bluuebunny/crossref_metadata_2025 huggingface dataset:
CBTE in Elementary Mathematics Education
Authors: McKillip William D.
Published: October 2020

Some aspects of competency-based teacher education (CBTE), as they apply to the preparation of teachers of mathematics, are explored in this article. Essential and distinguishing features of CBTE are examined and related to the University of Georgia experience in CBTE, and some nonessential features of CBTE are identified. A “competency” and how competencies may be identified are discussed, along with the effects of a competency orientation on methods courses, student teaching, and internship experiences. Some research trends related to CBTE are also touched on. And finally, the development of a competency is described.
Making a Problem of Junior High School Mathematics
Authors: House Peggy A.
Published: October 2020

Junior high school mathematics is problem enough for many students. Why, as the title suggests, try to make it more so? One answer to this question is that frequently the problem with junior high school mathematics is that there is too little problem solving.
Ideas
Authors: Jacobson Marilyn Hall , Tabler M. Bernadine
Published: October 2020

The IDEAS for this month consists of two problem-solving posters with a Halloween theme. Some of the problems can be easily solved and have only one solution. Others will take students more time, especially if they find all the possible solutions
Why Blame the Kids? We Teach Mistakes!
Authors: Jencks Stanley M. , Peck Donald M. , Chatterley Louis J.
Published: October 2020

Experienced teachers in both elementary and secondary schools can depend on encountering children's mistakes like those in figure l. Why are these and other mistakes like them so pervasive that every teacher recognizes them? Could it be the incorrect methods children use were inadvertently taught to them? Evidence gathered by the authors suggests this is the case.
Mathematics and the Spanish-Speaking Student
Authors: Castellanos Gloria G.
Published: October 2020

From time to time, many teachers have in their classrooms students who began their education in Spanishspeaking countries. Thus certain aspects of the students' training in mathematics may be significantly different from what is standard in this country. Three such differences are discussed here.
Cross-Number Puzzles
Authors: Orletsky Ann E. Trahanovsky
Published: October 2020

A cross-number puzzle can be used as a learning device or as a means of evaluation. If it is used as a test, the fact that it is a puzzle may reduce the fear of taking a test. Checking a crossnumber puzzle test is an easy task for the teacher since the answers are in a definite position.
Geometry Word Puzzle
Authors: Gerbe Warren S.
Published: October 2020

The idea for this puzzle came from the many others in magazines and newspapers. This activity has been such a success in my classes that the students even went so far as to make puzzles of their own.
Sweeten Mathematics with M & M's
Authors: Lunde Henry M.
Published: October 2020

Are you still searching for ideas for presenting different mathematical concepts with concrete and semiconcrete materials and ways that will capture the children's attention? Try M & M's. Children like the candy and are intrigued with the idea of using them for mathematics.
Mathematics and Language
Authors: Earp N. Wesley , Tanner Fred W.
Published: October 2020

In speaking of the measurement of academic achievement, Thorndike (1912, p. 1) said, “As you well know our measurement of ability in arithmetic actually is a measure of two things: sheer mathematical insight and knowledge on the one hand; and acquaintance with language, on the other.” Present-day teachers often contend that many students do not read well enough to do mathematics. Yet it seems that there are matters other than the sheer ability to decode and comprehend printed matter that relate to reading in mathematics.
Mathematics and Saltine Crackers
Authors: Sanok Gloria
Published: October 2020

One saltine cracker can give a student a taste for whole numbers, common fractions, decimal fractions, percents, and money—geometrically and rationally speaking, of course. A saltine cracker can illustrate several mathematical concepts.
What Do Children See in Mathematics Textbook Pictures?
Authors: Campbell Patricia F.
Published: October 2020

In communicating with words it is obvious that if the receiver does not know the language he will not be able to decode the message. It is obvious that reading is a skill which must be learned. It is not obvious—indeed it is sometimes completely unnoticed—that a parallel condition exists in the case of pictures. Children must learn bow to “read” pictures.
Fractions Taught by Folding Paper Strips
Authors: Scott Wayne R.
Published: October 2020

The folding of paper strips into equal segments is an excellent model for conceptualization of operations with fractions, both simple common fractions and mixed numbers.
Dinosaurs and Arithmetic!
Authors: Weinstein Pauline Smith
Published: October 2020

Children in a grade one classroom sat with eyes wide open, mouths agape, as the teacher related a story concerning dinosaurs, those “terrible lizards” who lived on earth about two hundred million years ago. The very physique of the dinosaur, its shape, strength, and enormous size captured the imagination of the children. They wanted to learn more about these reptiles. Many children were motivated to read about these creatures, so books specifically designed for their reading level were made available. Some children were fascinated by the names of the different dinosaurs—Brontosaurus, Camptosaurus, Stegosaurus, Allosaurus, Triceratops, among others. The words had an interesting ring to their ears. Each child also seemed to favor one type of dinosaur over the others.
MISCELLANY: Sara's Pattern
Authors: Juraschek William
Published: October 2020

