bluuebunny/crossref_metadata_2025 huggingface dataset:
72 Addition Facts Can Be Mastered by Mid-Grade 1
Authors: Rightsel Pamela S. , Thornton Carol A.
Published: October 2020

We made it fun and made it work! Children in our first-grade classes mastered 72 of the 100 addition facts by the middle of first grade. The facts learned were of four types: “count ons” (facts having addends of 1, 2, or 3), “zero” facts, 10 sums, and doubles. Mastery was defined as a twosecond response to a given addition fact. The school district also lent its support and gave permission to delay the formal teaching of subtraction until the second semester. The foHowing sequence of activities serves as an outline of the approach that was taken.
A “Fair” Way to Discover Circles
Authors: Cangelosi James S.
Published: October 2020

The National Council of Teachers of Mathematics (1980) has recommended that schools should focus on developing students' abilities to use principles creatively in realistic, everyday situations. However, many published schemes for categorizing cognitive levels of learning suggest that a student cannot learn to use a principle creatively without having first discovered the concepts underlying that principle (Bloom et al. 1956; Guilford 1959; Bruner, Goodnow, and Austin 1967; Skemp 1971; Cangelosi 1982). This article discusses techniques for helping students in the primary grades discover geometric concepts for themselves.
More Magic with Palindromes
Authors: Whitin David J.
Published: October 2020

I didn't know what I was getting into. Palindromes seemed simple enough—numbers that could be read the same both forward and backward, like 66 or 343 or 2662. For that reason they were often called mirror numbers. I suspected that any number could become a palindrome by merely reversing its digits and adding the two resulting numbers together.
Students + Tournament = Motivation
Authors: Clark Alice
Published: October 2020

“My students aren't interested in anything,” or “the only things they're interested in are sports.” These comments were typical remarks of teachers at my school. I agreed with them. I knew that if I didn't think of something—and soon—I could “wrap it up” for the year.
One Point of View: Let's Diagnose the Child and the Curriculum
Authors: Underhill Bob
Published: October 2020

Many children benefit only nominally from much of the first- and second- grade curricula even under specially designed conditions. After we diagnose children's characteristics, we must look at the curriculum and ask whether it fits the learner. The curriculum and the learner must have a two-way fit. It makes little sense to force children to master curricula that are inappropriate for them or to waste large blocks of instructional time on areas in which research has demonstrated the general futility of such a course of action.
Math-Facts Memory Made Easy
Authors: Greene Gary
Published: October 2020

There comes a time when children in the primary grades are expected to increase the speed and accuracy with whlch they perform computational tasks. Mastery of basic addition and subtraction facts greatly facilitates a student's ability to achieve this objective. Although some children are able to learn math facts without individualized instruction, others require extensive support. For the latter students, teachers typically prescribe extra drill-and-practice activities (e.g., flash cards), often leading to disappointing and frustrating results for both the teacher and the child.
Folder Electric Boards
Authors: Harvin Virginia R. , Welch Ronald C.
Published: October 2020

We know that immediate reinforcement of behavior faci litates learning. Teachers can easily make a device that provides immediate positive reinforcement—the electric board.
Jeopardy
Authors: Klenner Hedy
Published: October 2020

Teachers can use games to motivate even reluctant students. Most students look forward to class when they know they will be playing a game. They may not be so enthusiastic, however, when they know they will simply be reviewing material they learned earlier. I have used Jeopardy for nearly ten years in my mathematics classes in grades 5–8. In my experience, students can benefit from the review that the game format provides, and they can have fun at the same time. Students frequently ask, “When are we going to play Jeopardy again?”
Y Is for Yacht Race: A Game of Angles
Authors: Butzow John W.
Published: October 2020

This article describe an activity approach for teaching upper elementary school students the concept of angles. It is a departure from the usual approach in which student are taught the use of a protractor, which show only 180°. ln thi activity student practice reading and drawing angle from oo to 360° as they simulate the behaviors used to navigate a sailboat. The activity is used in the form of a game to heighten the interest in a skill area that is often less than stimulating. The activity is also designed to help teachers infuse marine education into the study of mathematics.
Mathematics Attitudes of Elementary Education Majors
Authors: Becker Joanne Rossi
Published: October 2020

A recent article by Bulmahn and Young (1982) in this journal discussed an important topic, the mathematics anxiety of future elementary school teachers. For a long time many mathematics educators have decried the poor attitudes toward the subject of those who will teach young children. Unfortunately, relatively little data have been published documenting these poor attitudes and anxieties (see NCTM 1982). Perhaps Bulmahn and Young have such data, but they did not present them in their paper. Instead, they discussed the results in rather broad generalities that make it difficult to compare results with those of other samples or to determine if the elementary education majors in their sample were substantially more anxious about mathematics than the non–education majors in their sample. The authors made the problem of mathematics anxiety seem more severe than I judged it to be from my experience teaching mathematics to students majoring in elementary education. I decided to gather data to substantiate or refute that judgment. This article presents data on the mathematics attitudes of elementary education majors and compares them to data obtained from other populations.
Geometry and Geometric Measurement
Authors: Clements Douglas C. , Battista Michael
Published: October 2020

