seems to be common that the development of students' problem-solving abilities is one of the most important goals of mathematics education. In view of the importance of problem solving, it is templing to argue that problem solving and mathematical thinking are in fact different names tor the same activity. However, such an argument would provide too narrow an interpretation of mathematical thinking and too broad a view of problem solving. The purposes of this article are to describe one view of “mathematical thinking” and to describe the characteristics of a problem-solving program necessary to develop this kind of thinking.
Ideas
Authors: Shaw Jean M.
Published: October 2020

Elementary school students at all evels are interested in reptiles. This month's IDEAS uses reptiles as a Iheme for practicing skills in computation. measurement, comparison, reading, and problem solving, Teachers can use the worksheets for ordinary mathematical activities or as complements to the study of reptiles in science.
Patterns in the Multiplication Table
Authors: Tierney Cornelia C.
Published: October 2020

In elementary school, great importance is placed on memorization of number facts. In teaching fifth through eighth graders, 1 have assumed that most of my students had made a concerted effort to memorize facts in earlier grades. I have observed. however, that children who have had a similar amount of practice have a great range of recall. A few students complete tests of 100 multiplication or division facts perfectly in less than three minutes, whereas others are made miserable by the whole process. They skip many problems, look around the room to compare their progress with that of other students, and finally give up with few correct answers. Although those who have memorized the facts do better than others at whole-number arithmetic, they do not always do well in work with fractions.
Research Report: Improving Multiplication Skills
Authors: Suydam Marilyn N.
Published: October 2020

Did you hear that students' knowledge of multiplication basic facts improved decidedly between the second national mathematics assessment in 1978 and the third assessment in 1982 (NAEP 1983)? Average scores of nine-year-olds rose from 60 percent to 66 percent, ranging from 70–85 percent on easier facts to 50–60 percent on harder facts. Fourth graders performed about forty percentage points better than third graders. By age thirteen. scores were 90 percent or above on both assessments. That's the good news. The bad news is that results were not as good for conceptual, computational. or problem-solving items.
What's Going On…
Authors: Hopkins Billy L.
Published: October 2020

Elementary computer loan program. John H. Bayne Elementary School in Capitol Heights, Maryland, has implemented a program in which students can check out a computer for use at home. The three-component computer-literacy program is financed by a donation from Prescription Learning, an instructional firm in Springfield, Illinois. The program's components consist of computer literacy for kindergarten through second-grade students, skill reinforcement for students in grades four and six as a follow-up to reading and mathematics programs, and computer use at home for students in grades three and five. In the at-home component, students use the computers from four to six weeks. For more information contact Joyce Thomas, Principal, John H. Bayne Elementary School, 7010 Walker Mill Road, Capitol Heights, MD 20743 (301/336-1200).
Up Fractions! Up nm!
Authors: Kalman Dan
Published: October 2020

Have you ever wished for a simple and direct method for adding fractions? Would you be inte rested in a method with visual appeal? I have such a method to share, but I am reluctant to do so. I am not an experienced arithmetic teacher, and I am uncertain how to gauge the usefulness of my method. Perhaps by combining my idea with your classroom experience, we can come up with a useful contribution to teaching arithmetic.
Build a City
Authors: Reynolds Jean A.
Published: October 2020

Could I find a new angle for the old geometry lesson? This thought cro sed my mind as I prepared to teach a geometry unit to my class of fifth and ixth graders. The more I pored through old copies of teaching magazines and books, the more I became convinced that to give my students some tangible evidence that geometry is alive today in various careers. I would have to create the experience I ought for them. As a result, J designed a week-long build-acity project to let my students become familiar with the history of the five Platonic solids and then use these solid to create a city.
Ideas
Authors: Williams David E.
Published: October 2020

The IDEAS this month uses license plates to give students experiences in solving problems, following directions, developing numeracy, and writing number sentences. Students may find themselves using “guess and test” or “work backward” strategies as discussed in “Problem Solving: Tips for Teacher” (May 1985 and September 1984).
Mathematics Contest Stimulates Students
Authors: Cohen Lainie
Published: October 2020

Picture children excitedly doing mathematical calculations because they want to, not because they have to do so. Does this sound impossible? It can be a reality when winning a mathematics contest is at stake. This article describes a mathematics contest, from conception to completion, that can serve as a model for others.
Ensuring That Practice Makes Perfect: Implications for Children with Learning Disabilities
Authors: Moyer Margaret B. , Moyer John C.
Published: October 2020

Many teacher use the adage “practice makes perfect” to justify large quantities of drill-and-practice activities. Textbook authors use similar reasoning when they provide page after page of the same kind of problems. In the process, the quantitative aspect of practice is overemphasized while the quality of the practice activities suffers.
Mathematics Vocabulary and the Culturally Different Student
Authors: Garbe Douglas G.
Published: October 2020

Over the past few years, teachers have increased their efforts to identify and demonstrate the application of mathemat ics to life's activities, but many students still perceive mathematics as merely the manipulation of symbols governed by rules. Perhaps if these students had studied more applications of mathematics, then mathematics would be more meaningful to them. But even then I suspect that they would have been hindered by a lack of reading skills and an insufficient understanding of the vocabulary of mathematics.
One Point of View: Increased Time in School—Increased Learning?
Authors: Nichols Eugene D.
Published: October 2020

The years 1983 and 1984 saw several publications aimed at arousing the public's conscience about the status of American education. The headliner among them was the often quoted accusation directed at ourselves, the American people: “If an unfriendly foreign power had attempted to impose on America the mediocre educational performance that exists today, we might well have viewed it as an act of war. As it stands, we have allowed this to happen to ourselves.” (A Nation at Risk, National Commission on Excellence in Education, April 1983, p.5)
Math around the Clock
Authors: Joyner Jeane M.
Published: October 2020

Good programs in elementary school mathematics should include activities for building enthusiasm for mathematics as well as teaching basic concepts. Special projects offer teachers opportunities to motivate their students while children practice computational skills. When a mathematics act ivity involves children in ways in which each individual can be successful and feel that his or her contribution is as valuable as the next child's, then the students feel good about themselves and about mathematics. Teachers can capture the interest of children who are not self-motivated and build enthusiasm for mathematics in the classroom through projects.
Readers' Dialogue
Authors: Austra Joan L. , Whitney Susan Mount , Wright Janice A. , Loeffler Charles , Griffen Donna E. , Jamski William D. , Schaefer M. Geralda
Published: October 2020

In many years of teaching mathematics on the elementary school level. I have had occasion to introduce subtraction of frdctions with regroupmg. The concept of regrouping a whole number as one less plus an appropriate equivalent for “one” (3/3, 5/5, etc.) is difficult for many Mudents. particularly those with learning difficulties. I have used the following method successfully through the eighth grade.
Discovering Fractions on a “Fraction Table”
Authors: Wiebe James H.
Published: October 2020

Number lines have been used for many years to help students understand fractions. Another useful technique for developing understanding of operations on fractions has been the use of folded strips of paper (Scott 1981). By combining these two excellent models, we can create even more powerful materials to lead students to discover many important concepts about operations on fractions. The result of this combination of models is called a Fraction Table. It consists of large number lines taped to a table. Strips of paper that represent fractions can be manipulated on it to solve problems.