bluuebunny/crossref_metadata_2025 huggingface dataset:
Some innovations in the professional preparation of teachers
Authors: Lowry William C.
Published: October 2020

There is currently much ferment in the field of teacher preparation. New programs are being designed, and considerable emphasis is being placed on the use of new media. For example, see references [13] and [6].* The specialization in mathematics of both elementary and secondary mathematics teachers has received a great deal of attention over the past few years, particularly through the work of the Panel on Teacher Education of CUPM [16] and the Cambridge Conference on Teacher Training [12]. The subject-matter preparation of a teacher, however, cannot be entirely disassociated from his professional preparation. It is widely accepted that knowledge of mathematics by a mathematics teacher is but a necessary, not a sufficient, preparation for his job.
Problem solving: some suggestions from research
Authors: Riedesel C. Alan
Published: October 2020

As you have noted by now, the feature topic of this month's Arithmetic Teacher is problem solving. For over fifty years researchers have been exploring the improvement of instruction in this area. Many practical findings from these research studies have not as yet filtered into the elementary school classroom. Therefore, this month's column is devoted to a listing of suggestions that researchers have found to be aids in the improvement of problem solving. The comments are made informally. However, a list of selected research sources is provided for the reader who wishes to explore research findings in depth.
An analysis of the effects of arithmetic homework upon the arithmetic achievement of third-grade pupils
Authors: Maertens Norbert
Published: October 2020

A substantial part of the elementary student's day is commonly devoted to the preparation of home-study assignments. A National Education Association Teacher Opinion Poll [7]* revealed that 83.5 percent of all elementary teachers surveyed favored the use of homework in the teaching of elementary school students. G. W. Bond [1] surveyed 77 school districts in the state of New York to determine their homework practices. He found that 90 percent of those schools surveyed had formal homework beginning by the fourth grade or earlier. Students in Grade six were expected to complete an average of 50 minutes of homework daily, while those in the lower grades had proportionally less homework assigned. When one considers that the elementary school day is usually less than six hours, the addition of up to one hour's work at home represents a significant part of the total educational effort. The importance of homework was stressed by the Educational Policies Commission of the National Education Association [4], which listed homework as one of ten contemporary issues in elementary education.
“Though this be madness,…”
Authors: Havenhill Wallace P.
Published: October 2020

The number line is a powerful tool that can be used to illustrate the arithmetical operations and their relationships. Unfortunately, when the topic of multiplication and division involving two negative numbers occurs, there seems to be little or no information regarding how to represent these problems on the number line. With the use of two interpretations for the + and − signs, both multiplication and division involving negative numbers can be easily represented and their inverse nature illustrated.
The effect of sequence in the acquisition of three set relations; an experiment with preschoolers
Authors: Edward Uprichard A.
Published: October 2020

By its very nature, mathematics content has an inherent logical tructure. An instructional analysis of a mathematics concept or principle would consist of a list of prerequisite mathematical learnings deemed necessary for the logical development of the given concept. Inherent in the analysis would be hierarchal relationships between and among various prcrequisite learnings based on the structure of the discipline. Hence it is generally agreed that when teaching mathematic one should follow the structure of the content in determining instructional sequence.
Number patterns
Authors: Carman Robert A. , Carman Marilyn J.
Published: October 2020

We have a recurring daydream, shared with many other teachers, of somehow “turning on” our students, stirring in them a wild, reckless enthusiasm for the subject being taught. In this flight of fancy students attack the simplest, dullest assignments with eagerness and beg for more. Our reverie is punctuated with cries of triumph from ultrazealous tyros. Unfortunately, when the bubble pops we are back at the eternal teacher's game of trying to make eagles out of fledglings who would rather become parrots.
The Original Counting Systems of Papua and New Guinea
Authors: Wolfers Edward P.
Published: October 2020

Different groups of Papuans and New Guineans have used a wide variety of devices and techniques, as well as systems of numeration, to tally and, less frequently, to record quantities of goods and multiples of people, shells, days (until a meeting or ceremony), and animals. It is as yet impossible to provide a comprehensive guide to the counting systems of Papua and New Guinea or to provide a key to their geographic distribution as K. W. Galis has done for West Irian. Readers who wish to enquire into the systems employed by specific groups of people or into the distribution of a particular method or device should consult the bibliography that follows. This article is confined to a survey of the kinds of tallying, recording, and counting systems used, with examples only of each major type provided.
A note on correctness and incorrectness: Mathematical systems and their relationships to the real world
Authors: Brumfiel Charles
Published: October 2020

In the November 1970 issue of the Arithmetic Teacher there appeared my article, “Mathematical Systems and Their Relationship to the Real World.” One point I made is that mathematics provides us with a vast array of symbols and concepts to use in solving real-life problems. When we use mathematics to solve a real problem, we make certa in mental associations between mathematical symbols and real objects. I suggested that arguments sometimes arise because two persons may make different associations, mathematical symbols to real objects, and each thinks his associations are correct while the other person's are incorrect.
Three games
Authors: Godsave Bruce F.
Published: October 2020

