bluuebunny/crossref_metadata_2025 huggingface dataset:
Sneaking in Some Drill
Authors: Richardson Lloyd I.
Published: October 2020

Classroom situations that help students strengthen a mathematical skill while they are enjoying a mathematical activity should be an objective of all teachers. And yet, quite often, classroom periods devoted to maintaining mathematical skills become days devoted to dull drill. On the other hand, the mathematics lessons that students enjoy most seem to be those involving mathematics games with limited overt computations. What is needed then are games that covertly require computation.
“Fertilizer” Is Important!
Authors: Beattie lan D.
Published: October 2020

It is somewhat paradoxical, but at a time when there is increasing concern for mastery of basic arithmetic skills, there is a growing recognition of the fact that the able child is a neglected child. It is true that the basic program in most elementary schools probably includes optional segments that are intended to remedy this neglect and they are generally referred to as enrichment. However, although these optional segments are intended to be challenging and interesting, their very nature seems often to suggest that the term enrichment is a misnomer.
Multiplication Football
Authors: Tolman Marvin N.
Published: October 2020

During nine years as a teacher in the elementary schools, the author acquired a rather substantial bias in favor of the practice of requiring students to memorize the basic mathematics facts. He found that students in his classroom who had not mastered the basic facts were handicapped, as indicated by the relative performance of the same students following mastery.
Ideas
Authors: Scheuer Donald W. , Williams David E.
Published: October 2020

Ideas for this month consists of four worksheets that can be used to provide experience in classifying numbers according to attributes such as initial letter of the number name, size, divisibility (factors), and special characteristics such as prime and perfect squa re. These worksheets can be adapted to any level by changing the Lists of numbers to be classified.
An American Teaches in Shanghai Middle School #2
Authors: Smith Eugene P.
Published: October 2020

Imagine yourself in front of fiftyfive bright-eyed, attentive thirteenand fourteen-year-old Chinese adolescents in Shanghai Middle School #2. You speak no Chinese and, as far as you know, the students speak no English. If you were invited to work with this group, just what kind of lesson would be interesting as well as educative? The author thought that a SLIM presentation would be just the thing. SLIM is an acronym for a “Silent Lesson In Mathematics.”
Weighing Milk Cartons
Authors: Willcutt Bob
Published: October 2020

Here is a new version of a standard old problem: You are given nine milk cartons and are told that one of the nine cartons weighs slightly less than the other eight. If you use a balance scale, how can you find the one carton that weighs less than the other eight? What is the fewest number of weighings that you will need to make in order to always find the Light carton?
Place Value and Probability (with Promptings from Pascal)
Authors: Stone Janine S.
Published: October 2020

For several years my sixth-grade and seventh-grade students have enjoyed a simple number game involving place value. I have developed a deeper appreciation of the game as I have watched the students employing various str ategies to win. Since the game is superficially simple. it appeals to all levels of my students, from basic to gifted. (It is a modification of the Pl ace-Value Game found on page 64 of Mathematics: Modern Concepts and Skills by Dilley and Rucker; Raytheon Education Co.: Lexington, MA, 1968.) The materials needed to play the game are readily available. The student needs only paper and pencil.
Problem Solving Plus Role Playing Equal Interest Plus Basic Skills in Mathematics
Authors: Heck Shirley F.
Published: October 2020

Learning is more likely to occur when the learner can relate what he is learntng to the fulfillment of a real need or purpose in his life. Thus, there a need to build into a set of learning activities a mechanism that will encourage a compelling desire to understand some topic or subject more fully. It is this desire to learn, this hunger for knowledge, that teachers need to nurture in students. Providing the setting promote this kind of intellectual hunger can be exciting and captivating both learner and teacher. But more often than not, the success or failure of the learning environment rests on the teacher's ability to encourage this kind intellectual curiosity and interest. This is certainly true in mathematics if students are not intrinsically motivated learn basic skills.
Ditton's Dilemma, or What To Do About Decimals
Authors: Kidder F. Richard
Published: October 2020

Mary excitedly waved a shiny new minicalculator at her third-grade teacher exclaiming, “Mr. Ditton, Mr. Ditton, see what Daddy gave me for my birthday.” Sharing her enthusiasm, Mr. Ditton examined the calculator carefully, “Isn't this terrific? Now you can work all those long messy problems that you have always hated to do.” Mary's elation quickly subsided, “But I can't Mr. Ditton, I can't. I don't know what all these numbers mean.”
A Case for Rolling Zeros, or How to Determine If a Zero Is Necessary
Authors: Wilkey Bell Cathy
Published: October 2020

The answer is 10.4. “Teacher, teacher! I have 10.40. How come I missed it?”
Designs from Finite Arithmetic
Authors: Jacobson Herbert R.
Published: October 2020

