bluuebunny/crossref_metadata_2025 huggingface dataset:
A Mathematical Finger Exercise
Authors: Kent David
Published: October 2020

Finger counting or finger reckoning is an ancient practice. Almost any history of mathematics will include references to humans' use of their fingers in calculations and some histories will also include descriptions of systematic finger reckoning. Society now has more efficient ways of making calculations so finger reckoning is no longer a basic or familiar skill, but it does have interesting mathematical implications. And children may enjoy and benefit from experiences with finger exercises like the ones described here.
Your “Ace in the Hole” for Teaching Mathematics
Authors: Greenberg Joanne Cecelia
Published: October 2020

Almost every child has access to a deck of playing cards. Even children who might be labeled “slow” can amuse themselves for hours with a simple deck of cards. Furthermore, children seem to have no difficulty learning card-game rules from one an other. Seeing children enjoying a game of Fish or War is a familiar sight; seeing children using playing cards in a mathematics class is not so common. Regular playing cards can be used, however, to reinforce and even teach some mathematics skills.
Sexual Stereotyping in Mathematics: Beyond Text books
Authors: Reyes Laurie Hart
Published: October 2020

The May 1977 issue of the Arithmetic Teacher included three articles that discussed some of the issues involved in the problem of sex-role stereotyping and mathematics learning. Fennema and Sherman reviewed and analyzed the sex-related differences in mathematics learning and studying that have been found in research. They hypothesized that many females elect not to take mathematics in high school and college because mathematics is perceived as a male area of study and therefore inappropriate for females. The other two articles—one by Kepner and Koehn, the other by Kuhnke—examined the extent of sex-role stereotyping in elementary mathematics textbooks. In the latter two articles there was a sense that (a) things are changing on their own so we have nothing more to do and (b) once sex-role stereotyping is removed from elementary mathematics texts we will have provided equity for females in the study of mathematics.
Calculators in Elementary Schools
Authors: Wheatley Grayson H. , Shumway Richard J. , Coburn Terrence G. , Reys Robert E. , Schoen Harold L. , Wheatley Charlotte L. , White Arthur L.
Published: October 2020

With the widespread availability of inexpensive calculators, educators and parents have expressed concern over the effects of calculator use on basic mathematics skills. They want to know the impact calculators will have on learning before they sanction the use of calculators in the classroom. On the other hand, proponents of calculators in schools cite increased motivation and better understanding as potential benefits of calculator use.
Teaching Base Three? In a Pig's Ear!
Authors: Hardin Daniel D.
Published: October 2020

Teachers in the middle school grades often introduce the study of numeration systems different from base ten. Counting in different bases and writing numbers in different numeration systems are experiences that can strengthen students' understanding of the principles of the base ten positional system.
“Do You See What I Hear?” A Look at Individual Learning Styles
Authors: Speer William R.
Published: October 2020

The notion that students learn in uniquely individual ways has long been recognized by classroom teachers. Each child brings to each learning situation certain content and attitudinal predilections which, when mixed with individual “information processing tilasters,” paint a picture of the child's individual learning style. This style, in deturn, is reflected in stated preferences and observed behaviors. The results of observing and analyzing individual learning styles can be of considerable help in planning for and implementing instruction.
Test Failure and Mathematics Failure There is a Difference
Authors: Gregory John W.
Published: October 2020

A research study is central to this article, but what follows is not intended to be a formal research report. The results of this particular investigation are in themselves interesting, but it is equally important for classroom teachers to realize that in their daily work with children they, too, may come upon researchable questions. Once such a question has been identified, assistance in carrying out an investigation, if teachers want it, is usually as close as the nearest university. All of us, classroom teachers and teacher educators, need to become more involved in the kind of research that may lead to more favorable practices in mathematics education.
Readers' Dialogue
Authors: Trotter Terrel , Gross Lawrence P. , Averbuch Mindy , Longston Lisa , Flora Sharla
Published: October 2020

I can “second the motion” that the motivational effect of palindromes, as described by Nichol io “Addition through Palindromes” in the December 1978 issue is indeed great. And the instructional spio-offs not touched upon by the author provide many opportunjties for further learning.
Let's Do It: Without Pencil and Paper
Authors: Nelson Glenn , Leutzinger Larry P.
Published: October 2020

The circumstances of our daily lives are often such that we are forced to perform arithmetic calculations mentally. At a grocery store, on a trip, in a hardware store—there are many occasions on which we need to be able to calculate exact or approximate answers in our heads. Thus, the ability to do mental arithmetic is a very useful skill.
A Look at the Past
Authors: Brown Sue Dreiling , Brown Donald E.
Published: October 2020

A look at old mathematics textbooks used in the United States provides not only interesting insights into earlier historical periods, but also a different, and sometimes amusing, perspective on current practices. The earliest textbooks used in the American colonies were written and printed in Europe. Later, the works of these European authors were printed in the United States, so the European influence on the education of young Americans lasted a long time. By the 1790s, there were local authors.
A “Friend” in Need
Authors: Warburton Jacqueline W.
Published: October 2020