Geometry is the study of objects, motions, and relationships in a spatial environment. We use it to examine containers, buildings, cars, and playgrounds—familiar things that students see, touch, or move. Because students are naturally interested in these things, geometry can be a highly motivating topic.
Models: Help or Hindrance?
Authors: Touger Hallie Ephron
Published: October 2020

Modeling mathematical operations using pictures and other concrete materials is a valuable technique to help children develop an understanding of mathematical concepts. A teacher feels secure that a child understand an algorithm when the child can build or draw a model of it. But a model that work for one child, that is, one that helps him or her to see a solution more easily, may make a problem seem more difficult for another child.
Talking with Young Children about Multiplication
Authors: Katterns Bob , Carr Ken
Published: October 2020

Research indicates that interviewing children is a powerful technique to tap their mathematical thinking. Lankford (1974), for example, used interviewing to learn about children's computational strategies, and Erlwanger (1975) uncovered useful information about their mathematical misconceptions. Clinical interviewing of individual student3 can reveal significant evidence about the actual effect of curriculum from the learner's point of view; it thus aids individual diagnosis and program evaluation (Codd 1981; Schoen 1979).
The Extended Subtraction Table: A Search for Number Patterns
Authors: Litwiller Bonnie H. , Duncan David R.
Published: October 2020

The subtraction table is a mechanism sometimes used to display the results of subtraction. In the following simplified version of a subtraction table, the answer in the body of the table is achieved by subtracting the number in the top row from the number in the left column.
One Point of View: Let's Teach Mathematics
Authors: Dubisch Roy
Published: October 2020

I find very little evidence that the present challenge to improve mathematics instruction is being met; instead, evidence shows an emphasis on rote learning as in the past. What is new, of course, in the mathematics instruction of the 1980 is the computer.
Symmetry the Trademark Way
Authors: Renshaw Barbara S.
Published: October 2020

Pepsi-Cola, Shell Oil, Chevrolet, Mattel, Westinghouse. What possible link could exist between these companies and the teaching of mathematics in the classroom? Interestingly enough, the trademark designs of these and other companies can provide a familiar yet innovative way for students to look at a number of mathematical concepts. These concepts include symmetry, mathematical curves, geometric shapes, similarity, angles, graphic representation of numerals, reflections, and translations. Though all these topics lend themselves to further analysis and interpretation, this discussion is limited to how two common type of symmetry—line and rotational—can be taught using some familiar trademarks. In particular, the article focuses on how trademarks and symmetry can be presented through the bulletin board.
Estimation and Mental Computation It's “About” Time
Authors: Reys Barbara J.
Published: October 2020

Mental computation and estimation are topics we keep hearing about. Although mental computation is not a stranger to the history of mathematics education, estimation is a relative newcomer to the curriculum. The history of mental computation dates back to when arithmetic was first taught. Historically, it was emphasized bccause of its social utility—shopkeepers needed to “cipher” total of grocery bills quickly. The current emphasis on both mental computation and estimation has a different origin. As teachers, we want students to take advantage of whatever computatonal tool is most appropriate for the situation at hand. Yet unless students have developed the skill both to compute mentally and to estimate and the awareness to take advantage or whichever is appropriate, we will not see it happen.
Research Report: The Cognitive Content of Elementary School Mathematics Textbooks
Authors: Callahan Leroy , Nicely Robert F. , Fiber Helen R. , Bobango Janet C.
Published: October 2020

Students' acquisition of higher-order thinking skills has long been a goal of mathematics educators. The National Council of Teachers of Mathematic (1980). in recommending that “problem solving be the focus of school mathematics in the 1980s.” noted that students must learn to “formulate key questions, analyze and conceptualize problems, define the problem and the goal, discover patterns and similarities, seek out appropriate data, experiment, transfer skills and strategies to new situations, and draw on background knowledge to apply mathematics” [emphasis added]. It is imperative that the reource teachers use to teach tho e skill be equal to the challenge of this goal.
One Point of View: Computation—It's Time for a Change
Authors: Trafton Paul R.
Published: October 2020

Considerable rethinking of elementary school mathematics is occurring. Exciting new directions and emphases are being recommended. One major stumbling block, however, to a more appropriate mathematics program for K–8 students is computation.
Uninterrupted Sustained Arithmetic: USA
Authors: Edge Douglas
Published: October 2020

