bluuebunny/crossref_metadata_2025 huggingface dataset:
Teaching Mathematics with Technology: Activities to Introduce Your Class to Logo
Authors: Taylor Lyn
Published: October 2020

Papert (1980) developed Logo to encourage exploration, creativity, and discovery. The following classroom-tested, guided-discovery activities exemplify this spirit and further the goals of the NCTM's Curriculum and Evaluation Standards (1989). These activities are appropriate for use at the primary, intermediate, and middle school levels, as well as with older students.
One Point of View: The Least Common Denominator
Authors: Esty Warren W.
Published: October 2020

Many people of all ages have difficulty adding and subtracting fractions. I think that the usual emphasis on finding the least common denominator is at fault.
Calendar Mathematics
Authors: Chancellor Dinah
Published: October 2020

The calendar is designed to speak directly to students by giving them open-ended questions intended to engage them mathematically in high-interest activities. Students ore encouraged to work on the activities individually, in pairs, or in small groups. No answers are given for the calendar questions so as to encourage students to look to themselves as the mathematical authority and to develop the confidence and critical-thinking skills necessary to validate their thinking. The activities in this calendar involve mathematics integrated with various school subjects.
Using Performance Assessment to Determine Mathematical Dispositions
Authors: Collison Judith
Published: October 2020

The proliferation of information and information technology demands educational change, especially in mathematics. The emphasis must shift from mere acquisition to the use of information to deepen mathematical understanding and appreciation. The NCTM 's Curriculum and Evaluation Standards (1989) envisions a new curriculum. Among its goals are the development of “mathematical power,” or “numeracy” (National Research Council 1989) and an appreciation of the beauty and power of mathematic (NCTM 1989). Mathematics instruction must not merely expand students' knowledge of mathematics but must also foster intellectual courage and a set of positive personal attitudes, or dispositions, that enable and empower students.
Calendar Mathematics
Authors: Chancellor Dinah
Published: October 2020

The calendar is designed to speak directly to students, giving them open-ended questions intended to engage their intellect through their interests. Students are encouraged to work on the activities individually, in pairs, or in small groups. No answers are given for the calendar questions so that students are encouraged to look to themselves as the mathematical authority, thereby developing the confidence and critical-thinking skills necessary to validate their thinking.
IDEAS
Authors: Sammons Kay B. , Kobett Beth
Published: October 2020

The IDEAS section for this month presents activities that involve measurement as it relates to the Olympic Games. Activities involve nonstandard units of measure, linear measure, and time measurement. An at-home activity related to the Oiympic Games is also furnished. These activities should help heighten awareness of mathematics related to the forthcoming summer Olympic Games.
Ideas
Authors: Hopkins Martha H. (Marty)
Published: October 2020

The “IDEAS” section for this month focuses on computation, estimation, and mental mathematics. Some correct and some incorrect solutions to problems involving computation are presented. The student, acting as judge, is asked to review each solution carefully and to pronounce a verdict—is the problem solved correctly? In some “cases” the verdict may be in favor of the solution, and in others the solution may be deemed incorrect. In either situation the student is asked to justify the verdict by explaining how the decision was made. Students are encouraged to review each solution process as well as the end product.
Book Review: Test Review
Authors: Dam Robert Van
Published: October 2020

New York Test of Arithmetical Meanings, Levels One and Two by J. Wayne Wrightstone, Joseph, Justman, Morris Pincus, Ruth H. Lowe, Yonkers-on-Hudson, New York and Chicago, Illinois, World Book Company, 1956.
Reading in Mathematics
Authors: Streby George W.
Published: October 2020

Sometimes the teacher thinks that the students cannot work verbal problems because they do not have the ability to read. This is a vague statement because the act of reading is very complex, involving many skills and understandings. What docs the teacher mean when he says the student cannot read? Does this mean that the student cannot pronounce well, does not read smoothly, does not understand the concepts, or does not understand the technical words used in the problem? Stating that a student cannot read is making use of the catch-all word that may mean any number of things.
Arithmetic with Frames
Authors: _ _
Published: October 2020

The project of the university of Illinois Committee on school Mathematics is primarily concerned with students in grades nine through twelve. Frequently, the Project staff is asked if its work with high school students has implications for students in earlier grades, that is, if in attempting to work out better ways of presenting material to high school students, ideas have occurred for better ways to present mathematics to elementary school students.
An Approach to Problem Solving
Authors: Wisely Edna
Published: October 2020

Problems—story problems—experience problems—sentence problems—word problems are all used to designate a situation in which children must read and then decide which process or processes are to be utilized in arriving at the solution of the question proposed. To the adult this seems a relatively uncomplicated matter especially if he does not recall clearly his own school days. Unfortunately many children approach problem solving in a state of bewilderment induced by fear and failure. Here are no neat little sign or directive words to offer security to the agile manipulator of number. The child is truly confronted by “problems” not the single problem which is stated. His problems often are: Do I add? Subtract? Multiply? Divide?
100% Automatic Response?
Authors: Ulrich Louis E.
Published: October 2020