Sara is bright and learns quickly. One day, when she was four, she was enthusiastically displaying her newly acquired ability to recognize and name the digits. That evening as I read stories to her I decided to try an informal teaching experiment. Through guided discovery with appropriate reinforcement we would extend her new skill to bigger and better things.
Ideas, Ideas, Ideas from IDEAS: An Annotated Bibliography
Authors: Hirsch Christian R. , Meyer Ruth A.
Published: October 2020

The IDEAS section bas been a regular feature of the Arithmetic Teacher since January 1971. Each section contains several worksheets and suggestions for teaching strategies appropriate for use with pupils at various levels in elementary and middle schools. The worksheets are arranged so as to be easily removed and reproduced for use with individuals, small groups. or a total class. This annotated bibliography of IDEAS was compiled to provide the classroom teacher an easy way to identify content-specific activities that could be included in a planned program of instruction. The compilation includes aU LDEAS published through May 1980.
NEEDED RESEARCH: Mathematics for the Talented
Authors: Osborne Alan
Published: October 2020

It is appropriate that interest in the development and nurture of creative mathematical talents be renewed after several years of limited attention to and concern for the special needs of the gifted. Do we have sufficient research to guide decisions about what should be taught to talented children, when it should be taught, or in what setting? Do we know enough to make prudent commitments of resources? If not, what type of research is needed to improve the state of our decision making?
Ideas
Authors: Jacobson Marilyn Hall , Tabler M. Bernadine
Published: October 2020

The IDEAS for this month provides experiences with concepts of basic probability. The understanding of likely and unlikely events, and the ability to make predictions based on information about a particular situation is an important skill for children to develop.
”Top Ten” Mathematics
Authors: Siwakowsky Evelyn
Published: October 2020

Bored? In a rut? A good change of pace is “The Top Hits of the Week” lesson. I have found this lesson to be highly motivating and beneficial for my students who have trouble applying skills and concepts learned in mathematics class to situations outside class.
Painless Division with Doc Spitler's Magic Division Estimator
Authors: Spitler Gail
Published: October 2020

In the February 1978 issue of the Arithmetic Teacher (p. 55) Charles clearly identified the feelings we all have about long division: “Students complain when a long division problem is assigned. Teachers grumble when their classes approach the chapter on long division. Parents wonder why students complain and teachers grumble.”
Ideas
Authors: Jacobson Marilyn Hall , Tabler M. Bernadine
Published: October 2020

The IDEAS for this month consists of two problem posters. The problems focus on the usc of information from a chart to find a solution. Some of the problem can be easily solved and have only one solution. Others will take student more time. especially if they find all the possible solutions.
Computational Skill in Division: Results and Implications from National Assessment
Authors: McKillip William D.
Published: October 2020

Division exercises in the most recent mathematics assessment conducted by the National Assessment of Educational Progress (NAEP) are the subject for discussion this month. The report of student performance on selected exercises testing computational skill with division is followed by some suggestions for improvement in the teaching of division.
Share and Cover
Authors: Peck Donald M. , Jencks Stanley M.
Published: October 2020

Fractions (both common and decimal) pose many difficulties to students. The authors have spent a great deal of effort over the past several years investigating the conceptual notions of fractions held by students and developing materials to build adequate understandings. The purpose of this paper is to outline, in general, the results of the investigations and to describe a method of approach that holds considerable promise.
BASIC Programming for Gifted Elementary Students
Authors: Wiebe James H.
Published: October 2020

The content wof this article is the result of a class taught through a summer program run by the Tempe (Arizona) Parents Gifted Association (TPG). During the summer of 1979, gifted students from the Tempe Elementary School District and other interested students from the fifth through eighth grades were allowed to enroll in a variety of classes. One option was a course in BASIC programming. Instruction in the class was based on the book BASIC for Beginners (Bitter and Gateley 1978).
A Money Center
Authors: Weir Merlene J.
Published: October 2020

The Money Center was originally planned for a third-grade class with low to average abilities. The students had been introduced to coins and their values in this order: penny, nickel, dime, quarter, half dollar, one dollar, and five dollars. They had been counting money and identifying equivalent coin values in class exercises. They had also been taught the concept of regrouping in both addition and subtraction, but these skills all needed to be reinforced.
Ideas
Authors: Tabler M. Bernadine , Jacobson Marilyn Hall
Published: October 2020

The IDEAS this month focuses on finding two-dimensional geometric shapes in designs and three-dimensional objects. The ability to isolate some elements from the total environment is an essential process for every phase of mathematical learning. These activities also encourage looking for geometric shapes in everyday surroundings.
Number Walks
Authors: Shaw Jean M. , Cliatt Mary Jo Puckett
Published: October 2020