Each year in my mathematics classes, when we came to the section on perimeters of plane figu res, I fou nd misunderstandings. Although most of my students had been introduced to the concept of perimeter, many of them had misconceptions about it. The most common confusion seemed to come from the fact that they had been well drilled in finding area and by habit, especially in the case of quadrilaterals, automatically wanted to multiply length by width. The second most common error may also have stemmed from a confusion with area. In this case they would add one length to one width, thereby producing a semi-perimeter or in cases of figures with many sides, a very short pan of the distance a round the figure. The third error was the mislabeling of the units in the answers as square units or cubic units, or of not labeling them at all.
ADAM Comes to Nueva
Authors: Laycock Mary
Published: October 2020

Adam is a “first of its kind” computer with a language of English words out of which children can “teach” ADAM to do their bidding with a minimum of instruction. The Nueva Learning Center was host to ADAM for two months. ADAM's inventor, John Peers, arranged the loan and visited Nueva to talk with the fifth- and sixth-grade children about things of the future and the unbelievable role of computers of the fu ture in their lives. With the help of one of the instructors from ADAM's home base, the children were able to master the basic capabilities of the machine.
Is It Necessary to Invert?
Authors: Feinberg Miriam M.
Published: October 2020

Dividing fractions seems to be one of the most common areas of difficulty for students. Once having been taught to invert and multiply, many students start inverting in performing other operations with fractions.
ONE POINT OF VIEW: Girls Need Mathematics, Too
Authors: Skypek Dora Helen
Published: October 2020

Sex-related inequities in mathematics education have been documented in many contexts. Less than one-third of the females among the freshman classes at our major universities have the prerequisites in high school mathematics to qualify for the range of undergraduate majors offered. The options for males are much wider. Two thirds of them have completed the minimum number of high school mathematics courses (including trigonometry) prerequisite to admission to any program.
CSMP: A New Alternative in Elementary School Mathematics
Authors: Woodward Ernest
Published: October 2020

The Comprehensive School Mathematics Program (CSMP) is in the eighth year of the pilot study of its elementary school mathematics program. For the first two years, only elementary schools in the area of Carbondale, Illinois, were involved. In the extended pilot study, approximately 170 schools in eighteen states and the District of Columbia, with over one thousand teachers and over thirty thousand elementary school students have participated. For the extended pilot schools, sequential materials are available for grades kindergarten through four. Sequential materials for grades five and six were planned for use in the falls of 1978 and of 1979, respectively. Thirdand fourth-grade entry programs also have been completed for students who have not previously studied from CSMP. CSMP is asking teachers to evaluate its program and is revising as a result of teacher feedback. The final version of the kindergarten materials was completed in the fa ll of 1976. Completion of the final version of the first-grade materials was scheduled for the 1978 79 school year, with the materials for other grades to be completed one grade at a time on an annual basis.
Rolling for Meters
Authors: Skinker Judith A.
Published: October 2020

Fourth graders generally have little difficulty remembering how many millimeters are equivalent to one centimeter, how many centimeters are equivalent to one decimeter, and how many decimeters are equivalent to one meter. For those who need help, however, and to reinforce these relationships for others, “Rolling for Meters” bas been a real success in our class.
Fractions and Popsicle Sticks
Authors: Carlisle Earnest
Published: October 2020

That inexpensive and abundant aid, the Popsicle stick, can provide an excellent “concrete” model for multiplication and division of fractions. To effectively use the sticks in modeling fractions, we need to dye one set of sticks so we have sticks of two different colors.
ONE POINT OF VIEW: Aren't We Doing Something Right?
Authors: Wilson James W.
Published: October 2020

There is plenty wrong with our mathematics programs and our mathematics teaching. I do not wish to deny this fact. But, I feel the more serious problem is that we mathematics teachers have come to seek out and emphasize the negative. There are several pitfalls in this attitude.
Ideas
Authors: Scheuer Donald W. , Williams David E.
Published: October 2020

Ideas for this month consists of two posters that can be used to provide experience in recognizing patterns in sequences of numbers. The posters have been made with blank spaces for the numbers to be written in. If the posters are laminated or covered with a clear plastic, they can be used over and over again with different sequences of numbers.
Let's Do It But It Can't Be Done
Authors: Leutzinger Larry P. , Nelson Glenn
Published: October 2020

Teachers in elementary classrooms throughout the country often hear students say, “I can't do it.” The statement does not imply that the problem or exercise being attempted has no solution but, rather, that the student does not have the skills necessary to complete it, or that the student has forgotten how to determine the answer.
Results and Implications of the Second NAEP Mathematics Assessments: Elementary School
Authors: Carpenter Thomas P. , Kepner Henry , Corbitt Mary Kay , Lindquist Mary Montgomery , Reys Robert E.
Published: October 2020