It was not so lonc ago that statements such as the following were current: “The only right standard for drill is the 100% standard and this is easily possible in arithmetic because the processes calling for drill are few. The harm done by a lower standard is immeasurable and defeats the chief purpose of drill. The drill load must be small to make the 100% standard possible for every child.” 1 This writer, in his capacity as a teacher, administrator, and researcher finds it difficult to agree with the above quotation
Book Review
Authors: Gunderson Agnes G.
Published: October 2020

Each page of concepts and captions written by Lowry W. Harding is illustrated by a cartoon on the opposite or facing page. These cartoons were drawn or designed by Michael Dooley.
Arithmetic in the Total School Program
Authors: Curtin James
Published: October 2020

Effective arithmetic instruction is not confined solely to arithmetic periods. The demands placed upon the arithmetical knowledge of the children are inherent in all subjects in the elementary school curriculum. In some areas of study these demands are enormous while in others they are less significant. However, if we can generalize at all, we can say that knowledge of arithmetic or a knowledge of quantity is necessary in every subject that is taught in the elementary school. Indeed, we might go further to say that the understandings derived from studying the sciences, social studies, even spelling, music and art are dependent in some measure upon the quantity involved.
Help Children Discover Fraction Facts
Authors: Glenn William H.
Published: October 2020

IN TEACHING ANY MATHEMATICAL Concept, it is always well to begin with experiences which children already have had, in order that their ideas can be freely expressed and certain words can easily become a natural part of their conversation.
Exploring Geometry
Authors: Claus Alison
Published: October 2020

This unit began as a favor for a friend who needed some examples of children writing about mathematics. but it ended as a marvelous activity for the first week of school. The unit consisted of a series of lessons that furnished my fifth-grade students with a review of geometry and problem solving using geometric concepts and allowed them to communicate with each other about these concepts both in writing and orally.
Stimulating Communication in Mathematics
Authors: Greenes Carole , Schulman Linda , Spungin Rika
Published: October 2020

Recently, a great deal of interest has been shown in communication in mathematics. The National Council of Teachers of Mathematics, in its Curriculum and Evaluation Standards for School Mathematics (1989), states that at all grade levels, students must learn to communicate mathematically. Science for All Americans: A Project 2061 Report (American Association for the Advancement of Science 1988) describes effective teaching of mathematics as teaching that emphasizes the development of students' abilities to communicate clearly in both oral and written work. Turning Points: Preparing American Youth for the Twentyfirst Century (Carnegie Council on Adolescent Development 1989, 43) encourages middle-grade teachers “to promote a spirit of inquiry and to stimulate students to think about and communicate ideas.”
Teacher to Teacher: The Learning Connection: Talk-throughs
Authors: Kay Vetter R.
Published: October 2020

For the last two years, I have been implementing as much peer teaching as possible in my fourth -grade classroom. Teaching in a self-contained room, I have seen benefits in all subject areas, but I have to say that the area of most benefit has been mathematics.
Getting the Most From a Problem
Authors: Fulkerson Paul
Published: October 2020

While coaching a team for the national MATHCOUNTS competition, I found the following problem in the test for the Sprint Round of the 1988–89 national contest.
Integrating Mathematics and Literature in the Elementary Classroom
Authors: Kliman Marlene
Published: October 2020

Imagine a class of fourth graders sitting at their desks at the start of the school day. The teacher announces that she is going to read them a story about adventures in a land of giant people and things. The story, a popular children's book, is replete with descriptions of size. For example, the story describes a staircase in which each stair is 6 feet high, a table top that is 30 feet above the tloor, a serving dish that is 24 feet in diameter, and a ten-year-old child who is 45 feet tall
Angle Sense: A Valuable Connector
Authors: Rubenstein Rheta N. , Lappan Glenda , Phillips Elizabeth , Fitzgerald William
Published: October 2020

To empower students through con-nections in mathematics, we need to identify those fruitful nodes in the mathematics network from which many new understandings can be derived. For these nodes or connectors to help students move from familiar ideas to new ones, they need to have certain qualities.
Calendar Mathematics
Authors: Morrow Lorna , Chancellor Dinah
Published: October 2020

The calendar is designed to speak directly to students, giving them open-ended questions intended to engage their intellect through their interests. Students ore encouraged to work on the activities individually, in pairs, or in small groups. No answers ore provided for the calendar questions so that students ore encouraged to look to themselves as the mathematical authority, thereby developing the confidence and critical-thinking skills necessary to validate their thinking.
Ideas
Authors: Usnick Virginia , Miller Phyllis Knerl , Stonecipher Danna , Brahier Daniel J.
Published: October 2020