The students in my fourth-grade class were having difficulty completing a multiplication table for a 7-clock— we were working on a unit of clock arithmetic. In order to help them, I reviewed multiplication on a number line and demonstrated multiplication by 3 and 4 on the line. (Fig. 1) Then I drew a 7-clock and repeated the process. (Fig. 2)
Ideas
Authors: Tabler M. Bernadine , Jacobson Marilyn Hall
Published: October 2020

The IDEAS this month provide practice for addition, subtraction, multiplication and division of rational numbers.
From the File
Authors: Shores Danna
Published: October 2020

On 3-by-5 cards, one figure on each card, make four copies of each of the figures shown. Include the name of the figure on each card.
Identifying the Gifted Student in Mathematics
Authors: Greenes Carole
Published: October 2020

We are witnessing a surge of interest in the gifted child. This is evidenced by the increasing number of special educational programs, curriculum materials, professional articles, lectures, and research projects devoted to the subject.
Providing for Able Students at the Local School Level
Authors: Shufelt Gwen
Published: October 2020

In the early history of education in the United States it was only the capable student who remained in school. At that time mathematics was considered a subject appropriate for the intellectually elite and the needs of a predominantly rural culture did not include extensive education for the majority. However, with the spread of the Jeffersonian ideal of democracy based on universal education, by the middle of the twentieth century, education for all was becoming a reality.
Teaching Mathematics: Implications from a Theory for Teaching the Language Arts
Authors: Skypek Dora Helen
Published: October 2020

Researchers have investigated the influences on mathematics achievement of general reading ability, of instruction in special reading skills, of knowledge of vocabulary and syntax, of listening skills, of the verbal styles of teachers, and of verbal interactions within the classroom. In most cases, the investigators found evidence of a significant relationship between measures of mathematics achievement and measures of selected language skills. Thus, it seems appropriate to ask the question, Do the practices in teaching language have implications for teaching mathematics?
From the File
Authors: Iovino Rose Marie , Ahrens Carole
Published: October 2020

Five computation problems done correctly are as good as fifty. (If you can do five, you can do fifty and, of course, the converse is true.) Don't overdo mathematics assignments and use them as busy work.
National council of teachers of mathematics: Annual Financial Report
Authors: Stipanowich Joseph J. , Egbers Elden B. , Choate Stuart A. , Immerzeel George , Crosswhite Joseph , Gates James D. , Tewell James R.
Published: October 2020

Each year it is the responsibility of the Financial Policies Committee (FPC) to prepare and to recommend to the Board of Directors a balanced budget for the next fiscal year. The budget as submitted or as modified to reflect the priorities of the Board is adopted and becomes a plan for use of the revenues available during that fiscal year.
Let's Dolt A Poster–Board Balance Helps Write Equations
Authors: Van de Walle John , Thompson Charles S.
Published: October 2020

The word equals is an illusive word with a very simple meaning: “Is the same as.” Equals is illusive since few children have any contact with the term prior to its use in first-grade mathematics workbooks. Interviews with children in grades 1, 2 and 3 indicate a weak or inappropriate concept attached to the equal sign (=) even though all seem to know what it is called. One child said, “It keeps the teacher from getting the answer confused.” Other responses indicated that, in general, many children believe that the principle use of the equal sign is to separate problem and answer.
Spatial Relationships and Young Children
Authors: Baust Joseph A.
Published: October 2020

“Jane, would you please look under the table next to the wall for my crayon and bring it to me?” To young children, this sentences communicates quite an intricate set of directions that may ultimately help them to find an object in a chaotic environment. Being able to know the position of someone or something in the adult world and being able to discriminate or even crudely measure where these things can be found, is where spatial words and mathematics play a crucial role.
Calendar Bingo
Authors: Barson Lois H.
Published: October 2020

“Calendar Bingo” is a game that helps children become familiar with a calendar. A large, poster-size calendar for each month is useful for class discussion and reference. lf the large calendar is not available, each student should have a copy of the calendar for the current month. A transparency of the current month could also be used.
Extracting Square Root Made Easy
Authors: Chow Paul C. , Lin Tung-Po
Published: October 2020

“What's the square root of 219.04?” asked the professor. There was no response from the class.
How Mathematics Supervisors can use the Arithmetic Teacher
Authors: Rowan Thomas E.
Published: October 2020

Most people I know agree that some kind of team approach is the most effective avenue to good mathematics teaching and learning. Mathematics teachers and supervisors are members of one of the kinds of teams that can produce highly effective mathematics instruction. The purpose of this article is to say something, however briefly, to mathematics supervisors about another member of the team that can make things easier and even more effective—the Arithmetic Teacher. Of course, having a team member like the AT is not just having one additional member on your team; it's a variety of additional members. Although it may be a case of stating the obvious for most supervisors, I believe it is worthwhile to briefly enumerate some of the ways in which the AT can help supervisors.
Let's Do It: Strategies for Learning the Basic Facts
Authors: O'Neil David R. , Jensen Rosalie
Published: October 2020