When René Descartes sat up in bed one day and created coordinate geometry, he did a fantastic thing for mathematics. Many students and teachers believe that much of mathematics came to us in a manner similar to that of the Ten Commandments. In fact, something like the coordinate system was made up by a mortal man, in much the same way that man created Monopoly. It would be difficult, if not impossible, to devise an intuitive way of learning the rules of Monopoly. We are told the rules, and after we learn them, we use our skill and intelligence to send our friends to the “poorhouse.” The same is true with coordinate geometry and most other mathematical concepts: we need to learn the rules.
Division by zero
Authors: Duncan Hilda F.
Published: October 2020

In the teaching of elementary arithmetic we introduce the students to 100 addition facts, 100 subtraction facts, and 100 multiplication facts. When it comes to division, however, most teachers and books present or discuss only 90 basic facts. Many children will not think to question this nonsymmetric arrangement, but what about those who do? What explanation can we give the alert and inquisitive child who wants to know why we have omitted 10 division facts from our list?
Let's go one step farther in addition
Authors: Sanders Walter J.
Published: October 2020

Children spend a great deal of time finding answers to addition problems. In the beginning, the problems are related to classroom activity or to manipulative materials, which most children enjoy. Since answers are usually determined at this stage by counting, it frequently takes a child quite a bit of time and effort to do one problem. As the child becomes familiar with “addition situations,” emphasis shifts to skill in adding “pure numbers.” The addition facts are memorized, and column addition is introduced. Practice using column addition is coupled with applications through word problems.
Individualized instruction: Distinguishing characteristics
Authors: Graham Evelyne M.
Published: October 2020

Individualized instruction—what's that?” This question was frequently asked five or more years ago. Today, there is not a good educator around who has not heard the two magic words: individualized instruction. However, to have heard about individualized instruction and to know what it means are two different things. There are an infinite number of interpretations of the meaning of individualized instruction; in other words, it means different things to different people. The Winston Senior Dictionary (1957) defines individualize as “to characterize with distinctive qualities” and defines instruction as “the act of teaching; knowledge imparted.” To put these two together would give a feasible definition of individualized instruction—“teaching with distinctive qualities.” However, this definition is very inadequate, since the distinctive qualities are not described; the definition would also fit poor instruction.
Things you can try: A Pythagorean puzzle
Authors: Hall Gary D.
Published: October 2020

This puzzle was constructed as a project for a graduate course. It has been used in teaching sixth-grade mathematics.
A “limited” approach to the sum of the angles of a triangle
Authors: Bruni James V.
Published: October 2020

One of the exciting discoveries children can make about triangles is that the sum of the measures of the angles (in degrees) of any triangle always equals 180. Teachers often lead them to “discover” this phenomenon by having them make all sorts of triangles, use a protractor to measure each of the angles, record the measure of each angle for individual triangles, and look for a pattern or rule. This method gives the child the opportunity to practice using the protractor for measuring angles.
Using stream flow to develop measuring skills
Authors: Knight Carlton W. , Schweitzer James P.
Published: October 2020

A small stream, irrigation canal, or drainage ditch can easily become a focal point of exciting mathematical field experiences. Students can demonstrate the practical application of various measuring skills by computing the surface velocity and volume flow of a nearby stream. These measurements can be related to ecological phenomena by studying (1) changes in the volume of flow by season, (2) the effects of different amounts of rainfall on the volume of flow, and (3) the effects of precipitation in more distant parts of the watershed.
A regular classroom plus a mathematics laboratory
Authors: Beuthel Donald G. , Meyer Phyllis I.
Published: October 2020

For years we taught arithmetic using “just a textbook” with the few variations of games, visual devices, and limited activities that could be used to individualize instruction in the confines of a single classroom.
Teaching Arithmetic with Calculators
Authors: Schaughency Mildred D.
Published: October 2020

When you were a youngster in school, would you have given up a play period for a chance to stay indoors and do arithmetic?
More Rationalizing Division of Fractions
Authors: Brickman Benjamin
Published: October 2020

The december, 1954 issue contained an article entitled “Rationalizing the Division of Fractions” by my colleague, Prof. Sam Duker. In the Editor's Note, following the article, readers are invited to indicate their reaction and to submit better methods.
The Role of Experiences in Arithmetic
Authors: Nadelman Goldie , Paskins Elsie B.
Published: October 2020

In Every Modern Elementary School, there are many natural situations which provide opportunities for children to think about and to use numbers. Classroom and school experiences are important because they pave the way for planning a program of meaningful mathematics. Teachers welcome suggestions which help them in recognizing and utilizing experiences effectively, in setting up situations which create a stimulating learning environment, and in stimulating children to play an active part in the learning activities.
Learning Arithmetic from Kindergarten to Grade 6
Authors: Ratanakul Suchart
Published: October 2020