In its document, the Curriculum and Evaluation Standards for School Matheniatics (1989), the National Council of Teachers of Mathematics recommended instruction connecting mathematics to other content areas. The “IDEAS” section for this month presents activities that offer connections between mathematics and the visual arts.
See it, Change it, Reason it Out
Authors: Shaw Jean M.
Published: October 2020

When we attended the Smithsonian Museum's traveling exhibition on kaleido-scopes at our University Museum, several undergraduate students made an interesting discovery. Pan of the exhibit featured a device with hinged mirrors and colored objects that could be arranged on a table; participants arranged the objects and explored the different effect that they could see reflected in the mirrors. When the students placed a colored strip between the ends of the mirrors and looked directly into the mirrors, which were positioned to create an angle with measure 90 degrees, they saw a square (fig. 1a). When they changed the angle of the mirror, they saw a regular pentagon or hexagon.
Teacher To Teacher: Take-Home Kits
Authors: Franklin Joyce , Krebill Joyce
Published: October 2020

Our half-day kindergarten did not permit us to extend and enrich our mathematic program the way we wanted to pre ent it. Therefore, we decided to develop take-home kits. They were intended to be of high interest, fun, and yet simple enough that a student could do the activities alone. For a student fortunate enough to have help, extended activities were included. Each kit contained a pictorial evalumion sheet that could be completed by the tudent. The evaluation were intended to keep us infanned about the appeal of the activity and the abilities of the students. The evaluation sheets were filed and made into a book for each student to take home at the end of the year.
Connecting Learning and Teaching Through Assessment
Authors: Moon C. Jean
Published: October 2020

We are beginning to understand that the teacher-as-researcher role encourages a teacher to reflect on teaching practices and students' learning, which is a promising strategy for changing the way mathematics is taught, learned, and assessed (Tobin 1989). When teachers actively participate in evaluating classroom lessons, they can begin to create new, more effective frameworks in which to help their students make mathematical connections.
Using Biographies to “Humanize” The Mathematics Class
Authors: Dakin Voolich Erica
Published: October 2020

Using biographies of mathematicians can successfully bring the human story into the mathematics class. What struggles have these people undergone to be able to study mathematics? Who developed the ideas that we continue to study today? How extraordinary were these mathematicians? Could one of today's students be the next Sonya Kovalevski or Carl Friedrich Gauss? Does your class have a hero or role model waiting to be discovered?
Promising Research, Programs, and Projects: Current Projects and Research Programs—a Federal Perspective
Authors: Lacampagne Carole B.
Published: October 2020

This is the first article to appear in a new section in the Arithmetic Teacher called “Promising Research, Programs, and Projects.” This new section will give teachers a view of research, actions, and projects that will affect teaching and learning mathematics at the K–8 levels. Readers of the Arithmetic Teacher are encouraged to submit suggestions or short articles for this section. Of particular interest are projects with developed materials or papers, which the project director will send to readers. (Write to Carole Lacampagne, United States Department of Education, OERI, 555 New Jersey Avenue, N.W., Washington, DC 20208, for article guidelines.)
Becca's Investigation
Authors: Whitin David J.
Published: October 2020

As my eleven-year-old daughter, Becca, was doing her mathematics homework one night, she called me into her room. “Dad, do you think'36 × 8' is the same as '48 × 6'?”
AT Classic: Twentieth Century Mathematics for the Elementary School
Authors: Engen H. Van
Published: October 2020

In this article. H. Van Engen goes directly to the bottom line and places the responsibility for the problem that exists in elementary mathematics on elementary, secondary, and college teachers, Now, thirty years later, all these groups must share the blame. With few exception, the three groups are not cooperatively working toward improvement. At all levels, “answer-mindedness” has blinded mathematics educators to the need to search for the fundamental structure of the problem situation. Van Engen was right—elementary teachers need to know more mathematics but only if that instruction leads to more understanding, less fragmentization, and a realization that computation is not the end product in mathematical thinking. In thirty years we should have made much more progress.
Calendar Mathematics
Authors: Ajose Sunday A.
Published: October 2020

The calendar is designed to speak directly to students, giving them open-nded questions intended to engage their intellect through their interests. Students are encouraged to work on the activities individually, in pairs, or in small groups. No answers are provided for the calendar questions so that students are encouraged to look to themselves as the mathematical authority, to develop the confidence and critical-thinking skills necessary to validate their thinking.
Strategies for Estimating Discrete Quantities
Authors: Crites Terry W.
Published: October 2020