Children require a great deal of reinforcement for each new mathematics concept they encounter. One exposure is insufficient to ensure mastery. Children need opportunities to encounter a new idea in many different ways until they become facile and confident with its use.
Motivational Activities in Elementary Mathematics
Authors: Geralda Schaefer Sister M.
Published: October 2020

Unquestionably, the key to success in learning elementary mathematics is through meaningful experiences and practical applications. The skills of computation, however, need to be nurtured by a variety of systematic practice and drill, which build accuracy, efficiency, and retention. An abundance of mathematical games is available commercially and games are relatively easy to devise by the classroom teacher. The use of other forms of practice has also been found to be advantageous.
Ideas
Authors: Tabler M. Bernadine , Jacobson Marilyn Hall
Published: October 2020

Ideas this month focuses on computers, how they are used and some aspects of how they work. The more ubiquitous computers become, the more important it is that citizens understand the computer's possibilities and its limitations. Knowing something about how computers operate can help to increase this understanding. A discussion of the uses of computers and occupations that use computers would be a good way to introduce any of the IDEAS.
What Makes a Triangle?
Authors: Damarin Suzanne K.
Published: October 2020

The triangle is one of the basic shapes to which children are exposed quite early in the curriculum, and often even before they enter school. However, although children learn the word “triangle” and some of the properties of triangles in kindergarten or first grade, their concepts of a triangle often remain very meager throughout the elementary grades.
Miscellany: Mathematical Competency for Indiana Elementary Teachers circa 1920
Authors: Jamski William D.
Published: October 2020

Try visualizing yourself in the following situation. It is a cold March Saturday morning in Indiana. The year is 1923.
Miscellany: Mr. Manning's Money
Authors: Writt Elinor J.
Published: October 2020

Here is a little problem that clearly demonstrates how the use of a calculator, although performing an amount of computation formidable if done “by hand,” does not obviate the need for careful analysis of a problem and precise mathematical reasoning for its solution. This problem was written several years ago by Jack Thornton who was at the time in the seventh grade at Brunswick Junior High School in Brunswick, Maine.
Miscellany: Working Backwards to Achieve Understanding
Authors: Miller Goeffery
Published: October 2020

Recently, while sorting through my file cabinet to make room for a new set of folders, I came across an article I had clipped and saved for future reference. The article, “Check Your Calculator Computations,” by Charles D. Friesen appeared in the December 1976 issue of the Arithmetic Teacher.
A Million! How Much Is That?
Authors: Burnett Peg Hampton
Published: October 2020

The population of the United Sates is approximately 230 million! I've got a million things to do today! But what is a million? In talking with eighth-grade students and other individuals of all age ranges, I discovered how loosely and freely we attach numbers to our expressions. I became intrigued with the idea of “one million.”
One Point of View: A Sign of Strength: Admitting a Weakness
Authors: Rubillo James M.
Published: October 2020

As we enter the 1980s the news media is bombarding the public with stories of incredible advances in computer technology. The home entertainment market has been revolutionized by “computer” games. Horror stories about computer mistakes make front page news. The use of the computer in transmitting photographs of Saturn left the public with a feeling of awe. As a result of this mixture of fact and fiction about computers, the public has developed an ambivalence toward the devices. On one hand, they see the growing use of computers in their daily lives as threatening. On the other hand, the public believes that the computer is a marvelous tool that should be integrated into the educational programs of their children.
Mathematical Concepts for Very Young Children
Authors: Hollis Loye Y. “Mickey”
Published: October 2020

During the 1970s interest in the mathematical abilities of young children increased. This resulted partly from a proliferation in kindergartens, which became an integral part of existing programs in schools. More very young children entered school causing the number of nursery schools and day-care centers to increase. This resulted in a larger financial investment and an increased public interest in preschool curricula. One aspect of this interest was concern about the mathematics that can be learned by young children and how it should be taught.
Let's Do It: Some Aids for Teaching Place Value
Authors: O'Neil David R. , Jensen Rosalie S.
Published: October 2020

Understanding our numeration system and the paper-and-pe ncil algorithms for the four fundamental operations requires that students have a mastery of the concept of place value. This month we suggest a variety of teaching techniques and materials that wiU help assure students' knowledge of this vitally important concept.
Money—A Key to Mathematical Success
Authors: Sullivan Karen Werley
Published: October 2020

In a poll reported several years ago on the Phil Donahue Show, children rated money as the most important item on a list that included peers, school, and family. Children are fascinated with money from a very early age, so why not capitalize on this prevailing interest in money by using money to teach other topics such as fractions, percents, decimals, and non-decimal numeration.
High Finance at Trilby School
Authors: Swartz Karen
Published: October 2020

“Dad, I've outgrown my football cleats again this year and here is a pair that costs only $15.99. If you don't have the money with you, you can write a check or charge it.” This statement is typical of a child's attitude toward money. How many children of today, who will be the consumers of tomorrow, are thoughtfully educated in the use and management of money? By presenting real-life situations to our students, we helped them in gaining a practical understanding of banking and money management. They also enjoyed the experience.
Readers' Dialogue
Authors: Kim Maeve , Gilbert Carolyn B. , Scott Wayne R.
Published: October 2020