After I Started to go to school, my life seemed to be the most unpleasant one. I had a very moody and terrible teacher. In my point of view, she never had good temper. She taught me arithmetic and everything else.
Ten Years of Meaningful Arithmetic in New York City
Authors: Eads Laura K.
Published: October 2020

During The Past 10 Years meaningful arithmetic has become the generally accepted method of teaching and learnjng in the elementary schools of New York City. This means that some 20,000 supervisors and teachers are now making varying efforts to help children think mathematically and to undetstand the mathematics they learn. It means also that these supervisors and teachers are learning or have leamed the meaning of arithmetic themselves.
Going metric in Hawaii
Authors: King Irv , Whitman Nancy
Published: October 2020

Be it resolved by the House of Representatives of the Sixth Legislature of the State of Hawaii, Regular Session of 1972, that the College of Education of the University of Hawaii be requested to develop a pilot program for teaching metric in the schools of Hawaii as the primary language of measurement.
Things you can try: Filops, hahas, zobos, gripees, zillies, and dingbats
Authors: Dreyfuss Joan
Published: October 2020

As teachers, we have all read countless books on educational theory. We know that positive reinforcement breeds future successes and that negative factors, such as failing grade, sometimes lead to feelings of inadequacy, a diminished concept of self-worth, and a lessened desire to succeed the second time around. Any teacher who has taught low-achieving mathematics student!. knows that they often enter the class with pre et ideas about their problemolving inabilities. These ideas come from a cries of past failures, and these past fa ilures frequently block the student's ability to solve new problems. All of the pedagogy is well known to teachers, yet the application of this very theory to the classroom situation is often overlooked. For this reason I would like to share an experience.
Cultural considerations in mathematics education in Arizona
Authors: Smith Lehi T. , Bitter Gary G.
Published: October 2020

Two groups of people with cultures that are unique and as different from the dominant way of life in Arizona as they would be in any other state, are the Spanishspeaking and the Indians.
Ecology, rapid transit, and graph theory: An intuitive approach for middle and upper elementary grades
Authors: Jacobson Herbert R.
Published: October 2020

It is important for students to learn that identifying a problem is only half their responsibility; they should also feel an obligation to provide a possible solution. It is the purpose of this exercise to reinforce the students' desire to seek solutions to problems and to emphasize the importance of mathematics skiUs as a tool for solving complex, modern ecological problems.
Sixth-grade enrichment final
Authors: Cornell Robert W.
Published: October 2020

The enthusiasm that students at the sixthgrade level can give to a new challenge is amazing to observe. I have found this to be true with classes of children of a low socioecomonic background in southwestern United States as well as with the affiuent children attending the International School of The Hague, Netherlands.
Happy time mathematics
Authors: Chilcote Elinor , Blaine Jeannie , Nason Nancy
Published: October 2020

Mathematics is a happy time when it is approached in a fun way, is practical, and relates to the child's world. The real secret to successful learning is the teacher's resourcefulness and enthusiasm. The teacher whose background includes a wealth of readily available games and activities that are fun for children finds that her classes enjoy learning mathematics. This creates a climate in the classroom that “turns children on” and makes the teaching of mathematics a happy time.
Laboratory experiences with perimeter, area, and volume
Authors: Moon Leland
Published: October 2020

The topics of perimeter, area, and volume are included in the study of measurement in most elementary mathematics programs. With the mounting concern for the impending conversion to the metric system, these topics arc likely to receive more rather than less emphasis in the future. The author's experience teaching sixth-grade mathematics has shown, however, that the study of perimeter, area, and volume can pose serious difficulties for learners.
Braided polyhedra
Authors: Malcom Paul S.
Published: October 2020

The construction of various polyhedra provides an interesting classroom activity in mathematics. Construction of these polyhedra is usually performed by sketching a pattern, cutting it from heavy paper, and then assembling it with glue or tape. An unusual alternative to this method was discovered in the mid 1800s by John Gorham (1888), an Englishman with an interest in crystallography. Gorham found that by braiding strips of paper together he could form many of the polyhedra found in nature.
Calculator ideas for the junior high classroom
Authors: Ockenga Earl
Published: October 2020

One of my seventh graders wagered, as he handed me his calculator. “Betcha don't know how many times my heart has beat in the last year.” “About 36 792 000 times,” he said in response to my surprised look. “This newspaper ad isn't correct,” announced another student as she showed me her calculator. “The ad says 20% off on all items. but it's really only 16.7% off on the dishes.” Comments such as these occur when hand-held calculators are made avai lable in the classroom.
Check your calculator computations
Authors: Friesen Charles D.
Published: October 2020

