bluuebunny/crossref_metadata_2025 huggingface dataset:
Using Research in Teaching: Notes from National Assessment: word problems
Authors: Carpenter Thomas P. , Coburn Terrence G. , Reys Robert E. , Wilson James W.
Published: October 2020

Learning to solve word problems is a significant hurdle in learning mathematics. Failure to learn the skills needed to solve such problems can significantly inhibit a child's progress in school mathematics. Therefore, it is important that the solving of word problems occurs as a meaningful and successful part of each child's mathematical education.
Multipurpose mathematics games from discards
Authors: Sowell Evelyn J.
Published: October 2020

Wait! Don't throw that game away just because some of the pieces are missing. With ingenuity and time you can transform it into a first-class instructional aid. The mathematics games pictured in figures 1 and 2 were made from discarded boards from commerical games. (The games were designed and constructed by mathematics education students at the University of Houston.) When the games were subjected to reality testing, pupils played both games enthusiastically.
Magic squares for average learners, too
Authors: O'sullivan Ellen P.
Published: October 2020

It seems that the use of enrichment materials and activities for “making math fun” are too often geared to rapid learners. Granted, we must stimulate and motivate such students, but how about mathematics fun for average learners?
Let's Do it!: Taking advantage of the hand calculator
Authors: Bruni James V. , Silverman Helene J.
Published: October 2020

If you have experienced the excitement of a group of children who realize they will be using a hand calculator, you will agree that the calculator should have a role to play in the elementary school classroom. In stant motivation! The most “ reluctant” learner is anxious to have a chance to use the calculator.
What's going on…
Authors: Gawronski Jane Donnelly
Published: October 2020

Peer teaching was the special feature of two-week workshops held at three sites in Oregon this past summer. The “hands-on” workshops were part of a new program enabling Oregon teachers who are leaders in mathematics education to conduct graduate-credit mathematics workshops for other teachers under the auspices of The Math Learning Center in Salem. The workshops presented many useful classroom ideas and materials covering a variety of mathematical topics, with emphasis on problem-solving and laboratory approaches. Peer teaching was used to create a friendly, unpressured atmosphere in which “mathephobes” could discover the fun of mathematics. More workshops are planned for next summer. Additional information can be obtained from David Raskin, The Math Learning Center, 325 13th Street, N.E., Room 302, Salem OR 97301.
Instructional games with calculators
Authors: Judd Wallace
Published: October 2020

This is a brief collection of calculator games that I have played with kids (and adults) over the last two years. Each game can be explained simply enough for first or second graders to understand, yet the games can be played with variations difficult enough to make most mathematics teachers stop and think.
Selecting a minicalculator
Authors: Caravella Joseph R.
Published: October 2020

As long as the number of minicalculators in use continues to increase and the quality of their hardware and software designs remains in a state of flux, a systematic means of differentiating between and evaluating the various machines will be needed. The checklists that follow are designed to help educators select an appropriate minicalculator for their individual or group situation.
Hand calculators: where do you stand?
Authors: Shumway Richard J.
Published: October 2020

It has often been proposed that the Mathematics Teacher and the Arithmetic Teacher publish careful a rguments for and against a particular proposal to stimulate thought and air honest differences regarding issues relevant to the teaching of mathematics. Such pro and con discussions have been difficult to organize. At the risk of being accused of being on the wrong side of an issue by everyone, I would like to raise what appear to be the arguments proposed for and against the use of hand calcul ators in school mathematics.
Mystic primary squares for pupils
Authors: Moon Leland , Moon Sharon Pearl
Published: October 2020

What is a mystic square? Mystic squares are similar to magic squares because both contain rows and columns of numbers that yield the same sum when added, but mystic squares differ from magic squares in two ways. First, all mystic squares contain four numbers while the smallest magic square contains nine. The second difference is that sums of numbers on each diagonal of a magic square must equal the sums of the numbers on each row and column; this need not be true for the diagonals of mystic squares. A mystic square and a magic square are shown in figure I. Notice that in the magic square the sum of the numbers in each row, column, and diagonal is 15. On the other hand, in the mystic square the sum of the numbers in each row and column is 5, while the sum of the numbers on one diagonal is 6 and on the other it is 4.
Mathematics is fun! It's in the cards for you!
Authors: Herrmann Jeanne Throckmorton
Published: October 2020

Almost all children have ordinary playing cards available in the home. Early in the fall, ask each child to bring a deck of new or used playing cards for use in the mathematics class. Even broken and damaged sets can be used. Because children like card games, the response will be positive.
Slow or learning disabled—is there a difference?
Authors: kurtz Ray , spiker Joan
Published: October 2020