The National Assessment of Educational Progress (NAEP) has completed its second mathematics assessment. This article focuses on the results from this second assessment of 9-year-olds and 13-year-olds. A companion article in the May 1980 Mathematics Teacher examines the secondary school data.
Some Guidelines for Teaching Geometry Concepts
Authors: Charles Randall I.
Published: October 2020

The types of examples and nonexamples used for teaching a concept and the manner in which they are used influence the extent to which a student understands that concept. This is evident in the following two situations, which were selected from situations observed in elementary school classrooms.
Ideas
Authors: Scheuer Donald W. , Williams David E.
Published: October 2020

Ideas for this month deals with problem solving. Too often problem solving in the elementary grades is concerned only with getting a correct answer rather than with the process involved in reaching a solution. Analyzing information, identifying the question, and selecting pertinent facts are skills that need to be developed in the process of problem solving.
Metric Week Celebration All Year Long
Authors: Schussheim Joan Yares
Published: October 2020

In anticipation of the celebration of Metric Week 1980 (5–9 May), a collection of metric activities from a math lab is presented in this article. The activities were selected as being most suitable to grades two through six and easily adaptable to classroom mathematics.
Funny Letters: A Discrepant Event
Authors: Juraschek William , McGlathery Glenn
Published: October 2020

We would like to share with you an activity that is fun for youngsters and grown-ups alike. For maximum appreciation we ask that you first experience this “discrepant event” yourself.
Miscellany: Please, My Dear Aunt Sally
Authors: Shoemaker Richard W.
Published: October 2020

The purpose of this note is to repair a serious omission in many modern arithmetic and elementary mathematics teacher-training texts. I refer to the almost universal absence of mention of a rule defining the order of application of the fundamental operations of arithmetic. The young computer, expected as he or she is to get the correct answer, must know the rule.
Let's Do It: Paper Dot Plates Give Numbers Meaning
Authors: Thompson Charles S. , de Walle John Van
Published: October 2020

When children are learning early number concepts, teachers want them to learn a variety of subconcepts.
This is us! Great graphs for kids
Authors: Sullivan Delia , Ann O'Neil Mary
Published: October 2020

September has arrived, and before you is a list of the names of your new pupils. Once again you are faced with the tasks of quickly learning everyone's name, of helping the children become acquainted with one another, and of easing individuals into their roles as one among others. You are concerned with meeting the children individually, allowing them to be themselves and comfortable with their own self concepts. and yet helping each widen personal horizons as he or she adjusts to being a group member
One Step to Learning
Authors: Thornton Carol A. , Bazik Edna F. , Barnard Janet K.
Published: October 2020

Children with learning difficulties have a chance to feel successful when they are learning “one step” at a time. The ONE STEP idea helps children focus on small parts of problems, which, taken separately, they can handle.
One point of view: Effective Instruction and Productive Learning
Authors: Trafton Paul R.
Published: October 2020

The quality of mathematics instruction is a major influence on how much mathematics students learn, how well they learn it, and their ability to apply what is learned. Effective mathematics instruction, in other words, leads to productive learning. There are two sources of support for this statement. First, recent studies of teacher effectiveness identify a variety of factors that are related to effective mathematics instruction as measured in terms of student learning. These studies document the powerful influence of the characteristics of the teaching, rather than of the teacher, on the learning of the students. Second, studies of students' learning of specific content, such as place value or fractions, provide information on the kind of instruction and the sequencing of the instruction required for students to learn the content.
Frame Geometry: An Example in Posing and Solving Problems
Authors: Walter Marion
Published: October 2020

“Close your eyes and try to see your favorite picture. Then open them and draw it.” Children who do this will usually enclose their pictures in a rectangle or frame and often take great pride in the details of their drawings
Let's Do It: Concepts, Art, and Fun from Simple Tiling Patterns
Authors: de Walle John Van , Thompson Charles S.
Published: October 2020

A tiling pattern (or tessellation) is a repetitive pattern, something like a mosaic, using one or more geometric shapes. The tiles in a tiling pattern should fit together so there are no holes or gaps between them. They are placed in a repeated pattern so that once begun, a huge plane surface could be covered by simply repeating the pattern over and over.
Say It with Pictures
Authors: Ann Dirkes M.
Published: October 2020

Pictures and concrete objects serve to communicate mathematics in a way that words and symbols do not match. Some students claim that many concepts are understood only when they are illustrated through objects, diagrams, or pictures. A study of individual abilities suggests that these students might benefit most from drawings which they themselves produce.
The Monsters in Multiplication
Authors: Bolduc Elroy J.
Published: October 2020

The September 1978 issue of the Arithmetic Teacher included an interesting article on multiplication. The author, Vigilante, discussed several different ways to provide “access” to the basic multiplication facts. Along with using all of the devices and methods suggested by Vigilante, I would like to suggest a learning pattern for the multiplication facts. My pattern is not intended for an introduction to multiplication (though with some modification it may be useful), but rather for older students who should have learned the facts, but have not.
Ideas
Authors: Hall Jacobson Marilyn , Bernadine Tabler M.
Published: October 2020