Perform the indicated computations on a calculator. To check your answer turn the calculator upside down and read a word answer. A clue is given for each problem.
An approach to teaching numeration systems
Authors: Verbeke Linda M.
Published: October 2020

Of what use is the study of different numeration systems? There are at least two answers to this question: Numeration systems are interesting in themselves and important from the historical standpoint. The study of numeration systems gives students a better appreciation and understanding of the development of the decimal system, in much the same way that the study of a foreign language helps students to understand their mother tongue.
Your Council at Work: Annual financial report
Authors: Smart James R. , Wells David W. , Kriegsman Helen , Devlin John , Stipanowich Joseph , Gates James D. , Tewell James R.
Published: October 2020

The National Council of Teachers of Mathematics further strengthened its sound financial position during the 1975-76 fiscal year. In spite of a projected deficit, a soaring rate of inflation, and necssary expenditures beyond those budgeted, NCTM ended the year with receipts over expendjtures totaling $27 511
Rx for Verbal Problems: A Diagnostic-Prescriptive Approach
Authors: West Tommie A.
Published: October 2020

Why can't children solve verbal problems? “They can't read,” respond some teachers. “They can't think,” reply others. “They are careless,” say some. “They can't decide what to do,” answer still others.
President's Report: Is the NCTM Really Helping the Classroom Teacher of Mathematics?
Authors: Egsgard John C.
Published: October 2020

It is my belief that the majority of men and women who teach mathematics are interested in improving their knowledge of mathematics and their ability to teach it, and I am convinced that the most important task that the Council has is to assist them in doing so. Therefore, I think it is necessary to examine critically the importantquestion, “Is the NCTM really helping the classroom teacher of mathematics?”
The Plight and Might of Number Seven
Authors: Avital Shmuel
Published: October 2020

It was a few minutes past midnight. The daily toil had taken the better of me, and I slumbered at the table with the Arithmetic Teacher as a cushion. A knock on the door made me jump. Who could it be at that time of the night? Through the peephole I saw the huddled figure of Seven leaning on the doorframe.
Minicalculators in the Classroom—What Do Teachers Think?
Authors: Palmer Henry B. A.
Published: October 2020

Are attempts to introduce minicalculators in the classroom, particularly at the lower elementary grades, likely to be greeted with the same kinds of responses that previous innovations have encountered? Teachers were, and many still are, deeply concerned about the effects of such innovations as programmed instructional materials, computer-assisted instruction. contingency management, and behavior modification. Investigations of the reasons for their caution revealed the following: (1) erosion of the teacher's role—machines taking over teaching functions; (2) impersonalization of the teaching-learning process—reduction or elimination of the humane aspects of teaching and learning: (3) stifling of creativity—emphasis on precision, measurement. and mechanization inhibits creative expression.
The Diagnosis of Learning Styles in Arithmetic
Authors: Hopkins Martha H.
Published: October 2020

Individualization, diagnostic teaching, remediation, prescriptive instruction-all these terms and many similar to them are undoubtedly in the minds of educators and the textbooks of education students throughout this country today. By effectively meeting the needs of individuals in our classrooms and by teaching our students, as opposed to teaching our curriculum guides, it is believed that education will be more meaningful, and therefore more useful, to the children.
Let's Take Another Look at Teaching the Metric System
Authors: Fowler Mary Anne
Published: October 2020

As one facet of some recently completed research involving over six hundred fifth-grade students, I discovered that regardless of the many concerted efforts to teach the metric system—state mandates; federal encouragement. even in the form of grants; university preservice training; and local inservice training—the children in all the schools included in my project were woefully lacking in any knowledge or the metric system.
Equation Hangman
Authors: Kilhefner Dale Z.
Published: October 2020

Probably everyone has played the game called Hangman. Johnny thinks or a word and writes down blanks to indicate the number of letters. Susie guesses a letter. If it is a letter in Johnny's word, he writes it in the correct blank. If it is not, he draws a portion of a stick figure of a man being hung. Susie's goal is to discover the whole word before the hangman drawing is complete.
Chisanbop: Just another kind of finger reckoning?
Authors: Knifong J. Dan , Burton Grace M.
Published: October 2020

Increased concern for children's achievement in mathematics is evident in the press and in both formal presentations and informal conversations at professional meetings. Although such concern has been longstanding, it has of late focused on the “failure of modern math” to provide for the “basic skills.” Since basic computation is the center of so much attention, the time is ripe for the introduction of any new approach that would either (a) help teachers teach “the basics” more quickly or (b) help students compute more quickly and more accurately. The claim has been made that a new finger-reckoning system called Chisanbop will do both.
Today's Elementary School Teachers Are Better Prepared in Mathematics
Authors: Pigge Fred L. , Gibney Thomas C. , Ginther John L.
Published: October 2020