A student's ability to estimate discrete quantity has important implications for the development of mathematical power. Hofstadter (1985) and Paulos (1988) both suggest that the ability to estimate is intimately tied to the growth of understanding large numbers. This “feel” for large numbers allows students competently to consider questions about the relative magnitude of two quantities, realize absurdities when confronted with facts that are illogical, and become better-informed citizens when making decisions about important social policies (e.g., our country's $1 trillion budget, the number of trees it takes to produce a day's supply of newsprint, and how many tons of garbage are produced each week by our largest cities).
Forecast: Changing Mathematics Curriculum and Increasing Pressure for Higher-Level Thinking Skills
Authors: Niess Margaret L.
Published: October 2020

There's a lot of exciting new technology that the weather service plans to incorporate in the next decade. But, to do that, positions in the weather service will have to be upgraded from technical to scientific. people with a higher level of skill in using and interpreting the new data available” (Oregon State University ews Service 1990. 3). Technology is affecting the work force. changing not only the skills that are needed but also the level of those skills. Thus, the education of those workers assuming the newly defined positions must reflect the changes.
Mean or Meaningless?
Authors: Korithoski Theodor P. , Korithoski Patricia A.
Published: October 2020

The arithmetic mean is not really mean to students: the mean is merely meaningless to students if they really do not understand what the mean really means. Confused and tongue-tied? Read on and see what the authors did with a group of fifth graders to help them understand the arithmetic mean.
Critical Thinking During The December Holidays
Authors: Raphel Annette
Published: October 2020

In a conscious effort to make mathematics more open-ended and relevant and to dispel the myth that the discipline is a series of easily solved and discrete experiences, the curriculum has been reshaped in the author's school to allow for some more lengthy investigations and projects. These lessons take more than one period, ask students to extend their thinking, and require them to relate several disciplines to mathematics. Many of the experiences start with sketchy ideas and without firm notions about answers on the part of the teachers. These experiences become the foundation for deep understanding and appreciation of the power of mathematics beyond computation.
Daily Activites for Data Analysis
Authors: Hitch Chris , Armstrong Georganna
Published: October 2020

Statistics, tables, charts, and graphs abound in our daily world. We see them in advertisements, in newspapers, and on televised weather forecasts. However, many students are not exposed in school to experiences using statistics and graphing. One goal of the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) is to give students experiences that allow them to “collect, organize, and describe data: construct, read, and interpret displays of data; formulate and solve problems that involve collecting and analyzing data” (p. 54). Children develop mathematical concepts by seeing them in a variety of settings. Our challenge is to find many ways to help our students understand these concepts. The following activities enable students to understand the power and usefulness of data analysis.
One Point of View: Planning for Instruction Involves Focusing on Children's Thinking
Authors: Rathmell Edward C.
Published: October 2020

Too often when teachers plan for instruction, such mathematical skills as two-digit subtraction, multiplication facts, and equivalent fractions take precedence over thinking-and-reasoning strategies. Planning for instruction that promotes the development of children's thinking and reasoning about mathematics not only helps them make sense of the content they are studying but also helps them learn ways of thinking that later will enable them to make sense of new content.
Calendar Mathematics
Authors: Porter Jeanna
Published: October 2020

The calendar is designed to speak directly to students, giving them open-ended questions intended to engage their intellect through their interests. Students are encouraged to work on the activities individually, in pairs, or in small groups. No answers ore provided for the calendar questions to encourage students to look to themselves as the mathematical authority, to develop the confidence and critical-thinking skills necessary to validate their thinking.
Planning for Classroom Portfolio Assessment
Authors: Lambdin Diana V. , Walker Vicki L.
Published: October 2020

Three years ago, the mathematics teachers from grades 4-12 in our school met for two weeks during the summer for an in-service program related to assessment and decided to begin using portfolios with our students in the fall. I was enthusiastic, although I had no idea at that time how drastically my approach to assessment—and to teaching in general—would change a a result of the portfolio decision.
Exploring Estimation through Children's Literature
Authors: Whitin David J.
Published: October 2020

Estimation is a crucial mathematical strategy that can be woven throughout the entire mathematics curriculum. The strategy can certainly foster the development of many of the goals advocated by the NCTM's curriculum and evaluation standards (1989). Since approximately 80 percent of real-world applications of mathematics involve estimation or mental computation, the goal of becoming an “informed electorate” requires us to use and analyze various estimation strategies.
Implementing the Professional Standards for Teaching Mathematics: The Influence of Teachers' Beliefs and Knowledge on Learning Environments
Authors: Lubinski Cheryl Ann , Vacc Nancy Nesbitt
Published: October 2020

Seth was sitting in his second-grade classroom on the third day of school. He'd just finished writing on his paper after his teacher, Ms. Kates, had given the class a problem to solve.
IDEAS
Authors: Chessin Debby A. , Shaw Jean M.
Published: October 2020

The “IDEAS” section for this month focuses on connections among mathematics, concern for the environment, and conservation of natural resources. Each activity allows opportunities for communicating, reasoning, and problem solving as students become personally involved in helping to conserve natural resources. This investigative approach that connects mathematics to students' everyday lives is recommended in the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989).
Color as an Aid in Teaching Concepts
Authors: Erickson Leland H.
Published: October 2020