The IDEAS for this month provide experiences with using the calendar as one does in daily life. The calendar experiences in the primary grades usually include learning the months and recognizing the date, but little attention is given to learning how to read the calendar. The following activities provide both calendar reading and problemsolving experiences.
Silence is Golden
Authors: Huff Sara C.
Published: October 2020

Have you ever tried a silent lesson? You will be amazed at the concentration of all of your students.
ONE POINT OF VIEW: Action for Middle Schoolers
Authors: Worth Joan
Published: October 2020

The policy recommendations for the mathematics curriculum of the 1980s contained in An Agenda for Action* are most demanding, roost important, and therefore most exciting at the middle school level. For if many of the recommendations are going to be acted upon, that action will occur with middle schoolers, and the results could be dramatic.
The Language of Calculators
Authors: Williams David E.
Published: October 2020

This article deals with the learning of a language, the language of a calculator. What makes the study of languages interesting is that a word or phrase might signify one thing in one language and something entirely different in another. For example, the statement, “Let x = x + 1” is valid in BASIC, a computer language, but incorrect in the Language of algebra.
CLASSROOM ACTIVITIES FOR ABLE STUDENTS: In Fifth and Sixth Grades
Authors: Economopoulos Marjorie P.
Published: October 2020

Mathematically able students in the fifth and sixth grades a re beginning to evidence logical think ing skills which you can nourish and encourage. Problem-solving situations should be introduced to these bright students to develop these skills and to acquaint them with the depth and practicality of the content they are studying. Challenging problems related to applications of mathematics can motivate them and expand their awarenesses of mathematical topics.
CLASSROOM ACTIVITIES FOR ABLE STUDENTS: In Seventh and Eighth Grades
Authors: Humphries Casey
Published: October 2020

Too often it is assumed that mathematically talented students, through some sort of magical osmosis, are inherently good problem solvers. This is not true. Bright junior high school students need to have opportunities to systematically develop, practice, and refine their analytical thinking skills.
Let's Do It: Give Bean Sticks a New Look
Authors: Van de Walle John , Thompson Charles S.
Published: October 2020

Good manipulative materials need not be commercially made, expensive, or in short supply in your classroom. Some of the very best teaching aids are made by teachers and their students. We would like to use this article to encourage you to take a fresh look at a manipulative that has been around for years, is easily and cheaply made in your classroom, and can be produced in sufficient quantities for all of your children. Most importantly, it is quite useful in teaching the major topics, number, place value, and computation.
From the File
Authors: Mort Janice K.
Published: October 2020

Match me a card game for 2 or 6 players that gives your children experience in recognizing likenesses.
David's Algorithm for the L.C.D.
Authors: Thiessen Diane
Published: October 2020

We were in the midst of discussing how to add fractions with unlike denominators. It was an eighth grade remedial mathematics class that met the last period of the day. The students had breezed through adding and subtracting fractions of like denominators. In discussing fractions with unlike denominators, we had drawn pies and cakes (circles and rectangles) to represent the various fractions (fig. 1).
Mastering Basic Facts of Addition: An Alternate Strategy
Authors: Lazerick Beth E.
Published: October 2020

If 2 + 2 = 4 today, then it had better equal “4” tomorrow. This may seem trivial to adults who have memorized the basic facts of addition, but this is anything but obvious to the first-grade child who is beginning to struggle with the intricacies of memorizing the basic facts of addition. Fortunately, what once was called the “one hundred basic addition facts” has been mercifully whittled to about fifty-five ”real” facts and a few simple rules. (Heddens 1980, Underhill 1972) How is this done? Quite simply, thank goodness. Since nobody argues with the need to memorize the basic facts of addition, children should at least be able to do it in the simplest possible way. One alternative method for doing this is outlined here.
A Different Attribute Game
Authors: Scott Thomas L.
Published: October 2020

When I read about the “Concept Game” in Recreational Computing magazine, I realized that this was a very good way to get my students involved in logical thinking in game situations. The game was originally described by Schwartz (1978).
Talking mathematics with children
Authors: Rudnitsky Alan N. , Drickamer Priscilla , Handy Roberta
Published: October 2020

Teachers should “talk” mathematics with their students more often. The key premises of this paper are (I) that teachers can more effectively help children learn arithmetic if they understand what a child knows, (2) that this understanding is best arrived at through dialogue with children, and (3) that the dialogues themselves are valuable instructional episodes.
Using Calculators to Discover Simple Theorems—An Example from Number Theory
Authors: Padberg Friedhelm F.
Published: October 2020

Frequently the calculator is considered to be merely an auxiliary device for the solution of numerical problems and its use in classes is limited to that.
Let's Do It: Meaningful Linear Measurement
Authors: Jensen Rosalie , O'Neil David R.
Published: October 2020

