bluuebunny/crossref_metadata_2025 huggingface dataset:
The “Transformation Game”
Authors: Sicklick Francine , Turkel Susan B. , Curcio Frances R.
Published: October 2020

In recent years, the elementary school curriculum has seen the advent of some new topic. One such topic is tran formation geometry. At the elementary school level. this topic. treated informally, includes the study of location, direction. and di stance (Kidder 1977). Instructional games give sllldents concrete experiences to explore concepts in a new way. The transformation games offers an opportunity for students in grades 4-6 to sharpen their spatial abilities and enrich their geometrical experience. It pre ent s such concepts as reflection, translation, and rotation (i.e., flip. slide. and turn, respectively).
Teacher-Computer Interaction in Teaching a Mathematics Lesson
Authors: Andersen Lyle E. , Allinger Glenn D. , Abel Jean P.
Published: October 2020

Elementary school teachers are being encouraged to use the computer for mathematics instruction (NCTM 1980). Many are seeking appropriate methods for integrating the computer into their mathematic lessons. Unfortunately, much of the pre ent software must be altered or creatively adapted before it can be incorporated into teacher presentations. The lack of computers in individual classrooms and the lack of regular acce to computer laboratorie are other tumbling blocks that di courage the u e of computers in a regular lesson. The estatement are supported by a survey conducted in Minnesota (Andersen 1984) that showed fewer than 5 percent of the K-8 teacher who responded had ever used the computer for teaching mathematics.
Applying Pick's Theorem to Randomized Areas
Authors: Hawkins Vincent J.
Published: October 2020

Elementary school students enjoy working with different shapes. The appeal of these activities is not surprising considering student familiarity with Cuisenaire rods, attribute blocks, geoboards, and other manipulatives that promote concept development.
Making Division Meaningful with a Spreadsheet
Authors: Dubitsky Barbara
Published: October 2020

Long division is such a complicated procedure that it takes most students many years to learn all the variations. Even with a great deal of practice, many get so bogged down in the manipulation of numbers that they lose sight of what they were trying to solve. Students often come up with absurd answers and don't question their correctness.
Probability and Combinations for Third Graders
Authors: Vissa Jeanne M.
Published: October 2020

Typically, third graders are expected to associate common fractions with shaded parts of equally divided whole regions. Giving simple experience with probability to children of this age can extend their understanding of the need for fraction in everyday life. If the correspondence of equal chances to equal parts of a figure is emphasized. then fairly difficult problems can be approached through diagrams. The following activities involving probability and combinations build on language-arts experiences and incorporate concepts in multiplication. graphs, and fractions.
Developmental Algorithms Have a Place in Elementary School Mathematics Instruction
Authors: Stanic George M. A. , McKillip William D.
Published: October 2020

Perhaps the two most neglected elements of elementary school mathematics instruction are getting children ready for the formal introduction of a concept or skill and giving students the opportunity to develop an understanding of the concept or skill before mastery is expected. Both of these elements—readiness and development—have been given too little time in the classroom. This article deals with one aspect of the developmental period—the use of developmental algorithms to teach a rithmetic skills. During the developmental period in teaching children arithmetic skills, children make the transition from using concrete materials to using a standard algorithm. Given the changes taking place in elementary school mathematics instruction due to calls for the increased use of calculators and computers (e.g., Conference Board of the Mathematical Sciences [1975]; National Council of Teachers of Mathematics [1980]), we need to ask whether developmental algorithms are helpful or unnecessarily confusing for children.
By Way of Introduction
Authors: Thompson Charles S. , Rathmell Edward C.
Published: October 2020

Recent efforts to change the mathematics curriculum emphasize the development of number sense. Professional organizations and state and local curriculum planners identify several aspects of learning and refer to them as number sense.
Number Sense and the Importance of Asking “Why?”
Authors: Whitin David J.
Published: October 2020

When children ask the “why” quest ion in their mathematics classroom, they are on their way to strengthening their number sense. An atmosphe re that promotes curiosity about numbers encourages children to test their own hypotheses and pursue their own predictions. In this way children develop a broader understanding of why numbers act the way they do; they develop a number sense from the inside out because they are encouraged to be questioners and thinkers in their own right.
Step into Problem Solving with Cooperative Learning
Authors: Rosenbaum Linda , Behounek Karla Jeanne , Brown Les , Burcalow Janet V.
Published: October 2020

Problem solving has clearly emerged as a central emphasis for elementary school mathematics to facilitate our students' transition into the twenty-first century. Few teachers would argue its importance. How the primary-level teacher can translate these noble aspirations into actual classroom practices often becomes an area of consternation and concern.
One Point of View: Tracking Is Inconsistent with the Standards
Authors: Mumme Judy
Published: October 2020