Elementary teachers are fully aware that in every heterogeneously grouped classroom there are a few children who have an extremely difficult time with mathematics. Teachers struggle through the entire year, and yet feel that little progress was made by this group. These children are the ones who always seem to have messy papers with wrong answers. Even though teachers want to help these children overcome their deficiency in mathematics, all too often their attempts produce little measurable success. Frequently, past attempts at diagnosing children who experience difficulty in mathematics have tended to categorize them as slow learners. A careful examination of the group having difficulty shows that not all meet the technical definition of a slow learner, i.e., with an IQ in the 80-90 range. Many of these children have average or better intelligence scores. There is an encouraging movement presently underway to provide a somewhat different thrust from that used in the past to meet the needs of children who chronically experience difficulty with mathematics.
Let's Do It!: Using classification to interpret consumer information
Authors: Bruni James V. , Silverman Helene J.
Published: October 2020

In their daily lives children are showered with information presented in the form of schedules. tables, checklists, and charts that can be very puzzling unless the children have specific skills for interpreting the communications. Some materials come to children in no special order and may appear haphazard; the children then need to arrange the data in ways that show some pattern or format. Other materials may come arranged in some order, but children frequently do not know how to interpret the data that is provided.
Using flowcharts with first graders
Authors: Hubbard Sherry P. , Ashlock Robert B.
Published: October 2020

As teachers work increasingly with individuals and with small groups, children need to be able to work independently. As a result, teachers need a method of communicating with independent workers, a method that does not require much of a teacher's attention. Primary teachers often find written communication difficult because the reading vocabulary of primary children is limited. Would it be useful to nowchart directions?
Let's Do It!: Using rectangles and squares to develop fraction concepts
Authors: Bruni James V. , Silverman Helene J.
Published: October 2020

The first formal experiences that children have with concepts of fractions involve examining the whole/part relationship between models of circular regions and parts of those regions.
Graphing and prediction in the elementary school
Authors: Pereira-Mendoza Lionel
Published: October 2020

If we wish students to become better problem solvers, we must lay the foundation in the elementary school. In particular, within the framework of the mathematics curriculum students must be given the opportunity to make and test educated guesses. One of the most fruitful areas for this is graphing. Graphing provides ideal situations in which children can make predictions and then see if their predictions come true. Three examples of graphing-and-predicting activities that can be used with elementary school children are described here. These examples are meant to act as catalysts for ideas. Children may well suggest alternative graphs or other activities based on the initial idea.
Your Council at Work: Nominees for the 1978 election
Authors: Hardgrove Clarence E. , Elliott Mabel M. , Hill Thomas J. , Kent David , Price Jack , St. Clair Irene , Smith Eugene P. , Smith Louise , Taylor B. Ross
Published: October 2020

The Nominations Committee needs your help in selecting nominees for the 1978 election. At that time four new members for the Board of Directors will be elected.
Let's Do It!: From blocks and model making to ratio and proporation
Authors: Bruni James V. , Silverman Helene J.
Published: October 2020

The dynamic avenues for learning in the preschool and kindergarten can be vehicles for the learning of mathematics by older children. The background of experiences gained from these activities of early childhood, coupled with maturation, provides a base from which to explore new ideas with familiar materials. Block building and model making are two rich areas to consider.
Generating patterns from transformations
Authors: Johnson Martin L.
Published: October 2020

Many current elementary textbooks and curriculum guides are placing increasing emphasis on the teaching of transformational geometry. This topic, however, is still relatively unfamiliar to many classroom teachers, and ways of helping teachers and students acquire a “feel” for simple, basic transformations are needed.
IDEAS
Authors: Ockenga Earl , Duea Joan
Published: October 2020

The experiments on these pages actively involve students in generating data, drawing their own hypotheses from the data, organizing their information, and arriving at their own solutions. These activities may take more time than usual textbook problems, but the learning is well worth the time expended. We suggest that you pick the experiments most appropriate for your students, reproduce the copy, then encourage the students to develop their own methods of solving the problem.
Is one picture worth one thousand words?
Authors: Poage Melvin , Poage Esther G.
Published: October 2020

Is it true that “a picture is worth a thousand words”? Experiences indicate that while the statement may be true, very few people see and understand all “thousand words” when they look at a particular picture. In fact, most people see not only just a portion of the thousand words but different sets of words. Stated another way, pictures must be interpreted, and people interpret pictures differently. In the education of young children this situation is compounded. According to Piaget, children do not think and reason as adults do, yet we ask children to interpret adult-made pictures. To determine the importance of pictures in elementary mathematics one has only to flip through the textbooks or scan other teaching materials and note the great number of pictures. Teachers use materials containing pictures to convey ideas with a high degree of frequency, particularly in the lower elementary grades. Is there anything wrong with using pictures to teach mathematics? Experience seems to dictate two answers-no and yes. No, there is nothing wrong with using pictures to convey ideas. In fact, it seems a worthwhile and profitable format. Yes, there is something wrong with many of the pictures we use since children often come up with completely different ideas from those intended by authors. Pictures or pictorial representations used in mathematics lessons do not always convey the intended ideas to children. Examples of pictures that illustrate this problem are numerous and can be found easily. When the problem is brought to the attention of teachers, most of them can identify examples from their own classrooms. The examples cited in this article are not necessarily the most misleading ones; they have been selected to suggest several different facets of the problem.
The language experience approach to story problems
Authors: Davidson James E.
Published: October 2020

