bluuebunny/crossref_metadata_2025 huggingface dataset:
Calendar Mathematics
Authors: Chancellor Dinah
Published: October 2020

The calendar is designed to speak directly to students, giving them open-ended questions intended to engage their intellect through their interests. Students ore encouraged to work on the activities individually, in pairs, or in small groups. No answers are given for the calendar questions so that students ore encouraged to look to themselves as the mathematical authority, thereby developing the confidence and criticalthinking skills necessary to validate their thinking.
By Way of Introduction
Authors: Elliott Portia C.
Published: October 2020

I have chosen to begin this “By Way of Introduction” to this focus issue in a rather unorthodox way, spoofing the popular television game how “Jeopardy.”
IDEAS
Authors: Passarello Lisa M. , Fennell Francis (Skip)
Published: October 2020

This month's IDEAS emphasizes connections between science and mathematics by using a performance-, or authentic-, asessment format. The month of February is close to the heart of many students and teachers. The activity sheets and the extensions offer a different approach to the valentine month. Students have the opportunity to explore applications involving their own personal valentine—the heart. The activities involve number sense, problem solving, measurement, and statistics. Additionally, this month's IDEAS involves a variety of important mathematics concepts and ideas in a performance-based setting. The activity sheets are designed to be used in multiple grade levels. The activity sheets can be completed by individual students or groups of students. The at-home-activity sheet is designed to connect school-mathematics learning with the home. Encourage students to complete this activity sheet as a parent-child experiment.
Readers' Dialogue
Authors: Labuskes Kenneth G. , Hollingsworth Caroline , Schmidt Pauline , Ewbank William A. , Cooke Linda B. , Ronshausen Nina L. , Shatz Erica J. , Van Erp Jos W. M.
Published: October 2020

A fellow teacher posed a problem to me that inspired an interesting mathematics lesson. She had heard Mr. Wizard say that it was impossible to fold a piece of paper in half more than eight times. Naturally, I tried the experiment. Students stood around to watch the transaction, apparently very interested in the problem. They were invited to try the folds also. I found it impossible to fold in half more than eight times an ordinary sheet of eight-and-one-half-by-eleven-inch paper, but eight folds might be possible with other sizes of paper.
Teaching Mathematics With Technology: The Four Directions Indian Beadwork Design with Logo
Authors: Bradley Claudette , Taylor Lyn
Published: October 2020

Four Directions Indian Beodwork Design is o computer project using logo Writer created for American Indian middle school students attending summer-camp computer classes. The primary purpose of this project was to learn mathematics and logo concepts by writing procedures and creating o turtle-geometry project. The secondary purpose was to employ American Indian beodwork designs, which ore familiar to the students.
Teaching the Digit Zero
Authors: Shuster Carl N.
Published: October 2020

The literature of arithetic is filled with such absurd expressions as “zero is only a place holder.” As a result thousands of arithmetic teachers are teaching this nonsense and doing a vast amount of harm.
Group Methods in Primary Grades
Authors: Greco Anthony J.
Published: October 2020

Every teacher tries to give students as much individual attention as possible. But there is always the time problem, especially if classes are large.
The Role of Experiences in Arithmetic
Authors: Nadelman Goldie , Paskins Elsie B.
Published: October 2020

IN EVERY MODERN ELEMENTARY SCHOOL, there are many natural situations which provide opportunities for children to think about and with which to use numbers. Classroom and school experiences are important because they pave the way for planning a program of meaningful mathematics.
The Day Camp and Arithmetic
Authors: Goodrich B. J.
Published: October 2020

The day camp project of a fifth grade class at Little River School which was held at Greynolds Park, Miami, Florida, on April 17, 1956, afforded many pleasant educational experiences.
The Gifted Ones—How Shall We Know Them?
Authors: Junge Charlotte
Published: October 2020

A few years ago a teacher could be reasonably certain that lhr majority of the studets in his classroom were capable of maintaining the minimum level of achievement suggested by the curriculum. Today the situation is very different. Universal education brings togethe all the children of all people. They represent widely different capacities and interests which cannot be sa tisfied chrough unjform content and method. Perhaps one of the most important steps toward understanding the modern school is to realize the range of ability with which the teacher must work. Rsearch indicates that when the average group of six-year olds enter school that two per cent of them will be below the average for four-year olds in general mental development and two per cent will be above the average for eight-year olds. Considering only the middle 96% of the class there is still a four year range in general intelligence. This same range of ability will be found in achievement in any particular area. Furthermore, this range in achievement tend to increase as the children progress through school. A typical range of ability in arithmetic is shown by the following data.1
Developing Ability in Mental Arithmetic
Authors: Flournoy Frances
Published: October 2020