Most of the standard units of measure in use today were developed over a period of centuries. In early civilizations people used parts of the body, (e.g., foot) or common materials (e.g., grain) as arbitrary units to measure objects. Because of variations from person to person and from place to place in size of feet, bands, and so forth, the need for standard units arose as civilizations became more complex.
How Teacher Educators can use the Arithmetic Teacher
Authors: O'Daffer Phares G.
Published: October 2020

Would you want more information if you received a letter containing this announcement?
The National Math Football League Game
Authors: Connelly Ralph D. , Stygall Peggy
Published: October 2020

Over the years I have seen several ideas for incorporating the game of football into the mathematics classroom (Karau 1956, Fennell 1970, and Demchik 1973), but I have never seen one that combines the excitement and strategy of a football game and mathematics as effectively as the one I received as a game idea from one of my preservice students. Since the cards controlling movement on the “football field” are independent of the problem cards, the game can be used to practice any desired mathematical concept.
Ideas
Authors: Fennell Francis (Skip) , Houser Larry L. , McPartland Donna , Parker Sandra
Published: October 2020

Ideas for this month presents two posters. The first features baseball applications of addition, subtraction, and number concepts. The second uses a baseball setting for some problems in logic.
Amelia Bedelia's Apple-Math
Authors: Timberlake Pat
Published: October 2020

Amelia Bedelia is a magic name to elementary pupils. Perhaps one reason Amelia Bedelia is so popular is because she is a complete literalist. When Mrs. Rogers, her employer, tells her to “dress the chicken,” Amelia Bedelia does precisely that—complete with overalls and socks. Children can see the humor in Amelia Bedelia's predicament even before she can.
The Big Pumpkin Count
Authors: Coplestone-Loomis Lenny
Published: October 2020

Halloween isn't just a time for ghosts, goblins, and Jack-o-lanterns in my second-grade classroom at Rosemary Hills Primary School. It's also a great time to introduce counting by tens above one hundred. What do we count? Pumpkin seeds, of course!
Using Children's Books to Teach Mathematical Concepts
Authors: Smith Nancy J. , Wendelin Karla Hawkins
Published: October 2020

Children's books can be an enjoyable way for children to learn mathematics in the primary grades. Books can serve as a supplement to the traditional mathematics materials and are useful with individuals and with groups. They are relatively easy to obtain, from the school media center or from the public library, and require no special expertise for use. The purpose of this article is to suggest specific books and to discuss bow they may be used in the mathematics program.
Big Numbers in a Classroom Model
Authors: Brumaugh Frederick L.
Published: October 2020

Almost daily exposure to activities in outer space arouses children's interest in the “big numbers,” referring to great distances between the earth and other celestial bodies. Space vehicles have visited several of the solar planets, the sizes of which, likewise, lend themselves to studying numerical values different from most everyday activities of earthbound children. The writing of numerals representing these measurements can have much more meaning and significance if the major bodies of the solar system are assembled in a proportional physical display representing sizes of the bodies and the distances between them.
Readers' Dialogue
Authors: Lassman Barbara
Published: October 2020

The currency of letters to the editor of a journal like the Arithmatic 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. letters about an article that appears in a January Issue will amost never appear Mfore lbe following fall. The publication schedule alone dictates such a spread of time. and other factors can intervene to further delay publication of a letter.
Get the Most Out of “Word Problems”
Authors: Charles Randall I.
Published: October 2020

The emphasis given to mathematical problem solving has generated a number of discussions concerning the purpose of typical textbook word problems. The following exercise is an example of what most teachers and students refer to as a word problem. This particular example is from the end of a lesson concerned with division with one-digit divisors.
Making Averaging Easier
Authors: Smith Michael S.
Published: October 2020

The average of two numbers is the number that is halfway between them. Normally we compute averages by adding the two numbers and dividing the sum by two. Alternatively, we could take half of each number and then add the halves.
Books Can Make a Mathematics Fair
Authors: Swinger Alice K.
Published: October 2020

One answer to midseason mathematics doldrums is the creation of a mathematics fair. A fair—with games, magic tricks, food, manipulative objects, music, puzzles, and social interaction—can be a source of creative enjoyment for both peer groups and the community.
Distortions: An Activity for Practice and Exploration
Authors: Battista Michael T.
Published: October 2020

Facility in working with two-dimensional coordinate systems is an important objective for middle school mathematics. This skill is needed for reading and constructing graphs, using maps, and graphing functions. After students have been introduced to locating a point, given its coordinates, and finding the coordinates for a given point, they should be given frequent opportunities for practice. The activity described here can be used to provide one such opportuoity. What is more, most students find the activity fascinating, so it can be used to motivate students to get involved in a number of valuable exploratory investigations.
More Reflections on Teaching Mathematics for Elementary School Teachers
Authors: Billstein Rick , Lott Johnny W.
Published: October 2020