Children fail at solving story (verbal) problems for many reasons. Some of the reasons are low reading comprehension, lack of experience with the problem situation, unfamiliarity with the language of the situation, and irrelevancy of the problem, to name a few. The “language-experience” approach to teaching children to solve story problems is one method that short circuits these reasons for failure. When this approach is used, children are given the experience of writing their own problems in their own language and using their own previous experiences. The children, therefore, are familiar with the problem situation, know the language of the problem, have no trouble reading the problem, and can relate to the information in the problem.
Your District Needs a Policy on Pocket Calculators!
Authors: Munson Howard R.
Published: October 2020

A quick glance at professional journals dealing with teaching generally, and with mathematics teaching specifically, reminds us that miniature calculators have become a concern and an item of great interest. Articles dealing with the major question, “Should minicalculators be used in schools?”
Teaching Word Problems to Graders
Authors: Underhill Robert G.
Published: October 2020

The results of five studies of addition and subt raction story problems are brieOy presented here, and then some implications for improving problemsolving skills of first-grade children are considered.
Hawaii's Inservice Metric Program
Authors: Whitman Nancy C.
Published: October 2020

In 1972 and l973 the legislature of the State of Hawaii mandated the development of a program for teaching the metric system and for its implementation in the schools of Hawaii. In response to this mandate. a program of inservice education has been developed by the College of Education of the University of Hawaii and the State Department of Education. The program consisted of a series of works hops. The co ntent of these workshops was devel oped by Mildred Shimizu of the State Department of Education and the author in consultation with Irvin King. Director of the Hawaii Metric Project, and Frederick Braun of the Curriculum and Instruction Depa rtment of the Un iversity of Hawaii.
Greater Than and Less Than
Authors: Barcus Rita
Published: October 2020

Adults and children alike know that the color red, when seen on a traffic light. stands for stop, and green means the opposite. However, let us suppose th at the first traffic light was somewhat different. Imagine that the inventor had cho en the color orange to mean go and red to mean stop. It is obvious what might have happened. Since these two colors looked so much alike. many accidents would have occurred. These would not result because the driver did not know how to stop and go but because of the similarity between the two colors. We would hope that after the inventor realized the problems, he would devise a better traffic light using two colors that would be more easily distinguishable.
Homemade Device for Quick Recall of Number Facts
Authors: Hutcheson James W. , Hutcheson Carol E.
Published: October 2020

Elementary and junior high teachers in the Muscogee County School System are using a homemade device to assist them in developing quick recall of mathematics by their students. Teacher-made material should always be both durable and flexible. That is, it should survive many uses and serve many purposes. The particular item our teachers are using is a permanent transparency of random digits in rows and columns (fig. I). A master was made using a primary typewriter to insure digits of the proper size for viewing. The transparency is placed on the overhead projector, and rows selected at random are identified by covering other rows with sheets of paper (fig. 2).
Mathematics for Special Education Teacher Trainees
Authors: Hofeldt Ellen J. , Hofeldt Larry L.
Published: October 2020

College students and university mathematics professors frequently ask, “Do special education majors need detailed training in mathematics?” This article will assert and delineate the necessity of an all-encompassing background for special education teacher trainees. The special education teacher trainee certainly needs no less thorough training in any area than a regular elementary teacher trainee.
Patterns in Divisibility
Authors: Parkerson Elsa
Published: October 2020

Teaching tricks for recognizing multiples of the low numbers is always fun for both me and my students. This kind of teaching also provides opportunities for discoveries about numbers, as one of my sixth-grade classes found out.
The Use and Misuse of Mathematical Symbolism
Authors: Lichtenberg Donovan R.
Published: October 2020

This paper is written with the hope that it will cause some reaction and bring about some discussion among mathematics educators regarding the issues raised and the points of view expressed. The motivation for it came from discussions with colleagues while working on the Florida State Assessment Program. These discussions concerned whether or not something like that shown in figure I constitutes an appropriate multiple-choice test item. With today's excessive emphasis on assessment and accountability, millions of students across the United States are undoubtedly being asked to respond to such items.
What's Going On
Authors: Gawronski Jane Donnelly
Published: October 2020