It is a matter of common experience and observation that life presents many uses for mental a rithmetic in a rriving at quick solutions to arithmetical situations. Paper and pencil should seldom be necessary for interpreting many of these quantitative situations. Because activities of every-day life require competence in mental arithmetic, schools must provide pupils with opportunity to learn to think without paper and pencil in solving problems involving simple computation, making approximations, and interpreting quantitative data, terms, and statements.
Non-Occupational Uses of Mathematics Mental and Written—Approximate and Exact
Authors: Wandt Edwin , Brown Gerald W.
Published: October 2020

A widely accepted principle of Curriculum construction states that school curricula should include experiences similar to, and in preparation for, the problems encountered in adult life. In this regard two aspects of social usage of mathematics have received reletively little attention in curriculum construction or in educational research. These aspects are: (1) the role of mental mathematics, and (2) the the role of approximate solutions to problems.
Book Reviews
Authors: Slaugh Robert
Published: October 2020

Each book is attractive, and with the exception of Grade 2, each book contains a carefully prepared index. The grade level is indicated, not by a numeral, but by the number of letters in the first word of the title of each book.
Some Questionable Arithmetical Practices
Authors: Spitzer Herbert F.
Published: October 2020

Many ideas and procedures presented in children's arithmetic books and those used by teachers of a rithmetic are seldom examined critically. This situation is due, in thema in, to two factors: first, practically all the ideas and procedures used in teaching arithmetic are, for the most part, satisfactory, and second, they have become so familiar to teachers that they are taken for granted. Since there are some arithmetical procedures and some statements of what are purported to be facts that are either erroneous or of doubtful value, it seems worth while to look critically at a few of these questionable practices.
British Teachers' Reactions to the Cuisenaire-Gattegno Materials: The Color-Rod approach to Arithmetic
Authors: Howard Charles F.
Published: October 2020

During the fall of 1956 a Study was made of the Cuisenaire-Gattegno color approach to arithmetic as it was used by several teachers in infant and junior schools in the area of London, England. The purpose of the study was to secure the teachers' reactions as to the effectiveness of the approach under everyday classroom conditions.
A Place-Value Game for First Graders: A Teacher-Made Device
Authors: MacRae Irene R.
Published: October 2020

Many teachers find that place value is one of the more difficult number concepts to explain to small children. The following game was devised to help reinforce the understanding of place value after it has been introduced by the use of the Hundreds, Tens and Ones Chart. This chart is familiar to primary teachers. The game uses the same pocket device used in the chart. Thus children can reinforce their initial learning by practice under conditions similar to those in which the learning took place.
Grouping in Arithmetic in the Normal Classroom
Authors: Ivie Claude , Gunn Lilybel , Holladay Ivon
Published: October 2020

As a part of the curriculum re-study initiated in the Meridian Public Schools in 1955, an experimental revision of the mathematics program, grades 1-14, is under way.
“Meaning” in Arithmetic
Authors: Hill Jane M.
Published: October 2020

There are so many meanings in arithmetic that the only difficulty in writing on this subject is one of selection. The following ideas are miscellaneous rather than organized.
A Self-Evaluation Study in Grade Seven
Authors: Stenbol Marvel
Published: October 2020

Under the chairmanship of L. E. Hambrick a committee of teachers took an honest look at their work in arithmetic during the school year 1956-1957 and decided to improve the arithmetic weaknesses within grade seven. Early in the study they listed the following weaknesses and then decided what they would do to correct them.
The Use of Graphs for Retarded Children
Authors: Willerding Margaret F.
Published: October 2020

Graphs are very early mediums of a term which in today's education holds a prominent spotlight— VISUAL EDUCATION. Everyone likes pictures as evidenced in the popularity of such magazines as Life, Look, Click, and others. A graph is also a picture. Graphs are pictures measured to exact and comparative scales. They enable adults and children alike to see at a glance facts that it might take several paragraphs of words to describe to the point of full comprehension.
Why Teach Bank Discount?
Authors: Riedesel Alan
Published: October 2020

One of the areas in today's elementary school curriculum that has undergone revision in the past twenty years is the arithmetic program. While there has been much progress much work remains to be done if we are to make the experiences offered of value to the child now and in his adult life.
RESEARCH INTO PRACTICE: Estimation and Mental-Imagery Models in Geometry
Authors: Happs John , Mansfield Helen
Published: October 2020

Analogies are frequently used as mental models to introduce new concept in a number of subject area (Gentner and Gentner 1983). For instance, an electrical circuit can be likened to a water pipe so that students can visualize electricity as “flowing” through the wire in the electrical circuit.
TEACHING MATHEMATICS WITH TECHNOLOGY: Computation and Estimation
Authors: Parker Janet , Widmer Connie Carroll
Published: October 2020