The NCTM Standards (Commission on Standards of School Mathematics of the NCTM 1987) articulate a clear vision for mathematics education, containing the central ideas of mathemat ics we wish all students to understand. Achieving the fundamental changes these Standards envision will require educators to reexamine many existing practices. Efforts to improve mathematics instruction interface with the broader issues facing education.
Project Hands-On Math: Making a Difference in K–2 Classrooms
Authors: Fielder Dorothy R.
Published: October 2020

How does one go about convincing teachers of early childhood mathematics that the hands-on manipulation of meaningful models by children is essential to concept development? That was one of the primary goals of Hands-On Math, a developmental project funded from 1985 to 1987 by the state of Georgia through a grant by the 1985 Quality Bas ic Education (QBE) Act.
Principles For Principals: Steps toward Building a Successful Problem-solving Program
Authors: Parish Bunny , Charles Randall I. , Martin Jane
Published: October 2020

Teachers interested in making problem solving an integral part of instruction can make any program work for a while! Unfortunately, even the most committed teachers cannot make problem solving a lasting part of their program unless all components needed for success are in place. Here's a checklist of components needed for a successful problem-solving program. Address each of these factors as you work with teachers in your school to develop a plan to make problem solving the focus of instruction.
Basic Facts Drill—Card Games
Authors: Campbell Melvin D.
Published: October 2020

Two major challenges confront teachers of elementary school mathematics. One is to teach, practice, and reinforce the basic facts of arithmetic. The other is to deal with the different ability levels of students within the same classroom. The following card games have been designed to address both of these difficulties. A number of students from the Ooltewah Adventist School, Ooltewah, Tennessee, in grades 4 through 6 played the games together in spite of differences in age and ability. This preliminary activity indicates that the basic facts can be practiced and reinforced in groups of students of varying ability in an enjoyable way.
One Point of View: Calculating the Influence of Tests on Instruction
Authors: Chambers Donald L.
Published: October 2020

Implementing the NCTM's curriculum and evaluation standards will require a change in the beliefs of many mathematics teachers and widespread acceptance of a fundamental premise of the Standards: that “appropriate calculators should be available to all students at all times” (Commission on Standards for School Mathematics of the NCTM 1989. 8). It will require widespread acceptance of the use of calculators in testing, for as the Standards observes, “until tests provide for the appropriate use of calculators, many teachers will continue to prohibit their use in the classroom. Without changes in how mathematics is assessed, the vision of the mathematics curriculum described in the standards will not be implemented in classrooms, regardless of how texts or local curricula change.”
Metric Mall
Authors: Fay Nancy , Tsairides Catherine
Published: October 2020

At Petrosky Elementary school in Alief Independent School District, Houston. Texas, a unique mathematics and science unit was developed for third-, fourth-, and fifth-grade students. The students worked in stores in this “Metric Mall.” These “retail” experiences gave them opportunities to work with measuring tools and ordinary, but motivating, materials.
Math Action Books: For Young Readers
Authors: Bohning Gerry , Radencich Marguerite C.
Published: October 2020

Primary-grade children delight in using three-dimensional action books. Why not build on this interest to help them to practice their counting and basic mathematics facts? Action books have movable parts and are often called pop-up or pop-out books, lift-the-flap books, or surprise books. Children lift flaps, pull tabs, slide panels, move wheels, or turn pop-up pages to initiate a three-dimensional movement. Mathematics three-dimensional action books offer skill practice in a helpful and exciting format. Children can add apples that slide into baskets, subtract airplanes that disappear behind lift-flap clouds, count pop-up crabs that crawl on the shore, or move hands on a clock to show when it is lunchtime.
Research into Practice: Teachers Researching Their Mathematics Classrooms
Authors: Pateman Neil
Published: October 2020

Teachers typically are treated as consumers of what other people produce. For example, as a consumer, the teacher is supposed to work from ready-made materials, using accompanying teacher's guides, even though the entire curriculum has been prepared in a different place. Such material are often characterized as being “teacher proof.”
Introducing Multiplication
Authors: Remington Jim
Published: October 2020

My third-grade student learn multiplication through many kinds of lessons intended to help them make sense of the process. It is most important for numbers and symbols to have meaning for students if they are going to use mathematical ideas to solve problems in the real world.
Ideas
Authors: Silverman Helene
Published: October 2020

The IDEAS ection this month focuses on the attributes of flags. Student compare the designs of flags and discover geometric properties of various flags. Centime ter squares are used to find area, perimeter, and proportion. Color charts of national flags and a large world map are recommended to encourage further observation and investigation. These aids can be found in most almanacs and encyclopedias.
Females In Mathematics: Erasing A Gender-Related Math Myth
Authors: Tracy Dyanne M. , Davis Susan M.
Published: October 2020

