bluuebunny/crossref_metadata_2025 huggingface dataset:
Hula-Hoop Math
Authors: Leach Junella
Published: October 2020

An “interest meter” (if such an instrument existed) would show record highs in my first-grade classroom whenever I take the hula hoop from it hook to begin a mathematics lesson. Hands stretch and wave for attention, and everyone wants to be picked for a turn using the hula hoop. 1 no longer think of it as a toy, because it has become indispen able. Most of the mathematics concept taught at this level can be enhanced by using one or two of these simple plastic circles.
Division with Base-Ten Blocks
Authors: Hall William D.
Published: October 2020

A paper-and-pencil approach tends to predominate in the teaching of division. As a consequence, the division algorithm is not meaningful to students. If the concept and usefulness of divisio n is to be understood, children must be required to go beyond simply computing with paper and pencil.
Some Thoughts on Teaching and Learning Mathematics
Authors: Greenwood Jay , Anderson Robert
Published: October 2020

Looking back at the “new math” (or if you prefer, “modern math”) era and reflecting on the emotional debates that occurred during that period, it is curious that the “back to basics” movement has been accompanied by essentially the same highly charged discussions.
The Sum of 1 + 2 + … + 99 + 100
Authors: Anderson Delores
Published: October 2020

What is the sum of the first one hundred counting number? This is the problem that I assigned to my gifted seventh-grade class. This is the problem that was solved by the great mathematician Carl Friedrich Gauss when he was eleven years old. lt did not take Gau much time to find the pattern and to present the answer to his teacher.
Counterpoint: A Reaction to “One Point of View”
Authors: Stanic George M. A.
Published: October 2020

In an interesting and thought-provoking piece published in the “One Point of View” section of the May 1983 issue of the Arithmetic Teacher, Zalman Usiskin asks: “once the calcuator is in the classroom, what consistent policy can justify learning partial-product multiplication and other time-consuming algorithms?” Usiskin suggests that, in fact, no consistent policy can justify placing restrictions on the use of calculator in the classroom.
The Third National Mathematics Assessment: Results and Implications for Elementary and Middle Schools
Authors: Lindquist Mary Montgomery , Carpenter Thomas P. , Silver Edward A. , Matthews Westina
Published: October 2020

The public has renewed interest and concern about education and those of usin the field must be prepared to answer question. One of the question is usually related to student performance. The National Assessment of Educational Progress (NAEP) is a primary source to which we can turn for support of our answer.
Computer Corner: Growing Numbers
Authors: Shumway Richard J.
Published: October 2020

A look at exponential growth provide an interesting setting in which student can explore new computer idea. At the same time they can become better acquainted with large numbers and cientific notation. The following sequence of activities and question will be interesting for your student to explore.
Report of the International Study Group on Minimal Competencies in Mathematics
Authors: Riehs Robert J.
Published: October 2020

The pressure to define minimal levels of competence in mathematics and the challenge to devise teaching strategies that ensure student achievement of those levels are two of the most pressing problems facing mathematics educators today.
Subtraction Drill with a Difference
Authors: Ewbank William A. , Ginther John L.
Published: October 2020

The subtraction algorithm has traditionally been more difficult for students to learn than the one for addition. Concrete demonstrations that are convincing are harder to arrange for subtraction as well.
Chalk Up Some Calculator Activities for Rational Numbers
Authors: Ockenga Earl
Published: October 2020

Would you like to get students thinking and talking about fractions? Sounds difficult? It's not. The activities that follow are ways that the calculator can be used to create interest in the study of fractions
Computer Corner: Try This: Computer Counting
Authors: Shumway Richard J.
Published: October 2020

One way to introduce students to computer counting is with a program such as the following:
Divisibility—Another Route
Authors: Gardella Francis J.
Published: October 2020

The rules for divisibility are studied at almost every grade level. As soon as a child learns to count by 2s, the conceptual basis for divisibility has begun. The purpose of this article is to offer an alternative to individual divisibility rules by generating a general process that can be applied to establish divisibility by any number
Assigned Readings from Professional Journals—a Suggested Procedure
Authors: Schmalz Sr. Rosemary
Published: October 2020

