bluuebunny/crossref_metadata_2025 huggingface dataset:
Individualized instruction—who needs it?
Authors: Wegener Dallas D.
Published: October 2020

From an elementary principal's point of view, few changes in education have created as many joys or headaches as the contemporary implementation of individualized instruction. It is easy to spot an elementary school principal who has recently inaugurated an individualized-instruction program. In all probability, he is slightly paranoid; his professional life is a delirious mixture of smiles and heartaches. At the same moment that he is basking in success, he is sweating out accountability. The broad smile on his face is tempered by welts of criticism. Academically, he patterns himself like a David: armed with the research of Piaget, Gagne, and Bruner, he daily encounters the Goliath of traditional educational practices. He does what he does because he honestly believes that his school exists for the kids.
The Decimal is More Than a Dot
Authors: Arnold Frank C.
Published: October 2020

Missouri Must Be The Birthplace of all teachers since the constant cry of each is “Show Me.” We in District 45 and 46 under the aegis of Assistant Superintendent Max Gewirtz attempted to do just this in our t raining program for newly appointed teachers. (Districts 45 and 46 are part of the r ew York City school system. There are 37 elementary and junior high schools with approximately 25,000 pupils and 1,100 teachers.) The demonstration teacher in each case was helped by the Elementary Mathematics Coordinators. The following is an account of one of the mathematics lessons which the neophytes of the 5th and 6th grades viewed.
The case for a more universal number-line model of subtraction
Authors: Werner Sister Marijane
Published: October 2020

The use of a number line as a model for the four fundamental operations of mathematics has become a fairly common and effective teaching strategy. The number line has been the means to guided discovery for many pupils in the elementary school mathematics program. However, the model of subtraction of whole numbers on the number line that authors and editors of textbooks for teachers and pupils have commonly used has severe limitations. The single exception to this observation is the thirtieth yearbook of the NCTM, More Topics in Mathematics for Elementary School Teachers (1969), but the approach used there has not caught fire. Perhaps we need to rekindle the fire.
Recorded recollections of the study of mathematics
Authors: Lipsey Sally Irene
Published: October 2020

What does the layman remember of his mathematics lessons? What impressions remain after formal mathematics education has ceased? Biographical and autobiographical literature provides a view of mathematics education as it existed for some and as it is being documented for posterity. The recorded recollections of the subjects suggest the need for continued sympathetic attention to and careful research on the psychology of teaching mathematics.
Things you can try: A mathematics attitudinal device
Authors: Fellows Martha M.
Published: October 2020

A child's attitude toward mathematics and his self-concept of his ability to succeed in mathematics are factors that affect the progress and the receptibility of the child. However, these concerns, within the affective domain, are often shunted aside in concentrating on the acquisition of skills.
Experiences for metric missionaries
Authors: Viets Lottie
Published: October 2020

For the past 180 years, the United States of America has been inching along toward the almost universally adopted metric system of weights and measures. Certain sectors of our society—science, medicine, engineering, and athletics—are in various states of transition at the present time. Some important developments and major decisions of the United States government regarding metrication, including a conversion date projected by the National Bureau of Standards, are shown in figure 1.
Manipulatives in the classroom
Authors: Fennema Elizabeth
Published: October 2020

Statements concerning the efficacy of manipulative materials in facilitating the learning of mathematical ideas abound in current mathematics education literature. Partly in response to such statements, mathematics laboratories, or activity-based curricula that include a heavy reliance on the use of such materials, are becoming more and more prevalent. This belief that manipulative materials do indeed enhance the learning of mathematics has gained much validity from learning theories such as those suggested by Bruner, Dienes, and Piaget. These theories strongly support the idea that children need physical involvement, such as might be provided by hands-on experiences with manipulative materials, in order to add new ideas to their cognitive structure. However, attempts to translate such theories into classroom practice and to empirically measure the results have not provided evidence that the use of such materials by teachers does indeed result in better learning than the use of symbols alone (Suydam and Weaver 1970; Kieren 1971; Fennema 1972). This difference between theory and research findings indicates that manipulative materials are no panacea; the use of materials does not automatically ensure that mathematics learning will follow. However, even without strong empirical support, a strong case can be built for the inclusion of manipulative materials in an elementary school mathematics program.
Why I don't have any examples of negative numbers
Authors: Schultz James E.
Published: October 2020

Today is our day to start discussing negative numbers. So I should have some examples. But these last few days have been really hectic.
Things you can try: Paper, pencil, and book
Authors: Lulli Henry
Published: October 2020

This is a mathematical game that has been used successfully in the classroom. It was tried with various levels of seventh and eighth grade classes at an inner-city school.
Is the “new math” really better?
Authors: Cowle Irving M.
Published: October 2020