TEACHING ARITHMETICAL CONCEPTS would be a simple task if all children learned alike. It would be a relatively simple teaching situation, for example, if all children responded equally effectively to the same stimulus in learning compound subtraction. One device or one situation would serve the needs of all learners. The fact that all children do not respond in the same manner to all stimuli, and that quantitative concepts are not discovered in the same way by all learners is now accepted by all educators. The thought patterns of children which determine the acquisition of number concepts and arithmetical processes are different in many ways. Teachers are familiar with the reasons underlying these differences in learning, some of which are mental ability, experiential background, previous number concepts, methods used in teaching previous number concepts, insights, ability, interest, aptitude and attitude. For these reasons elementary teachers must be certain that children have all kinds of experiences in dealing with numbers and number processes.
Counters? Yes, But…
Authors: Tuttle Ruth H.
Published: October 2020

IT IS GENERALLY ACCEPTED as sound theory that our number system is the result of an evolution of numbers through several progressive stages. It seems probable that primitive man counted his possessions by the aid of his ten fingers; that when he had counted ten and used all his fingers he substituted a stone or other object to which he assigned the value of ten and resumed his counting by his fingers. When he had as many tens-counters (stones, or what had he!) in his tens pile as he had fingers, he again substituted a stone (perhaps a larger one), assigning to it a value of one hundred and resumed his counting by his fingers to more ones, tens or hundreds.
The Neglected Role of the Decimal Point
Authors: Mueller Francis J.
Published: October 2020

The Modern Approach to elementary arithmetic places considerable emphasis upon the basic structure of our Hindu Arabic system of number notation. It is felt that upon such a foundation the algorismsthose rules of procedure by which we combine, separate and compare numbers by working with the numerals that represent these numbers—can best be understood.* It is almost trivial to state that understanding, not rote manipulation, is the keystone of this modern approach.
How Profitable Is the Usual Problem Work in Arithmetic?
Authors: Wilson Guy M.
Published: October 2020

There are at least three distinct types of material in arithmetic,—drill, problem, and apprecia tion. Each type of material carries a distinct aim.
Report of the Membership Committee
Authors: Rogers Mary C.
Published: October 2020

This has been a remarkably successful year in National Council membership growth. Needless to say, we are very happy about it. We are confident that all of you, our current members, share this feeling with us.
Psychology Applied to the Teaching of Arithmetic
Authors: Koenker Robert H.
Published: October 2020

IN THE LAST TWO DECADES NUMEROUS studies and experiments in the field of psychology have given us many sound principles of learning which are readily applicable to the teaching of all subjects. These principles have no doubt been successfully used by many teachers; however, to the best of the writer's knowledge, no organized statement of these principles of lea rning as applied to the teaching of arithmetic has been published. The writer will attempt in this article to draw together some of these principles of learning and then apply them to the teaching of arithmetic.
Another Look at Problem Solving
Authors: Berglund Dorothy , Boyd Margaret , Cocke Elizabeth , Durrenberger Camilla , Rader Eunice
Published: October 2020

As a result of an inservice education program, the authors of this report undertook an extensive investigation of ways in which pupils' work with story problems could be improved. At the outset, it was recognized that this was an area of arithmetic instruction about which many teachers were concerned. After a thorough review of literature, including research articles as well as other reports, the authors hypothesized that “experience problems” would provide, at least, a partial answer to this problem. Experience problems were defined as those problems which provide a quantitative experience outside the regular textbook. In five classrooms in grades four, five, and six, extensive experience problem projects were undertaken.
Teachers Look at Arithmetic Manuals
Authors: Folsom Mary
Published: October 2020

IN 1931, THE National Society for the Study of Education devoted a yearbook to a report on the textbook, and the authorities conceded that the textbook is the most valuable single piece of instructional equipment available to the teacher.2 However, the fact that manual material has become a large factor in the preparation and selection of arithmetic textbook series has not been similarly recognized nor has any serious attempt been made to evaluate arithmetic manuals in light of teacher needs and usage.
Art and Arithmetic
Authors: Ragland Elizabeth
Published: October 2020

It all started with the theme for the ninth grade class day progam. The subject was Our Flower Garden. Six homerooms were to represent six different flowers. The speeches and songs were to correspond with the central theme. It was suggested that the back auditorium wall would be a wonderful place for a scenic view.
Developing Creativity through Arithmetic
Authors: Delong Arthur R. , Clark Richard M.
Published: October 2020

When making arrangements for taking her fourth grade class through a local manufacturing plant, Miss Bliss was told that plant guides would take a group of eight children at a time through the plant. Since Miss Bliss had become concerned about whether she was developing creativity, she asked each member of her class to figure out how many groups of eigh't would be formed from the class of thirty-two children, and to work out this problem in as many different ways as they could.
Building Algebra Readiness in Grades Seven and Eight
Authors: Mueller Francis J.
Published: October 2020