One complaint often voiced by elementary teachers is that some of their students are unable to readily grasp new concepts because they do not have sufficient command of the basic facts. This month we are suggesting some strategies teachers can use to help their students master the basic addition facts. The same strategies can be adapted to the memorization of basic facts for the other operations.
Transitional Division Algorithms
Authors: Laing Robert A. , Meyer Ruth Ann
Published: October 2020

“Long division is the most difficult process taught in the elementaryschool mathematics program.” During the past decade, this statement has been cited as a justification for poor performance on standardized tests. Could it be that the manner in which the process is developed in the elementary-school program is the culprit, and not the inherent level of difficulty of the process itself? Test results reveal only the effect. It is the purpose of this article to suggest the cause.
A Visitor from SQ
Authors: Richards W. S.
Published: October 2020

Our last week of vacation was great! While Jennie and Michele, my granddaughters, and I were camping in the hinterlands of northern Michigan, we learned about SQ. They also made a new friend, Connie Cubic. The area in which we were camping is accessible only be canoe. There were no roads close enough for us to even hear the sound of traffic. Anyway, on with the story.
Note on Philosophy of Teaching Arithmetic
Authors: Fehr Howard F.
Published: October 2020

More and more the only services which human beings can offer to society and which society will need will be intellectual. Just as in the last 100 years mechanical skill superseded and to a great extent outmoded manual labor, in the next few years the automatic machine will supersede and to a great extent outmode mechanical skill (not entirely but mechanical skill will be cheap, comparatively to brain power). The age of automatons, for their development, construction, and maintenance, demands from society greater brain power.
How Are Your Nines?
Authors: Bane Robert C.
Published: October 2020

Have you ever wished for an abundance of computational material whose accuracy could be verified when teaching the fundamental operations of addition, subtraction, multiplication and division? All of us have, no doubt, yet I tremble to think how many times I have overlooked the t remendous possibilities inherent in the casting out of 9's before I ever made any extended use of this princi ple for checking the accuracy of arithmetic computations.
Introducing Mr. “0” and Mr. “Decimal Point”
Authors: Ernst Richard
Published: October 2020

PROBABLY THE BIGGEST problem that faces 7th grade teachers is to find some way to stimulate the pupils' interest as well as aid his learning of a subject. I was faced with this problem while intering in a junior high school. My directing teacher suggested I teach the unit on decimals. He warned me that 7th grade students were often afraid of decimals and as a result of this, interest was often low. I took this warning to heart and made up my mind to find a way to introduce the unit in such a manner as to create interest and also to teach place value and the use of the decimal point.
What's in a Rhyme?
Authors: Tuttle Ruth Hodges
Published: October 2020

I DISCOVERED THE EFFECTIVENESS of using little poems and rhymes to help children acquire number meanings when Bobby was six years old. Bobby was the first of 1B's to have a birthday after school opened in September. It was a big event. A birthday! A thrill for every child in the room, for each had at least five birthdays behind him. And each child had either recently become six or was about to do so.
Teaching Verbal Problems in Arithmetic
Authors: Peeler Harry
Published: October 2020

What is a problem? A problem consists of a situation which has no ready-made solutions. An arithmetic problem is a special quantitative situation involving perhaps size or amount. It involves a special vocabulary—the language of numbers. And the solution is reached through use of special techniques—one or more of the fundamental processes. Morton refers to a problem as “an arithmetical situation in which the operation to be performed is not indicated but must be decided upon by the pupil.” 1
Measures Make Arithmetic Meaningful
Authors: McKeen Gene
Published: October 2020

“MEASUREMENT IN LIFE” was the title of one of our recent units in arithmetic. Prior to studying this unit, most of our class members had only vague ideas about the real value of measurement in everyday living. At the beginning of the unit, we discussed some of our own ideas as to where and how measurement was used throughout the world. We knew, of course, that carpenters measured with rulers and tapes and some in the class mentioned that the housewife used measurements when she used recipes in cooking and baking. As our study of measurements progressed, however, our knowledge of measurement and its value in many occupations took on more and more meaning. Our teacher, Mr. Norton, asked each member of the class to search the house for any measuring device that could be brought to school. Believe me, we soon discovered that the ruler and yardstick weren't the only measuring devices being used. Some of the class members brought instruments that most of us had never heard of or seen before. For example, three boys brought micrometers. Although most of the class had not heard of the micrometer before, all of us soon learned that the “mike” was a precision instrument used by many different people such as the machinist, geologist, metal worker, and factory worker. All of us learned the parts of the “mike” and also how to measure with it. We were really surprised to find that we could measure the thickness of a hair on our head; mine was 3/ 1000 of an inch thick. Some of the class members had difficulty in learning to read the instrument at first, but it wasn't long before all of us knew all about the “mike.” In the process of finding out the interesting things about the “mike,” we studied and learned how to work with decimal fractions. My sister had told me that decimals were hard, but I didn't think so even though arithmetic was one of my hardest subjects last year. In fact, I thought decimals were fun and you certainly have to know them to use a micrometer.
Let's Do It: The Versatile Hundred Board
Authors: Horak Virginia M. , Horak Willis J.
Published: October 2020