Is the ‘new math’ really better? I have heard this question literally hundreds of times, both in my primary function (that of teaching mathematics education to students preparing for careers in the elementary school) and on the occasions when I spoke to parent groups or conducted workshops for teachers who are already in service. People are still asking, “Just what is the ‘new math’?” One also hears repeatedly, from those individuals who once loved mathematics and did so well, “Until the new programs came along …, then I was all mixed up.”; And there are numerous instances in which a highly competent parent who majored in mathematics in college, or is an engineer, relates how he could always help his youngster with homework, “but now, I don't know what they're talking about.”
Making √2 seem “real”
Authors: Jacobs Judith E. , Herbert Elizabeth B.
Published: October 2020

What is √2? Ask this question of many students in junior high or even high school and the most frequent replies will be “1.414” or “I'd have to look it up.”
An analysis of teaching percentages
Authors: Cole Blaine L. , Weissenfluh Henry S.
Published: October 2020

For years that “demon” percent has plagued both teachers and students in sixth, seventh, and eighth grades. Unless careful consideration is given to the approach in teaching percentages, the problem will be with us for some time.
Scuba: Some challenging un-boring arithmetic
Authors: Fitting Marjorie A. Pickering
Published: October 2020

In this age of Jacques Cousteau and his film reports of the wonderful world beneath the sea, many a student's interest is peaked by the mention of scuba diving. When my three boys and I recently took a course and became certified divers, I was amazed at the amount of arithmetic that was absolutely essential to our safety as divers. It is understanding the pressures, being able to read gauges and tables, and being accurate arithmetically that brings us back to the surface, alive, after each dive. This article illustrates some applications of arithmetic to scuba diving.
Readers' Dialogue
Authors: Reys Robert E. , Davies Pauline , McLeod Don , Laird Virginia , Oliver William J.
Published: October 2020

I read “Fun with Geometry through Straw Construction” in the November issue of the ARITHMETIC TEACHER. This was an interesting yet disappointing article. It is good to share activities that provide for child involvement and that can also develop mathematical ideas, but the article did not go far enough. I did not find any specific suggestions that would enable a classroom teacher to link this model (the stellated dodecahedron) with the “concepts” listed at the beginning of the article. Maybe this would be too pedantic; or maybe it would be an insult to the knowledge of elementary teachers or maybe it is expecting too much in the limited space of an article. I don't think so!
Things you can try
Authors: Masse Marie
Published: October 2020

Would you like to drill some fun into your mathematics class? Put aside the usual mathematics drill and get out an electric drill, some scrap wood, some golf tees, and some dice. From these inexpensive materials you can develop a variety of mathematics games, even some that accomplish the same results as the usual mathematics drill, but in an unusually enjoyable way.
Rays and angles
Authors: Meggison Glynn W.
Published: October 2020

During a discussion of angles and how they are formed by rays, my sixth-grade students became curious about the number of angles that would be formed by a given number of rays.
Sex bias in elementary school mathematics texts
Authors: Jay Winifred T. , Schminke Clarence W.
Published: October 2020

Don't close your eyes. It won't go away. Subtle sex bias in elementary schools isn't likely to disappear unless you do something about it. One way to begin is by recognizing that sex stereotyping may exist in the instructional materials used in elementary schools, or more specifically within elementary school mathematics textbooks.
IDEAS
Authors: Burns Marilyn
Published: October 2020

Patterns in graphs is the theme for April's IDEAS. Counting is the only skill prerequisite to learning to name points on a grid; all that's needed for each point is a pa ir of numbers. The French mathematician, Rene Descartes, invented the coordinate graphing system in the 17th century and provided a way to link geometric figures to algebra ic equations. Children at all levels can have some experience with this important idea of ma thematics, and graphing activities reinforce concepts of number.
Concentration
Authors: Crouse Richard
Published: October 2020

The rules for this game are similar to the rules for the television game. A “Concentration” board is needed. On a large piece of cardboard, rule off a number of squares (or rectangles)—the number will depend on the ability and grade level of the class the teacher is teaching. The examples used will depend on the kind of drill the teacher wants to provide. Suppose a teacher wants to drill students on equivalent fractions. Then the board might look like the one in figure 1.
Individualized instruction: it can't be done with a screwdriver
Authors: Clark H. Clifford
Published: October 2020

Have you heard the story of the elementary school principal who individualized his school over the weekend with a screwdriver? In less than two hours he removed all the “grade” signs above each classroom door and replaced them with “level” signs. When the teachers returned Monday morning, as if by magic, they were all nongraded and individualized.
Self-paced mathematics instruction: how effective has it been?
Authors: Schoen Harold L.
Published: October 2020