Pythagoras, Eratosthenes, Euclid, Boole, and Einstein are familiar names to many mathematics students. It is interesting that these and other names of famous mathematician identify males, whereas names of female mathematicians remain unfamiliar. The fact that females have made and are making significant contribution in the field of mathematics is somehow obscured in a society that admit a history of traditional role expectations
IDEAS
Authors: Silverman Helene
Published: October 2020

In this month's IDEAS, students learn to obtain information from maps and to use scales and legends. They learn to interpret and record information on charts.
Teaching Mathematics with Technology: Measurement in Geometry with Computers
Authors: Edwards Nancy Tanner , Bitter Gary , Hatfield Mary M.
Published: October 2020

Work with a protractor or compass can be frustrating for students because accurate measurement requires the proper placement of the apparatus at all times. It is difficult for a teacher to check each student's work as every angle or circle is being constructed. Using Logo programs allows the students to check their own constructions immediately
Research Into Practice: Dialogue and Conceptual Splatter in Mathematics Classes
Authors: Stanic George M. A. , Easley Jack , Taylor Harold A. , Taylor Judy K.
Published: October 2020

We have studied first- and second- grade mathematics classes in Japan and the United States in which story problems and problems about mathematical concepts were used to promote higher-level thinking. Our re earch leads us to question the common a umption that teachers should aim each le son at a particular conceptual goal for all pupils and expect nearly all of them to succeed and to understand the same concept. Instead, a teacher's aim should be as close as possible to accepting conceptual diversity or “splatter” among pupils. We believe that steady work on such an aim through problem solving and dialogue will lead to outstanding conceptual power in pupils. In this article, we present three examples from lessons that reflect this aim, as well as suggestions that we have drawn from these and other lessons.
Teaching Arithmetic Averaging: An Activity Approach
Authors: Goldman Phyllis H.
Published: October 2020

In my experience as a mathematics teacher of fourth, fifth, and sixth graders, I have found that the concept of the mean, or arithmetic average, is difficult for many youngsters. I therefore devised several smallgroup tasks in which the students had to redistribute materials to find the means, or arithmetic averages. These tasks were completed by the students within three class periods.
A Unified Approach to Multiplying Fractions
Authors: Ott Jack M.
Published: October 2020

Some have mistakenly advocated that the multiplication of fractions should be taught before the addition of fractions because the multiplication of fractions is easier. The mistaken notion that the multiplication of fractions is relatively easy is based on the fact that for most students the standard multiplication algorithm for fractions is easier to perform than the tandard addition algorithm.
Get in Touch with Shape
Authors: Juraschek William
Published: October 2020

When discussing spatial visualization we often mention using our mind's eye to form and transform images of objects. The expression “mind's eye” reflects the obvious association between our sense of shape and space and our sense of sight. However, we seldom associate our sense of shape and space with our sense of touch; but as anyone who has been blindfolded knows, when we cannot see we must rely heavily on our sense of touch. Relying on our sense of touch to explore an unseen object forces us to attend carefully to sensory images, and this careful attention often results in the formation of an object's image in our mind's eye. This phenomenon is the basis for the following kinesthetic activities, designed to exercise and develop students' sense of shape and space. The activities have all been used successfully in primary grades, middle schools, and college classrooms.
Using Patterns to Practice Basic Facts
Authors: Feinberg Miriam M.
Published: October 2020

Memorizing the basic addition and subtraction facts becomes an insurmountable problem for many pupils, and finger counting remains their basic counting tool in the middle and upper grades. However, if they recognize and use patterns, they can develop a better understanding of the number system. An understanding of patterns then becomes an important tool as they progress to increasingly complex mathematical problems.
The Naive Expert Challenges the Limits of Young Learners
Authors: Timpson William M. , Schlelein Marty , Jones Barbara A. , Stephens-Carter Sherri
Published: October 2020

Our schools threaten to drown us all in a “rising tide of mediocrity,” producing conditions we would never tolerate if imposed by an outside force. This statement is the provocative concluion of the National Commission on Excellence in Education's Nation at Risk (1983).
Teaching Mathematics With Technology: Teaching about Exponents with Calculators
Authors: Baker Delores , Edwards Rhonda , Marshall Catherine
Published: October 2020

Calculators can move students from manipulative, concrete activities to symbolic, abstract representations (Berlin and White 1987), and they can be used to give meaning to concepts and help students develop explanations of mathematics topics. Calculators allow students to examine many examples and nonexamples; the speed and power of calculators can make problems more realistic and interesting. In short, calculators help focus students' attention on mathematical processes (Comstock and Demana 1987). The worksheets in this month's “Teaching Mathematics with Technology” show how we have used calculators to introduce, and then expand, instruction on powers of numbers.
The Writing Process: A Strategy for Problem Solvers
Authors: Ford Margaret I.
Published: October 2020