USSR, an acronym for uninterrupted sustained silent reading, is a strategy developed to give students quiet time to practice silent reading and to increase their abi lity to read silently for longer periods of time. During this activity, everyone in the room reads silently, without interruption, for a specified length of time. This article highlights the essential features of USSR and describes how this strategy was adapted for use in mathematics classes and clinics.
Ideas
Authors: Zawojewski Judith S.
Published: October 2020

When a region model is used to represent fraction, an a sumption is made that the parts, or regions, are of equal area. This assumption can be reexamined in grades 1–8 with activities similar to the one given here. Activitie uch as the e also provide an opportunity for children to review the meaning of fraction as they work with regions. An additional payoff is that measurement and geometry are also used.
Learning with Logo “Instantly”
Authors: Clithero Dale
Published: October 2020

A group of second-grade tudents huddle around a computer. They use the simple commands of F, R, L, and B to teach the turtle to draw a creature that they have designed. No, they are not involved in a clandestine activity that must be hidden from their teacher. Rather, they are completing part of their a signment in the In tant Logo unit.
Lattice Multiplication and Division
Authors: Broadbent Frank W.
Published: October 2020

We often find solutions to new problems in older methods This pattern may hold for the use of a newly revised algorithm for multiplication and division. The original historical algorithm was the lattice method of multiplication used in Europe as early as the fifteenth century and later made more useful by John Napier and his bones in the sixteenth century. Lattice algorithm are easy to teach, and students are fairly uccessful with them. Unfortunately, they require more time to teach than our standard algorithms. Now that any calculation requiring a significant amount of time is done on calculators or computers, the present standard algorithms, which are highly efficient but difficult to teach and prone to error, need to be reconsidered.
Research Report: Learning Probability Concepts in Elementary School Mathematics
Authors: Shulte Albert P.
Published: October 2020

Many curriculum groups and individual have recommended the inclusion of topics in probability in the elementary school mathematics program. In “A Case for Probability,” an important position statement in this journal, Jones (1970) recommended probability because (a) the subject deals with idea and pattern that grow over time; and (b) evidence suggests that appropriate units can be taught in the elementary school.
Calculators in the Classroom: How Can We Make It Happen?
Authors: Reys Barbara J. , Reys Robert E.
Published: October 2020

Although curriculum and teaching method change slowly, we have witnessed some major changes in mathematics instruction over the last ten years, most notably the emphasis placed on the problem-solving process. We've also observed vast amount of resources funneled into microcomputer equipment for young students. In part because of this interest in microcomputer technology, we may have overlooked a technological device that has even more potential for revitalizing and enhancing mathematics instruction for children. Simple four-function calculators have been hoved to the back burner (or rear shelf of the school storeroom) in the past few years, but interest in them is reviving as evidenced by this focus issue.
Calculators and Connecticut's Eighth-Grade Mastery Test
Authors: Carter Betsy Y. , Leinwand Steven J.
Published: October 2020

An Agenda for Action (NCTM 1980) recommends that “mathematics programs take full advantage of the power of calculators and computers at all grade levels” and that “the success of mathematics programs and student learning be evaluated by a wider range of measures than conventional testing.”
Using Reflections to Find Symmetric and Asymmetric Patterns
Authors: Bidwell James K.
Published: October 2020

The concept of line symmetry is usually introduced in the elementary school by folding shapes, using mirrors, or drawing lines on a picture. Good follow-up activities are needed to give the student enough time to explore this concept of symmetry adequately.
Factors and Primes with a T Square
Authors: Dearing Shirley Ann , Holtan Boyd
Published: October 2020

Students often have difficulty determining all the factors of a number and finding out whether a number is prime or composite. The “T square” technique can make these processes easier. It has been successful with advanced sixth graders and average eighth graders. The T-square technique enables studetns to find all the factors of a number and to express the factors using set notation. The “T” idea comes from the T in factor and is the shape of the table that is used to record the factors.
MATHSTUFF Logo Procedures: Bridging the Gap between Logo and School Geometry
Authors: Battista Michael T.
Published: October 2020

Much enthusiasm has been generated about students' investigating and exploring the world of Logo's “turtle graphics” to learn geometry. This enthusiasm is easy to understand, since the computer screen in which the Logo turtle moves represents a small portion of a mathematical plane. As it is taught in middle and junior high school, geometry is essentially the study of such a plane and the objects that exist within it. So creating shapes with the turtle clearly involves geometric thought. However, the geometric ideas encountered in Logo are many times not covered in the standard curriculum; thus, integrating Logo activities with textbook topics can be difficult. This article will describe how teachers familiar with Logo can employ some special procedures (or programs) that allow students to explore and use traditional geometric topics within the context of the exciting environment of Logo.
Using a Metric Unit to Help Preservice Teachers Appreciate the Value of Manipulative Materials
Authors: Johnson Gretchen L.
Published: October 2020