The January 1972, issue of the Arithmetic Teacher was devoted to individualizing mathematics instruction in the elementary schools. Most of the articles in that issue dealt with self-paced, modularized approaches to individualization. Proponents of this approach have argued that mathematics achievement is increased, or at least not decreased, and that gains in the affective domain far outweigh the extra cost and teacher effort needed to implement a self-paced program. To date very little research testing this argument has appeared in educational journals. However, nearly one hundred recent unpublished studies, mostly doctoral dissertations, have been conducted in which the effectiveness of a self-paced mathematics program was examined. Studies that compared a self-paced program with traditional approaches to mathematics instruction in the elementary school have been summarized in another paper (Schoen 1975[a]). The major findings in that summary and some further studies that help to explain those findings will be included here. Due to space limitations, the individual studies will not all be cited. The interested reader may refer to the longer paper just cited.
Analysis of questions teachers ask about teaching modern mathematics in the elementary school
Authors: Green Robert W.
Published: October 2020

Modern mathematics, ushered into the mathematics curriculum in the latter part of the 1950s and persisting through the decade of the 60s, received much publicity and was vigorously taught, or at least attempted, across the entire country-from the largest city system to the smallest village school. Unfamiliar subjects and symbols were introduced, and expressions and terms were used that were heretofore foreign to the elementary school. Expressions such as commutative, associative, distributive. teaching for understanding. and mod were but a few of the new expressions heard in elementary education circles. Bases other than ten, modulo arithmetic, and set language represent some of the new subjects that made up “modern elementary mathematics.”
The electronic calculator—another teaching aid?
Authors: Rogers Joy J.
Published: October 2020

Fifteen years ago schools seemed to find it very easy to get grants to install language labora tories. Seven years ago I attempted to do a paper (Rogers 1969) on what had become of a ll those language laboratories. The paper was quite a challenge because published references to language laboratories had dwindled to nearly none. An exciting, promising teaching aid had, in the span of only a decade, been relegated to the dustiest corners of the school along with the supply of Pressey punchboards, wire recorders, and instructional radio receivers. This paper is not just about electronic calculators—or even about language laboratories. The paper is intended to identify some issues that appear to be responsible for the all-too-rapid and unforeseen obsolescence of any teaching aid. It is hoped th at the paper might offer some useful suggestions to the manufacturers of new teaching aids—in this case electronic calculators—in the hope that some of the mistakes of the past may not be infinitely repeated. Secondly, it is hoped th at this paper might offer some useful suggestions to educators considering large-scale purchases of electronic calculators on how to avoid, ten years from now, being the butt of other adm inistrators' jokes about their horde of these push-button white elephants.
Sexual stereotyping and mathematics learning
Authors: Fennema Elizabeth , Sherman Julia A.
Published: October 2020

Although many questions are being asked about the teaching of “modern mathematics,” two important ones are seldom asked: Is modern mathematics teaching providing equal opportunity for both boys and girls to learn mathematics, and if not, why not? This paper attempts to provide a partial answer to the first question and a viable hypothesis concerning the second.
The Right Hemisphere's Role In Problem Solving
Authors: Wheatley Grayson H.
Published: October 2020

Recent brain research has revealed a remarkable fact-man has two brains instead of one. The two hemispheres of a person's cerebral cortex are specialized for different modes of thought processing. Differences in the functioning of the two hemispheres has been known for many years. When a person sustained a head injury on the left side, he lost speech capability: when the injury was to the right side, speech was not affected. The nature of the capabi lity of the right hemisphere, however, was not understood.
Hey Mister! It's Upside Down!
Authors: Gilbert Robert K.
Published: October 2020

Children live in a world in which mathematics is an integral part of the environment and society, and they seem to possess a curio ity and eagerness to learn about the world. Biggs and MacLean (1969) have set down three aims of learning mathematics in Freedom to Learn: (1) to free students to think for themselves, (2) to provide opportunities to di cover the order. patterns, and relations that are the very essence of mathematics, and (3) to train studen ts in the necessary skills. It seems reasonable, too. that classroom teachers hould develop students' interest in using mathematics to better relate to the world around them.
The Learning Disabled Child—Learning the Basic Facts
Authors: Myers Ann C. , Thornton Carol A.
Published: October 2020

It happened. time and again—a learning disabled (LD) child frustrated by inadequate fact mastery. We faced the problem repeatedly in the Clinical Teaching Center and in other classroom situations in which we worked. Our concern for LD children led us initially to investigate the whys of their failures. Interviews with children successful in fact mastery provided some clues. They revealed that the “successful” child often used easy facts to find answers to harder ones (e.g., 6 + 6 = 12, so 6 + 7 is one more. 13: or 2 × 6 = 12, so 4 × 6 is twice as much, 24). Perhaps what appeared to be a memory problem for an LD child was actually a failure to use relationships to aid his recall of facts. An analysis of the arithmetic texts and of current teaching practices further indicated that many helpful relationships were not emphasized during instruction. The successful student was to discover these for himself.
Metric Round Robin
Authors: Trusty Kay
Published: October 2020

Metrication is here and current literature suggests that the job to be done must be tackled by the public schools. “Metric round robin” was a successful attempt to do just that.
Ideas
Authors: Bright George W.
Published: October 2020