In his article, “Some Reflections on Teaching Mathematics for Elementary School Teachers,” (November 1980 issue of the Arithmetic Teacher), Lowell Leake suggested that mathematics educators share teaching ideas, successes, and failures in courses for elementary school teachers. This article is a response to his suggestion.
A Microcomputer Minicurriculum
Authors: Feeney John E.
Published: October 2020

These ten activity cards are designed to introduce students in the upper elementary grades to the elements of programming BASIC through the subject of mathematics. The concepts and skills involved in the programming correspond to the students' knowledge of mathematics and aids in the reinforcement of mathematical concepts and skills.
Football—All Year Long?
Authors: Massey Tom E.
Published: October 2020

“It's Friday! Will we play Football today?” “May I call the coin?” These and similar questions are the first greetings that I get from my sixthgrade students every Friday all through the school year. For several years I have been playing “Football” with my sixth-grade students almost every Friday of the school year. “Football” is a game that I have used with my classes for general review, for review of recently taught topics, or for introduction of new material. “Football” is a vehicle for class-size instruction and the nature of the game contributes to participation by aU students.
Games People Play
Authors: Barson Alan
Published: October 2020

I enjoy playing games! I particularly enjoy studying the history of ancient board games and discovering their strategies. In their purest forms, games can be classified into three categories: formation games, chase games, and elimination games.
How to Teach Problem Solving
Authors: Burns Marilyn
Published: October 2020

Our charge as elementary teachers has been made clear—problem solving is the number one focus for school mathematics of the 1980s. And that's exactly as it should be. It would be hard for anyone to deny that the major responsibility of schools is to help children become effective problem solvers, preparing them to face the myriad of day-to-day problems of living they'll face as adults. But it's also hard for teachers to relate that responsibility to what happens in the mathematics curriculum on a daily basis. This article aims to deal with just that issue—how to incorporate problem solving as an integral part of the mathematics program in the classroom.
Writing an Effective Arithmetic Test
Authors: Long Lynette
Published: October 2020

In an age of competency-based instruction and teacher accountability, reliable measures of student achievement seem more critical than ever before. Teachers need to know whether their students have achieved lesson, unit, and yearly objectives so that they can accurately plan future instruction. Performance indicator also provide students and their parents information about whether certain objectives were achieved by the students. For the successful student, these test results reinforce the students' efforts. For the slow student, they highlight the areas where fu ture work is needed.
What's Going On…
Authors: Hanel Ann Marie
Published: October 2020

Microcomputers in Education. The Robbinsdale Public Schools in Minnesota are in the third year of a Title IV-C project to develop and test microcomputer programs for grades K-6. The programs are suggested by teachers, programmed within the project by students, and classroom-tested with the appropriate age group. Inservice training has been provided for all the staff and key teachers. All 120 programs run on the Commodore 8K PET, with selected programs available for the APPLE and ATARI. The programs are available for purchase. For more information contact Bill Heck, Microcomputers in Education, Robbinsdale Schools, 4148 Winnetka Avenue, N., Minneapolis, MN 55427.
Basic Computational Facts: A Problem and a Procedure
Authors: Brulle Andrew R. , Brulle Christine G.
Published: October 2020

Many teachers of arithmetic have expressed the lament, “If only they knew their facts, then the learning of the processes would be so much easier!” As all educators know, however, the learning of the basic computational facts has long been a problem for many students.
Doubles Up—Easy!
Authors: Thornton Carol A.
Published: October 2020

Easy facts first, then harder ones! This is the natural route to take in the mastery of basic addition facts, and addition doubles are certainly among those “easy” facts. Using objects to help children “picture” each double makes learning the doubles even easier and a lot of fun. That at least has been the experience of children enrolled in the Illinois State University Mathematics Learning Clinic for area children with learning difficulties in mathematics.
Implications of a Guidance and Counseling Program
Authors: McDaid Elmer W.
Published: October 2020

THE MAJOR PURPOSE of this discussion is to cite background thinking, basic assumptions, and techniques that have grown out of a program of Guidance and Counseling Testing introduced a number of years ago. The Detroit Public Schools foster and supervise this continuing program of periodic testing through the Division of Instruction and the Department of Instructional Research. Although the program cuts across a number of subject matter lines (except in the introductory background statement), I will attempt to point my remarks to our major interest — the testing program and its implication to mathematics instruction and programming.
Classroom Experiences with Recreational Arithmetic
Authors: Nies Ruth H.
Published: October 2020

Much of the so-called dislike for arithmetic in the intermediate grades is only pretense. Attitudes of a pathy and hatred can be changed to contagious enthusiasm when methods of recreational arithmetic are employed. When pupils participate in the healthy enjoyment of number games, they are not ashamed to admit their enjoyment to the world in general. Original puzzles, tricks, and recreational units devised by pupils prove that working with numbers is not really distasteful.
An Introductory Activity
Authors: Heathcote Andrene G.
Published: October 2020