Review and extension of computational processes learned in the elementary grades, mastery of one important new topic —percentage—and the informal introduction of basic geometric concepts are generally accepted as the pr incipal mathematics responsibilities of grades 7 and 8. Less frequently recognized, but of increasing importance, is an added responsibility: building an algebra readiness.
Arithmetic and “Block Work” in Primary Grades
Authors: Johnson Lois V. , Whipple Avis S.
Published: October 2020

Arithmetic and the content fields are frequently used in a mutually supporting relationship in the middle and upper grades. Arithmetic is used when it is needed in the social studies or science class, and vice versa. The content fields and arithmetic complement each other to the benefit of the children's understandings of both arithmetic and tbe content field. This is in accord with a major objective of arithmetic that children should be sensitive to number whenever and wherever it occurs and that they should develop the habit of using number effectively in such situations.*
Arithmetic for the Academically Talented: The Arithmetic Program in the Member Independent Schools of the Educational Records Bureau
Authors: Erhart M.
Published: October 2020

In his recent report on the American High School Dr. Conant1 gives careful consideration to the comprehensive-type school, for he is of the opinion that this type of school satisfies the needs of the greater part of the nation's youth. However, he also gives proper recognition to other types of schools in our society: “I cannot emphasize too strongly the differences I have found between industrial cities, suburban areas, and the districts I have visited in certain large cities … improvements must come school by school and be made with due regard for the nature of the community.”1 In his discussion of the schools found in suburban districts—and he includes certain metropolitan schools in this category—he mentions two chief characteristics. First: the students in these schools are markedly superior in academic abiJity as measured by scholastic aptitude tests; and secondly: the majority of these students are preparing for college.
The Impact of the Maryland and Yale Programs
Authors: Genise L. Roland
Published: October 2020

I BELIEVE MY REASONS FOR CHOOSING this topic are good ones. First, as they say in the T.V. detective stories, K-12 and beyond is “my beat.” As supervisor of mathematics education for the Brentwood Public Schools, it is my primary responsibility to provide the leadership for the development of a comprehensive and modern mathematics program for the young citizens of the Brentwood community. Second, we have, this past year, had some of our students enrolled in the University of Maryland Mathematics Project. Third, our Junior High School will have many more students enrolled in both the UMMaP and Yale SMSG 7th and 8th grade programs.
Tables and Structures
Authors: Jackson Humphrey C.
Published: October 2020

Experienced teachers know the value of tables of number facts as a means of helping students discover relationships. There is value in directing the student to make his own tables, but often in the interest of saving time, tables already prepared may be placed in his hands. Some of the tables suggested here have been used by accelerated fourth grade classes, others in the seventh grade.
The Abacus and our Ancestors
Authors: Flewelling Robert W.
Published: October 2020

Although not generally appreciated, the history of the abacus in the development of western civilization makes an interesting and effective vehicle for integrating mathematics and social studies in the classroom. The average American, if he knows about it at all, probably thinks of the abacus as a toy for children or an antiquated gadget that is used by some Orientals to “figure with.” Many teachers are little better informed even though abacuses are common in elementary classrooms.
A Combined Content-Methods Course for Elementary Mathematics Teachers
Authors: Phillips Clarence
Published: October 2020

Colleges and Universities have the responsibility of training prospective elementary teachers in the teaching of elementary mathematics. These teachers must be trained so that they can teach elementary school mathematics for meaning and understanding. In addition to training prospective elementary school teachers, the colleges and universities also have the responsibility of acquainting teachers in-service with the “newer” approach in teaching elementary mathematics. In this article, I will use “elementary teachers” as including both groups.
How Well Do 158 Prospective Elementary Teachers Know Arithmetic?
Authors: Fulkerson Elbert
Published: October 2020

For the Past Several Years the College of Education of Southern Illinois University has required its students majoring in elementary education to take a course known as Mathematics 210, which is described in the University Bulletin as a “professional treatment of the subject matter of arithmetic methods and a study of trends and current literature on the teaching of arithmetic.” This course is offered by the Mathematics Department of the College of Liberal Arts and Sciences and carries four quarter hours of credit. I ts prerequisite is a general mathematics course which does not count toward a major or minor in mathematics but which does include, however, a careful study of the real number system and other topics providing a better understanding of arithmetic and elementary algebra.
The Meaning of Two Times Two
Authors: Buckland G. T.
Published: October 2020

For a Large number of people, laymen, students, as well as teachers, two times two has always meant four. The reason for this seems to be “just because it has always been that way.” Actually two times two has two other products equally as good as the common four. Sometimes the product could be 10 or 11. These answers are not to be confused with the numbers ten and eleven involved in our common base of operation, the decimal base.
Historical Conflict—Decimal Versus Vulgar Fractions
Authors: Jones Emily
Published: October 2020