Preservice teacher in my elementary mathematic method class often find it difficult to imagine how much help manipulative materials or an activity approach can be to a chi ld in learning a new concept. To help them understand, I teach them the metric ystem-for many an intimidating subject- using the ame materials and approache that would be used with children, although covering the material in a shorter period of time. If the e method help the preservice teachers learn the metric system, then they hould be convinced that the same approaches will work with chi ldren. ln turn, they will be more likely to use manipulatives in their own classrooms in the future.
An Infinite Variety of Names
Authors: Schiller Diane
Published: October 2020

An elementary school mathematics program can be structured to allow students to practice computational skills and also become familiar with concepts that need to be mastered in algebra. A basic notion needed for successful work in algebra is the idea that any number has an infinite variety of expressions. This same idea occurs in elementary school mathematics. For example, 10 = 9 + I = 8 + 2 = 7 + 3 = 6 + 4 = 5 + 5 = 100/10 = 2 × 5 = 90/9 = … = 20/2. The isolated knowledge that 3 + 7 = 10 is far less important than the chain of relationships in the previous sentence. An elementary school teacher can give students practice in computation (finding the sum to 10) while beginning to develop this idea of multiple names for any number. The activities described in this article begin with students' life experiences, continue through concrete and pictorial experiences, and conclude with abstract activities and problem solving.
Learning about Odd and Even Numbers
Authors: Boyd Barbara Vogel
Published: October 2020

The number charts described in this article have been used sucessfully with elementary students as young as first graders to teach the concept of even and odd numbers. Students construct charts and then answer a series of questions about the patterns that they observe. The teacher can guide the dicussion by uing overhead transparencies.
Using Historical Materials in the Mathematics Classroom
Authors: Arcavi Abraham
Published: October 2020

The arguments advocating the use of the history of mathematics in mathematics education have become widespread in recent years. Theoretical and practical guidelines for using history have also appeared, some of them accompanied by the description of actual experiences (see, e.g., the review by Booker [1985]).
Two-sided Pies: Help for Improper Fractions and Mixed Numbers
Authors: Rees Jocelyn Marie
Published: October 2020

Although empha is on the development of fraction concepts is increasing, it occur in the early grades when the discussion is limited to proper fractions. When improper fraction and mixed number are introduced, far less attention is given to the development of a sound conceptual base. It is not unusual to find a pupil who can draw a repre entation of five-sixth but not of even-fourth. Even more infrequent is a youngster who can illustrate the equivalence of two and two-third to eight-third. Failure to acquire a clear understanding of fraction greater than one and their mixed-number equivalents severely limits pupils' meaningful use of these number and results in a weak background for the development of mixed numbers. This article suggest a model for improper fraction and mixed numbers and describes some activities for working with them at the precomputational level.
Research into Practice: Microcomputer Use in the Elementary School
Authors: Wilson Patricia S.
Published: October 2020

Current software in elementary mathematics offers tutorial and practice programs as well as more openended activities, such as simultations, games, utilities, and problem solving. In addition to software, elementary school students are using student- and teacher-made programs (BASIC or Logo) to explore mathematics. Owing to the wide range of lessons, researchers have found it necessary to adopt a variety of methods for studying mathematics learning, including case studies, classroom observations, and large-scale data collection. Although it is difficult to compare such diverse studies, results support the following conclusions.
Microcomputers in the Primary Mathematics Classroom
Authors: Campbell Patricia F.
Published: October 2020

Picture a school-board meeting or a meeting of a school district's elementary curriculum committee. Raise the issue of integrating microcomputers into the elementary school's mathematics curriculum, and a debate will ensue. Focus the discussion on the use of microcomputers in the primary classroom, and the remarks will become intense and passionate. Although the diversity of comments prompted by such a discussion cannot be anticipated, two views will probably be voiced. Seeking the promise of a supposed competitive edge, one faction will favor microcomputer use while questioning whether the calculator threatens children's learning of the basics, that is, arithmetic. Citing the added danger of producing socially isolated children who are obsessed with the lure of microcomputers, another group will reject any form of technology in the primary classroom.
Ideas
Authors: Barson Alan , Barson Lois
Published: October 2020

Because this issue concerns early childhood education, IDEAS for this month consists of activities for the primary grades. The grids offer practice with patterns, number and shape identification, and computation.
Ideas
Authors: Barson Alan , Barson Lois
Published: October 2020

Ideas this month uses newspapers as a source of data from which students design, read, and use tables, charts, and graphs. Proficiency in interpreting data is one of the essential skills necessary for successful problem solving. The following activities provide teachers with both short- and long-term projects.
The Continuing Calculator Controversy
Authors: Dick Thomas
Published: October 2020