Over the past decade, mathematics educators have promoted problem solving as the goal of school mathematics. Yet in 1987, the National Assessment of Educational Progress revealed that our nation's schoolchildren are still falling short of our goals for their problem solving abilities. Many students dislike word problems in mathematics, and many teachers report feeling frustration and discouragement in helping their students learn how to solve such problems (Ford 1988). What can teachers do to improve students' attitude toward problem solving and to realize the goal of helping students become better problem solver?
Parents Can Help Children Learn Mathematics
Authors: Ashlock Robert B.
Published: October 2020

All parents want their children to enjoy school and succeed with schoolwork. They are eager to help children learn mathematics, but many are not sure how to proceed.
Teaching Mathematics with Technology: Problem Solving with a Spreadsheet
Authors: Hoeffner Karl , Kendall Monica , Stellenwerf Cheryl , Thames Pixie , Williams Patricia
Published: October 2020

As mathematics education adapts to the needs of a changing society, the use of technology becomes increasingly important. Technology can play a valuable role in developing problem-solving capabilities in students by freeing them from tedious computations. Thus, higher-level thinking skills can be emphasized. An electronic spreadsheet can calculate rapidly, generate data from which patterns can be found, show relationships between two or more variables, and investigate “what if?” questions with ease.
A Script For a Mathematics Lesson
Authors: Kelly Margaret
Published: October 2020

While Juan monotonously finishes reading the text, six students are doodling in their notebooks, four are staring at the clock trying to anticipate how long it will be until lunchtime, three are arguing about their softball game in notes passed among them, and a few are still shuffling in their desks to find their mathematics books.
Using Commercial Games to Design Teacher-Made Games for the Mathematices Classroom
Authors: McBride John W. , Lamb Charles E.
Published: October 2020

Paul hated mathematics. He was a bright child, but he was behind in his work and was not doing well. He particularly disliked the monotonous pages of drill for homework. He took hours to complete them (when he did them), and he usually missed most of the problems.
Research into Practice: Giving Pupils Tools for Thinking
Authors: Davis Robert B. , Clements Douglas H. , Battista Michael T.
Published: October 2020

Pupils often invent mathematical ideas and methods that go beyond what has been taught in class. The inventiveness is frequently noted in research studies based on careful observation of pupils talking about mathematical problem.
Implementing the Standards: Redefining Computation
Authors: Van de Walle John A.
Published: October 2020

Pencil-and-paper computational skills have long dominated the elementary school curriculum. For over ten years we have been hearing that the emphasis on these skills must be reduced because in our technological society they are much less important than in previous times. Furthermore, a valid, frequently voiced argument suggests that the time spent on computation is the one “fat” area where cuts can be made to allow time for the many new concepts and higher-order processes that are more important.
Teaching Mathematics with Technology: Teaching Mathematics Using Calculators
Authors: Pagni David L.
Published: October 2020

The last three years has seen a marvelous resurgence of interest in the use of calculators for teaching mathematics. Much of the credit goes to professional organizations like the National Council of Teachers of Mathematics that have promoted the use of calculators. The renewed interest in the use of calculators in schools coupled with the sale of over 250 million electronic hand-held calculators in the last ten years in the United States (about three for each household) suggests that an opportunity exists for a revolution in mathematics education.
Multicultural Mathematics Education For The Middle Grades
Authors: Zaslavsky Claudia
Published: October 2020

Why are many young women and minority-group students less likely than white males to continue their study of mathematics? Among the reasons cited by researchers are these:
Implementing The Standards: Making Connections in Mathematics
Authors: Dolan Dan
Published: October 2020

At a recent meeting of a group of elementary mathematics leaders in Montana, one of them said, “I wish all elementary school teachers could realize how much mathematics they teach when they are not teaching the mathematics lesson. So many connections could be made between mathematics and the other subjects.”
Helping Students Understand Place Value
Authors: Gluck Doris H.
Published: October 2020

Teaching mathematics is much like building a house: if we do not lay a strong foundation, innumerable difficulties appear later. Too often we see a nice facade, with papers done accurately or algorithms copied and performed well, but like a house on a poor foundation, the student's understanding does not hold up when he or she tries to learn the next logically connected concept. The same student who can add and regroup for two-digit numbers cannot seem to understand how to add three-digit numbers. The student who can subtract with regrouping in the tens column is unable to subtract accurately when asked, and even shown how, to regroup in the hundred column.
Parents and Mathematical Games
Authors: Tregaskis Owen
Published: October 2020