As we prepare for the day envisioned by the Curriculum ond Evaluation Standards for School Mathematics (NCTM 1989), when every student will have a calculator and every class will have at least one computer available at all times, we need to reexamine the roles of computation, estimation, and mental mathematics in the teaching and practice of mathematics. It is true that calculators and computers can perform virtually all computations, relieving us and our students of much drudgery; however, this is not their only role. Calculators and computers also make it easy for us to solve problems in a new mode, T-E-M-T-T: trial, error, and modified trial through technology.
ONE POINT OF VIEW: Let's Not Implement the Stanclarcls
Authors: Schroeder Thomas L.
Published: October 2020

Every now and again If ind my self stopping to reflect on the words and expressions that I use to think about and talk about things. Often, I become uncomfort able with what I discover through this process. I have been involved with an NCTM committee that was originally called the Committee for Implementing the Standards (later renamed the Standards Coordinating Committee). and I have noticed regular “Implementing the Standards” fea tures in both the Arithmetic Teacher and the Mathematics Teacher. But as this phrase has become more and more prevalent, I have found myself becoming less and less satisfied with the whole notion of “implementing the standards.”
Problem Solving with Combinations
Authors: English Lyn
Published: October 2020

When you're trying to choose from a selection of sandwich fillings at a lunch canteen or trying to decide which shirt will best match a pair of pants, you're dealing with combinations. Defined simply, the topic of combinations involves the selection and arrangement of objects in a finite et where the order of election does not matter (Jacobs 1982).
Supermarket Challenge
Authors: Axelson Sharon L.
Published: October 2020

Every so often teacher present a lesson that far exceeds their original expectations for students' learning. This delight occurred with a lesson I developed for my s ixth-grade mathematics class in an effort to implement the NCTM's curriculum standards. My objectives were to integrate mathematics with other curriculum areas and draw on a real-life situation to motivate and interest my students.
Using Logic Activities to Produce a Class Constitution
Authors: Monchamp Susan Strand
Published: October 2020

One of my major goals in mathematics is to have my student understand the relationship of mathematics to the real world. To this end, we begin the year in my first-gradeclass by doing a series of logic activities that lead to the production of our class constitution. The activities reflect three of the NCTM' curriculum and evaluation standards—Mathematics a Communication, Mathematics as Reasoning, and Mathematical Connections (NCTM 1989).
The Number 2 Challenge
Authors: Alterman Alan E.
Published: October 2020

Kids love computers. Kids love a challenge. Kid love to work together. The teacher's challenge is to channel all those positive feelings in mathematically significant directions. In the “number 2 arithmetic challenge” students work together to find as many different equations as possible using only the number 2. They are convinced that excepting 1, the easiest number with which to compute is 2, so they begin the challenge with confidence.
Research into Practice: Students' Use of Symbols
Authors: Carey Deborah A. , Campbell Patricia F.
Published: October 2020

Learning to communicate mathematically is one of the goals of the mathematics curriculum (NCTM 1989). One way to communicate mathematical ideas is through the use of symbols. In the primary grades, number sentences are among students' first introduction to symbolic representation. Number sentences include two kind of symbols: (1) numerals. which represent quantity, and (2) signs for operations, such as+ or −, or signs for relationships, such as=, that describe associations between or among quantities, Young student use these written symbols to record what is already known about an event or a situation (Hiebert 1989). For young students, symbol initially do not have meaning in and of themselves. Rather, meaning for symbols is developed through the process of interpreting and recording what is known about a problem and the solution. Symbols also supply students with a framework for investigating and understanding number. such as the part-whole relationship of quantity.
Assessing Reasonableness: Some Observations And Suggestions
Authors: Garofalo Joe , Bryant Jerry
Published: October 2020

Our friend Pat received a telephone bill of slightly more than $60000 and called the telephone company to report the error. When the company's representative suggested that she may have made more calls than she remembered during the month, Pat pointed out that it would take a very large number of calls to run up a bill of $60 000. The representative agreed and told Pat that her bill would be investigated. The representative then told her that in the meantime she should pay the full amount of the bill and that when the telephone company determined the correct amount due, any excess payment would be credited toward her next bill!
IDEAS
Authors: Moses Barbara E. , Proudfit Linda , Speer William R.
Published: October 2020

The “IDEAS” section for this month focuses on connections between mathematics and music. including both the interpretation of music and the creation of music and musical tones. Music is very special. As a child listens to music, he or she may feel happy and want to smile or may feel a beat and want to clap or dance or may feel contemplative and want to think or write down some thoughts. The activities offer a variety of classroom happenings that tie together a student's perception of music and some important strands of mathematics. The visions of the Curriculum and Evaluation Standards (NCTM 1989), including mathematics as communication, mathematics as reasoning, and mathematics as problem solving, are an integral part of these activities. Other emphasized standards are those on estimation, measurement. statistics, fractions, and patterns. The reproducible sheets for the “IDEAS” section are designed to be used by multiple grade levels. Included are four classroom activities and an activity sheet that involves parents and children in listening together to the radio.
Calendar Mathematics
Authors: Costas Hellen , Porter Jeanna
Published: October 2020