The hundred board is a manipulative aid that allows a teacher to build upon the recognition of number patterns to teach many basic mathematical understandings. Although young children are often familiar with various patterns, they need concrete models to help them grap the underlying structure of our number sytem. The associated activities decribed in this article provide a means to refine, develop, and extend these understandings.
The Newspaper: A Source for Applications in Mathematics
Authors: Fennell Francis (Skip)
Published: October 2020

The newspaper has long been recognized as a useful instructional aid, primarily in reading, language arts, and social studies. The newspaper can also offer valuable applications of mathematics in a number of topical areas to supplement day-to-day mathematics instruction. The intent here is to present a sampling of mathematics applications that use the newspaper and involve pupils in practical activities. The easy availability and popularity of the newspaper further enhance its uses in the classroom. The activities presented have been grouped by the applications suggested for classroom use.
Let's Do It: Making Measurement Meaningful
Authors: Horak Virginia M. , Horak Willis J.
Published: October 2020

Measurement experiences in the elementary grades should include everyday a pplication situations. With the current emphasis to THINK METRIC, it is necessary for children to have readily available references for the basic metric units. lt is also helpful and interesting for children to see how some metric measurements occur naturally in our environment. The activities in this article are divided into two categories, linear measurement and area measurement. The use of our bodies as a reference for metric estimation is stressed throughout.
A Variation on the Algorithm for GCD and LCM
Authors: Adams Verna M.
Published: October 2020

An algorithm sometimes presented for finding the least common multiple (LCM) of two numbers uses tbe technique of simultaneously finding the prime factors of the numbers. This technique is shown in figure 1. Both numbers are checked for divisibility by 2, then by 3, by 5, and so on. If the divisor does not divide one of the numbers, the number is written on the next line as shown in steps 4 and 5. This process continues until all numbers to the left and on the bottom are prime numbers, or it can be continued, as shown in figure 1, until the numbers across the bottom are all ones. The least common multiple is the product of all of the prime divisors. Thus, LCM (80, 72) = 24 · 32 · 5.
Developing Mathematical Concepts with Microcomputer Activities
Authors: Billings Karen
Published: October 2020

Ten-year-old students are wearing advertising buttons that read MICROS ARE THINKER TOYS. Teachers are bringing microcomputers into their classrooms and using them with students. Teachers are, in fact, investing large amounts of time and energy in learning the capabilities of the microcomputer hardware, in searching for appropriate software, and in experimenting with different computer uses to find out what is most effective.
Taking the First Step with a Computer
Authors: Gojak Linda M.
Published: October 2020

Several years ago. if a computer was available in a chool district. it was located at the high school—only to be used by students taking upperlevel mathematics courses. With advances in technology, the microcomputer i now affordable to most school systems. The added status of having microcomputers at the elementary level has led many administrators to purchase such unit for their schools. What better way to impres the voting public!
Readers' Dialogue
Authors: Mahan Ralph E. , Bidwell James K. , McDonald Jan , Riordan Dennis J. , Freier Judy
Published: October 2020

We welcome letters from readers, and will publish them to the best of our ability within the constraints necessarily placed upon us.
Ideas
Authors: Tucker Benny F. , Bazik Edna F.
Published: October 2020

Ideas for this month presents some problem-solving situations in various settings—a park, a carnival, a map, and a hardware store.
Areas of Polygons on Isometric Dot Paper: Pick's Formula Revised
Authors: Litwiller Bonnie H. , Duncan David R.
Published: October 2020

Many students and teachers are familiar with Pick's area formula for square dot paper. Can Pick's formula be applied to simple closed polygons drawn on isometric dot paper? The answer to this question is the focus of this article.
One Point of View: A Prescription for Dedicated Teachers
Authors: Frye Shirley M.
Published: October 2020

The discussion of Recommendat ion 7 of An Agenda for Action (1980) includes this statement: “Even the be t prepared, competent, and dedicated teacher must continue their development to keep abreast of changing needs, tools, and conditions.” This development could be accomplished by using the “preventive maintenance” theory advocated by home builders. dieticians, automobile mechanics,. dentist, and others. Just a the epecialist prepare a preventive prescription for their clientele, I have a prescription for our development and growth to keep us excited and exciting in our teaching.
One Point of View: Mathematics Equity: Computers
Authors: Johnson Martin L.
Published: October 2020

There is no disagreement that schools have changed since the introduction of the microcomputer. A glance at recent issue of professional journals will reveal many articles that describe ways to introduce and use microcomputer in school or classroom. Some article address issues, such as financial considerations and the selection of software, that need to be considered.
What's Going On…
Authors: Hopkins Bill
Published: October 2020