Educational needs assessment project in Wyoming is designed to assess discrepancies between the mathematical skills that Wyoming teachers believe graduating high school students should possess and the skills that such students can actually demonstrate. Fifty-six competencies were translated into test items that were administered to 869 of the state's approximately 6000 seniors. The students' performance on each item was compared with the expectations of the teacher committee, with a discrepancy of ten percentage points being considered “educationally significant.” For additional information contact Gayle Lain, Coordinator of Innovative Program Development, Wyoming State Department of Education, Hathaway Building, Cheyenne, WY 82002.
Mission: Division
Authors: Charles Michael
Published: October 2020

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.
Why the Continuing Resistance to the Use of Counting Sticks?
Authors: Anderson Alfred L.
Published: October 2020

It is a continuing source of wonder to us, when we visit first-grade classrooms, to see the number of teachers who are either not allowing the use of counting sticks and place-value boxes in their classrooms or are seemingly unaware of their instructional value. Certainly the use of manipulatives has been amply examined and strongly advocated in teacher-training classrooms and in current literature. And certainly the idea of manipulatives in teaching is not a new one. Deatsman (1976), for example, pointed out that the use of manipulatives was not a new topic in 1893, and that the value has been understood ever since then. Why, then, are so few teachers using counting sticks and place-value boxes in their classrooms?
Calculators in the Elementary Classroom
Authors: Drake Paula M.
Published: October 2020

Should hand-held calcu lators be used in elementary school classrooms? The question has become a controversial issue and the subject of much discussion. I discussed the question with my sixth-grade class, and they have put the issue to rest. We have formed a Calculator Club.
Manipulative Devices for Teaching Place Value
Authors: Shokoohi Gholam-Hossein
Published: October 2020

Since the appearance of the results of recent psychological investigations into the ways that children learn mathematics, and particularly since the acceptance of Piagetian ideas regarding the stages of development of children by the majority of those who are concerned with instructional activities, much emphasis has been placed on the value of using concrete models and manipulative devices in the early stages of the development of mathematical ideas. The purpose of this article is to describe briefly a method that we have used since 1963 with considerable success to teach place value in the Teacher Training College of Tehran and in many of the Iranian elementary schools.
Evenness and Oddness Extended
Authors: Ruderman Harry D.
Published: October 2020

A challenge for the mathematics class often becomes a ch allenge for the teacher. This happened with one of my bright seventh-grade classes.
Minicalculators and Repeating Decimals
Authors: Hobbs Billy F. , Burris Charles H.
Published: October 2020

The minicalculator can be used effectively in the class room to encourage student inquiry and creativity through experimentation with mathematical ideas. The benefit of the calculator is multiplied when the experimentation requires computations that are too difficult or time-consuming to be done by paper-and-pencil algorithms. (See “Minicalculators in Schools,” Mathematics Teacher or Arithmetic Teacher January 1976.)
Let's Do It: Make Counting Really Count: Counting Projects for First and Second Grade
Authors: Montgomery Lindquist Mary , Dana Marcia E.
Published: October 2020

To understand number sizes and the order of numbers, children need to do a lot of counting. At times we all need new or additional suggestions to motivate counting and to relate it to other concepts or subjects.
Simulating Problem Solving and Classroom Settings
Authors: Liedtke Werner , Vance James
Published: October 2020

The simulation of various classroom settings in which problem-solving activities occur is one aspect of the mathematics methods course for elementary teachers at the University of Victoria. By participating in these sessions, the students are made aware of some of the possible instructional settings that they might use as teachers and the important role that problem solving plays in the curriculum. Some of these settings and problems are described here and some results of the students' involvement in the program are illustrated.
Peg It!
Authors: Hardin Larry D.
Published: October 2020

Elementary school students need to experience physical interaction with objects. Such experiences facilitate cognitive growth. They should include novel activities with objects that are slightly above the cognitive level of the student in order to help the student advance to a higher degree of operational ability, which will eventually lead to the use of symbols. Peg numerals, for example, can be used in a sequence of activities that have been found helpful in developing mathematical understanding.
Compu-Kids: A Project for “Children” of All Ages
Authors: Statz Joyce A.
Published: October 2020

At Bowling Green State University, the reaction to seeing fifth and sixth graders working at teletype terminals is varied and interesting. “Look out, here come the kids for the terminals!” “What are those kids doing here?” “You're joking, those guys are learning BASIC!” Undergraduates look at the children with a mixture of wonder, annoyance, and curiosity-wonder at their abilities, annoyance when the terminal room is crowded, and curiosity as the children jump up and down when a program works.
A Common Cents Approach to Mathematics
Authors: Carr Karen D.
Published: October 2020

My sixth-grade mathematics classes seemed to need a change, something more than the routine of textbook assignments. We needed a program that would not only include some important “basics” but also show some practical a pplications in everyday life.
Story Numbers
Authors: Swafford Jane , McGinty Robert
Published: October 2020