The calendar is designed to speak directly to students, giving them open-ended questions to engage their intellect through their interests. Students are encouraged to work on the activities individually, in pairs, or in small groups. No answers are given for the calendar questions so that students are encouraged to look to themselves as the mathematical authority, thereby developing the confidence and critical-thinking skills necessary to validate their thinking.
Percents: Developing Meaning Through Models
Authors: Haubner Mary Ann
Published: October 2020

An important goal of the mathematics curriculum in grades 5-8 is the careful development of strategies and skills needed to solve problems using percents. Yet students still have difficulties in solving these problems, even when significant time and effort have been devoted to this topic. As we emphasize the development of meaning and understanding of concepts, we need to ask whether the me thods used to teach problem solving with percents are consistent with this trend toward greater understanding of content
Making Manipulatives Work: A Strategy For Success
Authors: Ross Rita , Kurtz Ray
Published: October 2020

As twentyfour second graders enter their classroom after lunch, each one eagerly grabs a playing card from a face-down deck containing only twenty-four cards. “I'm going to the five' table today,” announce Janet as she shows her five of hearts to her friends. Janet then proceeds to a child-sized table over which is suspended a large “5” rotating on a string. Each of Janet 's classmates follows the same procedure until they are seated in groups of four at six tables. The rest of the room is filled with many attractive centers and stations each directed toward the achievement of classroom objectives. Also apparent on countertops and tables are many basket, boxes, and bag full of colorful mathematics manipulatives. which are always kept accessible to the students for use when counting, classifying, patterning, constructing, and exploring.
IDEAS
Authors: David Keller J. , Speer William R.
Published: October 2020

The “IDEAS” section for this month focuses on connections between mathematics and football by using the Super Bowl. Students are asked to look at the Super Bowl not just as “the big game” but as an opportunity to apply mathematics to some interesting problems. The activities involve number sense, geometry, measurement, statistics, estimation, and problem solving. The activities are designed to be used in multiple grade levels. They can be used by inclividual students, small groups, or the entire class. Also included is an activity sheet to be used as a school-home connection. Encourage the family to complete this activity sheet as a family project.
Implementing The Professional Standards For Teaching Mathematics: Making Change in Schools
Authors: Gann Jeanette H.
Published: October 2020

The Editorial Panel welcomes readers' responses to this article or to any aspect of the Professional Standards for Teaching Mathematics for consideration for publication as an article or as a letter in “Readers' Dialogue.”
Teaching Mathematics With Technology: Patterns in Measurement
Authors: Parker Janet , Widmer Connie Carroll
Published: October 2020

Of fall the topics in the K-8 curriculum, perhaps none requires a more active, hands-on approach than does measurement. As advocated in the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989), essential concepts and skills must be developed by engaging students in examining, measuring, comparing, and contrasting a wide variety of shapes. Students must use measurements to investigate and solve real-world problems: “Measurement activities can and should require a dynamic interaction between students and their environment” (NCTM 1989, 116). Formulas should be de-emphasized as activities focus on exploration and estimation. Yet even in activities that focus on actively measuring concrete objects, calculators and computers are valuable tools for recording and organizing data and for extending measurement patterns to pose and test hypotheses.
Making Connections with Estimation
Authors: Lobato Joanne E.
Published: October 2020

During a recent visit to a sixthgrade classroom, students were observed estimating the sums of columns of multidigit numbers by first painstakingly computing the exact sum of each column of numbers on paper, then rounding the answers to obtain estimates. Apparently the students were not bothered by the fact that it didn't make much sense to round the numbers after already finding an exact sum. Furthermore, they seemed unaware that the power of estimming lies in the speed with which a person can obtain an amount that is close enough for the purpose at hand. Instead. estimation had been turned into a cumbersome process intended, at most, to satisfy the direction on a worksheet.
Multiple Strategies: Product of Reasoning and Communication
Authors: Gill Alice J.
Published: October 2020

The NCTM's Curriculum and Evaluation Standards (1989) supports the idea that problems can be solved in more than one correct way. This multiple-strategy approach contains the seeds of motivation, success, and mind stretching. The curriculum standards that focus on reasoning and communication skills are integral to delivering mathematics education that generates the cre ative, problem-solving, divergent thinker that the business community would like to employ.
Research Into Practice: Misconceptions about Multiplication and Division
Authors: Graeber Anna O. , Campbell Patricia F.
Published: October 2020

Multiply your options—divide and conquer— these and many other everyday expressions imply that multiplication always makes larger and division always makes smaller. In fact, these two ideas are so self-evident and so pervasive in many people's thinking that they are among the most notorious misconceptions about mathematics. Misconceptions or naive conceptions are commonly held ideas or beliefs that are contrary to what is fonnally acknowledged to be correct. Mathematics educators study misconceptions because if we can understand how students are apt to see mathematical ideas, we may be better prepared to offer instructional experiences that help them develop accepted conceptions. The two misconceptions just described have been the subject of many research investigations (see, e.g., Bell, Fischbein, and Greer [1984]; Fischbein, Deri, Nello, and Marino [1985); Greer [1987)).
One Point Of View: The Shadows of Mathematics
Authors: Flores Alfinio
Published: October 2020