Ford foundation mathematics project. Five northern New Mexico school districts are participating in the Ford Foundation Mathematics Project, which is designed to improve mathematics programs by training teachers in mathematics content and pedagogy.
Why Do Some Children Have Trouble Learning Measurement Concepts?
Authors: Hiebert James
Published: October 2020

Johnny is good at measuring. He usually gets all his worksheet problems right, especially when the problems involve using his ruler to measure things.
Ya Gotta Play to Win: A Probability and Statistics Unit for the Middle Grades
Authors: Fennell Francis (Skip)
Published: October 2020

Probability and statistic are part of our daily lives in an ever increasing number of ways. State lotteries, casino gambling, and sports at all levels continue to fascinate millions of people.
Cross-Numeral Roman
Authors: Pohl Victoria
Published: October 2020

Work this puzzle like a crossword, but in place of words write roman numerals for the indicated arabic numerals. The complete solution can be found on page 59.
“Hop-A-Long” Math
Authors: Belk Elizabeth Cravens
Published: October 2020

A game I use with kindergarten children is called “Hop-A-Long Math.” It's inexpensive and involves, both manipulative materials and physical movement.
Ideas
Authors: Jacobson Marilyn Hall
Published: October 2020

The “IDEAS” section this month provide problem-solving experience using a “things to do this summer” theme. The problems are related to a county fair, a summer reading program in the library, camp, and Summer jobs.
Teaching the Most Basic Basic
Authors: Burton Grace M.
Published: October 2020

Figure are found in the cave drawings from the Middle Stone Age of what the new-math programs popularized as “counting men” (Gundlach 1969). The early representation shown below illustrates how human beings took advantage of the natural configuration of the hands to develop an ever-ready recording device. It is often asserted, and seems plausible enough, that the reason we rely on a base-ten numeration system is that we are endowed with ten fingers. Some cultures have used other systems (notably, the Mayans, a hot-climate culture in which people went barefoot. used the base-twenty system), and our culture uses other systems for measurement, but, for the most part, ten is a universal base.
Olympiads for Elementary Schools
Authors: Lenchner George
Published: October 2020

Mathematics competitions are widely used to promote interest and enthusiasm for problem solving in programs for capable, talented, and gifted students at the secondary school and college levels. Such competitions are available at the national, state, and local levels. However, few competitions are available at the elementary school level. This lack may be related to some shortcomings of the elementary school mathematics program for capable, talented, and gifted children. Among the shortcomings are (1) a lack of agreement on what special topics and extensions of the curriculum are appropriate, (2) a shortage of teachers trained to teach such topics and exten ions where they exist, and (3) a lack of sources for related “good” problems.
Ideas
Authors: Shaw Jean M.
Published: October 2020

Making graphs and interpreting the results of graphs and polls are important mathematical skills. The following excercises give students opportunities to deal with many kinds of data as they make graphs and interpret their results.
Let's Do It: Promoting Mathematical Thinking
Authors: Walle John Van de , Thompson Charles S.
Published: October 2020

Let's Do It—activity approaches to teaching and learning mathematics in the primary grades, with extensions through grade six.
Mathematical Games: Antithesis or Assistance?
Authors: Harvey John G. , Bright George W.
Published: October 2020

Mathematical thinking can be characterized as thinking intended to solve problems using mathematical knowledge, skills, and techniques. This thinking is often convergent, and the problems being solved may not be mathematical ones, even though mathemat ical knowledge is useful in their solutions. Since the recall of facts and imilar cognitive skill is usually de cribed as a knowledge-level kill (Bloom 1956), it may seem that mathematical thinking and playing mathematical instructional games are at odd with each other, especially if the only effect ive usc of mathematical games i drill and practice of low-level skills. Certainly, such use of mathematical games should not be neglected, since games can be effectively used (1) to retrain students in basic skills at the beginning of the school year (cf. Bright. Harvey, and Wheeler [1979]), (2) to help students retain and improve their performance of basic skills during the school year (cf. Bright, Harvey. and Wheeler [1980]), and (3) to assist students in developing those skill (cf. Bright. Harvey, and Wheeler [forthcoming]).
Attitudes and Career Interests of Junior High School Mathematics Students: Implications for the Classroom
Authors: Pedersen Katherine , Bleyer Dorothy R. , Elmore Patricia B.
Published: October 2020

During the 1970s. various political, cultural, and academic factors joined to thrust the topic of sex differences in achievement in mathematics to national attention. At the same time, research has served to refine attitudinal instruments and to relate cultural and societal influences to sex differences in mathematics. The junior high school years are Important to study because sex-role identification becomes more prominent, and crucial educational choices are made at this stage. Surprisingly, a study by Benbow and Stanley (1980) has suggested that the mathematical experiences of both males and females are identical until the junior high school years. The junior high school teacher, especially, becomes cognizant that different foctors are Influencing students during these early adolescent years.
Teacher Education: Mathematics Methods in a Laboratory Setting
Authors: Sherard Wade H.
Published: October 2020

