bluuebunny/crossref_metadata_2025 huggingface dataset:
What's Going on…
Authors: Hopkins Bill
Published: October 2020

Family math. The EQUALS staff at the Lawrence Hall of Science, University of California, Berkeley, has developed a program of classes to involve parents in their children's future schooling and jobs. Information about careers and the importance of mathematics to future jobs and schooling is woven throughout the classes. Mathematics topics are drawn from measurement, probability and statistics, patterns and functions, geometry, arithmetic, and logical thinking, and activities are designed to supplement the classroom curriculum. Classes are given for specific grade levels, spanning kindergarten through general mathematics. A hands-on approach, used with emphases on problem solving and the enjoyment of mathematics, includes instructions for use at home. FAMILY MATH is funded by the Fund for the Improvement of Postsecondary Education. A dissemination workshop will train new leaders in the fall of 1984. For further information contact Virginia Thompson and Ruth Cossey, c/o EQUALS, Lawrence Hall of Science, University of California, Berkeley, CA 94720.
Young Children—Small Numbers: Making Numbers Come Alive
Authors: Liedtke Werner
Published: October 2020

When parents discuss the abilities of preschool children, they will frequently volunteer such statements as, “My child can count to______.” “My child knows the numbers to_____.” “My child can add numbers.” It is likely that these skills were taught at home, and it is more than likely that these parents frequently overestimate the level of understanding their young children possess. Elkind (1975) noted that “because young children are often so capable linguistically, adults often overestimate their capacity to think” (p. 1). This statement is especially applicable to comments that relate to rote counting, a procedure likely to consist of nothing more than the ability to match a name or sound to an object or a series of objects like those below.
Teacher Education: Techniques for Developing Positive Attitudes in Preservice Teachers
Authors: Larson Carol Novillls
Published: October 2020

Many college seniors entering a course in elementary school mathematics methods admit to having negative attitudes toward mathematics. For most of these future elementary schoolteachers, the course in mathematics methods will be their last encounter with mathematic prior to student teaching. Since attitudes can probably be transmitted from teachers to student, developing a positive attitude toward teaching mathematics is one of the major goals of the course. The course in mathematic method cannot be just a clinic on math anxiety however; other goals must also be realized. These other goals include (1) at taining knowledge of the curriculum and (2) being able to select and use appropriate teaching aids, in tructional trategies, classroom organizational patterns, and diagnostic and evaluative technique. Nevertheless. no conflict really exists between covering the usual content of a course in mathematic methods and at the same time encouraging positive attitudes toward mathematics and combating math anxiety. A principal ingredient is “to deal with feeling,” a well a wi th idea and teaching kills. This article describc technique that can be used to help change mathematical attitudes and that, at the aame time, accomplish the other goal of the course.
Let's Do It: Punchy Mathematics
Authors: Shaw Jean M.
Published: October 2020

Let's Do It—activity approaches to teaching and learning mathematics in the primary grades, with extensions through grade six.
Graphs and Microcomputers: A Middle School Program
Authors: Saltinski Ronald
Published: October 2020

Everyone agrees that students should learn about making and reading graphs. Even the national assessments on the topic indicate that students should use graphs for inferring and predicting (Bestger 1980). Yet, limited time and resources prevent most teachers from implementing classroom activities re lated to graphs. This need not be the case. The relatively new presence of microcomputers in the classroom can facilitate an innovative and rewarding program for teaching about graphs.
Ideas
Authors: Fennell Francis (Skip) , Houser Larry L. , McPartland Donna , Parker Sandra
Published: October 2020

Ideas for this month presents two possters that emphasize graphing in a Halloween setting.
Computer Corner: What Machine?
Authors: Shumway Richard J.
Published: October 2020

According to Time (3 January 1983), the best-selling computers for 1982 were Timex-Sinclair, VIC-20. Tl 99/4A, Atari 400, TRS-80 (model III), Apple II Plus, Atari 800, and the IBM personal computer with sale ranging from 1 000 000 to 2000. Many ask me which computer I would recommend for use in chool. My first answer is that I like all of them, and I ask what they want to do with it in their school. Many would prefer a question not answered with a question—so here goes. As of today. 28 April 1983. here is what I would do.
Research Report: Achieving with Calculators
Authors: Suydam Marilyn N.
Published: October 2020

You have probably heard it said that schools may be the last place where paper-and-pencil computation i used—while everyone else uses calculator! Concerns about the use of calculator led to over 175 studie, at least 75 of which explored the question of whether calculators harm achievement.
The Only Way to Do It Is to Undo It
Authors: Haigh William E.
Published: October 2020

Every day we “do” many activitie that we can “undo” by reversing the initial procedure. For instance, we turn on a light (do), and we turn off the same light (undo). We sit down (do). and we tand up (undo). In the evening, we go to sleep (do). and the next morning, we wake up (undo). Each undoing activity cancels or neutralizes what each doing activity ha accomplished. Figure I illustrate the relationship between doing and undoing.
But Why Does C = πd?
Authors: Ott Jack M. , Sommers Dean D. , Creamer Kay
Published: October 2020