At the beginning of each school year I am always amazed at how many students do not know fellow classmates. Another school year was beginning and I vowed that this year would be different. I developed the following introductory activity. I found that it not only introduces the students to each other and provides material to apply to developing mathematical concepts, but also creates a climate for an “our classroom” atmosphere.
Improving Spatial Abilities with Geometric Activities
Authors: Young Jerry L.
Published: October 2020

The role of geometry in the elementary school curriculum is a topic of continuing discussion. Even though every elementary mathematics text include some geometry, except for measurement, there seems to be little consensus as to which geometric topics should be included and how they should be organized.
National Council of Teachers of Mathematics
Authors: Sobel Max A.
Published: October 2020

There is good news and bad news to report with respect to the National Council of Teachers of Mathematics at the conclusion of my two-year term as president. The good news is that the ship of state is still afloat! The bad news, however, is that some of our members have jumped overboard. The sea is still very rough, and it might be prudent to wear life jackets. We are in for tormy weather ahead. and it's esential that we prepare ourselves for that storm brewing on the horizon.
The Little Hand Tells You When
Authors: DeLoach Ruby Haydock
Published: October 2020

Learning. the concept of telling time can be a very challenging and sometimes frutrating experience for some children. (My class was a primary, trainable. mentally handicapped class.) Aside from the orientation to a different system of movement, there is a large vocabulary to be learned. I decided to attempt a novel approach to the task of teaching time. My first step was to find omething very important to the children and incorporate it into my schema.
Readers' Dialogue
Authors: Kennedy Leonard M. , Chinn Phyllis , Wheatley Grayson H. , McCuiston Ronald S. , Sitarik Kenneth A. , Clay Gwendolyn V.
Published: October 2020

The currency of leners to the editor or a journal like the Arithmetic Teacher is always a problem. At the very best. four months will have elapsed between the time when an anicle is published and the time when a lener commenting on that an ide can appear in the journal. Sometimes the minimum time is even greater. For example, leners about an anicle that appears in a January issue will almost never appear before the following fall. The publication schedule alone dictates such a spread of time. and other factors can intervene to further delay publication of a lener.
TEACHING: Using a Directed Lesson
Authors: DeRidder Charleen , Dessart Donald J.
Published: October 2020

What does a teacher do to guide students in the development of specific mathematical skills? In this article we outline five steps—introducing, presenting, analyzing, practicing, and applying— that are designed to help teach a directed mathematics lesson.
Sharing the Wealth: Dividing with Meaning
Authors: Peterson Wayne
Published: October 2020

The major problem with most representations of the division algorithm, as opposed to the concept of division, is that students become lost in the mechanics of the manipulations and do not make the connection between the model and the process being modeled. The model described in thi article relates step by step to the standard division algorithm; the connection is immediate and obvious. It is a spin-off of a method presented by DiSpigno in the October 1971 issue of the Arithmetic Teacher. There are two major differences; one, the introduction of a story line; and two, the direct connection that is made between the representational model and the standard algorithm.
On the Transmission of Mathematics Anxiety
Authors: Bulmahn Barbara J. , Young David M.
Published: October 2020

The nature and quality of a child's early exposure to mathematics is a matter of ongoing concern in our profession. This concern has been amplified recently by the studies relating to “math anxiety” in children and adults (Tobias 1976). At the same time, research continues on the relative significance of biological and environmental factors on mathematical achievement (Fennema 1974, Hilton and Berglund 1974). The conclusions of these studies are in some cases confusing and even conflicting, but nearly all recognize that a person's environment has some effect on her or his mathematical ability and interest.
All Hands on Deck!
Authors: Lent Barbara C.
Published: October 2020

Take a minute to answer this simple true-false test.
Maybe We Should Be in the Model Business
Authors: Heikkila Frank L.
Published: October 2020

So often when we know that a student is learning disabled, we lower our expectations for the child. We assume that this student is not capable of dealing with abstraction, that we should concentrate on drill work since conceptual understanding will not be possible. But, are we being myopic? These students may be far more capable than we expect.
One Point of View: Problem Solving: If Not Now—Then When!
Authors: Newell Virginia K.
Published: October 2020

The NCTM recommendation that a major focus for school mathematics in the 1980s should be on problem solving is on target. Problem solving is the heart of school mathematics; it is an art to be nurtured and encouraged. Children's natural curiosity is evident early in their lives. Alert parents and teachers begin the process of problem sol ving at the onset of a child's questions.
Readers' Dialogue
Authors: Suenobu Dennis Y. , Jurgensen Marlinde , Farrar Paul M. , Brown Syd. , Maletsky Evan M.
Published: October 2020

The currency of letters to the editor of a journal like the Arithmetic Teacher is always a problem. At the very best, four months will have 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. letters about an anicle that appears in a January issue will almost never appear before the following fall. The publication schedule alone dictates such a spread of time. and other factors can intervene to further delay publication of a letter.
Grid Arrays for Multiplication
Authors: Robold Alice I.
Published: October 2020