The data from the first mathematics survey of the National Assessment of Educational Progress (NAEP) showed a mixed picture of strengths and weaknesses in our mathematics programs. An examination of the assessment data suggests that the current emphasis on arithmetic skills in undergraduate and graduate teacher education should be examined to find a proper balance between skill and understanding, as well as between arithmetic s kills and skills in measurement and geometry.
By Way of Introduction: Assessing Student Learning
Authors: Robinson G. Edith
Published: October 2020

The authors of this month's articles take a variety of approaches to our focus topic. At the same time, a central theme persists—assessment is an integral part of the learning process.
Using the Individual Interview to Assess Mathematics Learning
Authors: Schoen Harold L.
Published: October 2020

The main thesis of this article is that the individual interview is a useful tool for assessing students' mathematical thinking. In the first three sections, examples are presented to illustrate how the interview can be used for individual diagnosis, instructional planning for the entire class, and instructional program evaluation. In the last section, these uses are summarized and guidelines for when and how to use the interview methods are discussed.
Using an Hour Clock to Teach Time
Authors: Maertens Norbert
Published: October 2020

The concept of time is extremely complex, and perhaps a full understanding of its many facets comes only with the accumulation of many experiences. In the culture of North American life, time assumes a dominant role and every individual operates on some kind of time schedule. Recognizing this, teachers begin teaching children about time when they first enter school. This article seeks to examine some basic concepts of “telling time,” and to suggest a more effective way of teaching such a fundamental concept.
Stand Up and Be Counted
Authors: Scalzitti Joyce
Published: October 2020

Getting to know you, getting to know all about you, may be a fitting expression in 1980. Once again, the United States Government is undertaking the monumental task of counting and assessing information about our society and its people. The Bureau of the Census is in the process of gathering facts on population, housing, agriculture, industry, transportation, health, education, income, prices, and much more, as it continues the tradition begun in 1790.
Why not a mathematics quiz?
Authors: Beyer Jim , Sherman Jon
Published: October 2020

Competitions among students are time-honored traditions in American education. In our earliest history the spelling bee, and later, track meets and football and basketball games have been popular forums for competition. Only recently, however, has competition within the academic disciplines received any real acceptance.
It's About Time
Authors: Riley James E.
Published: October 2020

Recently I was patiently waiting for a clerk to help me in a jewelry store. The clerk, who was occupied by a couple who were buying a watch for a child, was doing his best to convince the man and his wife that a digital watch would be their best choice. “Just think,” he said, “how much easier it will be for teachers to teach the telling of time when only digital watches are sold.” How many teachers, like the sales clerk, believe that learning about time means only learning the “telling” of time?
Teaching Fourth and Fifth Graders about Computers
Authors: Zukas Walter X. , Berka L. H. , Martin Judith T.
Published: October 2020

One characteristic of our complex technological society is the ever-increasing interaction that computers have with our daily lives. For example, computers send us bills and run our telephone systems. Children are playing with computerized toys that provide a variety of experiences and offer immediate responses. The computer is fast becoming an accepted part of our society since it enables citizens to do many activities that would otherwise prove too time consuming and laborious. Computerized equipment and toys are also reasonably priced and readily available at the comer drugstore or toy store.
Students' Affective Responses to Mathematics: 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

Mathematics, for a number of reasons, is sometimes viewed as an unpopular subject, one that provokes strong negative responses among students. Results on questions about students' affective responses to mathematics administered during the second National Assessment of Educational Progress (NAEP) mathematics assessment showed, however, that for younger students, in particular, mathematics did not necessarily evoke strong negative feelings. In fact, mathematics was liked and enjoyed by a majority of respondents. Results for the 9-yearolds and some results for the 13-yearolds are reported in this article; similar analyses of results for the 13-year-olds and 17-year-olds are presented in the October 1980 issue of the Mathematics Teacher.
Problem Solving for Teachers
Authors: Zur Mordecai , Silverman Fredrick L.
Published: October 2020

Many teacher training programs in mathematics education have a weakness in common, namely, concentration on skills at the expense of thinking. This is true for both facets of the preservice education of mathematics teachers, for mathematical content and for pedagogy.
Calculators in the Elementary Classroom: How Can We Go Wrong!
Authors: Reys Robert E.
Published: October 2020

Hand-held calculators are widely available. The 1977-78 National Assessment of Educational Progress reports that 75 percent of 9-year-olds, 80 percent of 13-year-olds, and 85 percent of 17-year-olds have access to at least one calculator. State and local surveys document that this statistic increases yearly.
Calculators in Testing Situations: 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

Calculators are fast becoming a common and welcome computation tool in our society. The 1977–78 mathematics assessment of the National Assessment of Educational Progress (NAEP) revealed that over 75 percent of the 9-year-olds, 80 percent of the 13-year-olds, and 85 percent of the 17-year-olds bad access to at least one hand calculator. Clearly, calculators are available. Despite this widespread access to calculators, many questions regarding their use remain unanswered: How will calculators affect the mathematics proficiency of our youth? Should they be used in school settings? Will they alter the mathematics curriculum? (Suydam 1976, Esty and Payne 1976).
Basics—In Perspective
Authors: Collins William J.
Published: October 2020