In the November 1980 issue of Arithmetic Teacher. Lowell Leake describes his efforts and experiences in his class for prospective elementary teachers. Many of my efforts have been similarly directed, but I would like to respond to one point in particular: the assigning of readings from professional journals. Over the past years, I have worked out a system that I have found quite successful in making such assignments
Computer Corner: A Microcomputer and the Law of Small Numbers
Authors: Flores Alfinio
Published: October 2020

If we throw a fair die, we know the probability of tossing any one of the six numbers is 1/6. In the long run, we expect each side to appear approximately the same number of times.
Research Report: Fractions
Authors: Suydam Marilyn N.
Published: October 2020

All three NAEP mathematics assessments have indicated that student score far lower on fraction items than on whole-number item. When children are interviewed about their conceptions of fractions, their sometimes torturous explanations clearly indicate how little they understand.
One Point of View: Does Mathematics Teaching Have to Be So Awful?
Authors: Moser James M.
Published: October 2020

While going through my files a hort time ago, I found the article “Does Mathematic Have to Be So Awful?” (Bereiter 1971). As one might expect from the title, Bereiter overstated his case, just a readers of this column might think I have over tated mine. Yet the title ha enough truth in it for both of us to go on. The key notion is awful, a word with several meanings that are not necessarily disjoint. According to Webster's, awful can mean (1) inspiring, or filled with, awe, as in afraid, terrified, deeply respectful, or reverential; (2) extremely disagreeable or objectionable: or (3) exceedingly great.
Which Comes First—Length, Area, or Volume?
Authors: Hart Kathleen
Published: October 2020

If teachers of mathematics were asked to choose the five or six most important topics in the school mathematics curriculum, then measurement would be likely to appear on every list.
Let's Do It: Cut and Paste for Geometric Thinking
Authors: Walle John Van de , Thompson Charles S.
Published: October 2020

Some of the very best geometric activities can be accomplished with very simple materials and minimal preparation. Each of the activities suggested in this article requires nothing more than some colored construction paper cut into simple shapes, some paste or glue, and large sheets of newsprint or art paper on which to paste designs.
Ideas
Authors: Shaw Jean M.
Published: October 2020

If students are to become intelligent consumers, they must learn to read and interpret labels on food packages. The exercises in the IDEAS column this month guide students in examining labels and making sense of the information the labels provide.
Multilevel Metric Games
Authors: Jensen Rosalie
Published: October 2020

The goal of the games described here is the improvement of skills in comparison, estimation, and linear measurement. Because children are motivated by their interest in the outcome of the games, they do not associate the practice in them with the tedium of some drill problems. The materials needed are easy to make, and some of them can be made by the children themselve. Several sets of rules are given for each set of materials so that the games can be used on different levels. Children may wish to create their own rules once they have learned to play these games. They can be played alone or in small groups.
Problem Solving: Tips For Teachers
Authors: O'Daffer Phares G.
Published: October 2020

Draw a picture is a strategy that is very helpful in solving certain problems. Consider the following problem to see how this strategy is used.
From the File
Authors: Jamski William D.
Published: October 2020

You are to plan a route through a dungeon for Indiana Jones, who wants to search for a hidden treasure. This route must cover all rooms to make sure that the treasure is found, and it must contain a minimal number of turns to allow for a rapid search.
Children's Difficulties in Subtraction: Some Causes and Cures
Authors: Baroody Arthur J.
Published: October 2020