Ideas for this month consists of two posters that provide counting problems from geometry. Students will need several days to consider the questions. Supplementary activities can be found in the NCTM publication, Boxes. Squares. and Other Things. by Walters.
Festival Fun and Mathematics
Authors: Mikesell Jerald L.
Published: October 2020

What causes some of the sharpest students in the district to work harder than they have worked all year?
Subtraction: Decomposition versus Equal Addends
Authors: Sherrill James M.
Published: October 2020

At the end of each academic year at the University of British Columbia, the author teaches mathematics in some elementary school for two months. While he is in the school, there are many informal discussions with teachers concerning mathematics education. The inability of many students to do basic computation has long been a complaint of teachers. In a discussion centering on computational algorithms, subtraction requiring regrouping was identified as one area where teachers wanted some alternati
Solving Verbal Problems: Results and Implications from National Assessment
Authors: Carpenter Thomas P. , Kay Corbitt Mary , Kepner Henry S. , Montgomery Lindquist Mary , Reys Robert E.
Published: October 2020

Why can't children solve story problems? Two recent articles in the Arithmetic Teacher have opened with this question (West 1977; Zweng 1979). Results from the second NAEP mathematics assessment offer no definitive answers, but they do provide some interesting insights regarding children's ability to solve verbal problems (Carpenter et al., 1980). The assessment results indicate that the commonly held view that children cannot solve word problems may be an oversimplification. ln fact children were quite successful at solving some types of simple verbal problems. Performance was reasonably good on most problems that could be solved using a single operation of addition, subtraction, multiplication, or division. However, almost every problem that could not be solved by a routine application of a single arithmetic operation caused a great deal of difficulty.
Making and Interpreting Graphs and Tables: Results and Implications from National Assessment
Authors: Bestgen Barbara J.
Published: October 2020

The organization and presentation of important information takes various forms including graphs, tables, and charts. Vast amounts of data are presented to us each day as citizens, as consumers, and as interested individuals. The ability to process this information is not only an important skill, but also essential for making many everyday decisions. How knowledgeable are students in interpreting simple graphs and tables? Should reading a graph or table be the main emphasis of our instruction? Can students transfer the skill of reading graphs and charts to using them to make generalizations, predictions, and solve problems?
Decimals: Results and Implications from National Assessment
Authors: Carpenter Thomas P. , Corbitt Mary Kay , Kepner Henry S. , Lindquist Mary Montgomery , Reys Robert E.
Published: October 2020

Decimals are receiving more as well as earlier emphasis in today's elementary school mathematics programs. The increased use of calculators and metric measurement coupled with a reexamination of the appropriateness of the scope and sequence of common fractions provide impetus for such a change. The results of the second mathematics assessment of the National Assessment of Educational Progress (NAEP) can help us make this change effectively. They give some indication of how 9-year-olds handled decimals prior to much formal instruction and insight into areas of difficulty for 13-year-olds who have received instruction.
Calculators with a Constant Arithmetic Feature
Authors: Woodward Ernest
Published: October 2020

Different models of hand-held calculators react differently to the same series of “commands.” Tables 1 and 2 illustratet his fact for two Texas Instrument Company models. Notice in the sequences shown that if the = key is pressed on the SR-10 calculator the display does not change, but the display on the TI-1255 does change and continued computation results. Machines that continue to perform computations when the = key is pressed are said to have a constant arithmetic feature. In my opinion, this feature is a desirable characteristic for calculators that are to be used instructionally in elementary school mathematics classes.
Mathematics for the Overhead Projector
Authors: Arledge Jill E.
Published: October 2020

Mathematics can be interesting. As a matter of fact, mathematics can be presented in a way that makes it the most exciting time of a student's day. The key, I have found, is to get the student's attention. This can be done easily through the use of games.
Variations on Concentration
Authors: Tucker Benny F.
Published: October 2020

Most elementary school teachers are familiar with the card game, Concentration; many have used the game in their own classrooms. Concentration is simple to play. All you need to make a game is a set of cards that match in pairs. The simplicity with which one can make the game, teach the game, and play the game probably accounts for much of its popularity.
Classroom Problem Solving with Calculators
Authors: Duea Joan , Ockenga Earl
Published: October 2020

In An Agenda for Action the NCTM has made recommendations for the mathematics classroom. One recommendation is that “problem solving be the focus of school mathematics in the 1980s.” Another is that “mathematics programs take full advantage of the power of calculators at all grade levels.”
Readers' Dialogue
Authors: Schonemann Roberta , Wardrop R. F. , Guyden Martha J. , Moses Barbara , Owens Caroline , Willie Nancy A. , Sicklick Francine , Liedtke Werner , Preston Anne M.
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 months will have elasped between the time when an article is published and the time when a letter commenting on that article can appear on the journal. Sometimes the miminum 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.
An Investigation of Some Numerical Properties
Authors: Robitaille David F.
Published: October 2020