What do tudents really want to know when they a k why? Let us examine the question in the context of a teacher who is introducing a cia to the formula for the circumference of a circle.
Programming, Problem Solving, and Practice
Authors: Clements Douglas H.
Published: October 2020

We know that the microcomputer can be used effectively for drill and practice in arithmetic. It can, however, also foster student’ abilities in programming and problem solving. This article describes an activity in which studenh write programs for each other using a child-oriented programming language known as Logo.
Teacher Education: Using Microcomputers with Preservice Teachers
Authors: Schroeder Thomas L.
Published: October 2020

A presing issue facing teacher educators today is what work with microcomputers should be included in the program of preservice education for teachers.
Let's Do It: Making Graphs
Authors: Shaw Jean M.
Published: October 2020

Constructing graphs offers children many opportunities to make decisions and solve problems as they organize data and interpret their results. Making graphs is an interesting activity for children when it involves gathering data with other classmates.
Kids with Computers: An Enrichment Program for Elementary Schoolchildren
Authors: Bloomstrand Nancy L.
Published: October 2020

As director of the learning center of an elementary school situated in a midwestern city, I became involved in an enrichment program for mathematically advanced children. ln the fall of 1979, our School's principal consulted with his staff concerning the previous year's standardized test score for student in the third through sixth grades. Although the reading cores showed a fairly typical bell curve, the mathematics cores were clustered in the middle range. A few of our students were in the lowest percentiles, but no children had cored in the top range on the mathematic test.
It Followed Us to School One Day …
Authors: Williams Julie
Published: October 2020

It is no secret that Pac-Man and Ms. Pac-Man draw a more enthusiastic audience than most of the nation's schoolteachers. The competition for children's attention is strong, and educators feel the pressure.
By Way of Introduction
Authors: Williams David E.
Published: October 2020

Previous focus issues of the Arithmetic Teacher have concentrated on topics very appealing to mathematics educator. Last year, the focus was on microcomputer, and problem solving was featured in a focus. issue the year before.
One Point of View: Helping Children Understand Rational Numbers
Authors: Kieren Thomas E.
Published: October 2020

The natural number system is the first one that a child studies in school. Instruction builds on the child's knowledge of this system.
Ideas
Authors: Fennell Francis (Skip) , Houser Larry L. , McPartland Donna , Parker Sandra
Published: October 2020

Ideas for this month reinforces com-putational skills involving fractions and decimals. These skills are presented in a winter sports setting (the Olympic Games).
What Research Says
Authors: Driscoll Mark
Published: October 2020

When the recent National Assessment of Educational Progress (NAEP) showed that “only about 40 percent of the 17-year-olds appear to have mastered basic fraction computation” (Carpenter et al. 1981). it underscored a problem that is very familiar to teachers of mathematics at all school levels: learning fractions and teaching fractions are two very difficult tasks. Another NAEP conclusion may also be familiar to teachers, but it merits their constant attention: when computational skills with fractions have been mastered by age 13, students have little understanding of them. Once they have forgotten procedures for computing fractions, few teenagers can reconstruct them
Ten Often Ignored Applications of Rational–Number Concepts
Authors: Usiskin Zalman , Bell Max S.
Published: October 2020

When we speak of applications of rational numbers, we refer to those applications that involve more than just whole numbers or integers. Most textbooks outline such applications.
Mathematics Can Be Fun
Authors: Gross Lawrence P.
Published: October 2020

A large sign prominently displayed on my classroom windows declares that “Mathematics Can Be Fun” (see photograph). Assuming that one accepts the statement as a truth, certainly one reason for it is that “Bingo Can Be Better.” Without a doubt, the most popular recreational activity that takes place in my fifth-, sixth-, seventh-, and eighth-grade mathematics classrooms is “Math Bingo.” I use real (professional) bingo sheets that I get from a local bingo hall. An enormous amount of excitement is generated. especially toward the end of a game, and I'm certain that other teachers who try math bingo will experience similar results
Sum 9.9: A Game for Decimals
Authors: Priester Sharon
Published: October 2020

Recently I purchased a game called “ono 99,” put out by International Games. Our family found that once we understood all the rules, it was really a great game to play. The game “ono 99” gave me an idea for helping children with decimals
The Integer Abacus
Authors: Dirks Michael K.
Published: October 2020

Everyone knows the difficulty that secondary students [and even university students!] have in understanding the algebraic rule of signs—“minus times minus equals plul.”
Preschoolers and the Computer
Authors: Williams R. Ann
Published: October 2020

As four-year-old Eric enter the Living-Learning-Laboratory for Young Children, his eyes quickly scan the room. He excitedly calls to Shawn, who is still in the hall, “Hey, we get to computer today!”
Greatest Common Factor and Least Common Multiple
Authors: Lamb Charles E. , Hutcherson Lyndal R.
Published: October 2020