Even when they are presented with basic addition combinations (1 + 1, 2 + 1, up to 8 + 9, 9 + 9) and basic subtraction combinations (1 − 1, 2 − 1, up to 17 − 9, 18 − 9), primary-age children tend to reJy on informal counting strategies to obtain sums or differences (Ginsburg 1982; Resnick and Ford 1981; Steffe, Thompson, and Richards 1982). Indeed, without instruction, children invent increasingly sophisticated counting strategies for adding and subtracting (Baroody 1984a; Carpenter and Moser 1982; Groen and Resnick 1977). Moreover, informal arithmetic provides a developmental basis for more advanced strategies, such as reasoning out or recalling combinations of numbers (e.g., Brownell [1935]). As a result of their informal experience, children discover numerical relationships that can later be ued to deduce sums and differences, for example, 5 + 4 = 9 because 4 + 4 = 8 and 5 is 1 more than 4, or 6 − 4 = 2 because 2 added to 4 makes 6 (Baroody, Berent, and Packman 1982; Baroody. Ginsburg, and Waxman 1983; Rathmell 1978; Suydam and Weaver 1975). Only gradually are these relationships internalized, enabling children to generate basic addition and subtraction combinations automaticall y (Baroody 1983b; Brownell 1935). Thus, despite the emphasis placed in school on memorizing the basic addition and subtraction facts, primary-age children typically rely on their informal counting procedures to do basic arithmetic because, initially, these are more meaningful.
Ideas
Authors: Shaw Jean M.
Published: October 2020

Let's go shopping! Shopping for school supplies and items for school lunches is a common occurrence at this time of year. IDEAS features problems based on shopping experiences this month. The posters let c hildren make judgments, use their estimating skills, deal with prices, make change, and add up calories.
Report on Primary School Mathematics Education in the People's Republic
Authors: Madell Robert L. , Becker Jerry P.
Published: October 2020

In 1980, fourteen American mathematics educators visited the People's Republic of China. The visit, sponsored by the U.S.-China People's Friendship Association, followed a fall 1977 visit sponsored by the National Council of Teachers of Mathematics (Madell and Becker 1979). But significant changes have occurred in China since then. Of particular interest to teachers is that the system of education, jolted by the Cultural Revolution (1966-76), is now being thoroughly reorganized.
Computer Sorting with Kids
Authors: Thompson Carla J.
Published: October 2020

The need to prepare students to function in a computer-oriented world is an educational priority. For students to participate effectively in a computerized environment, they must have some Jnderstanding of how computers work. Learning about the computer and how it operates does not necessarily require access to one. Many tasks that a computer performs can be demonstrated in the classroom with students.
A Discovery Approach to Teaching Programming
Authors: Doyle William H.
Published: October 2020

This journal has recently featured articles that stressed the importance of having elementary school teachers and students learn to write simple computer programs. This emphasis suggests the need to share successful strategies for helping teachers to gain elementary programming skills. Teachers will then be more likely to introduce or offer direction for students' programming in their classrooms. One successful approach uses discovery learning and leads naturally to programming without creat ing inhibiting anxiety. The objective is not to produce expert computer programmers but rather to help teachers understand the elementary constructs of BASIC and to begin writing simple programs. The approach uses short programs that illustrate educationally sound uses of computers in the classroom. The central, elementary constructs of BASIC are taught through the simultaneous study of program listings on paper and program output on the monitor.
Research Report: Estimation and Computation
Authors: Suydam Marilyn N.
Published: October 2020

Most people use estimation every day-more often than they do paperand- pencil computation. Thus, computational estimation needs to be given more emphasis in school mathematics programs. Textbook analyses indicate that it has been one of the most neglected topics in the curriculum. It is therefore no surprise that students pe1forin poorly on estimation questions in national assessments.
Computer Corner
Authors: Hampel Paul J.
Published: October 2020

A very motivational classroom activity for both younger and older students involves the use of mazes. Mazes promote the development of precise language that is so necessary when one gives instructions to a computer. A real plus is that mazes can be used both on and off the computer.
Understanding Word Problems
Authors: Knifong J. Dan , Burton Grace M.
Published: October 2020