In our sequence of mathematics courses for th e elementary school teacher, mathematics content is integrated with discussion of teaching methods and materials. We have found that the methods portion of these courses, which concern the teaching of informal geometry, measurement, probability, and statistics, can be taught very effectively in a math lab setting, where the emphasis is on active involvement of the student and on the use of concrete, manipulative materials.
Building a Scope and Sequence for Early Childhood Mathematics
Authors: Mueller Delbert W.
Published: October 2020

Educators and parents agree that some type of mathematical experience should be part of an early childhood curriculum. Nursery school and kindergarten teachers plan activities that reflect a mathematical focus, but they ask questions such as, “What mathematics is best for preprimaryaged children?” “What kinds of experiences should be offe red?” “What nonnumber activities are recommended?” “When should I introduce number?” “Is there an approved scope and sequence to follow?”
What's Cooking?
Authors: Routledge Joan
Published: October 2020

When I Introduced the metric system of measurement to my class of fifth grader, I gave them ample time at the sand, the water, and the weighing centers for each activity level. They had poured material from one graduated container to another and had measured and compared volumes and masses of different materials. Yet when they attempted to follow a simple recipe to make cookie for a parents' visitation day, they seemed unable to tranfer the knowledge gained through the contrived activitie and to complete this practical task. These observations prompted me to examine carefully the role that food-preparation activities could play in the development of an under tanding of mathematical idea by middle school students. In this article I would like to share some of my conclusions.
More Patterns with Square Numbers
Authors: Whitin David J.
Published: October 2020

I have found this question to be one of the most important ones that I can ask as a teacher. The more I ask it, the more alert and observant my students become, uncovering many patterns that I had not noticed. Work with patterns must be an integral part of any mathematics curriculum.
Selection Criteria
Authors: Hynes Michael C.
Published: October 2020

The task of selecting materials for classroom instruction is a crucial one whether the decision involves textbooks (NCTM 1982), software (NCTM 1984), or other teaching aids. This article focuses on a variety of criteria for the selection of manipulative material.
Teaching the Process of Mathematical Investigation
Authors: Borenson Henry
Published: October 2020

Middle school students can gain an appreciation for the process of mathematical investigation if we can offer some simple examples to catch their interest. The key to the investigative process is the concept of inductive reasoning, that is, the proces of arriving at a generalization on the basis of a few specific instances.
Ideas
Authors: Payne Joseph N.
Published: October 2020

The ancient Egyptian numerals used as far back as 3400 B.C. had groupings by ten but no place values. The use of these symbols will help students understand our base-ten system and the efficiency of our place-value notation. The basic rules for writing ancient Egyptian numerals (Egyptians now use Hindu-Arabic numerals, as we do) are relatively simple.
The Power of Five: The Step before the Power of Ten
Authors: Flexer Roberta J.
Published: October 2020

In the 1960s, the teaching of basic addition moved from an emphasis on rote memorization of facts to teaching for understanding. Children were given counters to model addition problems, and they arrived at sums by counting them. This experience helped them to understand the concept of addition, but some people suspected that counting alone was not an adequate basis for teaching and learning addition facts.
Problem Solving: Tips for Teachers
Authors: Duea Joan , Ockenga Earl
Published: October 2020

The hand-held calculator is a powerful problem-solving tool. It can be used to develop concepts and explore mathematical topics. The speed and power of the calculator make more realistic and interesting problems accessible and allow students to work many more problems than possible with pencil and paper. The calculator focuses tudents' attention on mathematical processes. Numerical problem solving form the foundation from which algebraic ideas grow. This art icle give examples of calculator tablebuilding activities suitable for the middle school curriculum that develop problem-solving skills and mathematical concept and span the gap from arithmetic to algebra.
AT Classic: Meaning and Skill—Maintaining the Balance
Authors: Brownell William A.
Published: October 2020

The subject given me poses a question. It is no academic question arising out of purely theoretical considerations. It is a assumed that both meaning and computational competence are proper ends of instruction in arithmetic. It is implied that somehow or other both ends are not always achieved and that there is evidence that this is so.
Helping Children Understand Ratios
Authors: Quintero Ana Helvia
Published: October 2020

Temperature, velocity, acceleration, and density are but a few examples of scientific concepts that are expressed by a ratio. These topics are difficult for students to understand because they do not understand the mathematical concept of a ratio.
A Japanese Educator's Perspective on Teaching Mathematics in the Elementary School
Authors: Kroll Diana Lambdin , Yabe Toshiaki
Published: October 2020