My first glimpse of mathematics teaching in the United States was through conf ercnces and work hops in Mexico conducted by Donovan Johnson. How lively and enjoyable the learning and teaching of mathematics. could be! My vision was expanded when I became a member of the ational Council of Teachers of Mathematic and eagerly read the Mathematics Teacher, the Arirhmeric Teacher. the yearbooks, and other NCTM publications. What a wealth of ideas, what richness of approaches-discovery learning. mathematics laboratorie. games. activities with manipulative, applications. The myriad ways to con truct meaning!. shed light on the learning and teaching of mathematics. I expected that in the United States thi wealth of information would be reflected in the teaching of mathematics.
Mathematical Connections: Making it Happen in Your Classroom
Authors: Robicheaux Ray T.
Published: October 2020

Some years ago I heard past NCTM president Shirley M. Frye admonish her audience not to be “two-by-four teachers—stuck between two covers of the book and the four walls of the classroom.” This statement seems to lie at the very heart of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989), for it eems that teachers' efforts are basically aimed at changing school mathematics to more closely approximate realworld mathematics.
One Point Of View: The Next Question
Authors: Tucker Sally C.
Published: October 2020

All the mathematics educators I meet are concerned about implementing the curriculum and evaluation standards (NCTM 1989) in classrooms throughout the United States. As an elementary school principal and K- 6 mathematics coordinator in a large rural school district in central Illinois, I am particular! y concerned about the implementation in my own district's classrooms. How should we go about moving teachers and students toward achieving the greatest possible level of understanding and empowerment? I believe that the way we can move toward a higher and higher le vel of achievement is through asking and answering “the next question.”
Using Games to Meet the Standards for Middle School Students
Authors: Leonard Lisa M. , Tracy Dyanne M.
Published: October 2020

It is evident that our society as a whole needs to take a new look at the way mathematics is taught. The National Council of Teachers of Mathematics (NCTM) has publ ished documents to establish a broad framework that will lead to the transformation of the teaching and learning of mathematics. The Curriculum and Evaluation Standards (1989) calls for a reform in school mathematics based on societal and economic needs. The Professional Standards for Teaching Mathematics (1991) makes suggestions for teachers about ways to change their mathematics teaching behaviors on the basis of the curriculum standards. It will take time to educate teachers and administrators about both documents.
One Point of View: Supporting Instruction through Assessment
Authors: Joyner Jeane M.
Published: October 2020

The focus on alternative assessment is an exciting movement in education. In the effort to assess students' knowledge, the emphases on measuring what is valued and in a manner consistent with sound instructional practice are potentially powerful force for improving mathematic.
Language Connections in Mathematics: A Critical Part of Mathematics Instruction
Authors: Capps Lelon R. , Pickreign Jamar
Published: October 2020

In 1973, Bruner maintained that teachers need clear and correct mathematical words to describe problem situations, to question students' unreasoned statements in mathematics, and to encourage students' further research and reading in mathematics. Bruner insisted that “good mathematical language challenges—relights the flame of curiosity” and further said that people use words to resolve puzzling situations. He suggested, however, that using words correctly in solving problems is not easy. To encourage students to speculate, teachers need to help them to understand the use of the words.
Teaching Mathematics With Technology: Using the Video Camera in Mathematical Problem Solving
Authors: Kelly M. G. (Peggy) , Wiebe James H.
Published: October 2020

In the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989), technology, including the use of video, is discussed as a way to develop mathematical thinking and reasoning abilities, promote problem solving, and apply mathematics in the classroom. Effective use of the video camera and instructional television may help students construct meaning in mathematical situations. Video technology brings in the outside world and adds excitement to the classroom by contributing a visual element that is often lacking in class discussions.
ONE POINT OF VIEW: A Different Perspective
Authors: Jones Doug
Published: October 2020

Calvin, the quintessential first grader, is delightfully bratty and philosophical at the same time. He has much to say to mathematics teacher about valuing different perspectives and points or view (sec fig. 1).
On The Nature of Teaching and Assessing “Mathematical Power” and “Mathematical Thinking”
Authors: Greenwood Jonathan Jay
Published: October 2020

What exactly is “mathematical power” to omeone who has always identified mathematics as being the mastery of facts, such as the multiplication table, and procedures, such as the long division algorithm? What does it mean to “think mathematically” to a teacher who always struggled wit11 story problems as a student? To those teachers who fit these descriptions, and a sizable number do. assessing students mathematical power and mathematical thinking is even more bewildering.
Calendar Mathematics
Authors: Faught Leslie , GingerFreeze Ginger
Published: October 2020