The ability of nine- and thirteen-year-olds to solve word problems has declined significantly since the First National Assessment of Educational Progress in 1972–73 (Carpenter et al. 1980). This drop is unfortunate, because learning to solve word problems prepares students to use mathematics in the real world. Teaching children to think logically about word problems is at the core of the professional responsibility of mathematics educators.
Problem-solving Opportunities
Authors: Easterday Kenneth E. , Clothiaux Clara A.
Published: October 2020

The use of quetions by teachers to elicit response from students has been recognized as a sound pedagogical technique; however, insufficient attention has been given to the positive contribution that can be made by students' questions., Their questions add spontaneity to a class and can lead to better learning and more effective instruction. This article reports some questions that were asked by middle school students and the activities selected by the teacher to answer their questions.
Some Findings on Conceptual Development of Computational Skills
Authors: Swart William L.
Published: October 2020

With the prevailing wind of the 1980s blowing “back to the basics” and with the countervailing efforts by those mathematic educator who have long been fighting rote memorization of facts and algorithms. one is a bit reluctant to report data on students' ability to compute. However, the findings reported here on achievement in addition and subtraction by first-grade children help make the case for the conceptual rather than the mechanized approach to the operation. The results may not be startling. but the in truction that brought them about does suggest some strategies for teaching computation.
What Every Elementary School Mathematics Teacher Should Read-Twenty-two Opinions
Authors: Leake Lowell
Published: October 2020

If you could own only ten book on the teaching of elementary school mathematics, which would you choose? If your school's library suddenly acquired enough money to buy ten such books, which would you recommend? Which ten books on the subject would you suggest that new teachers purchase for their personal libraries? Such questions are more limited versions of the old idea of deciding which ten books you would want if you were marooned on a desert island.
Palindromes and the “Law of 11”
Authors: Dockweller Clarence J.
Published: October 2020

Several years ago, McGinty and Eisenberg (1978) described an extenive classification of numbers according to the number of step required to form a palindrome (a number that reads the same forward or backward, like 707 or 12021). The number 89. for example, requires twenty-four reversals and sum before the palindrome 8813200023188 is obtained. Although finding palindrome is intriguing in itself, other inte resting things can be done with them. Logical reasoning can be fruit fully applied to palindromic patterns. The patterns, related concepts, and discssuions are very appropriate for enrichment experience at the intermediate grade level with extenions for all higher levels. We shall consider several example that suggest the “law of 11.”
Geometry
Authors: Burger William F.
Published: October 2020

The elementary school mathemalics curriculum contains no substitute for the study of informal concepts in geometry. in geometry, children organize and structure their spatial experiences. Also, geometry provides a vehicle for developing mathematical reasoning abilities about visual concepts, for example, through the study of planar shapes. In this article, I shall focus on how reasoning can be developed through the study of two-dimensional shapes, their properties, and the relationships among them. Additional topics, such as tessellations with shapes, motions and symmetry, congruence, similarity, geometric constructions, and measurement, are also highly useful in developing reasoning in geometry. The Bibliography includes many materials that teachers have recommended on these topics.
One Point of View: Teaching Computer Science versus Using the Computer to Enhance Mathematics Teaching
Authors: Koetke Walter
Published: October 2020

Should English teachers be teaching reading or writing? The obvious answer is that they should be leaching both. Reading and writing continue to be essential skills in our society, and we have no reason to believe that their importance will diminish. A person without access to the basic tools of reading and writing is severely handicapped in the vast majority of pursuits, from earning a living to developing intellectually.
A Uniform Approach to Fractions
Authors: Ettline J. Fred
Published: October 2020

One of the main responsibilities of the mathematics teacher is to make mathematical manipulation and computation understandable. This article identities two dilticulties students have in computing with fractions. It recommends a procedure that will resolve these difficulties for students and increase their understandinu and retention.
Ideas
Authors: Shaw Jean M.
Published: October 2020

Calculators and active minds make an unbeatable combination for computation and problem solving. The IDEAS worksheets for this month present situations in which students can do some thinking first, then push the buttons on their calculators to get quick and accurate answers. The exercises are suitable for work by individual students. Pairs of students can also profit from working together to devise strategies for solving the problems and then sharing a calculator to answer them. Teachers might also duplicate and place the worksheets in their mathematics learning center so that students can work on them independently.
Pentagonal Patterns in the Addition Table
Authors: Litwiller Bonnie H. , Duncan David R.
Published: October 2020