“Back to basics!” “Ahead to basics!” The calls for a revitalized approach to the so-called “basics”, from whichever direction, have been making news for at least the past five years. In the face of declining standardized test scores, writers in both professional and general-interest publications have either condemned or defended educational innovations of the previous two decades. The debate has hardly spared mathematics. In many areas mathematics bas indeed been the eye of the hurricane.
A Bibliography of Articles on the Teaching of Mathematics in Special Education
Authors: Matulis Robert S.
Published: October 2020

A look at recent developments in the teaching of mathematics to special education students can benefit anyone interested or involved in the mathematics education of mentally retarded, learning disabled, emotionally disturbed, physically handicapped, or brain-damaged students. The following bibliography lists nearly two hundred articles from about fony periodicals. The articles include reports of successful practices, surv.eys, research summaries, suggestions, reviews, and opinions about mathematics for students with special learning problems.
Students Like Personalized Word Problems
Authors: Muller Adelyn C. , Kurtz Ray
Published: October 2020

Teachers everywhere ask, “How can I teach word problems so children will understand and enjoy them?” These teachers usually continue by stating that in addition to there not being enough problems in the book, those that are included are not relevant for their children.
The Need for Fully Trained Mathematics Diagnosticians in the Elementary School
Authors: Anderson Alfred L.
Published: October 2020

In our tratrung programs for prospective elementary school teachers, great emphasis has been placed on the acquisition of the skills necessary for the successful implementation of individualized programs in mathematics.
Classroom Activities for Problem Solving
Authors: Schmalz Rosemary
Published: October 2020

During the 1978-79 academic year, I took a sabbatical from teaching college mathematics to try my hand at teaching middle-grade mathematics. To emphasize problem solving and to use the immediate environment to create problem situations were two of my instructional goals for thls venture. Some of my efforts in thls area are described in the paragraphs that follow.
Networks—New York Subways, A Piece of String, and African Traditions
Authors: Zaslavsky Claudia
Published: October 2020

Children now growing up in our rapidly advancing technological society must be prepared to cope with problems that will arise not only in this century but also in the twenty-first century. Yet we ourselves do not know what kind of society today's children will face in the future. The best we as mathematics educators can do is to encourage children to deal with new situations, to be unafraid of challenges, and to learn to think.
Bar Graphs for First Graders
Authors: Johnson Elizabeth M.
Published: October 2020

Graphing is one means of developing and practicing both prenumeration and numeration concepts and skills. It provides experiences in matching, counting, one-to-one correspondence, comparing quantities, and helps children to develop an understanding of terms such as more than, less than, the same as, as many as, taller, shorter, longer than, shorter than, and so on. All such experiences help to lay foundations on which young children can develop further concepts of number.
Update on Research on Problem Solving: Implications for Classroom Teaching
Authors: Suydam Marilyn N.
Published: October 2020

Everyone seems to recognize the importance of problem solving—the members of the NCTM as the Council published An Agenda for Action; the teachers, principals, school board members, and parents who responded to the Priorities in School Mathematics (PRISM) surveys; the people who read the headlines about low scores on the second mathematics assessment of the National Assessment of Educational Progress (NAEP). How to refocus the curriculum and how to teach problem solving more effectively have become “hot topics.” Research also continues to focus on the nature of problem solving and how to help teachers.
The Elementary School Mathematics Library: A Selected Bibliography
Authors: Hutcheson Ruth , Mantor Edna , Holmberg Marjorie B.
Published: October 2020

Continual ohowth in understanding mathematical ideas is dependent upon a wide variety of experiences used to enrich and stimulate fmther interest and activity on the part of the learner. The elementary school library is an excellent source of quantitative ideas, described both pictorially and symbolically, that go beyond the systematic study materials used in most arithmetic classes.
Arithmetic for Those Who Excel
Authors: Grossnickle Foster E.
Published: October 2020

This topic deals with the problem of providing for the superior pupil in the field of arithmetic. Sometimes this pupil is designated as the fast learner, the gifted pupil, or by some other descriptive phrase. The title of this paper makes it comparatively easy to identify the pupils whose achievement in arithmetic is s ignificant. McWilliams and Brown1 recommended that superior pupils should be considered those in the upper 20 percent in general intelligence whose abilities lend themselves readily to intellectual pursuits. We shall not attempt to designate a fixed per cent of a class as belonging to the group which excels in arithmetic. Those students who understand the work and develop insight into the subject constitute the group who need some modification of the program which is designed for the average or below average in achievement in this subject. The problem is how to provide enrichment for the pupil who shows superiority in the field of arithmetic.
Addition and Subtraction Situations
Authors: Reckzeh John
Published: October 2020