The greatest common factor and the least common multiple are two concepts that are important in their own right as well as crucial to the development of other topics in mathematics. Unfortunately, these two topics can be difficult for students to understand even apart from the process of computing numerical values for them. This article discusses some strategies for avoiding misconceptions of these ideas and reviews some computational algorithms for them.
Readers' Dialogue
Authors: Buck Donna , Nanda Jayanta K. , White Mary Geraldine , Cline Starr , Ohlsen R. L. , David Elaine
Published: October 2020

Our fourth graders in the mathematics program for gifted students have been studying Cryptarithms by Josephine and Richard Andree. We discussed ways to approach digit replacement by carrying, observing several letters that remain the same, changing the operation, and so on. Several students were brave enough to try their own cryptarithms.
Using English Sentences and Pictures for Practice in Mathematics
Authors: Pereira-Mendoza Lionel
Published: October 2020

Every teacher accumulates, over a period of time, a collection of practice activities for use in the classroom. The best ones are those that can be adapted to many concepts. I have found the following activities to be extremely valuable and adaptable as self-checking tasks involving practice with whole-number operations.
One Point of View: Current Status of the Metric System
Authors: McGinty Robert
Published: October 2020

As you are well aware, it is 1984. and in some places and some respects, we arc in an Orwellian society (by one estimatc. over 100 of Orwell's 137 predictions have come to pass). The same thing can be said about the metric system. with the qualification that in most places and most respect. we are in a metric world. It would appear that compared to other countries, the United States has been the least affected by Orwell (fortunately) and the metric system (unfortunately).
Computer Power in Primary Grades: Mathematics with Big Trak™
Authors: Sawada Daiyo
Published: October 2020

All is quiet in the house. Even the cat, snuggled on his cushion beside the refrigerator, seems to be asleep. Suddenly, from the hallway, a vehicle emerges. chugging along quietly. It halts for a moment, a if getting its bearing, turn slightly to the left, traverses the island in the kitchen, turns right toward the refrigerator, and finally stop in front of the cat. Three flashes of light, accompanied by “space beeps,“ are launched to-ward a surprised cat. Laughter is heard in the hallway as the vehicle backs up and retrace its journey down the hallway (see fig. 1).
Predicting the Winner of the World Series
Authors: Fraser Don
Published: October 2020

Each fall the American League champions play the National League champions in the World Series. This article presents a simple system for predicting the winner of the World Series. Since 1969, when the American and National Leagues each were separated into two divisions, the system has worked for every year except two! That's an astounding success rate of 88 percent!
Research Report: Microcomputers in Mathematics Instruction
Authors: Suydam Marilyn N.
Published: October 2020

Many teachers are using microcomputers in their classrooms, trying out different programs and different ways of using them. Surveys indicate that most educational software is for mathematics, and thus microcomputers are used more frequently in mathematics lessons than in other subjects. Most of this software involves drill and practice for recalling previously learned facts, with no stress on higher-order skills. Few programs are designed to teach concepts or to develop problemsolving techniques.
A Different Kind of Preparation
Authors: Halpern Lynn
Published: October 2020

As preparation for the annual achievement test, teachers are reminded to emphasize how to take timed tests and multiple-choice tests. But little is mentioned about the structure of the test. What about the “trap”? What about the way proficiency in the different topics is meaured?
Computer Corner
Authors: Hampel Paul J.
Published: October 2020

This activity offers students a chance to practice mental computation and judge the effects of various rules for formatting output. Blank computer cards can be held up with different PRINT statements on them, and students can respond on paper (gridded maps of the computer's text screen) or simply explained orally. Practice with both written and oral responses to this activity is important. The ability to predict is an important problem-solving skill that can be practiced by using BASIC and the computer.
National Council of Teachers of Mathematics: President's Report: Mathematics Education 1984: Orwell or Well?
Authors: Willoughby Stephen S.
Published: October 2020

1984 Is here. For thirty-six years 1984 has been not only a number—not only a year—but a synonym for tyranny. When george orwell wrote his now famous novel, he was not predicting the future. He was calling our attention to the many good things we had and to how unpleasant life could become if they were taken from us. 1984 Was more warning than prophecy. An analyst recently announced that forty of fifty predictions made in the novel 1984 have come true. These include such things as the placement of television survey cameras in public places, The existence of a chemical agent to eliminate forests and crops, the use of outer space for military purpoes, and a single. title to replace the two title “Miss” and “Mrs.” that analyst missed the point, of course. Orwell was not so much interested in the technological and social details of the future as he was in the general condition of society. He was warning us that freedom was too much taken for granted and that we must constantly be vigilant to protect freedom—or we will lose it. He was not saying that 1984 was inevitable. He was saying, “don't let it happen. It depend on you.”
One Point of View: The “Rising Tide” of Educational Criticism
Authors: Vogeli Bruce R.
Published: October 2020