We welcome letters from readers and will publish them to the best of our ability. within the time and space constraints necessarily placed upon us. Some letter, too, include ideas that will be interesting to readers even though the readers do not have immediale access to the articles concerned.
Subtraction Facts with Pattern Explorations
Authors: Beard Earl M. L. , Richard Polis A.
Published: October 2020

The ideas in this article are designed for elementary and junior high school children, yet they are flexible enough to offer some challenge for high school students, particularly in an algebra class. The authors have tried these ideas with third and fourth graders by simply exploring patterns; with a group of gifted twelve year olds, the analysis and extension of patterns really caused some excitement. There are so many variations on this theme of pattern exploration that a creative teacher could design discovery sequences for almost any group of children and would find the result to be quite productive.
An Inductive Approach to Prime Factors
Authors: Hohlfeld Joe
Published: October 2020

An inductive approach offers an alternative sequence for the teaching of prime numbers and prime factors. The sequence can be used either as an introduction to prime numbers and prime factors or, in later years, when ideas about prime numbers and factors are needed and must be reviewed or retaught.
Some Thoughts for Teachers on Mathematics Anxiety
Authors: Brush Lorelei R.
Published: October 2020

My purpose in this article is to look at what research has to say to teachers about the development of mathematics anxiety and avoidance, looking specifically at opportunities for teachers to reduce anxiety and encourage more students to continue their study of mathematics beyond the minimal requirements in high school. The research in this instance is a look at students' responses on instruments that are used to measure mathematics anxiety. One of the best of these tests is the Mathematics Anxiety Rating Scale (MARS) constructed by Frank Richardson and Richard Suinn (available through the Rocky Mountain Behavioral Sciences Institute, Fort Collins, Colorado.)
One Point of View: “I Love to Teach” A Formula for Coping with Burn-out
Authors: Sobel Max A.
Published: October 2020

The decade of the 1980s is being called the decade of change. As a teacher of mathematics, I find it almost frightening to contemplate all that is demanded of us. The NCTM publication An Agenda for Action indicates that we are to become experts at teaching our students problemsolving skills, while at the same time developing their abi lities in a wide range of basics that go far beyond computation. Furthermore, we need to incorporate calculator and computer skills into the curriculum and then evaluate the success of our programs “by a wider range of measures than conventional testing.”
Let's Do It: Classical Problems for all Ages
Authors: Jensen Rosalie , O'Neil David R.
Published: October 2020

Most children in the later primary grades and throughout the middle grades are functioning at the stage of concrete operations. When they are faced with genuine problem-solving situations they need concrete and pictorial aids, as well as guidance from adults in organizing information and choosing strategies.
Problem Solving for the Primary Grades
Authors: Bruni James V.
Published: October 2020

“How can my children possibly be expected to do problem solving when they are only beginning to learn to read and to do basic arithmetic computation?” This is often the lament of primary-school teachers when urged to include problem solving in their mathematics programs. Developing problem-solving skills is often equated with training children to solve arithmetic word problems, but problem olving has a much broader meaning. It is not only possible for young children to become problem solvers but also, primary mathematics instruction can be organized to help develop problem-solving skills.
Problem Solving: Help in the Right Direction for LD Students
Authors: Thornton Carol A. , Bley Nancy S.
Published: October 2020

Until recently problem solving was stressed primarily in the middle and upper elementary grades. The focus in the lower grades was on memorizing basic facts and developing specific computational skills. When children reached the middle elementary grades it was often assumed that because they could compute they also would know when to apply the different operations in problem-solving contexts. Unfortunately this is not always the case. Problem solving involves more than incorporating computational skills. It primarily requires a great deal of decision making.
One Point of View: Teaching Effectively and Efficiently
Authors: Glenadine Gibb E.
Published: October 2020

The key to any efforts toward more emphasis on problem solving, expansion of the concept of what constitute basic skills, optimization of the use of calculators and computer in mathematics programs, increased flexibility in school programs, and a wider variety of ways to evaluate students' learning of mathematics is the teacher. As teachers we must not only understand the intent of these changes, but also translate them into learning experiences and changes in learning experiences for the children in our mathematics classes. Each of these characteristics in the teaching of mathematics encompasses effectiveness for what is learned and efficiency in the use of time for learning.
How a Resource Teacher can use the Arithmetic Teacher
Authors: Gilfoil Anne
Published: October 2020

Teachers at the elementary level are often overwhelmed by the diversity of subject matter they are expected to teach. Dedicated to maintaining continued professional growth, they frequently find it difficult to keep abreast of research and new developments in instruction and learning affecting all areas of the curriculum. The increased availability of materials is evidenced by the large number of professional journals and periodicals displayed in teachers' lounges and resource rooms in the elementary schools.
More Popsicle-Stick Multiplication
Authors: Dunkels Andrejs
Published: October 2020