In an increasingly technological world, parents are becoming more worried about the quality of children's learning of mathematics. Many parents become concerned about their own child's learning and visit the school to discuss the problem with the child's teacher. The result of this discussion is usually that the teacher confirms the parents' anxiety but offers few specific suggetions. If any help is offered. the parents are a ked to make the child practice more of the type of work done in school. This practice is often pitched at such a level that the parent have to do some teaching. At this juncture either the parent become confused because they do not know the method used in school or the child become confused because he or she is taught at home a method different from the one taught in school.
Introducing Division Through Problem-Solving Experiences
Authors: Burns Marilyn
Published: October 2020

Teaching computational procedures has traditionally been the goal of instruction in arithmetic. Instruction usually moves from developing the concept to introducing the notation and then to teaching the algorithm. The emphasis is on having pupils learn to do calculations. Applications to problem situations follow.
“Reality Math”
Authors: Moniuszko Linda K.
Published: October 2020

Junior high school and middle school students are a rare breed. They can be utterly charming one minute and yet extremely difficult to reach the next. Their minds seem to be everywhere but in the classroom. The far-off goal of high school graduation is too remote to entice some to hard work, and to others it must seem the impossible dream.
IDEAS
Authors: Irons Calvin , Irons Rosemary
Published: October 2020

The IDEAS section for this month involves students in cutting-and-rearranging activities in geometry. Students are asked to discuss, describe, read, and write about the activities. The emphasis on using components of language helps student build a broader vocabulary of geometry terms and understanding of spatial relationships because the new ideas match the language that the students already possess. The activities also help develop visualization and good spatial sense.
Group Management in the Mathematics Classroom: Exploring Pentominoes
Authors: Brown Sue , Jones Robert M.
Published: October 2020

In 1989 the National Council of Teachers of Mathematics published the Curriculum and Evaluation Standards for School Mathematics. A basic assumption shaping the K-4 standards is that “K-4 classrooms need to be equipped with a wide variety of physical materials and supplies” (p. 17). The 5-8 standards also make the assumption that “every classroom will be equipped with ample sets of manipulative materials and supplies …” (p. 67). In using materials in an elementary mathematics classroom, each student can be placed in a cooperative-task group, with each member of the group performing a specific function. This structure establishes a positive interdependence in which each student contributes significantly to the achievement of a learning goal. The following activity describes how this management system can be implemented in a mathematics classroom.
Activating Assessment Alternatives in Mathematics
Authors: Clarke David J.
Published: October 2020

The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989, 1, 2) emphasizes the role of evaluation “in gathering information on which teachers can base their subsequent instruction.” This strong sense of assessment's informing instructional practice is also evident in the materials arising from the Australian Mathematics Curriculum and Teaching Program (Clarke 1989: Lovitt and Clarke 1988, 1989). Both projects offer their respective mathematics-education communities a set of goal much broader than those traditionally conceived for mathematics instruction. The adoption of these goals by mathematics teachers and school systems demands the use of new assessment strategies if the restructuring of the mathematics curriculum and mathematics-teaching practice is to be effected. Mathematics education must not restrict itself to those goals that can be assessed only through conventional pencil-and-paper methods.
The Toronto Board of Education's Benchmarks in Mathematics
Authors: Clark John L.
Published: October 2020

Today, most school districts are increasingly being held accountable for the quality of their programs. The Toronto Board of Education, which has 114 elementary schools with approximately 41,000 students and 39 secondary schools with approximately 30,000 students, is no exception. In May 1987, the board mandated the development of s tandards for students' achievement in mathematics and language at the end of grades 3, 6, 8, and 10. Until this time no systemwide testing or standards had existed. Guidelines had been established for evaluating students and reporting to parents, but schools and teachers were left to work out their own procedures.
Implementing the “Professional Standards for Teaching Mathematics”: Evaluating the Teaching of Mathematics: The Read to Progress and Reform
Authors: Cooney Thomas J.
Published: October 2020

Questions abound whenever one's teaching is evaluated. Issues of context—both mathematical and otherwise, values, the definition of good teaching, and the very notion of what it means to do mathematics arise when teachers attempt to evaluate either their own teaching or that of others.
Teaching Students to Tell Time: Spatial Sense and the Construction of Abstract Units in Tiling
Authors: Androde Gloria S.
Published: October 2020

Recently I read that teaching the skill of telling time is unessential because, after all, “Is any adult unable to perform this task?” I can't agree with that reasoning because too many of my nine- and ten-year-old students are embarrassed by their inability to tell time.
Teaching Mathematics with Technology: Statistics and Graphing
Authors: Parker Janet , Carroll Widmer Connie
Published: October 2020