In the last few years, numerous articles extolling the virtues of the Japanese educational system have appeared both in academic publications and in the popular press (e.g., Cogan 1984: Morimoto 1982: Shimahara 1985). Although the United State and Japan together lead the industrial world in percentage of young people entering high school (both over 95%). Japanese mean scores on international or mathematics and science arc conently higher than those of any other country including the United Stste (Rohlen 1983) of such remarkable many American are quite interested in knowing more about education in Japan.
Ideas
Authors: Barson Alan , Barson Lois
Published: October 2020

lDEAS for this month focuses on the topic of problem solving using the strategies of patterning (grades 1 and 2); working backward (grades 3 and 4); making a chart, table, or graph (grade 5 and 6); and diagraming and elimination (grades 7 and 8). Teacher need to provide stude nts with problem that develop skill in a varie ty of problem-solving strategies. These activitic permit students to be creative in their methods of solving problems.
Assessing For Learning: Tests—a Tool for Improving Instruction
Authors: Trafton Paul
Published: October 2020

Tests … what purpose do they serve? So often their main purpose appears to be to grade, to sort, to label.
Research into Practice: Gender and Race Equity in Primary and Middle School Mathematics Classrooms
Authors: Reyes Laurie Hart , Stanic George M. A.
Published: October 2020

A number of concerns have been expressed about the mathematics performance of all students in our schools (see, e.g., McKnight et at. [1987]), but the performance of certain groups is particularly trouble-some. For example, on standardized tests of mathematics achievement, Hispanic students and black students consistently score below their white counterparts during the primary and middle school years. In addition, although female students perform at least as well as male students during the primary school years, some evidence suggests that gender differences in favor of boys begin to appear during the middle school years, particularly on problem-solving and applications task. Are female students black, and Hispanics naturally less able in mathematics? Or do families, schools, and the create of society offer experiences that create these differences? Individual differences in mathematics performance are normal, inevitable. and obviously related to natural ability; but no reason exists to believe that female students, blacks, and Hispanics, as groups, are by nature less able in mathematics. The problem is one of equity.
From Pattern-Block Play to Logo Programming
Authors: Newton John E.
Published: October 2020

Pattern blocks are the most seductive materials in my mathematics lab. All I need to do is dump them in front of children and interesting things happen. ldeas are explored, enhanced, and transformed until satiation: then other ideas arise. Children seem to have a continuoua source of inspiration. My role change from curmudgeonly taskmaster to welcomed facilitator.
A Television Programming Challenge: A Cooperative Group Activity That Uses Mathematics
Authors: Pagni David L.
Published: October 2020

Opportunities abound for acrossdiscipline activities that teach children Language arts, mathematics, science, and social studies in elementary school. In middle school or junior high school, where school subjects are departmentalized, the opportunities to give students experiences that integrate skills in the different disciplines are diminished. The Television Programming Challenge was designed for junior high school students to show applications of mathematics in the real world. It was piloted with sixty-four students in grades 7 and 8 as part of the Saturday Science Series at California State University, Fullerton. These presentations are made in mathematics, physics, chemistry, geology, and biology to selected students from local schools. Each presentation lasts three hours, from 9:00 A.M. to 12:00 noon.
Teaching Mathematics with Technology: Changing Variables Using Spreadsheet Templates
Authors: Edwards Nancy Tanner , Bitter Gary G.
Published: October 2020

Teachers can refer to the documentation of the software to prepare templates like those shown in figures 1–5 to help students solve word problems that have constantly changing variables. An advantage of using computer spreadsheets is that the students can answer a variety of questions based on one problem and see the relationships among the variables as numbers change.
More Magic With Magic Squares
Authors: Wood Eric F.
Published: October 2020

Many articles have appeared in the Arithmetic Teacher showing teachers how to use magic squares in their classrooms. Games (Bernard 1978), pattern searching (Atkinson 1975; Freitag and Freitag 1970), drill and practice (Bright 1977). and explorations (Wills 1989) are all activities that can be designed around magic squares. This article. however, serves a different purpose: to present the teacher with an easy method for constructing magic squares to use in these applications. In addition to explaining a method that can be carried out manually, a computer program that will do all the work is included.
Teaching Mathematics With Technology: Finding Number Patterns
Authors: Bitter Gary G. , Tanner Edwards Nancy
Published: October 2020

Students need to know which technological tool is appropriate to use with various kinds of problem solving. The computer is not always the most efficient device to use.
Spatial Sense
Authors: Grande John Del
Published: October 2020

Spatial sense is, in part, “an intuitive feel for one's surroundings and objects in them” (National Council of Teachers of Mathematic, Commission on Standard for School Mathematics 1989). outer world and people are really like.
Developing Spatial Thinking In The Middle Grades: Designing A Space Station
Authors: Moses Barbara
Published: October 2020

The recently published Curriculum and Evaluation Standards for School Mathematics (National Council of Teachers of Mathematics, Commission on Standards for School Mathematics 1989, 21) clearly states that educators should devote less attention to “ complex paper-andpencil computations” and “rote memorization of rules.” The time currently spent in the elementary school mathematics curriculum on these topics should instead be devoted to other areas, such as geometry and problem solving. Students should “visualize and represent geometric figures with special attention to developing spatial sense” and learn to appreciate “geometry as a means of describing the physical world” (p. 112). But elementary school mathematics textbooks typically contain few activities that deal with the development of spatial sense.
The Art of Tessellation
Authors: Giganti Paul , Cittadino Mary Jo
Published: October 2020