During the past year American education in general, and mathematics education in particular. came under attack to an extent not matched since 1957 when Sputnik led Americans to wonder if their chools somehow were inadequate. Critical reports directed “to the American people” were issued with such frequency that satirist Alex Heard ofrered readers of the New Republic advice on “How to Write an Education Report.” Heard emphaized the prospective critic's need not for facts or policy recommendations but rather for strong metaphors and a strident style. Unfortunately, too many educational critics seemed to have taken Heard' tonguein-cheek advice seriouly!
Mathematics in the Elementary Grades: The Soviet Experience
Authors: Moro Maria
Published: October 2020

In the Soviet Union, a complete ten-year education is free and compulsory for everyone. All Soviet schools teach the same mathematics curriculum for all ten years. The first three years comprise the primary schooling with classes conducted by one teacher. Teaching is done by subject specialists beginning in the fourth grade.
A Subtraction Algorithm for the Upper Grades
Authors: Grossman Anne S.
Published: October 2020

It took a long time for zero to be accepted as a number, and operations with it still confuse many people. Although my stude nts can pe rform the subtraction algorithm by the decomposition method, many of them make careless errors if they have to regroup or “borrow” in problems where one or more zeros occur in the minuend. Examples of this type occur frequently when we need to make change; $3. 95 s ubtracted from $5.00 or $798.00 subtracted from $ 1000.00 are typical cases.
Fun and Arithmetic Practice with Days and Dates
Authors: Richbart Lynn A.
Published: October 2020

Days, dates, and calendars, in general, provide an interesting setting in which to practice arithmetic. Students and adults alike are fascinated by the ability to determine the day of the week on which a particular date fell or will fall. All seem interested in finding out the day of their birth and that of their parents, brothers, sisters, and, of course, their teachers.
Research Report Homework: Yes or No?
Authors: Suydam Marilyn N.
Published: October 2020

Several of the national reports on educational improvement issued in 1983 suggested that children should be given homework on a regular basis. Is there evidence that homework in mathe matics promotes pupils' achievement?
By Way of Introduction
Authors: LeBlanc John
Published: October 2020

The decription of the goal of elementary chool mathematics is often made using a two-dimensional model. One dimension include the content objectives, the other, the process objectives. Content objectives include the topics in mathematics that are studied. whereas proce objectives are the behaviors, the procees that student hould develop and use as the content objectives are studied and mastered. One such model used in the 1981–82 National Assessment of Educational Progress (NAEP 1981) is shown in figure 1. As an alternative to thi framework. some groups have identified a set of basic-skill area to be studied in elementary school mathematics. The ten areas listed by the National Council of Supervisors of Mathematic (1977) arc as follow: (1) problem solving: (2) applying mathematics to everyday situations: (3) alertness to the reasonableness of result; (4) estimation and approximation; (5) appropriate computational skills; (6) geometry: (7) measurement: (8) reading, interpreting. and contructing tables; (9) using mathematics to predict; and (10) computer literacy. One important goal not specifically mentioned in either of these two cheme is that of mathematical thinking. yet the development of mathematical thinking in students should be a central goal of any mathematic program.
Mathematical Symbols: Insight through Invention
Authors: Sawada Daiyo
Published: October 2020

Over the years, like a pendulum. the emphasis in mathematics education has swung from a focus on concepts and understanding (e.g., the new-math movement) on the one hand to skill with facts and algorithms (e.g., the back-to-basic movement) on the other. Currently. children can adequately perform algorithms, but they may do so with little understanding of the underlying concepts (Resnick 1982, 136–55). In part, the difficulty lies in students having lo t sight of the role of symbols in mathematical thinking. The development of approache. that help children integrate the insight of symbolic understanding with the power of algorithmic technique should be of value. Accordingly, the intent of this article is to suggest how children can be guided to see and personally feel the power and simplicity that thinking with and about mathematical symbols can bring to their algorithmic competence. Although, for the sake of concretene and pecificity, attention hall be confined to computation, stress shall be placed on an approach that the reader may find generalize to other areas.
The Human Computer (Nudging Along Together)
Authors: Nelson Marvin N. , Clark H. Clifford , Tolman Marvin N.
Published: October 2020

Although the topic of bases in the elementary school may be wilting from lack of use, it is still potentially a very fruitful too for developing meaning and insights into our base-ten place-value system. Among prospective teachers who enter our mathematics methods classes, we find that most of those who have been exposed to bases have either strong positive or strong negative feelings about it. Few are neutral. Negative feelings are usually expressed by those whose experipassing It on to their students. we have found the following activity to be successful in helping pupils discover concepts about base ten using other bases.
One Point of View: Computer Training for Elementary School Teachers and Elementary School Computer Specialists
Authors: Richard Polis A.
Published: October 2020