A goal stated throughout the Curriculum and Evaluation Standards (NCTM 1989) is that all students be able to use mathematics to understand and interpret situations they encounter in the world around them. In this world, the proliferating use of computers has made statistics and graphs essential tools not just for students but for all of us. Every day we are deluged with statistical data generated by the computers used in all areas of society: political polls give us prevalent opinions on major issues; medical studies tell us the safety of new drugs; test scores indicate how our schools compare with the “average.” Often, capsules of the data are given as a graph; being able to interpret these graphs, to distinguish biased messages from reliable reporting, and even to create graphs to analyze data have become essential skills in our technological society.
Exploring Patterns, Relations, and Functions
Authors: Geer Charles P.
Published: October 2020

As teachers use NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) to develop programs that will prepare students for the twenty-first century, some are discovering that mathematics instruction is going to be very different in the 1990s. Many previous programs placed a heavy emphasis on paper-and-pencil proficiency with computational skills and learning mathematics by memorizing rules. Because of advances in technology, new knowledge about how learning occurs, and the changing needs of business and industry, future programs will focus on mathematics with meaning, problem solving, and higher-level cognitive skills.
Implementing the “Professional Standards for Teaching Mathematics”: Teachers Paying Attention to Students' Thinking
Authors: Maher Carolyn A. , Davis Robert B. , Alston Alice
Published: October 2020

The Professional Standards for Teaching Mathematics in its call for reform underscores the importance of teachers' knowledge of how students build their mathematical ideas. In our own work we have come to stress the importance of teachers' awareness of students' thought processes (Davis 1984; Davis and Maher 1990; Maher, Davis, and Alston 1991; Maher and Davis 1990). Teachers' knowledge of students' thinking is an important guide in planning effective lessons.
Research into Practice: Conquer Mathematics Concepts by Developing Visual Thinking
Authors: Hershkowitz Rina , Markovits Zvia , Wheatley Grayson H.
Published: October 2020

It seems that visual thinking will be the primary way of thinking in the future. In modern life the presentation of phenomena has changed from tables and formulas heavy with numbers and symbols to a dynamic visual presentation using computers. To understand, analyze, and predict, we will have to engage in some form of visual thinking. To communicate visually and to develop advanced visual thinking, we need certain linguistic elements—a language.
Pre-First Grade Arithmetic
Authors: Riess Anita P.
Published: October 2020

Children's earliest experiences with number are pleasurable ones. Before they use words or understand many words, children display responses to the manyness and numerousness of objects or events in their world-of-action and their worlds of seeing, hearing, touching, and moving. Their sensory reactions are so inextricably fused with their movements and manipulations that they are best chararterized as sensori-motor activities.
Introducing Our Numbering System in the Primary Grades
Authors: Hausdoerffer William H.
Published: October 2020

There are many objectives for the teaching of arithmetic in the primary grades. One of the most basic of these objectives is that of helping children to understand the place value principle of our number system. It is in the early grades that foundations of understanding are developed, but it should be pointed out that not until the student has studied exponents in high school is it possible for him to consummate these understandings in the richest possible way. It is the purpose of this article to discuss some of the fundamental approaches that can be used successfully in the primary grades.
Arithmetic at the Primary Level
Authors: Maloney John P.
Published: October 2020

At the curriculum center for Arithmetic for the City of Boston for several years a series of classes has carried on some rather interesting experimentation in the field of elementary arithmetic. An attempt has been made to develop in the children an appreciation of the stmcture of our decimal system, an insight. into the number relationships involved in t his system, and the ability to think creatively with numbers.
Mental Arithmetic
Authors: Lentz Donald W.
Published: October 2020

At a recent social gathering one of the guests was describing an experience involving an eminent scientist. “It was unbelievable that he could think through difficult higher mathematical computations without writing a thing, become so absorbed in the process that nothing else mattered, and after a period of mental gymnastics ‘out of this world’ he would set down a tentative result with a look of triumph and success in his eyes. It was wonderful to see.”
Report of the Membership Committee
Authors: Rogers Mary C.
Published: October 2020

The membership committee of the National Council of Teachers of Mathematics is very happy to report to you that the 15,000 membership goal toward which we have been working during the past two years has been reached. The membership count of December 17, 1956 received from the Washington Office indicates a total of 15,205 members. This achievement was received with considerable enthusiasm by the National Council Board and by many other persons in attendance at the Jonesboro meeting. We are confident that you, too, will be keenly interested in this news. It has been the a sistance of you as individuals which has largely made this accomplishment possible. The Membership Committee and the National Council Board are indeed grateful to you for your fine support and helpfulness.
Enrichment Units in Junior High School Grades
Authors: Norton Monte S.
Published: October 2020