The task of getting students excited about or interested in properties such as the commutative properties of addition or of multiplication of whole numbers can be a challenging one.
The Scientific Method of Problem Solving
Authors: Brewer Shirley Stillinger
Published: October 2020

Recently, while engaged in student teaching at The University of Texas, the author worked with a unique method of solving arithmetic word problems which was so successful that she wants to share this technique with other teachers.
Two-Digit Divisors Ending in 4, 5, or 6
Authors: Benz Harry E.
Published: October 2020

MOST TEACHERS FIND Che teaching of division with two-digit divisors a difficult task. The subject has been the occasion for a considentble amount of writing and discussion, and no little research has been carried out in efforts to find ways of organizing the topic for more effective instruction.
Levels of Learning: Planning in Depth
Authors: Moser Harold E.
Published: October 2020

A FEW YEARS AGO there was considerable emphasis on fine gradations of arithmetic skills as the key to improving instruction. According to this point of view much of the lack of success children experienced in learning arithmetic was attributed to a too-rapid exposure to the “special difficulties” of a given operation. Curricula of this period provided teachers with elaborate gradations of “easy steps leading to the mastery of arithmetic.”
Place It
Authors: Firkins John
Published: October 2020

Several studies of children's thinking in and out of the classroom have demonstrated that (1) learning can be interesting and fun for children, and (2) thinking is more closely related to the process than to the content of subject matter. Important intellectual skills depend far more on the experiences a child has had than they do on the child's age or grade in school. One of the sets of activities developed by the Elementary Science Study consists of attribute games and problems. These activities, like other games, provide an opportunity for the child to learn problem-solving strategies.
Developing Computer Literacy
Authors: Tobin Catherine D.
Published: October 2020

Do you consider yourself computer literate? Your first reaction may be, “I don't know” or “I' m sure that I am not,” or “Does it make any difference?” Statements like these are usually followed by some questions: “What is computer literacy?” and “How does it relate to me and my students?”
Educator's Lexicon of Computerese
Authors: Johnson Jerry
Published: October 2020

The steadily increasing number of computer term and acronyms is one of the few entities which can outdistance the rate of inflation. “Computerese” and “cybercrud” describe the jargon associated with the use of computer technology. In Up The Organization (1978), Robert Town end uggests that computer technicians “are complicator” not simplifiers … They're building a mystique, a prie thood, their own mumbo-jumbo ritual to keep you from knowing what they-and you-are doing, But is all this confusion really necessary?
Mathematics around the World
Authors: Smyth Mitzi
Published: October 2020

Why do our children, who live in one of the most affluent countries in the world, have such low mathematics scores? Why do so many children dislike mathematics? Do other countries of the world have the same problems? If not, how are they achieving success?
Special Characteristics of Rational Numbers
Authors: Skypek Dora Helen B.
Published: October 2020

The characteristics of rational numbers must be considered in a variety of interpretations and coding schemes. It is this variety that, if not sorted and carefully developed in appropriate contexts, results in confusion in teaching and learning about rational numbers. Although a discussion of interpretations necessarily involves the use of coding conventions, the two will be treated separately as special characteristics of the rational numbers. Another important charac-teristic. which is difficult to separate from interpretations and coding conventions. is this: unlike a whole number (or an integer), a rational number has an unlimited number of “behavioral clones.” These clones have different names, but they behave in exactly the same way. Still other Still other characteristics to be considered are the density and order of the rational number.
The Pythagorean Theorem Revisited: Weighing the Results
Authors: Hawkins Vincent J.
Published: October 2020

The Pythagorean theorem is one of the most important in mathematics. It is introduced differently by every teacher.
One Point of View: Manipulatives Are Good Mathematics!
Authors: Herbert Elizabeth
Published: October 2020

When asked, “Do you like mathematics? Why or why not?” at the beginning of each school year, a startling 80 to 85 percent of my middle school students would reply that they did not like mathematics because it was boring and because they did not understand it very well. Their negative attitudes appeared to stem from a lack of understanding based on plain boredom with uninteresting classes.
Problems with the Basic Facts May Not Be the Problem
Authors: Brumfield Robert D. , Moore Bobby D.
Published: October 2020

When mathematics teachers in grades 3–6 are asked why their students have difficulty with the addition and subtraction algorithms, many respond that the chief reason is that children do not know their basic number facts. It is true that in some cases students do not know their basic facts, and this would certainly inhibit their progress in mathematics. However, there may be other reasons.
Multiple Methods of Teaching the Addition and Subtraction of Integers
Authors: Chang Lisa
Published: October 2020

Many of us learned to obtain the correct answers to problems with integers by applying rules. Few of us had a good grasp of the meanings behind these rules. Yet we may be offering the same golden rules, with little meaningful explanation, to our own students.
Modeling Operations and Algorithms
Authors: Beattie Ian D.
Published: October 2020