Students need to experience the excitement and beauty of mathematics beyond numerical calculations. Introduce your students to tessellations, a project that combines mathematics and art. A tessellation is a tiling, made up of the repeated use of polygons and other curved figures to completely fill a plane without gaps or overlapping, just like the tiles on a kitchen or bathroom floor. See figure 1.
Teaching Mathematics with Technology: Data Base and Spreadsheet Templates with Public Domain Software
Authors: Edwards Nancy Tanner , Bitter Gary G. , Hatfield Mary M.
Published: October 2020

Good programs are becoming available through public domain software, software that can be obtained at little or no cost whose duplication is legal. An example is the Appleworks simulation program IMMIGRANT. It contains several programs, including the passenger lists of two ships from which the student is asked to “adopt” a family. The students help the family adjust to the housing, market, jobs, and budgets of the 1840s and 1850s. IMMIGRANT yields numerical information in two formats, data base and spreadsheet.
Remembering how to Read Decimals
Authors: Klein Paul A.
Published: October 2020

Even though some students have a clear concept of decimals and are able to carry out fundamental arithmetic operations with them, they may not be able to read or write decimals correctly. Their inability to read decimals is often caused by the way they “read” a decimal numeral. For example, the decimal 2.43 becomes “two point four three” instead of the more meaningful “two and forty-three hundredths.” The word-forword reading of symbols may, in fact, undermine their ability to determine the place value of digits in a decimal and to rewrite decimals in fractional form.
One point of view: The Spring Is Wound Too Tight on Our Spiral Curriculum
Authors: Jensen Robert J.
Published: October 2020

It is time to question the efficacy of the spiral mathematics curriculum. I believe that the spiral curriculum, in its current form, is hurting our efforts to improve mathematics education in this country. The crux of the problem is that we now typically have a curriculum so tightly spiraled that each year revisits almost all the content of the previous year. This approach necessitates so extensive a review component that only limited time remains for developing new material at a higher intellectual level. The resulting curriculum more closely resembles a tightly wound spring than the upward-moving spiral originally envisioned by educational proponents of a spiraled curriculum. This dilemma has been documented by Flanders (1987), who reports that the average percentage of new content in three popular mathematics textbook series is just 44 percent in the fourth grade and dips as low a 31 percent in the eighth grade.
Partitioning: An Approach To Fractions
Authors: Pothier Yvonne , Sawada Daiyo
Published: October 2020

Recent research reports show that students have difficulty solving fraction problems when using physical models or diagrams whether the units are sets of objects (Hunting 1983) or regions (Kieren, Nelson, and Smith 1985). These reports show that students are not familiar with fraction models, a finding that suggests that they do not have sufficient experience with nonsymbolic work in fractions. Competence in representing fractions concretely or pictorially would facilitate solving fraction problems and could serve to verify computations with symbolic fractions.
Research Into Practice: Experience, Problem Solving, and Discourse as Central Aspects of Constructivism
Authors: Yackel Erna , Cobb Paul , Wood Terry , Merkel Graceann , Battista Michael T.
Published: October 2020

Over the past five years, we have collaborated with teachers to develop forms of instructional practice in elementary chool mathematics that are compatible with a constructivist view of teaching and learning. Two key aspects of our work form the basis for this discu ion: first, the process of developing in tructional activities, and second. the importance of engaging students in mathematical discussion.
Ideas, Ideas, Ideas from “IDEAS”—an Annotated Bibliography
Authors: Browning Christine A. , Meyer Ruth Ann
Published: October 2020

In January 1981 an annotated bibliography of the “IDEAS” Section was printed. This compilation of activities began with the first “IDEAS” published in January 1971 and ended with the May 1980 issue. The bibliography was well received by preservice and in-service teachers and mathematics educators. Ten years and ninety-four more issues later, it's time for another compilation.
Pentagonal Tessellations
Authors: Clauss Judith Enz
Published: October 2020

Investigating tessellations can furnish enjoyable and exciting mathe matics-inquiry activities for elementary and middle school students. The word tessellation come from a Latin word meaning “to pave with tiles,” or “to make a mosaic of.” When polygons are fitted together to cover a plane with no spaces between them and no overlapping, the pattern formed is called a tessellation. Creating and studying these patterns helps students to investigate basic properties of angles and polygons. Additionally, students develop skills in using rulers and protractors.
The City Hall Park Study
Authors: Erb Clinton A. , Rathbone Charles
Published: October 2020

How could we teach elementary- and middle-level mathematics methods to college juniors in a manner that was engaging, relevant, and applied? That's the problem we faced.