The students could tell a prime number when they saw one, but they could not tell why it was a prime number. Obviously, the definition, “a prime number is a whole number with exactly two factors — itself and one,” did not mean much to fifth graders.
Mathematics in the Environment
Authors: Tucker Karen L.
Published: October 2020

We are all convinced that manipulative materials and concrete experiences are useful in teaching mathematics, and we have curricula which put this belief into action. We pretest and posttest, diagnose and prescribe; yet with all that, we may often miss the fun of everyday mathematics. We are so concerned with behavioral objectives for Unit 3, Lesson 2, at 1 o'clock, that we are not free to recognize the opportunities for mathematical learning and real enjoyment that arise for children in the kindergarten and primary grades in their daily art or dress-up activities.
Don't Give Up Yet!!!
Authors: Lazerick Beth Ellen , Harris Carolyn Karafin
Published: October 2020

Children who experience difficulty in understanding basic mathematical concepts and in learning standard algorithms are probably sitting in every classroom. Sometime these children are labeled “slow” and show symptoms of a child with learning disabilities or brain injury. Other times these children are the ones who have simply not been “reached” by teachers and they exhibit signs of frustration and a distrust of mathematics in general. Although the children who are working appropriately with grade level material may need continued review, practice, and reinforcement with materials and experience to learn concepts, children who are having difficulty with learning basic mathematics with conventional teaching materials and methods may need different or special techniques and aids to augment learning.
A Truck Driver Looks at Square Roots
Authors: Risoen John W. , Stenzel Jane G.
Published: October 2020

It was the end of summer and teachers were trying to get rooms ready for the coming year. Some weighed the pros and cons of new bulletin board ideas; others tried to remember where they had put last year's posters.
One Point of view: Mathematics in Urban Schools
Authors: Trafton Paul R. , Morgan Virginia R.
Published: October 2020

The limited achievement of many students in the schools of our nation's cities is a major concern today. The National Council of Teachers of Mathematics has made urban education a major priority and has established a Task Force on Mathematics in Urban Schools to focus on mathematics programs in these schools and to provide impetus to efforts to improve mathematics instruction and learning.
Aids for Learning Mathematics
Authors: Danforth Marion McC.
Published: October 2020

Mike, a seventh-grader with a visual memory deficit, had an excellent grasp of logical reasoning and problem-solving principles, yet he was unable to perform basic mathematical operations. In my efforts to meet Mike's special needs as a learning-disabled child, I found some procedures that are good teaching practices in the regular classroom.
Doing Arithmetic with Tangrams
Authors: Ajose Sunday A.
Published: October 2020

One of the most fascinating puzzles available today is the Chinese tangram. This ancient, seven-piece puzzle consists of five triangles in three sizes, a square, and a rhomboid. Through the years, the Chinese tangram has had many devoted players, young and old, including some renowned people like Lewis Carroll and Sam Loyd.
The why of arithmetic
Authors: Smart James R.
Published: October 2020

One of the hopes when modern elementary school mathematics was first introduced was that students would understand more about traditional ways of performing the operations of arithmetic. But simple answers to questions about the whys of arithmetic have been difficult to isolate in the complexities of technical language and abstraction. Here is a list of sixteen questions, with specific answers involving an example where possible. The purpose of this article is to provide a needed reference for teachers of arithmetic who want to answer some of the whys, but have a limited time to do it.
Geometry in the Primary Grades: Exploring Geometric Ideas in the Primary Grades
Authors: Silverman Helene
Published: October 2020

Many of the planned experiences for exploration of materials in the primary grades offer opportunities for the introduction of geometric concepts. After the initial exploratory activities, the teacher can guide the children into some of the more structured experiences that are described in the paragraphs that follow.
Geometry for the Intermediate Grades
Authors: Bruni James V.
Published: October 2020

If you examine current, upper-grade, mathematics textbooks, you will find that they usually include a good deal of geometry. But in actual practice geometry does not constitute a significant part of the mathematics programs in elementary schools. Geometry activities usually are considered a “frill,” a topic that is covered, if time permits. “Sure, geometry activities are great. But who has time? There's too much ‘basic’ arithmetic to do,” was the comment of one fifth-grade teacher.
A Case for Statistics
Authors: Shulte Albert P.
Published: October 2020

It would be hard to overemphasize the importance of statistics in the daily life of the ordinary citizen. The presentation and interpretation of statistical information plays a part in determining the television shows from which one may select, whether the local school millage election will pass or fail, whether the airplane is “overbooked” on one's next trip, how many fish one is allowed to catch each day while on vacation, and whether one's favorite professional athlete will be able to negotiate a raise in pay for the coming season. Through the daily paper, through news and analysis programs on radio and TV, through commercials, and continually throughout sportcasts, the person in the street is bombarded with statistical information (or misinformation) and presented with reasoning based on statistics
Statistics in the Middle School
Authors: Klitz Ralph H. , Hofmeister Joseph F.
Published: October 2020