The question of the relative importance of decimal and common fractions arose early in the history of arithmetic teaching in America. The proper emphasis that should be placed on each of these ropics, the space that should be assigned to them, and the order in which they should be treated claimed the attention of many of the first American textbook writers.
Helping Pupils Help Themselves Through Self-Evaluation
Authors: Norton Monte S.
Published: October 2020

Improvement in Arithmetic is dependent—dependent upon the individual's awareness of various weaknesses, a desire to improve in this area, and a knowledge of the procedures that possibly may bring about the desired improvement. This idea of self-improvement is carried on in arithmetic classes in our school through the use of our self-evaluation plan. Although rather simple in nature, this self-evaluation technique has proven a valuable device for helping pupils help themselves in arithmetic improvement.
Ancient Devices in Teaching Modern Arithmetic
Authors: Healy Daniel J.
Published: October 2020

Most of the Elementary School children throughout the United States learn arithmetic computation through methods evolved from Hindu and Arabic systems of mathematics. In this system basic number combinations are committed to memory and specific computation steps are done mentally. Therefore, number combinations and number facts are developed at early stages. Mental computation involves the process of “carrying” in addition and this process is to be mastered prior to the introduction of multiplication.
A Study of the Attitudes Toward Arithmetic of Students and Teachers in the Third, Fourth, and Sixth Grades
Authors: Stright Virginia M.
Published: October 2020

In the last few years many changes have occurred in the teaching of arithmetic, with the result that today arithmetic has a place of much greater importance in the curriculum. However, even with these changes, much of the current literature about arithmetic in the elementary curriculum gives one the impression that arithmetic is still a much disliked subject. Statements such as these appear in periodicals: “It is only too certain that today's mathematically ill-prepared teachers, many of whom are ill-disposed toward the subject, are infecting too large a number of our boys and girls with an enduring fear and hatred of mathematics, which can rarely be overcome later on in high school,”1 and “Most students who have a fear and dislike of mathematics met with some frustration in the elementary grades.” 2
Will you contribute to a forthcoming yearbook?
Authors: Hlavaty Julius H.
Published: October 2020

The Board of Directors of The National Council of Teachers of Mathematics at the April, 1960 meeting approved the preparation and publication of a yearbook to be devoted to the problem of the mathematical education of the talented student in grades K- 12.
In the classroom: Grouping—an aid in learning multiplication and division facts
Authors: Deans Edwina
Published: October 2020

As elementary-school children progress in their study of mathematics, they deal with numbers which are increasingly more complex and abstract. Around the third or fourth year in the grades, children's work with operations requires an understanding of numbers of two or more places and a knowledge of regrouping in terms of our basic unit of ten. Attention to grouping arrangements assists children in their discovery of multiplication and division facts, and it assists them in the use of these facts in the operations of multiplication and division.
Reviews: Books and materials
Authors: Hardgrove Clarence Ethel
Published: October 2020

This review is limited to the material on arithmetic in the World Book Encyclopedia. Other aspects of mathematics, such as algebra, calculus, and topology, are not discussed here since they are of primary interest in secondary school and college. Such topics, by the way, appear to have received good coverage.
Report of the Nominating Committee
Authors: Schaaf Oscar F. , Fawcett Harold , Ferguson W. Eugene , John Lenore , Karnes Houston T. , Lowry W. C. , Puett Ida B. , Sobel Max , Hunter Lottchen
Published: October 2020

The Committee on Nominations and Elections presents its nominees for offices to be filled in the 1961 election. The term of office for the two vice-presidents is two years. Three directors are to be elected for terms of three years.
Grouping by arithmetic ability—an experiment in the teaching of arithmetic
Authors: Pinney Grant C.
Published: October 2020

That children in the regular elementary classroom at every grade level vary widely in their interest and achievement in arithmetic is a well-known and accepted fact. With this fact in mind, the staff at Vieweg Elementary School felt that most of the difficulty in teaching arithmetic was due to the great span of ability found in a heterogeneous classroom of fifth- or sixth-grade children.1 In a sixth-grade class the grade placement ability on achievement tests ranged from 2.0 grade level to 10.0 grade level—eight full years. The problem, as we saw it, was to reduce the range of arithmetic achievement ability in each classroom.
Ordered pairs, patterns, and graphs in fourth grade
Authors: Driscoll Lucy E.
Published: October 2020

How many cuts will you make to cut a board into four parts?” “If Tommy is four years old when his father is twenty-four, his father is how many times as old as Tommy?” Although in itself this presented no apparent difficulty, someone then volunteered the statement, “Then when Tommy is six years old, his father will have to be thirty-six.” At this point there was some shaking of heads, much discussion, and a number of seemingly perplexed children.
Children are naturals at solving word problems: They love to solve puzzles. They love to explore.
Authors: Unkel Esther R.
Published: October 2020