Many mathematics educators and specialists believe that computer education at the undergraduate level should be concentrated in the mathematics and mathematics/education courses. However, the content in these courses is already crowded, and the prospective elementary school teacher still needs more mathematics than is currently taught. To add the necessary knowledge of computers to this overcrowded curriculum is unwise for two reasons. First, it could dilute rather than enhance the mathematics training, and, second, computers should be applied to all disciplines. I believe that a general education in the use of the computer needs to be introduced first and that applications should then be integrated across the curriculum. This approach will allow and encourage teachers to use the computer as a tool in each of the elementary chool subjects. This article recommends a program of computer education at the undergraduate level for elementary school teacher and elementary school computer specialists.
Research Report: Individualized or Cooperative Learning
Authors: Suydam Marilyn N.
Published: October 2020

From a recent study comes the conclusion that individualization of mathematics instruction using programmed materials with individuals or cooperative learning teams can be effective and manageable by a single teacher without an aide (Slavin, Leavy, and Madden 1984).
The Class Survey: A Problem-solving Activity
Authors: Newman Claire M. , Turkel Susan B.
Published: October 2020

Collecting, organizing, and drawing conclusions from data arc important aspect of chool mathematics for the 1980.
Research Report: Direct Instruction
Authors: Suydam Marilyn N.
Published: October 2020

A recent evaluation of direct instruction has indicated that such instruction is effective in teaching mathematics to disadvantaged students (Gersten and Carnine 1984).
On Patterns, Conjectures, and Proof: Developing Students' Mathematical Thinking
Authors: Thompson Alba G.
Published: October 2020

A useful strategy in solving problems is “look for a pattern.” In using the strategy, we start with simple cases or versions of the problem and from these cases discover a pattern or rule that can be applied to find the general solution.
Writing Techniques for Problem Solvers
Authors: Fennell Francis (Skip) , Ammon Richard
Published: October 2020

The decade of problem solving is upon us. The recommendations provided by the 1978 National Assessment of Educational Progress (NAEP), NCTM's An Agenda for Action, and the Priorities in School Mathematics (PRISM) Project all point toward greater emphasis on problem solving in elementary school mathematics.
One Point of View: Pressing Problems in Primary Mathematics Programs: Time, Texts, and Tests
Authors: Callahan Leroy G.
Published: October 2020

It is my point of view that the desired cognitive outcomes of an effective primary mathematics program are an integral blending of processes and products. observable mathematics performance (products) and the thinking strategies constructed by children that influence their performance (processes) are mutually inclusive aspects of a balanced primary mathematics program. I would like to consider three forces that can caues some disequilibrium in this blend and balance: time, texts, and tests.
Readers' Dialogue
Authors: Burdette Kathryn , Thompson Penelope , Brekke Stewart E. , Saxon John , Sheerin Inez , Buckler Rich , McClees J. Sheridan , Esch Ann McGee , Strowbridge Edwin D. , Coleman Julie , Jamski William D.
Published: October 2020

Last year our two classes of second graders spent an interesting week organizing and operating the “second Grade Pumpkin Company.” The project used mathematics, science, language arts, and economics. Some of the highlights of the activity follow.
One Point of View: Let the Learning Disabled Learn
Authors: Bley Nancy
Published: October 2020

The past ten or fifteen years have produced numerous changes in the field of education, particularly in mathematic. Many advances have been made in teacher education programs, in the use of mechanical aids, and particularly in the area of computers and computer-assisted instruction. At the same time awarenes has increased of the need to deal more effectively with students with special needs, or those more commonly described as having learning disabilities.
Mathematics for the Learning Disabled Child in the Regular Classroom
Authors: Sears Carol J.
Published: October 2020

Difficulties in mathematics are often the results of maladaptive behaviors or symptoms of underlying deficits in cognitive skills such as auditory memory, visual-motor coordination, or perception of spatial relationships. These problems can influence a child's normal development in such areas as number comprehension, ability to perform mathematical operations, and understanding of quantitative concepts. Mathematical difficulties can occur in combination with problems in reading and writing but, unfortunately, a large number of learning disabled children with disabilities only in mathematics do not receive the necessary special services “due to re liance on reading assesment scores as the sole or main criterion for referral for services” (Badian 1983, 235), and thus these services remain the responsibility of the regular classroom teachers.
The Low Achiever in Mathematics: Readings from the Arithmetic Teacher
Authors: Vance James H.
Published: October 2020

Since the Arithmetic Teacher began publication over thirty year ago, it has regularly published articles dealing with the challenging task of teaching mathematics to less able pupils. In teaching courses on diagnois and remediation of the slow learner in mathematics, I use many of these articles and refer my students to the journal to research a variety of topics. I have organized the articles into categories and filed them in three-ring binders, thus creating a book of readings on the low achiever. As new articles appear, I add them to the collection.
How Our Decimal Money Began
Authors: Clason Robert G.
Published: October 2020

Almost ten years ago, we celebrated the bicentennial of the American Revolution. A few years from now we will celebrate the bicentennial of our 1789 Constitution. During the era of these two major American event two hundred year ago our decimal monetary system was created. As arithmetic teachers, we are responsible for teaching children the fact of pennies, dimes, and dollars. Some background relating this arithmetic to American history can enrich both subjects.
One Point of View: Using Manipulatives
Authors: Bright George W.
Published: October 2020