The idea of using manipulative materials to model operation and algorithms is not new. The Arithmetic Teacher frequently includes articles on the topic, and its readers should have accumulated a wealth of excellent teaching suggestions. Current methodology books and school texts place great emphasis on the use of manipulatives. Thus one might expect appropriate manipulative materials to be a mainstay of every mathematics classroom, but evidence suggests otherwise. Although teachers believe that manipulative materials should be used for mathematics instruction and that the usc of such materials does develop understanding, the use of manipulative materials diminishes through the grade (Suydam 1984a).
The Turtle Deserves a Star
Authors: Billstein Rick , Lott Johnny W.
Published: October 2020

The National Council of Teachers of Mathematics recently published “The lmpact of Computing Technology on School Mathematics: Report of an NCTM Conference” (NCTM 1985). This report addresses the need for mathematics curricula and instructional methods to respond to the influence of computing technology. This report states that “the major influence of technology on mathematics education is its potential to shift the focus of instruction from an emphasis on manipulative skills to an emphasis on developing concepts, relationships, structures, and problem-solving skills.” The use of the computer language Logo offers an excellent opportunity to use technology to help develop the problem-solving skills advocated in mathematics. This article gives examples not only of how Logo might be used to teach some mathematical concepts but also of how it can be used as a problem-solving tool.
How to Check Elementary Mathematics Papers
Authors: Clark H. Clifford
Published: October 2020

The teacher sat quietly for a moment staring at a stack of mathematics papers she had collected that day in school, then proceeded to grade them. Red marks dotted each paper.
Gather, Organize, Display: Mathematics for the Information Society
Authors: Dickinson J. Craig
Published: October 2020

Perhaps it is time to rethink what we are teaching in elementary school mathematics. With many of our student having calculators on their ruler, watches, and key chains, should we pend so much time drilling them in the tep of arithmetic computation? With calculators, computers, and unlimited information becoming widespread, the gathering, organization, and display of mathematical data in meaningful way are perhaps more nece sary skills.
Beware of Tapping Pencils
Authors: Flexer Roberta J. , Rosenberger Naomi
Published: October 2020

Advocates of a new, “magical” method for teaching addition, subtraction, multiplication, and division are attracting the attention of many elementary chool teachers. The method involves teaching children to tap reference points on numeral to count out sums, differences, and products. Teacher like it because it's easy. Student catch on quickly and get the right answers. Even students who might have had trouble with arithmetic before can tap out correct answers. What's the problem, then? To a mathematics educator, the problem with the new “magic” is that a mechanical technique for getting answers is displacing learning with understanding.
Popsicle Sticks, Computers, and Calculators: Important Considerations
Authors: Abel Jean , Allinger Glenn D. , Andersen Lyle
Published: October 2020

Why, when, and how can teaching aids as varied as Popsicle sticks, computers, and calculators be used? To respond to these questions we developed three separate lessons on division for fourth-grade classes, the first using a traditional manipulative aid (Popsicle sticks), the second, the computer, and the third, the calculator. In each lesson the aid (1) helps children develop the concept of division, (2) assists in practice with the algorithm, and (3) moves students beyond the algorithm to applications.
Problem Solving: Tips For Teachers
Authors: O'Daffer Phares G. , Silver Edward A , Adams Verna M.
Published: October 2020

It is fairly common for students to believe that every problem has one and only one answer, that there is a correct algorithm or procedure to follow in solving any mathematics problem, and that all mathematics problems should be solved quickly, if they can be solved at all. It is important to offer experiences that broaden students' conceptions of mathematics and problem solving.
Boys' and Girls' Interest in Using Computers: Implications for the Classroom
Authors: Johnson Carole Schulte , Swoope Karen F.
Published: October 2020

As the United States moves toward being an information society, students must know more about computers and how to use them. Children who have access to computers from an early age are likely to develop skills and attitudes that will give them a distinct advantage over youngsters who lack this experience. Some authors have suggested that unless questions of equal access are addressed, the development of a technological elite could perpetuate or even exacerbate existing inequities based on socioeconomic status or sex (Johnson 1973).
Magic Squares and Magic Triangles
Authors: Sherrill James M.
Published: October 2020

For drill, many teacher use magic square, n × narrays of numbers in which the sums of the numbers in each row. each column, and each diagonal are the same. The only difficult y with magic squares is creating them. Once a specific magic square ha been used, it isn't much fun to use it again.
Ideas
Authors: Barson Alan , Barson Lois
Published: October 2020

Ideas this month presents activities to develop skills in estimation, a mathematics skill most frequently used in daily life. It helps us understand and deal with number sensibly and is an excellent aid in problem solving. The following estimation activities involve measurement, telling time, computation, and problem solving.
Learning, Teaching, and Standards
Authors: Dossey John A.
Published: October 2020