To use or not to use calculator in the elementary school classroom? That seems to be a question as contro-versial now as it was in 1975 when the National Advisory Committee on Mathematical Education offered the following advice: “beginning no later than the end of the eighth grade, a calculator should be available for each mathematics student during each mathematics class. Each student should be permitted to use the calculator during all of his or her mathematical work including tests.” In An Agenda for Action (1980), the National Council of Teachers of Mathematics (NCTM) recommended that “mathematics programs must take full advantage of the power of calculators and computers at all grade levels.” This recommendation was reaffirmed by the NCTM in a position statement (Calculators in the Mathematics Classroom, April 1986) with the further call “that publishers, authors, and test writers integrate the use of the calculator into their mathematics materials at all levels.”
One Point of View: An Active Approach to Geometry
Authors: Burger William F.
Published: October 2020

Every contemporary K–12 mathematics curriculum must contain a substantial amount of geometry. Geometry organizes and clarifies our visual experiences and provides visual models of mathematical concepts. Applications of geometry are ubiquitous—we encounter them daily. Thus, every student needs to study geometry. This idea is noncontroversial.
Digit Delight: Problem-solving Activities Using 0 through 9
Authors: Balka Don S.
Published: October 2020

Number puzzles of all kinds offer intriguing challenges to elementary and junior high school students. As the title suggests, this article presents several problem-solving activitie involving only the digits 0 through 9. For classroom use, sets of ten ceramic tiles (each 1-inch square) can be inexpensively made using marking pens, or plastic sets called “Try-A-Tiles” can be purchased. Each set can be stored in a small plastic bag for student use. Students will find the direction easy to follow. The teacher's guidance is helpful to direct students' interaction about their strategic and later to discuss maximum and minimum solutions. Problems can be shown on an overhead projector, as bulletin-board puzzles, or on individual sheets in learning centers.
Teaching Mathematics with Technology: Exploring Patterns
Authors: Bright George W.
Published: October 2020

One of the more exciting outcomes for a student to experience, or for a teacher to observe, is seeing patterns common to a collection of objects or data. Computer output and calculator displays can be used to lend opportunities to look for patterns. Some students are more successful with the graphics output, whereas other students see patterns in the numbers more readily. In either situation, encourage students to predict what the output will be and then to test their predictions. This activity will engage them more in the mathematics of the activity than simply using a trialand-error approach.
Explorations with Tessellating Polygons
Authors: Kaiser Barbara
Published: October 2020

Tessellations offer the intermediate-grade teacher an opportunity to incorporate a variety of geometric topics within one unit. This unit not only includes a review of two-dimensional shapes but also allows students to focus on relation ships among the shapes. Students can use their skills in angle measurement and apply transformations (slide, flips, and turns). Many opportunitie also arise for extension activitie to enrich student's learning either as individuals, groups, or a class.
Seeing Addition: A Diagnosis-Remediation Case Study
Authors: Tucker Benny F.
Published: October 2020

The value of physical materials as a tool for helping children “see” mathematical ideas is illustrated repeatedly when children have opportunities to use those materials. The following case study is just one of many that demonstrate this principle. The child, whom we shall refer to as Ann, was in the third grade. Ann's parents and teacher had reported that she had a fair grasp of all the basic facts for addition but consistently made errors when performing the operation with two-digit and three-digit number.
Teaching Mathematics with Technology: Logo and Geometry
Authors: Bright George W.
Published: October 2020

Interest in teaching geometry through Logo graphics is increasing. It seems reasonable to expect that geometry understandings will improve through exposure to such a visual environment, but the research has not given clear-cut evidence that the improvement is automatic. However, in two recent studies (Kelly, Kelly, and Miller 1986–87; Noss 1987) Logo showed a possible advantage in improving students' understanding of selected geometric concepts. This month's activities illustrate a way that teachers can give students explicit help in focusing on important geometric ideas.
Lesson Planning: The Key to Developing Number Sense
Authors: Thornton Carol A. , Tucker Sally C.
Published: October 2020

Building number sense starts by planning experiences that help children understand the size of number, operations on numbers, and relationships between numbers. The two example that follow illustrate children's use of good number sense.
Number Sense: The Role of Measurement Applications
Authors: Kastner Bernice
Published: October 2020

Mathematics educators may not universally agree on what number sense is, but most of us recognize it when we see it.
Yes You Can … Plan Appropriate Instruction for Learning Disabled Students
Authors: Meyers Marcee J. , Burton Grace M.
Published: October 2020

Matt is currently completing his senior year in high school and has achieved excellent grades in advanced literature and history courses. Because of these grades and his aboveaverage scores on college entrance exams, Matt has been accepted at both state univers ities to which he has applied. This feat probably does not seem extraordinary except for the fact that in second grade Matt was identified as having a specific learning disability and was placed in a special class for learning disabled children. Since that time, he has received mathematics instruction in regular classrooms, in resource programs, and from private tutors. The term learning disability covers many specific conditions and in itself communicates little about an individual's strengths and deficits. For example, tests showed that Matt is particularly strong in auditory language skills, but his visualspatial performance and visual memory are poor. These results mean that Matt understands and remembers what he hears but has trouble perceiving and remembering what he sees. Despite his strong motivation and his superior performance on an individual inteLligence test, he often receives below-average or failing grades in mathematics.
Facilitating Understandings of Geometry
Authors: Pappas Christine C. , Bush Sara
Published: October 2020