Manipulatives hold the promise for helping many student understand mathematic, but as with any “cure” they also hold the potential for harm if they are used badly. Careless use of manipulatives may convince students that two mathematical world exist, symbols and manipulatives, and that it is acceptable for these world to have different rules. An acceptance of this inconsistency is certainly harmful to the development of proper mathematical understanding.
Hands On: Help for Teachers
Authors: Trueblood Cecil R.
Published: October 2020

The preparation of prospective teachers to use manipulative in the classroom is a multidimensional task.
Research Report: Minorities and Mathematics
Authors: Stanic George M. A. , Reyes Laurie Hart
Published: October 2020

Concern is increasing about the performance of minorities in school mathematics. For example, the entire March 1984 issue of the Journal for Research in Mathematics Education was devoted to this topic. The reason for this concern is that certain minority groups are underrepresented in mathematics enrollments and have not achieved up to their potential.
Elementary School Activity: Graphing the Stock Market
Authors: Kelly Margaret (Peggy)
Published: October 2020

To most second-grade pupils, the Dow-Jones industrial average, as reported on the nightly news, might mean anything from a super-strength cleaner to an extra-large weight lifter. But I found that when McDonald's, Mattel Toys, and other familiar companies were mentioned, visions of hamburgers and toys made dealing with the complicated stock market more meaningful.
Finding the Area of a Circle: Use a Cake Pan and Leave Out the Pi
Authors: Szetela Walter , Owens Douglas T.
Published: October 2020

The fact that many students have misconceptions and misunde rstandings of the concept of area has been clearly documented (e.g., Carpenter et al. 1980; Jamski 1978). For example, one of the most common misconceptions held by students in grades seven and eight and even preservice teachers is that polygons with the same perimeter have the same area. Szetela (1980) found that fifty-four of ninety-four (57 percent) stude nts in grades seven and eight, when presented with diagrams of a regular hexagon and an equilateral triangle known to have the same perimeter, stated that the areas of the two regions were the same despite the fact that the hexagon contained 50 percent more area than the triangle. Even more astonishing are the results of a similar experiment by Woodward and Byrd (1983). They found that 157 of 258 (61 percent) students in grade eight stated that the areas of five different rectangles with the same perimeters were the same even though one of the rectangles was almost four times as large as another! If students have difficulty with the concept of area of polygonal figures, they can be expected to have even more difficulty with areas of irregular figures, “blobs,” and circular regions.
Help Your Students Read Mathematics
Authors: Gullatt David E.
Published: October 2020

Many student have difficulty recognizing the words in their assigned texts (Hollander 1977). Yet well over half the learning that takes place in school is based to some extent on reading. Some students who can read aloud do not understand the message the author is attempting to convey.
A Calculator-integrated Curriculum: The Time Is Now
Authors: Williams David E.
Published: October 2020

It is 1987. We have probed both far into space and to the depths of the oceans. Technology has enabled humans to walk on the moon several times; it has helped scientists to find the Titanic on the ocean's floor. Many of George Orwell's prophecies have come true, a number of them long before the year 1984. Technological advances have made the lives of many citizens easier and more productive. But elementary school students in classrooms across this country still are being taught the long-division algorithm using pencil and paper. Why?
Activities for Calculators
Authors: Hiatt Arthur A.
Published: October 2020

Even a cursory review of the literature reveal widespread use of the calculator in virtually every industrialized nation. Still, teachers need calculator activities that take advantage of its power as a tool to enhance learning. One of its key advantages is that it can generate correct data rapidly, per-mitting the learner to make observations and venture conjectures. In this role, the learner becomes the creator of mathematics rather than the passive onlooker.
The Calculator Is a Problem-solving Concept Developer
Authors: Comstock Margaret , Demana Franklin
Published: October 2020

The hand-held calculator is a powerful problem-solving tool. It can be used to develop concepts and explore mathematical topics. The speed and power of the calculator make more realistic and interesting problems accessible and allow students to work many more problems than possible with pencil and paper. The calculator focuses tudents' attention on mathematical processes. Numerical problem solving form the foundation from which algebraic ideas grow. This art icle give examples of calculator tablebuilding activities suitable for the middle school curriculum that develop problem-solving skills and mathematical concept and span the gap from arithmetic to algebra.
An Instructional Model for Integrating the Calculator
Authors: Berlin Donna F. , White Arthur L.
Published: October 2020

Advancements in the study of learning and educational technology in the last three decades have set the stage for revolutionizing educational theory and practice.
One Point of View: The Teacher Educator's Dilemma: Is More Better?
Authors: Berman Barbara , Friederwitzer Fredda J.
Published: October 2020

The current need for increased mathematics education at all levels has received many headlines and much attention from Congress, educators, and the general public. The National Commission on Excellence in Education recommended a greater number of mathematic courses for high school student and more stringent criteria for selection of mathematics teachers. The critics assert that emphasis must be placed on content, with rigorous instruction beginning at the elementary school level.
Research Report: Decimal Fractions
Authors: Hiebert James
Published: October 2020