Arrays are often used as excellent models for beginning multiplication examples, but sometimes are put aside when they become unwieldy for greater factors. L earners. therefore. may be deprived of the benefits of array models just when they need help with more challenging examples. The use of grid arrays, made from paper marked in squares, allows the learner to continue to benefit from array model and to follow a logical sequence of multiplication experiences.
A Look at Division with Fractions
Authors: Silvia Evelyn M.
Published: October 2020

Graph paper can be used for concrete representations of both fractions and operations with fractions. The combined use of graph paper and an overhead projector makes the presentation even more convincing. The paragraphs that follow are a description of how I have used graph paper to illustrate the algorithm for the division offractions. The activities on division were preceded by activ ities that covered equivalent fractions, as well as addition and multiplication of fractions.
The Gifted and the Micro-Will You Let It Happen?
Authors: Clemens Stanley R.
Published: October 2020

Meet Robbie; he is a bright-eyed first grader who in many ways is typical of his age.
Ideas
Authors: Tucker Benny F. , Bazik Edna F.
Published: October 2020

Ideas this month presents graphing activities. Students locate point on a coordinate system and name points by an ordered pair of numbers.
Readers' Dialogue
Authors: Scheding John C. , Sanders Walter J.
Published: October 2020

We welcome letters from readers, and will publish them to the best of our abillity with in the constraints necessarily placed upon us.
Learning Styles: Rx for Mathophobia
Authors: Hodges Helené L. B.
Published: October 2020

Have you ever heard any of your students exclaim, “I hate math! Can't we do something else?”, or “I'll never learn to do those problems. I give up!” Or better yet, “Can I have the pass to the bathroom?”
How to Teach Banking Basics
Authors: Lovejoy Patricia
Published: October 2020

As I open the classroom door, the impact of the noise forces me back into the hallway. My curiosity prevails, however, and once I am inside I am quickly caught up in the activity and excitement in the room.
Number Three Comes to See
Authors: Avital Shmuel , Grinblat Uri
Published: October 2020

A frightful ring of the phone pulled me out of a deep sleep. Heavens! Who can be calling at this time of the night?
One Point of View: Being a Real Teacher
Authors: Burton Grace M.
Published: October 2020

Teachers of mathematics, at every level, have a duty to not only know the topic they are teaching, but also to be real to their students. Being real means facilitating the development of both mathematical competence and positive attitudes, and respecting the inherent dignity and worth of each individual in the classroom. To the real teacher, how the individual child feels as well as what the child knows is important in planning effective instruction.
Let's Do It: Using Geometry Tiles As a Manipulative for Developing Basic Concepts
Authors: Horak Virginia M. , Horak Willis J.
Published: October 2020

Many of the out-of-school experiences young children have deal with geometrical concepts and understandings. Thus children have an intuitive feeling for much of the geometry content introduced in the lower elementary grades. The “geometry tile” described in this article can be used to develop and extend these beginning concepts. Through the use of handson materials like these tiles, children are better able to visualize geometric shapes and to communicate the involved spatial relationships. They are also able to begin dealing with measurement in a very concrete manner.
Ideas
Authors: Bazik Edna F. , Tucker Benny F.
Published: October 2020

Ideas this month focuses on the topic of measurement and on the concept of length, area, and volume. Children need experiences with estimating and with measuring. Active involvement of students is a necessity in teaching measurement.
What's Going On…
Authors: Hanel Ann Marie
Published: October 2020

Computer network to help manage instruction. A grant from the Arkansas State Department of Education has funded the development of a program for computer-assisted management of mathematics instruction for the Commodore PET Computer. The program contains data on each pupil--name, age, sex, teacher, grade, how much total computer time the child has, time spent on each test--and provides tests for all the basic skills' objectives for mathematics in grades K-4. The testing mode of the program generates four test items on each objective. The computer determines, tracks, and records progress on each objective for each student and updates the student's record. Mathematics instruction is given during a regular class period. The program is currently being piloted in grade 3 at North Elementary School in Jonesboro, Arkansas. The plans are to expand the system to cover mathematics K-8 and to begin using it in second grade. Teachers implementing the program were given training using the testing system and the computers. For more information contact Thomas Bishop, Arkansas State University, Box 70, Mathematics Department, State University, AR 72467.
Teacher Education: Helping Preservice Teachers to Teach Mathematical Concepts
Authors: Davis Edward J.
Published: October 2020

Teaching mathematical concepts is important. In a time when students' performance on basic skills is being emphasized, teachers must be alert not to stress computation at the expense of concepts. Understanding the meaning of a fraction differs from knowing how to add fractions. A lack of conceptual knowledge of a fraction can contribute to incorrect performance in computational skills with fractions. The same can be said about other mathematical concepts, such as percent, decimals, division, factoring, like terms, square root, and so on.