The calendar is designed to speak directly to students, giving them open-ended questions to engage their intellect through their interests. Students ore encouraged to work on the activities individually, in pairs, or in small groups. No answers ore provided for the calendar questions so that students ore encouraged to look to themselves as the mathematical authority, to develop the confidence and critical-thinking skills necessary to validate their thinking.
Teacher to Teacher: Loving Mathematics
Authors: Sepeda Arleen Nannette
Published: October 2020

Students in my fourth-grade class were having a frustrating time in mathematics. Since students of this age like clubs, I decided to start one in mathematics. Parts of the approach I used were reflected in “There Is a Mathematics Club in My School!” (Rogish 1991).
Dealing with Data and Chance: An Illustration from the Middle School Addendum to the Standards
Authors: Martin Hope M. , Zawoiewski Judith S.
Published: October 2020

Throughout life, people make decisions based on their own informal collection of data. For example, Alice has three convenient routes to her workplace. After a year of trials and experiences, Alice has settled on the route that she uses most often. When asked why she takes that route to work every day, she answers that she has found it to be the fastest way during rush hour. Her decision is based on the collection and analysis of data from past trial runs of various routes and on a recognition that travel time can vary.
Using Manipulatives Effectively: A Drive Down Rounding Road
Authors: Bohan Harry J. , Shawaker Peggy Bohan
Published: October 2020

A critical component of the use of manipulatives is making sure that students make the connection between the conceptual work done with manipulatives and the procedural knowledge that such work is supposed to support (NCTM 1989). To make sure that such connections are made, it is helpful to think of using manipulatives in the context of transfer of learning. Transfer of learning is a situation in which studying topic A will help in understanding topic B. The modern view of transfer suggests that transfer from topic A to topic B will happen only to the extent that certain conditions are met.
Thematic Webbing and the Curriculum Standards in the Primary Grades
Authors: Piazza Jenny A. , Scott Margaret M. , Carver Elizabeth C.
Published: October 2020

The National Council of Teachers of Mathematics's Curriculum and Evaluation Standards for School Mathematics (1989) reflects the importance of understanding the development of knowledge at the K-4 level. The standards document recognizes that current instructional and curricular content must focus on students' active construction of mathematical knowledge. Instructional practices need to be conceptually oriented, involve children actively, emphasize the development of mathematical thinking and application, and include a broad range of content.
From the File
Authors: Math Willard
Published: October 2020

Build a personal collection by reproducing this “From the File” on card stock and adding it to From the File Treasury, a collection edited by Jean M. Show and packaged in a colorful plastic file box with room to add your own favorites (1991, stock no. 476, $21.50; 20% discount for individual members; see the NCTM Membership Application and Order Form in this issue). Readers are encouraged to send in two copies of their classroom-tested ideas for “From the File” to the Arithmetic Teacher for review.
The Mathematics Textbook: How can it Serve the NCTM's Standards?
Authors: Rosemary Schmalz, S.P.
Published: October 2020

A few years ago I taught middle-grade mathematics in two schools for most of an academic year. I began teaching in the second school after Thanksgiving. On one of my first days there, I asked the students to open their books to page 106. Several objected. “We haven't done page 105,” they pointed out. When I told them that we weren't going to do page 105, one child was particularly upset. He gave me a disgusted look and said, ”You don't teach right.”
Making Connections with Teddy Bears
Authors: Beougher Cecile
Published: October 2020

These words were part of the commercial my class developed and presented to the other classes in our elementary school to advertise the cinnamon apple bear the children had produced for sale. Excitement ran high from the day that invitations were taken home inviting their teddy bears to visit school to the final day when we presented a check to a local “Toys for Tots” group. This successful integrated unit is detailed in the example of planning aids and unit plans given in this article.
Assessing Mathematics Learning for Students with Learning Differences
Authors: Cross Lee , Hynes Michael C.
Published: October 2020

The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) advocate the alignment of the mathematics curriculum with instructional practices and assessment techniques.
Calendar Mathematics
Authors: Shipley Lydia , Porter Jeanna , Chancellor Dinah
Published: October 2020

The calendar is designed to speak directly to students, giving them open-ended questions intended to engage their intellect through their interests. Students are encouraged to work on the activities individually, in pairs, or in small groups. No answers ore provided for the calendar questions to encourage students to look to themselves as the mathematical authority, to develop the confidence and critical-thinking skills necessary to validate their thinking.
Promoting Mathematical Explorations through Children's Literature
Authors: Whitin David J. , Gary Cassandra C.
Published: October 2020