In his article, “Which Way Arithmetic?” Professor Van Engen1 implicitly defines an additive or addition situation as one in which groups are joined to form a single group.
Using Hand-Operated Computing Machines in Learning Arithmetic
Authors: Fehr Howard F. , McMeen George , Sobel Max
Published: October 2020

Recent reports of experiments have announced rather startling claims concerning the great amount of ari thmetic learned in a rather short period of time. These researches made use of certain materials and devices. Since such great improvement in learning has not hitherto been thought possible, and since frequently such reports appear to be “headlines” rather than scientific fact, there is need for controlled scientific experiment to judge the values of these claims. In general there has been no royal road to improved learning in the past, only slow, careful and hard won progress. The following is a report of an experiment, scientifically designed to measure the value of the use of computing machines in the learning of arithmetic.
Arithmetic via Television: A Report of the Pittsburgh Experiment
Authors: Strueve Helen K.
Published: October 2020

5-4-3-2-1; THE INDICATOR on the television screen ticks off the minutes before the arithmetic lesson begins. Then, comes the 30 seconds' warning. At this point the children in the fifth-grade classes of the participating schools1 are ready and know that the lesson will begin momentarily. And now the television teacher is presenting the lesson of the day, the next in a series of sequential developmental lessons. Every morning, Monday through Friday, a lesson is presented from 11:05 to 11:30 over WQED, Pittsburgh's educational television station. A five minute period prior to the beginning of the lesson is used by the classroom teacher as a warm-up period. This may be in the nature of a review of number facts or a recall of the skill taught in the previous day's lesson. Following the television presentation, the teacher has fifteen minutes which she devotes to supplementing or implementing the lesson of the day.
Arithmetic in the Child's Future
Authors: Urbancek Joseph J.
Published: October 2020

THIS MORNING we shall talk about ARITHMETIC IN THE CHILD'S FUTURE and what it shall mean to the men and women of the future who presently are today's children. Indeed adults have a stake in this future too, be they teachers, parents or relatives, because possible new developments may well affect their own lives.
Teaching Geometry with Tangrams
Authors: Russell Dorothy S. , Bologna Elaine M.
Published: October 2020

What is the most neglected area of the elementary school mathematics curriculum? The answer, probably, is geometry. Too many people think of geometry as a formal structure, like the course they had in high school. As a result. they do not see its relevance to the elementary school mathematics curriculum. Activities that introduce children to geometric concepts provide experiences that help children develop and reinforce spatial perceptions.
Math Clinic: An Ideal Setting for Parental Involvement
Authors: Scheer Janet K. , Henniger Michael T.
Published: October 2020

The Diagnostic Math Clinic at Southern Illinois University at Carbondale is designed to diagnose students' mathematical learning difficulties and to provide remedial work to improve their deficient skills. The clinic is also an ideal setting for parental involvement in the educational process.
Fitting Games into a Mathematics Curriculum
Authors: Jones Sue M.
Published: October 2020

Games, when they are constructed and used appropriately, can supplement the mathematics program. They can be used to teach new mathematics concepts and to reinforce or enrich previously taught skills. Games can become an integral part of the mathematics curriculum if teachers become knowledgeable of the advantages of using games, and of how to construct games and to incorporate them into an existing program.
We Had a Math Day
Authors: Mason Carolyn Boysaw
Published: October 2020

What can be done to help students realize that mathematics can be used in all subjects, and that it is an integral part of daily living? Math Day—a day devoted to teaching mathematics in all subject areas—is one way to help accomplish this two-fold goal.
Calculators and Problem-Solving Instruction: They Were Made for Each Other
Authors: Bartalo Donald B.
Published: October 2020

One of the major reasons for teaching mathematics in school is to help all student Jearn how to solve common, everyday problem—those practical situations that all of us face as citizen and consumers. Elementary school teachers know the importance of teaching their tudent how to think through problems instead of guessing at possible solutions. Because of these two factors, technique for improving children's problem-solving skills de erve special attention.
Identifying and Teaching Mathematically Gifted Elementary School Children
Authors: Johnson Martin L.
Published: October 2020

The decade of the 1970s brought a major resurgence of interest in providing for the psychological and educational needs of gifted and talented students. Such emphasis is long overdue and should be applauded.
Teaching Mathematics with Microcomputers: Primary Grades
Authors: Heck William
Published: October 2020

“The school is getting some microcomputers next week. Would you like to have one in your classroom?” If your principal makes an offer like that, jump at it! Even if you have never touched a computer before! The self-contained classroom is an ideal situation for a microcomputer (or two or three).
Mathematics Students Have a Right to Write
Authors: Shaw Joan Guelig
Published: October 2020