Learning, teaching, and learning teaching—these prophetic words from George Pólya's (1963) title for his address to the members of the Mathematical Association of America nearly twenty-five years ago echo the questions that face our profession today (Curcio 1987). Pólya's legacy has not only touched our knowledge and abilltles in mathematics and problem solving but has also had a significant effect on our thoughts about teaching.
Language Activities That Promote Awareness of Mathematics
Authors: Cangelosi James S.
Published: October 2020

Developing students' abilities to rcason with mathematics and apply mathematics to the solution of problems occurring in the real world hould be a primary focus of school mathematics (National Council of Teachers of Mathematics 1980). However, most mathemati cal curricula seem to place more emphasis on memorization of fact and algorithm than on reasoning and problem solving (Romberg and Carpenter 1986). The mathematics education literature abound with ideas for reversing the emphasis on memorization and for guiding the teaching of mathematics so that it has real-life meaning for children. Included among the idea are the following:
Involving Parents in the Mathematics Education of Their Young Handicapped Child
Authors: Bruneau Odette J.
Published: October 2020

The greater the parental involvement in a child's education, the greater the effectiveness of the parent-school relationship. Parental participation is the cornerstone of success (Gargiulo 1985). Research has generally favored parental involvement in the education of handicapped children (Turnbull 1983). Parental involvement has often been linked to positive findings in the child's performance, parental satisfaction, and program success (Weigerink et al. 1984). Karnes, Zehrbach, and Teska (1972) asserted that parents serve an important role in helping their children reinforce and generalize school learning.
Bring On the Buttons
Authors: Whitin David J.
Published: October 2020

Have you ever entered an unfamiliar grocery store and had difficulty finding a particular item? I have. On what shelf is unsweetened cocoa? Some stores put it with flour and sugar because they consider it a baking product, whereas others place it beside coffee because it come from a bean. And what about Worcestershire sauce? I have found it grouped with Chinese food in some stores and with condiments in other stores.
Promoting Number Sense in School
Authors: Hope Jack
Published: October 2020

Number sense is considered a desirable trait to foster, although its meaning, as other notions of thinking, such as common sense, horse sense, and savoir faire, can be defined only broadly. It can refer to a feeling for number and their various use and interpretations, to an appreciation for various levels of accuracy when figuring, and to a common-sense approach to using figures to support an argument. It can refer to the ability to produce reasonable estimates, to detect arithmetical errors, to choose the most efficient calculating procedure, and to recognize number patterns.
Children Must Learn to Draw Diagrams
Authors: Yancey Anna V. , Thompson Charles S. , Yancey John S.
Published: October 2020

General agreement can be found that verbal problem solving is one of the most important yet one of the most difficult-to-teach topics in elementary school mathematics. Many authors have expressed the opinion that children perform better in mathematics problem-solving situations when diagrams or pictures of the problems are provided by the teacher to elicit appropriate mental images (e.g., Driscoll 1979; Nelson 1974; Riedesel 1969; Threadgill-Sowder and Sowder 1982).
The NCTM Standards—Challenges for All Classrooms
Authors: Frye Shirley M.
Published: October 2020

Just as the Curriculum and Evaluation Standards for School Mathematics generates excitement among our member and colleagues, the document also engender questions from them. Educators and colleagues have asked questions about the standards and the implementing procedure at conference and committee meeting, through the mail, on the telephone, and in personal conversations. From those submitted or posed. I have selected some typical questions to which to respond.
One Point of View: Fractions and Other Rational Numbers
Authors: Post Thomas R.
Published: October 2020

The results of national and international assessments indicate that students have significant difficulties in learning about rational numbers, in 1979 only 24 percent of the nation's thirteen-year-olds could estimate the sum of 12/13 and 7/8 given the following possibilities: 1, 2, 19, 21, and I don't know. Fifty-five percent selected either 19 or 21 as the estimated sum!
Multiplication and Division Word Problems: Improving Students' Understanding
Authors: Huinker DeAnn M.
Published: October 2020

Ryan, a fourth-grade student, was always the first to complete any basic-fact drill with 100 percent accuracy, but Ryan was also the most fru strated student in the class when he attempted to solve word problems. He merely picked out the numbers and guessed at which operation to use. Ryan had memorized his basic facts, but had little conceptual understanding of the operations and their applications.
Thou Shalt Not Divide by Zero
Authors: Sundar Viji K.
Published: October 2020

Many textbooks that deal with the basic concepts of division of whole numbers make a very clear statement that “division by zero is not permitted.” Henry (1969) states that “instead of completely avoiding the issue by merely telling the student that he must never ask about 6 ÷ 0, guide him to discover for himself that this operation is without meaning.” I agree. This article includes an approach to help elementary school teacher understand the difficulties involved in division by zero and some teaching suggestions to help teachers guide students as well.
Maximizing Implementation of Manipulatives
Authors: Hollingsworth Caroline
Published: October 2020