Setting out to convince restless middle schoolers that mathematics is a highly useful art, and not simply a parlor game for eccentric school teachers, can be a Herculean task. We would like to propose a short unit in statistics as one small step toward getting the job done.
Activities in Applying Probability Ideas
Authors: Choate Stuart A.
Published: October 2020

Probability has been recommended as a mainline curriculum topic for many years, but without wide acceptance; perhaps because many people view coin-flipping and dice-rolling as lacking purpose. Mathematics teachers need to carry the study of probability far enough for students to comprehend its many applications.
Let's Do It: Independent mathematics center for everyone
Authors: Lindquist Mary Montgomery , Dana Marcia E.
Published: October 2020

The idea of a mathematics center is very appealing to many teachers. At centers, you can have the ort of mathematics activity that is not done usually by children at their desk or by the whole clas at one time. Such activities can be fun as well as instructive and thought-provoking. Unfortunately, many cen ters take too much time and effort in preparation and can also require too much teacher direction. We have suggested several sample activities, appropriate for grades one through three. that involve minimal teacher preparation, materials, and direction.
Finger Multiplication
Authors: Balin Fred
Published: October 2020

Throughout history humans have used their fingers as number symbols and to perform simple computations. The Romans, for instance, devised a system of representing numbers from 1 to 10000 on the fingers of both hands. Menninger (1969) details how Arabian and East African merchants set the price of a transaction by touching fingers underneath a cloth to insure confidence. These techniques and others, which once attained great usefulness, are now all but obsolete.
Educational Implications of Dyscalculia
Authors: Flinter Paul F.
Published: October 2020

One of a child's finest attainments in his learning experience is the concept of number—ideas of quantity, weight, time. operation, numerical classification and problem solving. These principles begin early and develop as the individual grows. According to Gessell and Amatruda (1947) generalizations are made as early as in the first year with manipulations of various objects. Piaget (1953) observed acquisition of number concepts through a series of sequential levels depending upon the individual's readiness. A majority of children will acquire understanding of number and will encounter little difficulty. However, some will fail because of language disorders, faulty teaching methods, reading problems, or disturbances of qualitative thinking (Johnson and Myklebust 1967).
My Favorite Lesson: Speed Trap
Authors: Bork Ron
Published: October 2020

I have always felt that children were intrigued by the speeds of things, especially the speeds of cars and their own speeds. For this reason I am very excited about a lesson that I have been using in my mathematics classes for the past few years. I have used this activity, in one form or another, with students from the fourth through the eighth grades. The activity is done best out of doors.
Cutting across a Circle
Authors: Reid Joseph S.
Published: October 2020

Games have been in classroom use for sometime and are viewed by many as an effective teaching medium. In the area of mathematics, Allen and Main (1976) found a decrease in absenteeism when a game approach was introduced into the regular mathematics curriculum of an inner-city school. Edwards et al. (1972) reported that the achievement of classes using a game approach was significantly greater than that of a traditionally taught class. In the area of reading, many commercial and teacher-made games have been developed to teach reading skills. For example, “Grap,” “Split-word,” “Adlib,” and “Scrabble” are games that are used to develop a student's vocabulary. Vocabulary development can, of course, be more interesting when it is presented in a game format. Increasing a student's vocabulary is also an important goal of mathematical instruction, but learning technical terms can be difficult for many studen ts. The game described here was designed to make vocabulary learning more enjoyable.
What's Going On
Authors: Gawronski Jane Donnelly
Published: October 2020

Metric Education for Rural Southern Mississippi is being conducted by the Department of Curriculum and Instruction of the University of Southern Mississippi, under a grant from the United States Office of Education's Metric Education Program. The project seeks to provide inservice training in the metric system to elementary teachers in the rural counties of southern Mississippi and to involve those teachers in training community participants in its use. Further information may be obtained by contacting Jocelyn Marie Rees, MERUSM Director, Department of Curriculum and Instruction-Southern Station, Box 9224, University of Southern Mississippi, Hattiesburg, MS 39401.
Back to Basics the Magical Way
Authors: Flexer Roberta J.
Published: October 2020

Many mathematics educators fear that the “back to basics” movement will be translated into many hours of dreary drill for elementary school students. Although important and necessary, drill in the “basics” need not be dull. There are many reasons why drill should be made as interesting as possible and many ways to make it so.
Money Changer's Bingo
Authors: Elliott Portia C.
Published: October 2020