Providing more adequately for the rapid learner in arithmetic and mathematics has always been a paramount problem faced by administrators, teachers, and others interested in the education of our youth. Many schools are making excellent provisions for the academically talented in their charge through various enrichment activities, special classes, mathematics clubs, mathematics fairs and contests, and other activities designed to bring about the optimum development of each pupil.
The 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 announce that an all-time high in membership total has been reached, and wishes to thank you for your fine cooperation and support. It has been the assistance of each of you as individuals which has been largely responsible for this accomplishment. The Committee is indeed grateful to you for your helpfulness in this service to the Council.
Clifford Brewster Upton: May 10, 1877-September 25, 1957
Authors: Sanford Vera
Published: October 2020

Professor Upton is known to the younger generation of teachers as an author of textbooks in arithmetic, first the Strayer-Up ton series and currently the Upton-Fuller. They know him through his contributions to the literature of the teaching of mathematics, respecting his scholarship, his clear exposition and the artistry of his work, and regretting that these monographs are so few. His students—there were many of them in the thirty odd years that he was at Teachers College, Columbia University—are indebted to him for inspiration, guidance, counsel, occasional admonition, and for the standards of performance in study, teaching, and writing that he required.
One Point of View: The Dangers of Implementing the Standards; or, When Bad Things Happen to Good Ideas
Authors: Whitin David J.
Published: October 2020

A trhough I embrace the vision that the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) sets for us in the field of mathematics education, I am already worried about the way many people have begun to interpret it. My concerns echo those in the field of language education who fear the same fare for the writing process and whole language movement. Bad things can happen to good ideas, including the curriculum and evaluation standards, unless we are clear about what that document is and is not.
Math Pairs—Parents as Partners
Authors: O'Connell Susan R.
Published: October 2020

The need for students to be effective problem solvers is a primary concern of today's mathematics educators. The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) views problem solving as “a process that should permeate the entire program and provide the context in which concepts and skills can be learned”(p.23). The recognition of the critical role of problem solving in today's mathematics classroom challenges teachers to develop creative and effective ways to bolster students' problem-solving skills. At Hollywood Elementary School in College Park, Maryland, a program titled” Math Pairs—Parents as Partners” was developed in an attempt to tap available resources to meet the challlenge of teaching problem solving in mathematic.
Ideas
Authors: Brahier Daniel J. , Hodapp Shirley , Martin Rebecca
Published: October 2020

The “IDEAS” section for this month focuses on connecting and communicating in themes appropriate for the beginning of a new school year. Students use fami liar real-world experiences as the basis for problem solving, collecting and analyzing data, exploring pauerns and relations, and other mathematics-related activities both at school and at home. They communicate visually, orally, and in writing.
IMPLEMENTING THE “PROFESSIONAL STANDARDS FOR TEACHING MATHEMATICS”: The Role of Reflection in Teaching
Authors: Hart Lynn C. , Schultz Karen , Najee-ullah Deborah , Nash Linda
Published: October 2020

I do not believe it b possible for teachers to change their teaching practices if those practices arc not made the object of thought and consideration.
AT Classic: What Can a Teacher Learn about a Pupil's Thinking through Oral Interviews?
Authors: Lankford Francis G.
Published: October 2020

This article focuses on a too-often neglected aspect of teaching—listening to students. The decline in constructed-response testing and an detailed scoring of homework threatens to sever the last channels of communication from the individual student to the teacher. Hence, Francis Lankford's message is more important today than in 1974.

The subject of algorithms may seem passe in this age of calculators und computers. However, some error sources revealed by listening (lack of mastery of prerequisite skills, of a conceptual base, and of “number sense”) are no doubt present today and deter whatever mathematical learning we seek to achieve.
A Language Arts Approach to Mathematics
Authors: Nevin Mary Lou
Published: October 2020

Mathematics involves more than just com- putational skills. Mathematics includes reasoning, thinking, communicating, and solvingproblems. It involves skills that children have experienced during their preschool years. Preschool children are actively involved in their own learning and through informal learning activitie have experienced some of the processe expresed as verb and listed in the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) a important for student to be able to communicate mathematically—explore, represent. solve, construct, discuss, use, investigate, describe, develop and predict.
Reinforcing Place Value
Authors: Sherman Helene J.
Published: October 2020

One approach to improving mathematical achievement is to allow students the opportunity to make decisions, use alternative strategies, and communicate and reason—during practice sessions as well as during the developmental portion of instruction. Whereas traditional paper-pencil drill sessions might allow students the necessary opportunity to “fix” computational and place-value skills (Heddens and Speer 1988), many types of reinforcement activities do not require students to employ the problem solving, number-sense, and reasoning strategies learned when the content was introduced (NCTM 1989). Practice experiences can be made more meaningful if they offer elements of risk taking when choosing and using numbers so that the activities are indeed unique and challenging each time they are used.
Calendar Mathematics
Authors: 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 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.
One Point Of View: Mathematics Integration: Common-Sense Approach to Curriculum Development
Authors: Jacobs Heidi Hayes
Published: October 2020