After reading the article, “Fractions and Popsicle Sticks,” by Carlisle (Arithmetic Teacher, February 1980), I decided to tell my students about the idea. I did not have an adequate supply of Popsicle sticks, but I was able to purchase some tongue depressors at a drug store. I painted some of the tongue depressors red (any color would do).
Sticks and Stones
Authors: Lappan Glenda , Winter Mary Jean
Published: October 2020

Measurement has traditionally been a difficult topic for children to master. We believe that one of the major reasons for this difficulty has been the lack in the elementary grades of concrete experiences in attaching numbers to objects that “measure” those objects in some way. “Sticks and stones” are very effective, inexpensive materials to use when teaching students to subdivide measurement instruments for greater precision. We have used lengths of flat screen molding and a large supply of ceramic tiles to develop the concepts of linear and area measurement.
Teaching Time-Telling
Authors: Nelson Glenn
Published: October 2020

Rarely does anyone go through a day without making reference to time. Adults and children make time allotments for the day's tasks and use a clock or watch to measure such allotments. However, although nearly all children do eventually Jearn something about telling time and reading a clock, there is usually dissatisfaction about the effectiveness with which this topic can be taught. Reisman (1972) has noted this concern and has done much investigation of it.
Games for Mathematics Skill Practice
Authors: Ludeman Clinton , Sevier Bonnie
Published: October 2020

Mathematics games patterned after commercial games played on game boards have enjoyed great successes among elementary children in mathematics classrooms. The two games described here are examples of popular children's and adult's games that have been adapted from the original commercial games to fit the objectives of classroom instruction. These games have been played in Sevier's fourthgrade classes.
Bizz-Buzz Game in Arithmetic
Authors: Janicki George
Published: October 2020

The following game can be played in a class of the 5th, 6th, or 7th grade to test their knowledge of the multiplication tables.
A Modest Proposal: To the Teachers of Developmental Arithmetic for Solving the Many Problems that Beset Their Subject
Authors: Manheimer Wallace
Published: October 2020

IT IS A MELANCHOLY PROSPECT that the teaching of developmental ariithmetic presents to us. Educators could afford to scoff at the attacks upon the program by the least cultured elements of our country. However, insidious doubts spread fast in troubled times; and now even our children are starting to reflect the subtle poison.
Evaluation by Observation–Grade 3
Authors: Thomson Alice P.
Published: October 2020

At the end of grade three, it is possible to evaluate the pupil's knowledge of number facts and processes and of some understandings through written tests. However, there are some mathematical understandings that are better evaluated through observation. While children are engaging in their daily work and experiences you will find many opport unities for observation.
Enlarging Number Systems
Authors: Brumfiel Charles
Published: October 2020

Whenever we enlarge a number system S we employ one of two methods. Each method has the same ultimate aim. The difference lies wholly in the paths we follow to obtain our heart's desire. In each case we end up with a system R which contains the system S, symbolically
Arithmetic in New Zealand
Authors: Duncan E. R.
Published: October 2020

To understand new zealand Arithmetic Programme it is first necessary to recall certain things about New Zealand. It is necessary to remember, for instance, that it is a small country with a population about a quarter that of the city of New York, spread over two islands whose combined length is a litt le over 1000 miles and whose average width is about 100 miles. It is necessary also to remember that it is a young country, strongly conscious of its historic links with Great Britain.
A Teacher Plans Her Day
Authors: Albrecht Mary E. , Dunn Elva
Published: October 2020

I Consider it a pleasure and an honor to talk to a group of prospective and beginning teachers. Most of my time is spent in working with teachers who have taught less than five years. You have chosen a profession that not only gives you a great personal satisfaction and a livelihood but it also offers you the opportunity to work with all kinds of people, to develop leadership, to develop ideals, to stimulate ambitions, and best of all, to mold the character of our future citizens.
Arithmetic at the School Camp
Authors: Davis O. L.
Published: October 2020

Educators have long accepted as valid the principle that people learn best those things which they live. As teachers have tried to implement this basic belief, they have used various kinds of excursions, audio-visual aids, manipulative devices, and demonstrations in order that pupils may understand better what they are studying. In recent years, many schools have become more outdoorsminded and have taken classes to a school camp for varying periods of time. This school camping movement seems to be growing and many feel it serves an important function in making the world more real to the child who attends. By broadening and enriching his experiential background, the school camp provides many necessary situations out of which the pupil develops adequate meanings for himself.
Arithmetic via Television: Demonstration Lessons at Springfield
Authors: Glazier R. C.
Published: October 2020

Last spring the public schools of Springfield, Missouri presented two demonstration lessons in arithmetic. One of these was conducted by Mrs. Naomi Hall with her first graders at Sunshine School and the other by Mrs. Thelma Smith with a sixth grade from the same school.
The Ten-Tens Counting Frame
Authors: Smith Rolland R.
Published: October 2020