The game of “Money Changer's Bingo” is an activity for upper elementary school children who like competition and need practice in making and counting change. Children simulate making purchases of grocery store items and record their representations of excessive payments on game boards. Money Changer's Bingo is an exciting and fun-filled game, but it also has the educational value of reinforcing arithmetic concepts while children practice determining equivalent representations for various denominations of money.
Word Problem Skits for the Deaf
Authors: Hernandez Norma G.
Published: October 2020

In elementary school mathematics, teaching word problems is one task that causes as many difficulties for teachers as for students. Poor reading skills, lack of an adequate vocabulary, and lack of mastery of skills to perform the relevant arithmetic operations are often cited as major factors in students' inadequate and inappropriate attempts at solving word problems. On the other hand, teachers' lack of knowledge or familiarity with specific teaching strategies in mathematics may be major factors in students' unsuccessful attempts.
ONE POINT OF VIEW: Sense and Nonsense about Fractions and Decimals
Authors: Payne Joseph N.
Published: October 2020

With our certain, albeit slow, movement to the metric system and with the widespread use of calculators, there is general agreement that decimals wiU be introduced earlier in our elementary school mathematics curriculum. Decimals for tenths, for example, have been taught successfully in grade three. Nevertheless, there are major questions, substantial disagreements, and some sheer nonsensical statements being made about fraction concepts, fraction computation, and decimal computation.
When You Use a Calculator You Have to Think!
Authors: Meyer Phillis I.
Published: October 2020

We had just fini shed a semester of using simple handheld calculators in our fourth-grade mathematics class. I had given every student a sheet of paper and asked each to write what, for them, was the hardest thing about using the calculator. I got a variety of answers—pushing the wrong key and forgetting to “clear” it, turning the calculator off before a problem was finished. making a mistake and having to start a ll over again, and most revealing of all, “When you use a calculator you have to think.”
Errors That Are Common in Multiplication
Authors: Kilian Lawrence , Cahill Edna , Ryan Carolann , Sutherland Deborah , Taccetta Diane
Published: October 2020

Are there any generalities an elementary teacher can keep in mind while conducting group instruction in the use of the multiplication algorithm? Are there certain kinds of multiplication mistakes many children make and, therefore, of which teachers should be aware? Cox (1975) has investigated the errors made by children in addition and subtraction examples. He has proposed the foLlowing classification system for computational errors.
Let's Do It: With Powers of Ten
Authors: Leutzinger Larry P. , Nelson Glenn
Published: October 2020

The ease of converting from one unit to another is a major convenience of the metric system. Most of us find it much easier to convert meters to centimeters than to convert yards to inches. A skill needed for converting a measure from one metric unit to another is the ability to multiply or divide by a power of ten, often 10,100, or 1000. To change 6.32 meters to centimeters, for example, one has to multiply by 100. Some students, unfortunately, have to resort to a fairly long, time-consuming process (fig. 1). For these students, converting yards to inches is almost as easy and so, for them, a big advantage of the metric system goes unnoticed.
Ideas
Authors: Scheuer Donald W. , Williams David E.
Published: October 2020

The IDEAS this month is a series of exercises in classification and measure of various geometric shapes. Classification is done by size, number of sides, and the usual measurements of perimeter and area. Ratios of lengths of sides are also considered in the classifications.
Readiness of Eight-Year-Old Children to Understand the Division of Fractions
Authors: Shokoohi Gholam-Hossein
Published: October 2020

Several fine a rticles on the teaching of division of fractions have been written and published in the last twenty years. Some of the authors have proposed a mathematically valid method for teaching the topic, without considering the psychological factors that are so important for instruction in the elementary school. Other authors have given attention to the instructional considerations, but have neglected the psychological or mathematical aspects. And sti ll others, although familiar with both mathematics and psychology, have failed to exploit all the possibilities that these points of view can offer. An artithmetic teacher is in a difficult situation. He or she must be, in some measure, a mathematician, a psychologist, and an educator at the same time. The mathematician determines the content aims, the psychologist indicates the possibilities, and the educator chooses the best method, namely, the approach that satisfies the mathematician as well as the psychologist.
Cal the Calculator Can Help Parents Become Involved
Authors: Sovchik Robert J.
Published: October 2020

Classroom teachers have known for a long time that a child's parents are an important determinant of success in school. In a paper “Improving Mathematics Education in Disadvantaged Areas.” wh ich he presented at the 52nd Annual Meeting of the NCTM. Atlantic City, 1974. Williams stated that programs designed to improve mathematics achievement in disadvantaged areas must involve meaningful relationships between parents and teachers. Getting parents to make and use inexpensive mathematics games and activities with their children may be one way to help bridge the gap between home and school. This article describes one device that some parents have found enjoyable to make and use with their children. Cal the Calcu lator is an inexpensive. easy-to-make device that can help ch ildren practice basic skills in an enjoyable fashion.
ONE POINT OF VIEW: Face to Face with Tomorrow
Authors: Hill Shirley A.
Published: October 2020