Recently, Forman and his colleagues (Forman and Hill 1984; Forman and Kushner 1983) have offered important and useful ideas for applying Piagetian concepts in the development of curricula for young children. Central in their approach is the emphasis on the constructive nature of knowledge—that is, how an active mind constructs relationships among objects. In such a view of learning, questions such as, “What mental events explain how the child understands a complex problem?” and “What conflicting ideas must the child deal with in order to solve problems correctly?” are paramount (Forman and Kushner 1983, 10).
Algebra Can Be Elementary … When It's Concrete
Authors: Berman Barbara , Friederwitzer Fredda
Published: October 2020

Effective mathematics requires more than the use of symbols or numerals. All students, and even many adults, need concrete models to understand mathematical concepts. Elementary and middle school children can understand and master basic concepts of mathematics, including algebra, when concrete materials are used to model these concepts. This article presents a rationale for these statements and describes a model for teaching early algebraic concepts using manipulative materials.
Magic with Magic Squares
Authors: Wills Herbert
Published: October 2020

Johnny Carson docs a routine that is a take-off on the answer man. Instead of answering questions, however. Johnny is presented with an answer and he supplies a question having that answer. An analogous situation can be presented to youngsters. Let them play Johnny's part. the part of the question person. Suppo e that you orally give them, say, fifteen. This is the answer to a question that involves the addition of three different whole numbers. The students' task is to give the addition questions related to that sum.
Body Measurement
Authors: Allen Neufeld K.
Published: October 2020

In teaching the customary units of measure, the teacher risks offering two few activities that focus on measuring or on determining relationships among units. In the metric system, relationships among units are especially important and become clear to students when we offer them the opportunity to measure many familiar objects. The human body is made up of many parts that students measure with great interest. A student's knowledge of the measures of some of these body parts can be helpful in making estimates of the measures of other objects in his or her immediate environment
People Who Live in Round Houses
Authors: Zaslavsky Claudia
Published: October 2020

Mathematics comes alive when students participate in activities that illustrate how mathematical decisions arose from the needs of societies. An investigation into styles of building in different cultures is a valuable source of experiences with shapes and sizes, as well as with concepts of perimeter and area. At the same time, teachers have the opportunity to integrate mathematics with social studies, art. and other subjects.
Data Bases: In the Teaching of Elementary School Mathematics
Authors: Bright George W.
Published: October 2020

As the emphasis of elementary school mathematics moves toward more problem solving and more use of technology, students' understanding of concepts and ideas will become increasingly important. Without clear understanding of concepts and ideas, students are unlikely to be able to apply mathematics in everyday situations. This article illustrates one way to use data base software to develop conceptual understanding.
Some Observations of Seventh Graders Solving Problems
Authors: Garofalo Joe , Goodwin Vanere , Mitchell Robert I. , Mtetwa David J.
Published: October 2020

In viewing videotapes of four seventh graders working on verbal mathematics problems and subsequently being interviewed about their performance, we have noticed a variety of conspicuous and interesting behaviors being used to facilitate certain aspects of problem solving. We believe that these behaviors had not been explicitly taught to any of these students, yet they knew when to invoke them to aid their problemsolving efforts. Moreover, for the most part these students were aware of the behaviors and were able to talk about their usefulness.
Implementing the Standards: the Measurement Standards
Authors: Lindquist Mary Montgomery
Published: October 2020

Clear expectations for the measurement curricula of grades K–8 are expressed in the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989). The statements in figure 1 are discussed in the Standards. Central to both the K–4 and 5–8 standards is the process of measuring, which can help students build understanding about measuring and make connections among various measurement concepts and skills.
Flexible Straws
Authors: Prentice Gerard
Published: October 2020

Using drinking straws to construct geometric figures, has been a common activity for years. To join the straws, many different materials have been used—plasticine, marshmallows, paper clips. pipe cleaners. and so on. Here is a new twist, or should I say “flex.” to this topic.
Olympic Medal Counts: A Glimpse Into Humanistic Aspects Of Mathematics
Authors: Borasi Raffaella
Published: October 2020

Mathematics is too often perceived by students as a discipline in which results are always predetermined, exact, and absolutely right or wrong (Borasi, in press). This view of mathematics has some unfortunate implications. First, students may erroneously believe that school mathematics permits no space for creativity, imagination, or personal judgment. Second, they may place an unjustified trust in any position or statement that has been supported with mathematical data—as if the use of mathematics guaranteed absolute truth.
NCTM Standards for School Mathematics: Visions for Implementation
Authors: Crosswhite F. Joe , Dossey John A. , Frye Shirley M.
Published: October 2020