Have you ever received an extra-credit mathematics project that began with “The history of mathematics is …”? Boring, isn't it? Well, what do you expect? Students aren't in mathematic class to learn how to write. Right? Wrong! If we, as mathematic teachers, complain that on an objective test we can't get students to express themselves clearly or to write legibly, much less spell “associative” correctly, then we have an obligation to become teachers of writing as well as teachers of mathematics.
Using Hand Signs to Teach Basic Facts
Authors: LaSasso Carol , Mackall Philip L.
Published: October 2020

The procedure that is described in this article was developed several year ago for use with 12-to-15-year-old deaf student who could not remember basic addition and subtraction facts. Since its development, the procedure has been used successfully with numerous deaf children between the age of 8 and 17 years.
Tessellations and the Art of M. C. Escher
Authors: Zurstadt Betty K.
Published: October 2020

Relating mathematics to the world around us is one of the goals of the mathematics teacher. Plane geometry can be made relevant in the upper elementary years with a study of Escher's tessellations and how he created them.
The Difference between Problems and Answers
Authors: Lichtenberg Donovan R.
Published: October 2020

With the publication of An Agenda for Action (NCTM 1980). the Board of Directors of the NCTM took the position that problem solving should be the focus of teaching endeavors during this decade. Many mathematics teachers, undoubtedly, have been more than willing to endorse the Board's position.
Let's Do It: Dealing with Data
Authors: Shaw Jean M.
Published: October 2020

Children are surrounded by information. They must have ways to make sense of it—ways to organize and interpret the information.
Warm-Ups—Keys to Effective Mathematics Lessons
Authors: Williams David E.
Published: October 2020

Athletes do it, musicians do it, and so do chess players. They all engage in some form of physical or mental warm-up activity prior to their specialty, be it a 100-yard dash, a piano concerto, or an international chess match. The long-distance runner goes through a set of calisthenics to prepare for the rigors of a ten-mile run. A runner's ultimate success—making the distance—is dependent on this preparatory activity.
One Point of View: Elementary School Mathematics Specialists: Where Are They?
Authors: Dossey John A.
Published: October 2020

The multitude of national reports calling for the upgrading of the school cirriculum has once again brought the focus of educational reform on mathematics. The source materials for Educating Americans for the 21st Century (1983) contain the suggestion that school ystems “reassign intere ted teachers at the 4—6 grade level to become specialists at teaching mathematics … ” This call for mathematics resource teachers at the elementary school level is not new. However, it is an idea that has not received the attention it warrants.
Using a Problem-solving Approach in the Primary Grades
Authors: Campbell Patricia F.
Published: October 2020

According to the National Council of Teachers of Mathematics (1980), the focus of school mathematics in the 1980s must be on problem solving. Furthermore, computation is to be a tool for problem solving. The importance of problem solving as a goal in mathematics education cannot be disputed; however, the de-emphasis of computation may cause fee lings of uneasiness for many primary-level teachers. These feeling can be accentuated by such statements as “Primary-level curricula contain practically no mathematical problem-olving experiences” (Greenes 1981). Where does this dilemma leave the typical primary-level teacher, given the existing primary mathematics curriculum and the demands from pa rents and school administrators that young children develop a mastery of addition and subtraction?
A Study of Math Anxiety/Math Avoidance in Preservice Elementary Teachers
Authors: Kelly William P. , Tomhave William K.
Published: October 2020

In her 1972 study, Lucy Sells (1978) indicated that 92 percent of the female first-year students in the University of California had such inadequate mathematics preparation that they had effectively closed the door on 70 percent of the career choice available to them. Sell's conclusions and subsequent research on math avoidance were the bases for the resarch we conducted during the 1980-1981 school year at the University of Minnesota, Morris a liberal art college with an enrollment of 1700. This study was directed at documenting math avoidance among female students on the campus.
Research on the Role of Structure in Thinking
Authors: Carpenter Thomas P.
Published: October 2020

One of the most basic questions with regard to mathematical thinking is “What is mathematical thinking?” This question Is not the kind that is readily answered by empirical research. However, research can provide some perspective on the nature of mathematical thought if the question is rephrased: “What characterizes the thinking of individuals who have demonstrated a high level of ability in mathematics?” Research that compares the abilities of very capable mathematics students with those of less capable students or the problem-solving processes exhibited by experts and novices otfers some insights into this question.
National Council of Teachers of Mathematics: President's Report: An Agenda for Action: Continuing Commitments and Mid-Course Corrections
Authors: Crosswhite F. Joe
Published: October 2020

Five years ago the NCTM released An Agenda for Action, whose recommendations were intended as a framework to guide our efforts to improve school mathematics in the 1980s. We are now midway through that decade. It is an appropriate time to take stock of our progress—to ask if we are succeeding in translating our Agenda into a program of Action. We should also ask if the conditions that surrounded school mathematics when the Agenda was drafted have changed in significant ways and, if so. whether we should now reexamine our priorities.