Teachers of mathematics frequently wish to use nonroutine practice activities in their classrooms to review and maintain arithmetic skills. It is a serendipitous occurrence if students can discover patterns while practicing computation.
A Summer Professional Growth Experience
Authors: Hollis Loye Y. (Mickey)
Published: October 2020

It was probably not a unique experience, but it sure was fun, and more important, fifteen elementary school teachers improved their skills for teaching mathematics and did away with some anxiety about the subject. While they were about it, these teachers also increased the achievement in mathematics of forty-five elementary school students and showed them that mathematics can be a lot of fun.
Why Logo?
Authors: Shumway Richard J.
Published: October 2020

Logo is available on an increasing number of microcomputers, and many teachers arc considering Logo as an alternative to BASIC for young children. Should you consider Logo? By all means; Logo is an excellent language that can easily be learned by young children. But do not choose Logo as an alternative to BASIC, choose Logo as a companion language. Logo is excellent for some graphics, procedures, and structural programming and is available at an extra cost for some additional memory. For Cartesian graphing and most mathematics, BASIC is excellent and widely available at no extra cost. To illustrate Logo, let me introduce you to some elementary programs for your students.
Sticks and Bones
Authors: Hagan Michael
Published: October 2020

The proliferation of both teacher-made and professionally prepared games might easily tempt a teacher to conclude that using them to kindle a child's interest in mathematics is an end in itself. And yet the full riches of many games may lie undiscovered until children are challenged to go beyond their interests, to think about their actions, and to elaborate on them. From this perspective, the most valuable games are those that interest children and that have rich variations to encourage their growth.
Humanumerals
Authors: Hollingsworth Caroline
Published: October 2020

Although tracing numerals on sandpaper or felt or in a sandbox is often recommended as a way of learning their shapes tactilely, children rarely use more than their fingers and eyes in such an activity. Why not get their whole body into the act? Use body language to transform little humans into humanumerals! (See photos 0–9.)
How Do You Measure Up?
Authors: Mullen Gail S.
Published: October 2020

We hear a great deal about the United States going metric. Many busines es and indust ries have already done so. School mathematics texts increasingly feature metric measurement. Are you ready for the metric sytem? Do you understand it yourself, and can you teach it to other?
Testing Mental-Computation Skills
Authors: Reys Robert E.
Published: October 2020

Mental computation has always been useful. An examination of the elementary school curriculum during this century shows that mental computation has always been given some attention but that emphasis on it has varied. Currently, interest in developing better mental-computation skills is showing a resurgence.
Conceptual Understanding of Multiplication: Problems Involving Combination
Authors: Quintero Ana Helvia
Published: October 2020

Mistakes made by children in solving word problt:ms can have a variety of causes. One must identify these causes to help children surmount the ir difficulties. An a nalysis of the word problems given to c hildren can help in this task. This article will analyze multiplication word problems to identify the origin of children's difficulty. Emphasis will be given to problems involving the concept of combination.
Using the Memory Functions on Hand-held Calculators
Authors: Hannick Francis T.
Published: October 2020

Most inexpensive hand-held calculators on the market today have some memory functions, such as add to, subtract from, recall, and clear. Unfortunately, too few calculator users are familiar with the use of the e memory functions and, as a result, the opportunity to incorporate these calculator features into the elementary school mathematics curriculum is often overlooked. In the spirit of the recommendation in NCTM's Agenda for Action (1980) concerning the use of calculators in the classroom, this article demonstrates rhe use of the memory function by pre enting three activities that are appropriate for use in the middle grades (4–8). These activities are of interest to childrens, and their efllcient solution s are grea tly enhanced by the hand-held calculator's memory functions. (The constant arithmetic feature of the calculator is also required.) The calculator used in each activity is the Texas Instruments TI-1766. The particular memory key that will be di scussed are the AC, M+, and MR keys, which clear the memory and the di splay, add to the memory, and display (recall from) the memory, respectively. The use of the activities with other similar models may require minor modification.
Creative Problem Solving and Red Yarn
Authors: Wilmot Barbara
Published: October 2020