Children's literature can be an important vehicle to use when exploring various mathematical concepts (Whitin and Wilde 1992). Stories can help students understand the meaningful contexts that support mathematical thinking. They will see mathematics not as a prescribed set of algorithms to master but as a way of thinking about their world. Children's literature present a nonthreatening avenue to test out current notions about important mathematical concepts. The following two classroom scenarios occurred in Cassandra Gary's first-grade classroom in Irmo. South Carolina. She used two pieces of literature, The Line-up Book (Russo 1986) and The Doorbell Rang (Hutchins 1986), on two different occasions a springboards for mathematical thinking. The first book enabled her students to explore the concept of length, and the second story reinforced the concept of partitioning. Although each book ha a mathematical dimension, it is important to remember that they are, first and foremost, good pieces of literature. Each book is a unique literary experience and should be enjoyed for its own ake first. Gary read each story to the class cveral times and let the students voice their peronal. spontaneous observations and predictions. By so doing, the integrity of the literature is respected and preserved.
The Lunch-Wheel Spin
Authors: Mason Julia A. , Jones Graham A.
Published: October 2020

The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) recognizes the importance of having all students develop an awareness of concepts and processes of statistics and probability. In particular it proposes that experiences in statistics and probability should be offered that enable students to “formulate and solve problems that involve collecting and analyzing data” (p. 54) and “model situations by devising and carrying out experiments or simulations to determine probabilities” (p. 109).
Connecting Literature, Language, and Fractions
Authors: Conaway Betty , Midkiff Ruby Bostick
Published: October 2020

Because of the symbolic nature of fractions and the procedural operations required to manipulate fractions mathematically, the concept of fractions is often difficult for students in early grades to master (Van de Walle 1990). Perhaps this difficulty results in part from the numerical contradictions presented by fractions. Furthermore, fractions are part of a mathematsical language that is often foreign to students until they develop a personal understanding. “Children's literature presents a natural way to connect language and mathematics” (Midkiff and Cramer 1993, 303) and furnishes a foundation on which an understanding of concepts can be based. As students read, write, and discuss real-life situations requiring the use of fractions, they develop personal meanings for the abstract concepts.
Making Connections with Two-Digit Multiplication
Authors: Englert Gail R. , Sinicrope Rose
Published: October 2020

The mathematics curriculum in Norfolk Public School is arranged in a spiral, with concepts from twelve basic strands continually reviewed and developed. An emphasis is placed on connecting new ideas with previously studied concepts and on using models and manipulatives to understand the underlying operations.
Polydrons and Three-Dimensional Geometry
Authors: Woodward Ernest , Brown Rebecca
Published: October 2020

Empower—that word is key for mathematics teachers.
Teacher to Teacher: Learn about Statistics—Math League Baseball
Authors: Rosenberg Mitchell
Published: October 2020

I wanted an enjoyable but practical way to introduce concepts of statistics to my sixth graders while reinforcing fundamental arithmetic skills. This activity gives students hands-on experience in solving real-world problems while granting them the power to own and operate their own major league baseball team. The project took ten days and is easy to do.
Ideas
Authors: Renga Sherry
Published: October 2020

The “IDEAS” section for this month uses the theme of the postal service as a basis for connecting mathematics to art, social studies, children's literature, and real-life situations. The activities stress communication in cooperative groups.
Empowering Students with “The Math Connection”
Authors: Rosnick Peter
Published: October 2020

In Franklin County, Massachusetts, students, are making mathematical connections with “The Math Connection” television show, and the results are quite exciting.
Reviewing and Viewing: New Books: For Students
Authors: O'Shea Thomas , Whitin David J.
Published: October 2020

This counting book for young readers borrows it structure from “The Twelve Days of Christmas man.” A young boy and his sister watch various events unfold in twelve circus rings that feature animals, acrobats, and clowns.
Helping the Non-Learner in Grade One
Authors: Holinger Dorothy
Published: October 2020

In the first grade at our school we have a child who has no understanding of arithmetic and has not retained anything learned in this subject in the first five months of first grade. The class has covered addition and subtraction up to and including sums of ten.
Comments on Middle-Grade Arithmetic
Authors: Dickey John W.
Published: October 2020

MIDDLE-GRADE ARITHMETIC has made less change in recent years than has the primary-grade arithmetic; but the gains that have been made are in keeping with the newer philosophy of modern arithmetic. Modern textbooks on the teaching of a rithmetic, as well as the materials for the children, have also reflected these major changes in the philosophy, materials and methods. A brief look at the changes in content and methods is worthy of our attention.
Whither Research in Compound Subtraction? (A Second Communication to the Editor)
Authors: Johnson J. T.
Published: October 2020

After reading the article in the Octorber, 1955 issue of THE ARITHMETIC TEACHER entitled, “Comparison of Two Methods of Subtraction,” by Gladys and Joel Rheins and the one in the February, 1956 issue captioned, “Whither Research on Compound Subtraction,” by J. Fred Weaver, the writer cannot help but feel that there is a misunderstanding some place in regard to the teaching of meanings in connection with the compound subtraction technique.
Commercial Games for the Arithmetic Class
Authors: Johnson Donovan A.
Published: October 2020