Eight years ago I interviewed Mike, a second grader, and asked him to define “mathematics.” His response was that “math is something you do in the momjng.” I have referred to his answer in my workshops and writing as evidence of the isolation of the different subject areas (Jacobs 1989). Children viewed mathematics as a time of day, a textbook, or a change in teacher's attitude, given the predisposition of the teacher toward mathematics. But, eight years ago the NCTM curriculum and evaluation standards had not hit America's schools (NCTM 1989). Because of the declarations made in that document, today's students have a better chance of using mathematics through the course of their day. More students today view mathematics as a common, everyday activity. Through thoughtful integration of the curriculum, students use mathematics
Calendar Mathematics
Authors: Gates Eva
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 are encouraged to look to themselves as the mathematical authority, thereby developing the confidence and critical-thinking skills necessary to validate their thinking
IDEAS
Authors: Corwin Rebecca B. , Speer William R.
Published: October 2020

Many elementary and middle school mathematics teachers use a particular approach when planning mathematics units. We tend to match a mathematics concept that we want to teach with an activity or material that will convey the needed idea. When we teach fractions. we think of planning a pizza party or partitioning a geoboard. When we teach place value, we think of base-ten blocks or trading games. As we increase our teaching and planning repertoires over the year by adding more and more activities and materials, we make better matches among what we think of as basic curriculum elements: the students' needs. the mathematics topic, and choices of activities and materials. These elements, mixed differently year to year, facilitate many good mathematic lessons. But they may also give us a limited view of curriculum possibilities.
Research into Practice: Making Connections to Understand Fractions
Authors: Mack Nancy K.
Published: October 2020

Suppose you asked your students to solve this problem: If you have 3/8 of a pepperoni pizza and I give you 2/8 more of the same pepperoni pizza, how much of a pepperoni pizza do you have? Then suppose you asked them to explain how they got their answers. What do you think they would say? Several of them might respond, “I'd have ‘5/8’ because there's a pizza cut into eight pieces, and I got three of them and then you gave me two more of the eight pieces, so I have five of the eight pieces, or five-eighths of the pizza.” Several of them might respond, “The answer is ‘5/8’ because when the bottom numbers are the same, you add the top numbers and just put the bottom number down.”
Teacher To Teacher: Adding and Subtracting Integers on the Number Line
Authors: Çemen Pamala Byrd
Published: October 2020

Various models have been proposed for teaching addition and subtraction of integers (e.g., Grady [1978]: Dirks [1984]; and Chang [1985]), including money, two-color tiles, and the number line.
The Versatile Number Line
Authors: Buschman Larry
Published: October 2020

Teachers play many roles in the classroom. If we truly want our students to become lifelong learners, then one of these roles should be to encourage them to use strategies to construct new knowledge. The following activity demonstrates a teaching-learning model that the author uses in a second-grade classroom. When used as a teaching model, it serves as a prelude to the learning model that we want our students to adopt. Lt is my hope that by using such models, students will be able to experience more fully the learning process as well as its products.
Extending the Regular Curriculum Through Creative Problem Solving
Authors: Bohan Harry , Bohan Susan
Published: October 2020

Increased attention in school mathematics is also being given to creating a learning environment in which students can use prior knowledge and experiences to construct new knowledge for themselves.
Teacher To Teacher: A Videotaping Project to Explore the Multiplication of Integers
Authors: Cooke Marcia B.
Published: October 2020

My eighth-grade mathematics class was having some of the usual difficulties with beginning-algebra concepts. Because the students were becoming somewhat frustrated, I was looking for a way to present the multiplication of integers so that student could readily understand the concept. Relating this idea to the distance formula, which we had already tudied, would not only help put this idea into a more familiar context but also would review a formula that the students would often be using the next year in first-year algebra.
Teaching Mathematics With Technology: Family Math Enhanced through Technology
Authors: Bayliffe Janie , Brie Raymond , Oliver Beverly , Hynes Michael C.
Published: October 2020

What do you do when a parent asks you how they can help their child in mathematics? What if a parent wants to learn to use a calculator or a computer to enhance their child's knowledge of mathematics—how can you help? What about having some Family Math nights?
One Point of View: My Turn: A Talk with the Logo Turtle
Authors: Clements Douglas H. , Meredith Julie Sarama
Published: October 2020

What might be the role of using Logo in mathematics education, given the information in the Curriculum and Evaluation Standards (NCTM 1989) and the appearance of numerous new software packages? A recent rare interview with the Logo turtle may dispel some rumors and offer new insights into this question.
Ideas
Authors: Sovchik Robert , Meconi L. J.
Published: October 2020

Young students can gain valuable experience using such fundamental measurement units as centimeters, meters, and grams, as well as nonstandard units, during a short walk near their school.