This activity is one of the more stimulating and enlightening I have discovered. It has worked well and with similar results in classes of mathematically gifted students in grades 2–10, in a class of advanced high school seniors, and in in-service workshops for teachers! A wide range? Yes, and I feel certain that it would work in almost any situation. Using colored yarn, participants are asked to create geometric figures. Since yarn is not a familiar “output device,” it always supplies an ample number of problems.
An Invitation to Topology
Authors: Poggi Jeanlee M.
Published: October 2020

Topology—it's full of surprises! In this fascinating branch of mathematics, the inside becomes the outside, a doughnut is equi valent to a coffee cup, and four colors are all you need to color a map.
Symmetry and Tessellations from Rotational Transformations on Transparencies
Authors: Sawada Daiyo
Published: October 2020

The title of this article may be a bit ostentatious, but it describes a simple yet rather dramatic procedure for producing symmetrical tessellated patterns. I feel that mathematics is all around us if we would only care to look. It is easy to remind students of mosaic tiling patterns, hexagonal or other interlocking paving patterns, or Escher's work. Recently I discovered that simple dot grids in a square (fig. I) or in a triangle (fig. 2) can produce tessellations (interlocking patterns that cover a surface).
Research Report: Addition and Subtraction—Processes and Problems
Authors: Suydam Marilyn N.
Published: October 2020

Developing concepts, modeling, and solving problems form the core of essential learning about addition and subtraction. That we may make the task more difficult than necessary is the thrust of several recent studies.
Children's Conceptual Understanding of Situations Involving Multiplication
Authors: Quintero Ana Helvia
Published: October 2020

One-step word problems are usually included in the mathematics curriculum so that students can learn to apply a new arithmetic operation. Recent studies (Carpenter, Hiebert, and Moser 1979; Quintero 1980), however, point out that the main difficulty children have with these problems is understanding the situation described in the problem and not in determining the correct arithmetic operation to apply. So in teaching word problems, we should place more importance on helping children understand the situation described in the problem. To do this, we must be aware of the different situations that can be modeled by an operation as well as the different concepts needed to understand each situation.
A Rationale
Authors: Kennedy Leonard M.
Published: October 2020

Many teacher believe very strongly in the benefits of manipulative material in building a foundation for children's mathematical concepts: “I am firmly convinced that manipulative material improve children's understanding of the mathematics they learn. My classroom is well stocked with all sort of commercial and teacher-made materials. My children and I use them nearly every day.” Other teachers view them with skepticism and are less inclined to use them.
Cooperative Small Groups: A Method for Teaching Problem Solving
Authors: Gilbert-Macmillan Kathleen , Leitz Steven J.
Published: October 2020

If the objective is the development of abilities and skills which are problem-solving in nature, the least efficient discussion is superior to most of the lectures.
Summing It All Up: Pre-1900 Algorithms
Authors: Pearson Eleanor S.
Published: October 2020

In 1795 at the Ecole Normale in France, Joseph Louis Lagrange said in his lecture “The Operations on Arithmetic.”
Will the Real Division Algorithm Please Stand Up?
Authors: Bates Tom , Rousseau Leo
Published: October 2020

Most of the literature concerned with the division of whole numbers has dealt either with different variations of processes for division or with different strategies for teaching such processes to children. The index of almost any source dealing with the learning of elementary school mathematics contains the phrase division algorithm. However, the narrative to which it refers almost invariably reveals that the phrase refers to a description of some aspect of division as a process. All too frequently, one also finds that the particular process is referred to as “the division algorithm.” Such a descriptor is misleading, for there are many different division processes.
One Point of View: Curricular Improvement versus Standardized Testing
Authors: Leinwand Steven
Published: October 2020