This report summarizes what research says about the learning and teaching of decimal fractions and suggests some instructional strategies and activities to improve learning. Decimal fractions ordinarily are introduced in grade 4 or 5 and are treated intensively in grades 6 and 7. Research has focused on students at these grade levels, although some studies have included high school students. The following presents some of the significant findings obtained primarily from studies of students in conventional instructional programs in the United States and other countries.
Individualizing Mathematics Drill and Practice: Variations on a Computer Program
Authors: Vacc Nancy N.
Published: October 2020

In less than a decade, we have progressed from the rare situation of a school system having its own microcomputer to at least 85 percent of the schools in the United States having one or more microcomputers (Becker 1983). Although empirical studies supporting successful uses of microcomputers to supplement classroom instruction appear in the literature (e.g., Bradley [1982]; McDermott and Watkins [1983]; Ragosta, Holland and Jamison [1982]; Vacc [in press]), effective use of this new technology to assist with classroom instruction remains a concern. A major problem is inadequate available software. More than 90 percent of the educational computer programs reviewed by classroom teachers hired by a National Education Association foundation were found to be unacceptable (“Flunked Software” 1984), as were 95 percent of the language-arts software reviewed by subject-area leaders attending a meeting of the Association for Supervision and Curriculum Development (Otto 1984).
Division of Fractions: Developing Conceptual Sense with Dollars and Cents
Authors: Steiner Evelyn E.
Published: October 2020

One of the most difficult computational processes for students and teachers to conceptualize is division offractions. May (1974) indicated that “all learners of mathematics, regardless of age, need to be provided with models that will help to build bridges to the abstraction of mathematics.” This point was further emphasized in NCTM's An Agenda for Action (1980), which stated that teachers should incorporate situations into their mathematics lessons that “provide discovery and inquiry as well as basic drill” and use manipulatives “to illustrate or develop a concept or skill.”
Problem Solving in the Elementary Grades: Textbook Practices and Achievement Trends Over the Past Thirty Years
Authors: Nibbelink William H. , Stockdale Susan R. , Hoover Hiram D. , Mangru Matadial
Published: October 2020

The purpose of this article is to supply the reader with two sets of data, along with an invitation to ponder a question: Do textbook practices significantly affect achievement in traditional mathematical problem solving?
One Point of View: The Fundamental Problem of Arithmetic
Authors: Madell Robert
Published: October 2020

I haven't taught mathematics in quite some time, but I find it easy to recall some of my thinking about what I was tryi ng to do. First for me was alway problem solving. I liked to help children as they learned to “do mathematics.” To me it was obvious that such learning is important, above the detail implied by the question, problem solving about what? The processes that I was interested in can be exercised in a wide variety of domains—even in some that aren't usually thought of as mathematics.
Carnak the Magician: Sawyer's Number Tricks Revisited
Authors: Sovchik Robert J.
Published: October 2020

The art of motivating an elementary school mathematics class often rests on the teacher's ability to excite, mystify, and perplex students, Children like the mysterious (witness the popularity popularity of Halloween) and are often aroused to inquire about the origins of intriguing information.
One Point of View: Children's Right to Be Wrong
Authors: Labinowlcz Ed
Published: October 2020

A teachers, our view of learning is reflected directly in how we respond to children errors. A popular and long-standing belief among the majority of teacher is that errors and confusion have no educational value and, therefore, must be eliminated from the classroom. Hence, the teacher' role is interpreted as one that involves breaking learning down into such small teps that errors are not experienced. This role also includes modeling procedure explicitly and rescuing a child from period of confusion by quickly intervening with the correct answer or procedure.
Divide and Conquer: Unit Strips to the Rescue
Authors: Curcio Frances R. , Sicklick Francine , Turkel Susan B.
Published: October 2020

Yours is not to reason why, just invert and multiply … that's the stuff of sterile in-struction.
Estimation and Counting in the Block Corner
Authors: Singer Rita
Published: October 2020

Self-preservation caused me to begin using estimation and counting in my classroom block corner a a method of cleanup. A recent article about block-building in the Arithmetic Teacher (Carter 1985) gave me the impetu to hare my method. since cleanup is the bane of every early childhood classroom teacher. In my class of four-tosix-year-old, the children were allowed to keep their block constructions et up for the entire week. Their building consisted of airports. train stations, track, and roads; or hospital, Twin Tower, the Statue of Liberty, and tunnels, depending on the unit of study (e.g., transportation, health and nutrition, cities). We added accessories of trucks, trains, and people; named our constructions uing marker and construction paper; and wrote storie about our cities and towns. Then, on Friday, the “moment of truth” came with startling reality. We had to take down all these lovely buildings and put the blocks back in their proper places on the block shelves so that the custodian could clean the classroom floor.
Ideas
Authors: Barson Alan , Barson Lois
Published: October 2020