At an NCTM regional meeting, I attended a session for teacher educators that raised our awareness that the manipulatives to which preservice and in-service teachers are exposed in methods courses are all too often not used in practice. This predicament is especially unfortunate in the early grades.
Symmetry In American Folk Art
Authors: Zaslavsky Claudia
Published: October 2020

Symmetrical designs and repeated patterns are important elements in the arts of many cultures—in fabrics, masks, pottery, and wood carvings, to mention just a few examples (Appleton 1971; Chatley 1986; Harris 1987; Krause 1983; Larsen and Gull 1977; Zaslavsky 1973, 1979, 1981, 1987). Many examples can be found in the textile arts alone. Symmetrical patterns in quilts and rugs, the subject of this article, often have symbolic meaning and play a role similar to writing in conveying ideas. The artist, who is usually anonymous, may introduce variations on the traditional themes or may boldly create new designs.
Research Into Practice: Constructivist Learning and Teaching
Authors: Battista Michael T.
Published: October 2020

In reality, no one can teach mathematics. Effective teachers are those who can stimulate students to learn mathematics. Educational research offers compelling evidence that students learn mathematics well only when they construct their own mathematical understanding (MSEB and National Research Council 1989, 58).
Research into Practice: Calculators and Constructivism
Authors: Wheatley Grayson H. , Clements Douglas H.
Published: October 2020

Many conflicting views have emerged about the place of calculators in elementary school mathematics. Some teachers and many parents believe that the use of calculators will undermine mastery of the “basic” and thus should not be used, at least until students “know their facts” and are proficient with paper-and-pencil computations. Others suggest that in today's society, facility with calculators is essential. The National Council of Teachers of Mathematics has, for many years now, held the position that calculators hould be used at all grade levels.
Teaching Equations
Authors: Nibbelink William H.
Published: October 2020

At one time first encounters with equations like x + 5 = 7 belonged to ninth-grade algebra, a course devoted largely to extended uses for the letters of the alphabet. As adolescents, we thought of x simply as “the unknown,” persistently unknown to the less fortunate among us. We did not deal much in terminology like “truth set,” “universe,” “domain for the variable,” or “solution set.”
Ideas
Authors: Young Sharon L.
Published: October 2020

The IDEAS section for this month focuses on gathering, using, and interpreting data about bicycling as a basis for integrating mathematics, sports, and science. Measurement, ratios, and other relationships are explored through making graphs and finding bicycling speeds and in a parent-involvement activity sheet. This month the reproducible sheets for the IDEAS section are designed to be used by multiple grade levels. Included are an activity sheet for parents to use with their children, three class-activity sheets, and a data sheet. A teacher may want to reproduce and use several sheets.
One Point Of View: Reaching by Teaching
Authors: (Skip) Fennell Francis
Published: October 2020

A colleague of mine, a reading educator, of all things, loves to tell a story about her glimpse of mathematics teaching.
They Don't Like Math? Well, Let's Do Something!
Authors: Boling Ann Neaves
Published: October 2020

Chances are that many students in grades 4 and below will say that mathematics is their favorite subject. Students in grades 5 and above, however, are much less likely to identify mathematics as their favorite subject. In fact, the number of students identifying it as their least favorite subject increases as their grade level increases (Suydam 1984). Poll by the Weekly Reader and other source have found these results to be a seemingly national occurrence (Pedersen, Bleyer, and Elmore 1985).
Figurate Numbers in the Classroom
Authors: Norman F. Alexander
Published: October 2020

Students today are exposed to a more and more compartmentalized mathematics curriculum. The effect has been to offer fewer opportunities that require the integration of different mathematical skills. Yet we need to give our students opportunities to develop an awareness of mathematics as an integrated endeavor.
Research into Practice: Enhancing Mathematics Learning through Imagery
Authors: Wheatley Grayson H.
Published: October 2020

Mathematics is often seen as a subject in which rules are followed and symbols manipulated to achieve “correct” answers. Fortunately, this characterization of mathematics is changing, in large part because of NCTM's initiatives. As we move into the decade of reform in school mathematics, we should explore all options for enhancing mathematics learning. This article considers the role of visual imagery in doing mathematics.
Implementing The “Professional Standards For Teaching Mathematics”: What's All This Talk about “Discourse”?
Authors: Ball Deborah Loewenberg
Published: October 2020

Despite its title, the Professional Standards for Teaching Mathematics (NCTM 1991) should not be read as a set of prescriptions about how to teach. The document will not deliver on such expectations, not because it fails but because no document can prescribe good teaching. No set of standards can be expected to stipulate what teachers should do. The potential of the Professional Teaching Standards rests instead in its use as a set of tools with which to construct productive conversations about teaching. It should be viewed as a resource with which to build teaching rather than as a measuring stick by which to judge teaching. With new ideas about things to pay attention to in our classrooms, to ask ourselves, to wonder about, we would have increased power to analyze and improve our teaching — alone and as members of a wider community of educators. In this article I explore possible outcomes of using the Professional Teaching Standards in such ways.