“Amusement and Pleasure ought to be combined with instruction in order to make the subject more interesting. There should be games of various kinds such as a game played with different kinds of coins mixed together. There should also be problems connected with boxing and wrestling matches. These things make a pupil useful to himself and more wide awake.”—Plato
Meaning for Multiplication of Fractions
Authors: Ward Hoffman Hazel
Published: October 2020

Necessity is the Mother of invention,” so says an old adage. Thus it isn't until there is a real need to do something that most of us ever get around to doing it. It is the teacher who teaches multiplication of fractions who really gets down to finding the meaning of it when she must present it to her middle-grade class. Even so the children never find the meaning until they see the need. The need is self-explanatory with the meaning. Since they go hand in hand, we frequently omit both to present the method alone.
“I Like Math Because…”
Authors: Cross Bob
Published: October 2020

The Main Reason I like Math is that it has always elevated my opinion of myself. Every time I successfully work out a problem, I have finished one more little job that lies obscured in the countless small tasks that mark our everyday life. It is said that to complete a job is one thing; then to do it well is another. True, but there is only one way to complete a Math problem, and that is to find the right answer. Until then the task is incomplete and will remain incomplete as a nagging marker in one's brain.
Understanding Meanings in Arithmetic
Authors: Rappaport David
Published: October 2020

During the last twenty years a great deal has been written about “meaningful arithmetic.” Although there is some confusion over the terminology surrounding meaningful arithmetic as well as difference of opinion as to what constitutes a program of meaningful arithmetic, the term itself has been generally accepted by teachers and administrators. There is general agreement, expressed in the literature, that the basic meanings in arithmetic include the understanding of counting, place value, the decimal number system, the meaning of addition, subtraction, multiplication, and division with integers, fractions, and decimals, and the meaning of percentage.
Something New to Try
Authors: Torrance Arnold F.
Published: October 2020

Many youngsters who have asked me if there was any way of making long division palatable have discovered in this method an end to their former frustration and often surprisingly enough after a short trial period find they can endure and even like long division.
Manipulative Materials in Intermediate Grades
Authors: Fox Marion W.
Published: October 2020

Now that so many of our elementary teachers are well versed in child growth and in the over-all pattern of a developmental curriculum, they are increasingly aware of the need for providing a stimulating environment that will intrigue the child and evoke a desire to try, to achieve, to learn, and to share. Greater attention, therefore, is given today toward making available multi-sensory aids for learning. It is evident that there is a growing awareness of the values of manipulative materia ls as an aid in teaching arithmetic.
An Aid in the Analysis of Verbal Problems
Authors: Herriott Robert E.
Published: October 2020

The problem of teaching the solution of verbal problems in arithmetic has for many years been an intriguing one. Just about all points of view have appeared in the literature at one time or another. Yet today the question of what is best is still a very open one.
Directional Exercises as Preparation for Algebra
Authors: Mehl William G.
Published: October 2020

We who are teaching eighth grade arithmetic may find a stimulating method of aiding students in their preparation for algebra in a device which I have termed, The Directional Exercise. The material which might be incorporated into the drill is legion. It may be based entirely upon previous class experiences, or may relate to the introduction of new ones. Emphasis is placed upon implicit statements rather than upon explicit ones at this level.
National Council of Teachers of Mathematics: Report of the Membership Committee
Authors: Rogers Mary C.
Published: October 2020

The membership committee of the National Council of Teachers of Mathematics is happy to make this report to you, and to congratulate you for your achievement in bringing about the greatest membership total in the history of the Council.
Attitudes Toward Reading and Arithmetic Instruction: Why the Contrast?
Authors: Stevenson Gordon K.
Published: October 2020

There exists, and has existed for many years, an apparent difference in attitude toward instruction in the fields of reading and arithmetic. Should such differences exist? Is there any scientific evidence that it is justified? Is now a good time to do away with this difference in attitude?
Low Visibility, or, Ideas in a Fog
Authors: Morton R. L.
Published: October 2020

We all know that some children find arithmetic difficult. It is commonly assumed that children find arithmetic difficult because of an inadequate background of experience for the topic presented, or because they are relatively immature, or because they have insufficient native ability. Each of these reasons is doubtless a valid one in many cases.
Ideas for Your “Bag of Tricks”
Authors: Jackson Humphrey C.
Published: October 2020

The experienced teacher has a bag of tricks of the trade at her command every day and uses a wide variety of them in the daily work of the classroom. You have doubtless heard a great deal recently about the discovery technique because in the hands of a skilled teacher it is said to provide (1) interest for the learner, and (2) satisfaction to the teacher. In our modern world, methods used a generation ago do not seem to create the same interest on the part of the student. The student of today needs to feel that today's methods are the newest, best, and most effective. With the advent of television, scientific progress, electronic computing machines, space satellites, supersonic speeds, intercontinental missiles and the like, he has a right to expect teachers who are alert, well informed, specialists in their fields and who can employ effective, modern methods of instruction.