Ideas thi month is designed to give practice with rational numbers. The concepts of rational numbers are best under tood in practical application. The following activitie involve skills with common fractions, decimals, and percent.
By Way of Introduction
Authors: Fennell Francis (Skip)
Published: October 2020

What's the rush? Why are we pushing kids to mathematical abstraction so quickly? Do we really need to accelerate the mathematic curriculum so that some topic are introduced far too early while others are barely mentioned? Is it any wonder that many first and second graders impulsively complete mathematics activitie as rapidly as possible, for the mere satisfaction of being “done first”?
Assessing For Learning: Putting the Value Back into Evaluation
Authors: McKillip William D. , Stanic George M. A.
Published: October 2020

Evaluation is placing a value on something; one judges an outcome as good, fair, or poor or as acceptable or unacceptable. Evaluation is more than a score; in fact, a score on a test is not even necessary for evaluation. The meaning one places on some indicator, which may or may not be a score, is what constitutes evaluation. One can evaluate students, teachers, administrators, textbooks, curriculum, and many other aspects of schools; in this article, we concentrate on ways for teachers to evaluate the mathematics performance of primary school students. It is important to understand that teachers are evaluating students' performance, not the students themselves. This understanding helps one avoid permanently classifying a student as a good student or a poor student. Performance can and does change, and teachers should be alert to significant changes.
Assessing Understanding
Authors: Richardson Kathy
Published: October 2020

The rate of learning in the early years is dramatic. In just a few short months, children move from barely being able to stand alone to running across the lawn, from saying a few barely distinguishable words to chattering away using long, complex sentences. Parents and teachers are proud and happy to watch their young charges as they add to their list of accomplishments. When children enter school, parents and teachers are eager to see evidence of this learning and success, and their focus is on performance. “What can you do today that you couldn't do yesterday?” is the question, asked or implied, that children face daily.
What's Your Number? Developing Number Sense
Authors: Turkel Susan , Newman Claire M.
Published: October 2020

In a recent article in Newsweek, a mathematics professor bemoaned innumeracy, a widespread disability among otherwise sophisticated Americans. Such innumerate adults, he feels, have only a hazy understanding of numbers and the way they are used. These adults succumb easily to specious arguments that refer to numbers they do not understand. Many have no appreciation of number magnitudes—no grasp of very large numbers and little understanding of small ones (Paulos 1986).
Cross Sections of Clay Solids
Authors: Carroll William M.
Published: October 2020

This geometry exercise for intermediate and junior high school tudents has three goals for students: (1) to create three-dimensional clay figures; (2) to think in three dimension; and (3) to develop vocabulary. Working individually from pictures, students first construct geometric solids out of clay. Second, they attempt to visualize what happens when a solid is sliced at a particular location and angle. The type of solid and how it is sliced will determine the plane figure that will result—trapezoid, ellipse, and so on (see fig. 1). Third, students develop a geometry vocabulary by naming the solids they construct. For example, a cube is identified as a hexahedron; a doughnut is a torus. More important, students are asked to name or describe the cross section formed. Since they are not given the correct vocabulary, they must seek it out or develop it on their own. They will find that the terms rectangle and square are not adequate to name all four-sided polygon.
The AAN Calculator: A Tool for Enhancing Instruction
Authors: Embse Charles B. Vonder , Whiteman Frederick C. , Damarin Suzanne K. , Leitzel James R. C.
Published: October 2020

The utility of the hand-held calculator as an instructional tool is evident to the many teachers who use it. The usefulness and effectivenes of hand-held calculators in mathematics teaching is affirmed by the research literature (Suydam 1982; Hembree 1986). Nonetheless no learning tool, however general its uses and purposes might be, can serve all functions for all learners. The article The Inverse Tool Principle (Belland 1985) implies that novices often should be given more sophisticated learning tools than are needed by those who have become more expert in a field.
Golfing with a Protractor
Authors: Souza Ronald
Published: October 2020

Many junior high school students have a very difficult time using a protractor to measure angles. The following lesson enables students to practice estimating the measures of angles and to become proficient in using both a protractor and ruler.
Ideas
Authors: Barson Alan , Barson Lois
Published: October 2020

Ideas for this month presents activities to build concepts in measurement. Offering actual experiences with measurement tools is a most effective instructional method. The activities that follow require the use of rulers, scales, and clocks.
By Way of Introduction
Authors: Fennell Francis (Skip)
Published: October 2020

Did you see it? What? Why, the new subtitle, of course. Beginning with this volume, 36, the Arithrnetic Teacher will be subtitled “Mathematics Education through the Middle Grades.” Our subtitle accurately represents the content and intended audience of those articles published in the journal. The subtitle also attempts to publicize to our readership that a contemporary mathematics curriculum include attention to a variety of topic other than arithmetic.
One Point of View: Teaching Tomorrow's Skills Responsibly
Authors: Grouws Douglas A.
Published: October 2020

The educational reform movement will soon affect all school mathematics programs. It is hoped that the substantive changes that occur will reflect ca refully developed recommendation, such as those of the NCTM Standards Committee.