We can expect that the release of NCTM' Curriculum and Evalution Standards for School Mathematics (National Council of Teachers of Mathematics, Commission on Standards for School Mathematics 1989) (Standards) will become one of those memorable moments that mark the history of our Council. We may remember this event in any of everal ways.
Do You Speak Math?
Authors: Small Marian S.
Published: October 2020

Educators and parents are all aware of the importance of regularly talking to children to enhance their language development in particular and their intellectual growth in general. These experiences give children opportunities to experiment with language, to interact with others through a language medium, and to participate meaningfully in the world of ideas. When children learn language, they take pleasure in using words they hear from others in arrangements that express their own unique ideas and thoughts. They do not simply repeat sentences; they create them.
Communicating About Spatial Relationships
Authors: Sgroi Richard J.
Published: October 2020

Recently, the National Council of Teachers of Mathematics published the Curriculum and Evaluation Standards for School Mathematics (1989). It stresses the importance of developing spatial sense in students. The authors indicate that spatial sense can be nurtured by “constructing, drawing, measuring, visualizing, comparing, transforming, … discussing ideas, conjecturing, and testing hypotheses” (p. 112).
Research into Practice: Spatial Abilities
Authors: Stanic George M. A. , Owens Douglas T.
Published: October 2020

Look at figure 1 (Del Grande 1987). Which quadrilateral is different from the others? In figure 2 (BenChaim, Lappan, and Houang 1988), you are first given the back view of a building. Which of the pictures to the right of it represents the front view? These are two examples of tasks that involve spatial perception.
Implementing the Standards: Estimation—Direction from the Standards
Authors: Rowan Thomas E. , Reys Barbara J. , Reys Robert E.
Published: October 2020

Do you estimate? Of course you do. Everyone estimates. Research shows that estimation is used in real-world problem solving far more than exact computation. Furthermore, estimation relates to every important mathematics concept and skill developed in elementary school. It is a process that allows the user to form an estimate or to judge the reasonableness of a result.
One Point of View: Reclaiming School Mathematics
Authors: Elliott Portia
Published: October 2020

The framers of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) call for a radical “design change” in all aspects of mathematics education. They believe that “evaluation is a tool for implementing the Standards and effecting change systematically” (p. 189). They warn, however, that “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” (p. 252).
Implementing The Standards: Communication in Mathematics
Authors: Mumme Judith , Shepherd Nancy
Published: October 2020

The dictionary's definition of communication includes such phrases as succeeding in conveying information, having social dealings with, making connections, and making known. Our mathematical definition of communication parallels the general definition. We want our students to convey their ideas about mathematics, deal with it in social contexts, make connections, and make known their thinking as they learn and become involved in mathematics.
Research Into Practice: Constructivism and First-Grade Arithmetic
Authors: Kamii Constance , Lewis Barbara A.
Published: October 2020

For arithmetic instruction in the first grade, we advocate the use of games and situations in daily living in contrast to the traditional use of textbooks, workbooks, and worksheets. Our position is supported by the research and theory of Jean Piaget, called constructivism, as well as by classroom research (Kamii 1985, 1990).
National Council Of Teachers Of Mathematics: President's Report: Maintaining Momentum As We Reach New Heights
Authors: Frye Shirley M.
Published: October 2020

Recently I went back into my files to reminisce over the exciting and challenging years that have passed so quickly since Iris Carl, the chair of the Election Committee, invited me to accept the honor of a nomination for president-elect. There I found and read the position statement that I had written as a candidate in 1986 and decided that it was a most appropriate opening for these remarks.
Integrating Manipulatives and Computers in Problem-Solving Experiences
Authors: Brown Sue
Published: October 2020

In 1980, the National Council of Teachers of Mathematics stated that “problem solving must be the focus of school mathematics.” In 1989 the Council reaffirmed that belief with the Curriculum and Evaluation Standards for School Mathematics (Standards). Standard 1 for grades K–12 is “Mathematics as Problem Solving.” The Standards also asserts that “a computer should be available in every classroom for demonstration purposes, and every student should have access to a computer for individual and group work.” Also according to the Standards, “manipulative materials are necessary for good mathematics instruction.” In a typical classroom, problem solving may be taught, manipulative materials may be used, or students may be working at a computer. These functions, however, are usually completed as disjoint activities. Integrating these activities is possible, and this article illustrates how it can be done.
Using Concrete Models to Teach Large-Number Concepts
Authors: Joslyn Ruth E.
Published: October 2020

“I don't understand,” I often heard my fourth and fifth graders complain when I tried to teach them to read and write large numbers. Thinking that the problem might lie more in my presentation of the concepts than in their ability to understand, I began to look for a better way to teach these skills
Readers’ Dialogue
Authors: Fraps Judy C. , Carbotte Roger R.
Published: October 2020