Children have naturally inquisitive minds. They have the ability to shut out all other things in concentrating on the solving of a puzzle. They joyously answer a challenge. All this makes them naturals in solving word problems.
On the fraction as a numeral
Authors: Mueller Francis J.
Published: October 2020

In the December, 1960, issue of THE ArithmMETic TEacher, there is presented a rat her cogent case for the use of rate pairs and the definition of a fraction as a number.*
A time for decision: What shall be the mathematics in the elementary school?
Authors: Sueltz Ben A.
Published: October 2020

Mathematics is queen of the sciences and arithmetic is queen of mathematics. She often condescends to render service to astronomy and other natural sciences, but under all circumstances the first place is her due.” So wrote the great mathematician Gau s more than one hundred years ago. The queenly state is a high and noble estate with qualities such as those of beauty and charm, of authority and power, and of service to her people. This is the queen of t he sciences who begins to erve in the elementary school.
Sets and numbers in grade one, 1959-60
Authors: Suppes Patrick , Mcknight Blair A.
Published: October 2020

There are at least two major reasons for beginning first-grade arithmetic with the explicit introduction of the notion of set and appropriate notation for sets and operations upon them. In the first place, sets are concrete objects. Numbers are not concrete objects. Operations upon sets are more meaningful to the student than operations on numbers. The putting together of sets of physical objects, for instance, is a concrete operation. The addition of numbers is not an operation on physical objects. This is illustrated in the following example of the union of two sets.
Experimental projects and research: Geometry for primary grades
Authors: Hawley Newton S.
Published: October 2020

This program for teaching geometry in the elementary grades had its beginning in t he spring of I H58 when an iuformal experiment was conducted in the teaching of geometry in a first grade class. At that time the class received a geometry lesson lasting about twenty minutes each sc hool clay—usually in the early mornings. This first experiment lasted about two months. The material presented was based on Euclid's Elements but wa presented, of course, in a considerably modified manner.
San Diego's new arithmetic program
Authors: Wilson J. Fred , Self William , Chamberlin Don
Published: October 2020

The curriculum challenge of the 1960's is unquestionably the development of new mathematical material. The problems of bridging the gap between the traditional arithmetic content and methodology to the new and challenging modern mathematics approach will test the ingenuity of all concerned throughout this decade. What are the values of the present approach that should be retained? What criteria shall be used to select the newer mathematical experiences? How can some of the newer content be integrated into the existing curriculum? How can teachers become familiar with the newer mathematics? These are representative of the many questions and problems which must be solved before a new curriculum can be planned, written, and used effectively by the classroom teacher.
Planning an arithmetic fair
Authors: Gilman Dorothy F.
Published: October 2020

Each spring we have an exhibit to interpret to the parents of children in our school a particular subject-matter area from kindergarten through the sixth grade. In the past three years there have been a Science Fair, a Book Fair, and a Health Night at Wolf Swamp School.
Just plain drill
Authors: Coleman Josephine K.
Published: October 2020

Learning by repetition, in the early or later grades, has perhaps an undeservedly bad reputation that is based purely on memoritor work, lacking in motivation. The sorry but realistic allusions which have enriched ow- literature in the past two or three centuries from the pens of Lamb, Dickens, Captain Marryat, and Eggleston point up a succession of dreary, stolid, unimaginative educational experiences.
Division of fractions: A study of the common-denominator method and the effect on skill in multiplication of fractions
Authors: Capps Lelon R.
Published: October 2020

For some time there has existed a difference of opinion with regard to the effectiveness of the common-denominator and inversion methods of teaching division of fractions.
Deductive reasoning in the primary-arithmetic program
Authors: Foster James M.
Published: October 2020

One of the avowed aims of the elementary- school program is to teach children how to think. The ability to take a set of conditions and deduce logical conclusions is an essential skill in our modem society. Arithmetic instruction as an integral part of our total elementary program should make a contribution to the development of deductive reasoning.
Let them discover
Authors: Akins Thelma S.
Published: October 2020

Children enter the first grade with varying degrees of number understanding. Many six-year-olds have the ability to count to ten; some can count to one hundred. However, the ability to count by rote has very little relation to understanding of the number system. Because most children do memorize quickly and easily, there is apt to be some temptation on the part of the teachers to rest content with using that facile memory to cover the course in numbers. A whole class can become skilled and adept in addition and subtraction with very little or no understanding of the number system.
An open letter on teaching machines and programed instruction
Authors: Smith Leander W.
Published: October 2020

Each generation feels the pressure of time—to do, to make, to remake, and to perfect the world within a few short years. As each generation leaves its mark, large or small, the history of mankind records, and time slips away. The challenge persists. But few generations have been challenged as seriously as that of the present, for time itself seems accelerated.