IN THE NOVEMBER 1955 issue of the ARITHMETIC TEACHER there appeared and article entitled The Abacus as an Arithmetic Teaching Device. It dealt mainly with computation. This article does not compete with it for this has to do with the abacus (we call it a Ten-Tens Counting Frame) not as an instrument for computation but as a means of developing an understanding of our number system.
Decimal Versus Common Fractions
Authors: Johnson J. T.
Published: October 2020

COMMON FRACTIONS were being used in Egypt at about 1600 B. C. and Decimal fractions were invented about 1600 A. D. Thus the common fraction has had a 30,000 year handicap over the decimal by virtue of its priority in time. This handicap has been so strong that its influence is still in force as evidenced by the fact that the common fraction is taught before the decimal despite the evidence that decimals are easier to learn and to use.
More About Casting Out Nines
Authors: Moore Tabbie Mae
Published: October 2020

CONSIDERING THE RECENT INTEREST in proof by nines, one might conclude this is a mid-twentieth century discovery. Probably we can concede it is a rediscovery. In University Arithmetic by Charles Davies, LL.D., A. S. Barnes & Co., New York, 1868, the process is explained and is used throughout the book. In Advanced Arithmetic, Teachers Edit ion, G. A. Wentworth, Ginn & Co., Boston, 1898, the check by nines is called for and no explanation given, indicating it was expected to be part of a teacher's store of arithmetic knowledge.
Arithmetic Football
Authors: Karau Earl A.
Published: October 2020

ARITHMETIC FOOTBALL is a game of mental arithmetic. It is played without the aid of pencil or paper. A football field made of roll paper or oilcloth is laid out as shown in the drawing. It is 120 inches long and 36 inches wide. The line markers are ten inches apart for easy layout of the field.
Report of the Membership Committee: National Council of Teachers of Mathematics
Authors: Rogers Mary C.
Published: October 2020

The Membership Committee of the National Council of Teachers of Mathematics is pleased to report to you the results of the 1954–1956 Membership Campaign, and to thank you for your fine support and direct helpfulness in bringing about the generous increase in membership which was accomplished. It was this assistance on the part of each of you as individuals which has largely made this accomplishment possible. We are indeed grateful to you for your enthusiastic cooperation.
The Work of the National Council
Authors: Fehr Howard F.
Published: October 2020

THE NATIONAL COUNCIL of Teachers of Mathematics is deeply concerned with and interested in the teaching of arithmetic. It recognized that arithmetic is the basis of all succeeding study of mathematics. The Council has made sure that problems on teaching arithmetic will be given adequate attention by including on its Board of Directors a vice president at the elementary school level. Usually several other members of the Board of Directors are also directly involved in the improvement of instruction in arithmetic. There now exists a definite program of service to the instruction in elementary school mathematics. This program consists of three major areas, namely, publications, meetings, and committees.
One Point of View: Step-by-Step: What Are You Doing This Year?
Authors: Lindquist Mary Montgomery
Published: October 2020

Previous editorials on An Agenda for Action* have expressed many different points of view, but two themes were common: change in schools is a process that occurs step-by-step over time, and the teacher is a crucial ingredient in this change. We are now one-fourth of the way through the 1980s and beginning a new school year, so it is appropriate to ask yourself what you are going to do in this step-by-step process of change?
Readers' Dialogue
Authors: Trangmoe John , Beimler Gerald G. , Owens Caroline , Gatzke Alan , LaFrance Jacques , Stern Phyllis E. , Mills George W.
Published: October 2020

The currency of letters to the editor of a journal like the Arithmetic Teacher is always a problem. At the very best. four months will have elapsed between the time when an article is published and che time when a letter commencing on that art ide can appear in the journal. Sometimes the minimum time is even greater. For example, leiters about an article that appears in a January issue will almost never appear before che following fall. The publication schedule alone dictates s uch a spread of time, and other factors can intervene to further delay publication of a letter
Let's Do It: Collecting and Displaying the Data Around Us
Authors: Horak Virginia M. , Horak Willis J.
Published: October 2020

Young children are interested in answering questions about themselves and their surroundings—What colors of eyes do the children in our class have? How many in the class are left-handed? How many of our class were born in the spring, summer, fall and winter? Questions like these can be answered by constructing charts and graphs to present the information.
Readers' Dialogue
Authors: Mitchell Charles E. , Folk Mike , Robitaille David , Palmer Jacquelyn , Kunz Michael W.
Published: October 2020

The currency of letters to the editor of journal like the Arithmetic Teacher is always a problem At the very best, four months will have elapsed between the time when an article is published and the time when a letter commenting on that article can appear in the journal. Sometimes the minimum time is even greater. For example, letter about an article that appers in a January issue will almost never appears before the following fall. The publication schedule alone dictates such a spread of time. and other factors can intervene to further delay publication of a letter.
Developing Problem-Solving Ability with Multiple-Condition Problems
Authors: Greenes Carole E. , Schulman Linda
Published: October 2020