History and human experience do not really sort themselves into neat ten-year packages, but somehow the turn of a decade causes us habitually to take stock. Nowhere is this more evident than in the popular media which have been busily reviewing the seventies and speculating about the eighties for months now.
Painless Drilling Not Your Dentist, but the History of Mathematics
Authors: Krulik Stephen
Published: October 2020

Many of our students are far from receptive to the many problems of drill materials with which some teachers provide them. And yet, most students need some drill and practice before they can successfully master a new concept or skill. The history of mathematics can play an important role in making these apparently contradictory points of view compatible. Many of the concepts and ideas in the history of mathematics were developed from practical necessity rather than from a theoretical base; it is these same ideas that offer a great deal of practice material for our students. This ancient body of knowledge can provide drill that is interesting, satisfying, challenging. And, at the same time, it offers the necessary drill to achieve competence in fundamental skills and concepts.
One point of view: Change and Changelessness
Authors: May Lola June
Published: October 2020

Some of the changes made in the elementary and junior high school mathematics curriculum during the past twenty years have been good. Subtraction is presented as the inverse operation of addition. The words subtrahend and minuend are seldom used anymore. The words addends and sum are used for the numbers both in addition and in subtraction. It is hard to find anyone who wants to go back to teaching children the difference between a minuend and subtrahend and how to spell the words. Instead of being pure memory of isolated facts and operations, elementary mathematics has begun to evoke a friendly feeling for numbers. For example, by naming different ways to make the number five (3 + 2, 7 − 2, 5 + 0, and so on), young children get a feeling for five. They see that they can manipulate counters and write many names for a number. This type of teaching makes the number five come alive; it is not just the answer to some isolated facts.
Let's Do It Fractions with Models
Authors: Leutzinger Larry P. , Nelson Glenn
Published: October 2020

There is still value in learning about common fractions, even with the increased use of the metric system of measurement. In the past, much of the computation with common fractions has resulted from measurement situations with the customary system.
The Etiquette of Diagnosis
Authors: Scheer Janet K.
Published: October 2020

“Why can't you see?” said the frustrated student to the equally frustrated teacher. “Of course 32 − 9 = 37. To remediate an error like this, the student is too often given worksheets consisting of myriads of the same type of problem and is expected to practice until he or she is able to do that computation correctly. The more efficient and less frustrating procedure is to find out why the student persists in a particular error in computation and on the basis of that diagnosis, to plan appropriate remediating activities.
What's Going On…
Authors: Haynes Harriet
Published: October 2020

Great falls schools go metric. The Great Falls Public School System has launched a metric education program to train teachers and members of the community in the metric system through a hands-on approach. The program used seven portal leaders trained at the University of Wyoming to provide inservice work for teachers. Selected teachers then develop curricular mater ials and testing instruments, and act as in-school contacts. Portal leaders also speak to community groups such as PTAs and service clubs. For more information contact Alice Hemphill, Curriculum Coordinator, Great Falls Public Schools, P.O. Box 2428, Great Falls, MT 59403.
Multiplication and Division Algorithms in German Schools
Authors: Kulm Gerald
Published: October 2020

Giving attention to algorithms for arithmetic may seem strange at a time when paper-and-pencil calculations are giving way to minicalculators. There are, however, at least two reasons for doing so. First, it seems unlikely that competence in doing calculations with whole numbers will soon be thought unnecessary for most students. As long as this is true, it is useful to have alternative approaches available as instructional aids in teaching computation. Second, and more important, as the use of calculators becomes more common, students will have fewer arithmetic computational experiences on which to base their learning of algebra. For this reason, it is important that the arithmetic algorithms that are learned make as clear as possible the processes on which they are based.
A Case for the Calculator
Authors: Vannatta Glen D. , Hutton Lucreda A.
Published: October 2020

During the 1976–77 school year, 560 hand-held calculators were introduced into the mathematics instruction of tltirty-eight intermediate-level class-rooms in six Title I schools in the Indianapolis Public School System. Approximately 1000 students were involved and all teachers of fourth, fifth, and sixth grades in the six schools participated in the project. The project was continued during the 1977–78 school year, but during the second year teacher participation was entirely voluntary.
Superset '80
Authors: Brunelle Helen Mahoney
Published: October 2020

Want to end the school year with a burst of enthusiasm rather than a sigh of relief? Want to give all your students, no matter what their ability level, a sense of achievement? Want to capture the th rill usually reserved for athletic competition? Want to show your students how much they have learned du ring the school year?
Miscellany: Ice-Age Counting
Authors: Seligman Marc
Published: October 2020

Invention is the best teacher. If we harness this idea, we can have learning coexist with fun in our classrooms. Imagination and planning are all that are required to teach difficult concepts.