After reading in the April 1989 issue (p. 4) Harry Bohan and Peggy Dohan's article “Readers’ Dialogue: Keeping tabs on a million.” I decided to try the ac tivity.
A Program In Middle School: Problem Solving
Authors: Moody William B.
Published: October 2020

Recent literature concerned with the mathematics curricula for the elementary and middle school grades has st ressed the need for inclusion of more acti vitie involving problem solving and meaningful computational instruction. The authors of Curriculum and Elvaluarion Srandards for School Marhemarics (Srandards) (NCTM 1989) encourage the development of “an individual's abilities to explore. conjecture. and reason logically. as well a the ability to use a variety of mathematical methods to solve nonroutine problems.” (p. 5) They plea for intuitive approache to solving problem in the middle chool years as a foundation for solving problems in algebra. Mathematic competitions can be one way to create opportunities for developing interest and skill in problem olving and dealing with nonroutinc problems.
Not Just An Average Unit
Authors: Paull Sandra
Published: October 2020

In the fall of 1986 a colleague who teaches adult mathematics education courses presented me with a challenge. She asked me if I would like to collaborate in developing and teaching an interdisciplinary statistics unit to my class of fourth and fifth graders. The interest was prompted by her involvement in the project A Pilot Study on Cross-Discipline Statistics Education, an NSF-funded project under the direction of Robert F. Boruch of Northwestern University. Because my class was self-contained, the prospect of making the unit interdisciplinary was exciting. However, the thought of teaching stati tics was somewhat intimidating. In previous years I had taught some lessons on data gathering, graphing, and finding averages but had never combined these skills in a meaningful way. Thi collaboration cemed a wonderful opportunity to do so, and I accepted the cha llenge.
Parents: A Ready Resource
Authors: Goldstein Sue , Campbell Frances A.
Published: October 2020

“I never seem to reach every student when I am teaching mathematics.” “There is never enough time for practicing mathematics skills.” These laments by typical elementary school teachers are both real and abundant. Teachers would love to have more time and more help to work with students individually on developing and mastering mathematics skills. Involving parents in working with their children in mathematics is a ready method of obtaining an extra resource for teachers when individualizing mathematics instruction.
Higher-Order Thinking: A “Basic” Skill For Everyone
Authors: Chancellor Dinah
Published: October 2020

As I was walking down the hallway in one our our elementary schools the other day, one of the teachers rushed out of her room to catch me. “I love teaching this way!” she said with shining eyes. “The activities are exciting and challenging. The kids can't wait to do them. They are learning so much! I have really seen changes in how they attack problems. The only thing that bothers me is that I feel that all my students—not just the ones who have been identified as gifted— could benefit from these activities.
Rhombus Ratio Activities
Authors: Litwiller Bonnie H. , Duncan David R.
Published: October 2020

Mathematics is, in part, a study of patterns. Activities that involve students in investigating, conjecturing, and verifying patterns should be included in the mathematics curriculum.
Lima Beans, Paper Cups, And Algebra
Authors: Loewen A. C.
Published: October 2020

Manipulative materials have become an increasingly important part of mathematics instruction. The point has been argued that manipulatives make mathematics more intriguing, easier to understand, and even more fun to learn. The challenge for the mathematics teacher is to find new and interesting materials that help students better understand mathematics and better remember the mathematics that they have learned. Lima beans and small paper cups are one effective alternative for helping junior high school students learn how to solve simple algebraic equation.
Making Mathematics Meaningful With M&Ms
Authors: Knecht Paul S.
Published: October 2020

Taking the last M & M from a tiny packet, three-and-one-half-year-old Jonathan observed plaintively, “There aren't much in it.” And I began to wonder if M & Ms might not just lend themselves to the development of prenumeration skills. Clearly the problem of too few M & Ms is one of immediate relevance to children.
Calendar Mathematics
Authors: Chancellor Dinah
Published: October 2020

The calendar is designed to speak directly to students by giving them open-ended questions intended to engage them mathematically in high-interest activities. Students ore encouraged to work on the activities individually, in pairs, or in small groups. No answers ore given for the calendar questions so as to encourage students to look to themselves as the mathematical authority and to develop the confidence and critical-thinking skills necessary to validate their thinking.
One Point of View: Calculators in the Classroom
Authors: Kaiser Elizabeth
Published: October 2020

As we adopt the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989), we can expect to make more use of calculators in elementary school classrooms. This technology allows students to think about and solve problems without the burden of tedious written computations. Teachers will realize the importance of using calculators in elementary classrooms as they see students of all abilities regularly attempt higher levels of problem solving with increasing confidence. Students deserve the opportunity to learn to use calculators in their classroom and real-life situations. My experience with calculators in my classroom during the past three years has convinced me not only that such progress is important but that classroom teachers can and must take a leadership role in this area.