Results of the Priorities in School Mathematics (PRISM) survey and recent curricular recommendations by the National Council of Teachers of Mathematics indicate that problem solving should be the focus of mathematics education in this decade. Mathematics programs should be designed to teach students how to apply known skills to the solution of a variety of types of problems. This instruction in problem solving should begin early in a student's educational program.
What Do You Do with the New Computer?
Authors: Cooper Richard P.
Published: October 2020

Congratulations! Your school now has a microcomputer. It looks imposing as it awaits someone to turn it on and unleash its power.
Number Patterns and Bases
Authors: Peera Zehra
Published: October 2020

The well-known nurnber pattern in the nine-times taple in base ten is not peculiar to number nine. Multiplication by the highest single-digit number in any base, lower or higher than ten, will produce a similar order. The point is illustrated by the two tables, figures 1 and 2, in the nondecimal modern systems of numeration, one in base five and the other in base twelve.
Expanded Division
Authors: Patrick Sarah E.
Published: October 2020

ln a discussion on the developmental division algorithms with a class of prospective elementary school teachers, the following question arose: How do you justify the steps of the traditional division algorithm particularly bringing down a number, when presenting the algorithm to students?
Mind Sets in Elementary School Mathematics
Authors: Allinger Glenn D.
Published: October 2020

Delores panics when she doesn't find her bike parked in the rack but then remembers she walked to school that morning. Todd continues to leave the school building through the front door, even though his new classroom is located adjacent to another exit.
Learning Difficulties: Helping Young Children with Mathematics—Subtraction
Authors: Liedtke Werner
Published: October 2020

Most teachers in the primary grades, when they are asked to do so, have no problem identifying several chiidren in their classroom who are having some difficulties in learning mathematics. How can these children be helped? Before this question can be answered, and before any specific suggestions for remediation can be made, information about each child's strengths and weaknesses must be gathered.
Drama + Mathematics = Dramathics
Authors: Nave Tim
Published: October 2020

During my undergraduate days at Illinois State University I dreamed that I would some day be a language arts teacher in an elementary school. I pictured myself as having somewhat of a flair for the dramatic and I could expres myself in a variety of ways. Besides that, I was lousy in mathematics and hated science and social studies.
Ladies and Gentlemen, Start Your Engines
Authors: Cates Ward Mitchell
Published: October 2020

In teaching time/rate/distance problems to various less-than-enthusiastic students, I became aware of how mechanical was the approach they used to try to solve even simple problems. My students considered them not as in the context of real life, but as if they were complicated paper problems subject to lucky guesses and mechanistic solution.
A Psychologically Sound Primary School Mathematics Curriculum
Authors: Hendrickson A. Dean
Published: October 2020

What we know of how children learn has not been applied to the curriculum, with only a few exceptions. Children are given little time to think and to create their own ways. The need to “get inside the child's head,” to understand the kind of thinking done by the child, and to recognize that the child constructs knowledge, rather than accepting it as someone else's construction, must be satisfied before teaching can be useful to the child.
Fun with Geometry
Authors: Welch Ronald C. , Harvin Virginia R.
Published: October 2020

It was the middle of June and summer school for children in the Metropolitan School District had begun. Children who attended summer school were not remedial cases. The theme of the school was “enrichment in the basics.” Attendance was voluntary.
The Microcomputer in the Instructional Program
Authors: Hill Shirley A.
Published: October 2020

If you are a teacher, there is a microcomputer in your future. Perhaps you are one of the rapidly growing band of educators who have access to these remarkable. self-contained units and have integrated them into your instructional program. lf not, prepare to do so because even a conservative prediction is that they are destined to have a significant influence on instruction during this decade and a revolutionary impact by the last decade of this century.
Coping with the Challenge of Change
Authors: Caravella Joseph R.
Published: October 2020

Microcomputers, in school and at home, will be widely used as instructional aids, computation devices, and for telecommunication terminals to access database networks before the students in elementary school today graduate from high school. Whether you are a user or a soon-to-be user of microcomputers or other contemporary technology, consider the fo llowing resources and suggestions to establish your own system for coping with the challenge of change.
Put Some Probability in Your Classroom
Authors: Burns Marilyn
Published: October 2020

There is a weekly section in the sunday punch section of the san francisco chronicle called “the grab bag.” it's a collection of short ditties, usually of from three to ten lines each, compiled by L. M. Boyd. I like the section.
The Graph Examined
Authors: Slaughter Judith Pollard
Published: October 2020

Our modern technological age produces vast amounts of information. Facets of our culture—sports' scores, financial transactions, weather statistics, and economic conditions-—have features that are countable or measurable in some way. Graphs have become a means for organizing, displaying, and comparing this information.
In Search of Computational Errors
Authors: Shaw Robert A. , Pelosi Philip A.
Published: October 2020

One of the areas of mathematical skills defined a basic by the National Council of Supervisors of Mathematics (1977) is “appropriate computational skills.” The determination of a learner's computational strengths and weaknesses involves a search for the errors that the learner make and, subsequently, the development of learning experience that will e liminate the error (West 1971).
TEACHING: Making Middle School Mathematics Exciting
Authors: Brombacher Bruce
Published: October 2020

Each year, as teachers, we try to enhance and improve our effectiveness in the classroom. Many times the topics selected for discussion are determined by a textbook, by a district's K-12 curriculum guide, or by some set of minimum competencies. These are important considerations as we evaluate the current year and plan for the next year. But the interests of each child should really determine the instructional curriculum for students in the class. Meaningful instruction and learning take place when specific goals are relevant to the individual learner.
Put Your Students in the Picture for Better Problem Solving
Authors: Jones Billie M.
Published: October 2020

Teachers always are on the lookout for some way to use the natural interests of students in teaching them the basic skills they need to know. Most students—both girls and boys—love to read about, to hear about, and to discuss feats that set new world records. Commercial materials that make use of some of these records are on the market, but you may want to focus on certain types of lessons that the commercial material does not cover. One of the best uses of information about record-setting events is to combine reading and arithmetic skills in ways that will extend the students' understanding of solving word problems in arithmetic. Removing some of the mystery from word problems by helping students to create and solve their own word problems that use reports of world records in various areas of sports and in other fields is one good way of providing instruction and practice in solving word problems. Take a record and present it in an attractive format similar to the one that follows.
Another Use for Geoboards
Authors: Nelson Rebecca S. , Whitaker Donald R.
Published: October 2020

Geoboards, popular since the late 1960s, have been used frequently as a manipulative aid to teach geometric shapes, area, and perimeter; and to provide concrete visualization for irrational numbers such as and . An interesting fact is that the geoboard, together with a set of materials called “geo-islands,” can also be used to teach naming fract ions, equivalent fractions, and all four operations with fractions, as welJ as mixed and decimal notation. Unike many other models for fractions, the geoboard and geo-islands provide an area model that is both consistent and complete for the sequential development of all rational-number concepts.
One Point of View: Setting Our Sights High
Authors: Grouws Douglas A.
Published: October 2020

The way mathematics instruction accommodates the large technological changes sweeping society will profoundly affect the ability of young people to adjust to everyday life situations and perform efficiently in the skilled professions of the future. In particular, continued thoughtful attention must be given to the role of microcomputers in all aspects of the teaching of mathematics. Many significant issues in this area will need to be discussed and important decisions made in the months ahead. We need to set high expectations in these discussions and the decisions that follow from them. Settling for what can be done easily or selling short the talents of our students or our colleagues will be a mistake.
The Mathematically Talented Student Revisited
Authors: Vance James H.
Published: October 2020

Interest in the talented and gifted pupils in our schools has renewed recently. The need to challenge these young people academically and to give them opportunities to discover and develop their potential in various subject areas is receiving increased attention from both educators and the public.
Ideas
Authors: Fennell Francis (Skip) , Houser Larry L. , McPartland Donna , Parker Sandra
Published: October 2020

Ideas for this month focuses on the topic of whole-number numerati on using various resource materials. Teachers and media specialists who develop the use of newspapers, tables of contents, indexes, and almanacs will find these activities helpful for teaching writing, estimation, and the use of numbers.
Picking Apples
Authors: Lawhorn Lisa Anne
Published: October 2020

Picking apples is an enjoyable way to teach the concept of place value to young children. Make apples, pails, baskets, and apple trees using felt or construction paper and tape.
Graphs Can Motivate Children to Master Basic Facts
Authors: Miller Goeffery
Published: October 2020

For several years I stuck adamantly to the principle that competition in the classroom was a potentially damaging technique. Consequently, among other activitie, we flashed cards, played Quizmo and pinner games, listened to record, watched slides. set up and drilled on board exercises. and did timed fact sheets. The regular pats on the back and “atta boys” were also included. (All these techniques are till used.) The results were not as satisfactory aa I felt they should be. Some children continued to lag behind their expected achievement level in their acquisition of the multiplication and division facts.
Improving Verbal Problem-solving Performance
Authors: Wright Jone Perryman , Stevens Nancy Kight
Published: October 2020

Learning to solve problems is the principal reason for learning mathematics (Brodin ky 1977). Yet, the results of the National Assessment of Educa tional Progress (NAEP) released from 1972-78 indicate that one of the maj or weaknesse in mathematic achievement is problem solving (Carpenter et al. 1978; N AEP 1979). What are the difficultie with children's problem-solving performance? The NAEP results sugget that lack of computational skills was not considered to be a major factor in the weakness in problem-solving performance. Davidson (1977) believes that children cannot solve problem because they do not comprehend them. Some author have pointed out that difficulties in reading stem from the questions and the comparative language used in verbally stated mathematic problems (Hargis 1975; Knight and Hargis 1977; Zweng 1979).