By now, the question is familiar and anticipated.
Verbal Multiplication and Division Problems: Some Difficulties and Some Solutions
Authors: Hendrickson A. Dean
Published: October 2020

Verbal problems that involve multiplication and division are difficult for children to solve. Many of these difficulties arise because of their limited under tanding of these arithmetic operations. Their experience with the different kinds of situation that call for these operations is also limited. At the same time, these problem cannot be categorized easily because the situation that require these operations are varied. Nonetheless. multiplication is often taught only as “repeated addition” and division only as “repeated subtraction.” Children must have specific instruction in all the situation that require multiplication and division as arithmetic operations if they are to apply them successfully to verbal problems.
Mathletics: Adding Activity to Arithmetic
Authors: Mack Richard W.
Published: October 2020

Teachers are motivated to teach arithmetic. Students are motivated to participate in athletics. Why not teach arithmetic through athletics? With that premise in mind, the intermediate teaching team at the Ackerman Laboratory School on the campus of Eastern Oregon State College et about devising a method of using athletics as a springboard to teaching basic arithmetic skills.
One Point of View: Passports to Opportunity
Authors: Taylor B. Ross
Published: October 2020

We are preparing today's elementary school students to live in the information society of the twenty-first century. In that society, whether one is a “have” or a “have not” will be determined largely by one' s education; the ability to do mathematics and solve problems will be essential. Today we have dramatic racial inequities in employment and income. We also have great disparities by race in students' achievement and participation in mathematics. To reduce the inequities in society tomorrow, we must address the disparitie in mathematics today. In my opinion, this challenge is the major issue in mathematics education today.
Polygons, Stars, Circles, and Logo
Authors: Craig Bill
Published: October 2020

Many teacher are excited about the potential uses of Logo with elementary school students. The language give students access to mathematical topic they have not previouly explored. The following activitie uae Logo in the study of geometry, number theory, and problem solving. The activities assume that tudents are familiar with turtlegraphic commands (FORWARD, BACK, RIGHT, LEFT) and know how to define procedures. The activitie are designed for students in the upper elementary and middle school grades. The star procedure and explorations are adapted from Discovering Apple Logo by David Thornburg. The book contains excellent ideas for the use of Logo as a tool for mathematical explorations. See the Bibliography for additional resources.
Research Report: Effective Teaching
Authors: Suydam Marilyn N. , Driscoll Mark
Published: October 2020

In any field, one way to plan for a program's excellence is to study those programs that have been recognized for their excellence and to try to isolate the influential factors. During 1983 and 1984, the Northeast Regional Exchange (NEREX) engaged in “A Study of Exemplary Mathematics Programs.” The study, funded by the National Institute of Education, sought to “identify and describe factors and conditions associated with excellence in precollege mathematics.” Excellence was defined by student outcomes—test scores, awards, consistently high course enrollments, and so on.
Diagnosing a Student's Understanding of Operation
Authors: Sowder Larry , Threadgill-Sowder Judith , Moyer Margaret B. , Moyer John C.
Published: October 2020

Interviewer (after the pupil had correctly solved a story problem): How did you know to do it that way?
Astronomy, Geometry, and the Ancient Greeks
Authors: Mitchell Charles E.
Published: October 2020

In 1895, the Report of the Committee of Fifteen on Elementary Education cited two reasons for including arithmetic in the elementary school curriculum. The first. most often associated with this period, focused on the value of arithmetic as a mental discipline. This reason was soon to fall from favor.
Students' Creative Computations: My Way or Your Way?
Authors: Hamic Eleanor J.
Published: October 2020

My fifth-grade students had finished working through the concept involved in single-digit division and had been struggling with double-digit division for several days when I selected students to work at the chalkboard.
Don't Be Blue, Number Two
Authors: Avital Shmuel
Published: October 2020

It was 2:00 P.M. on 2 February. I had a free period; I had no pape rs to correct and no students to interview, and material for my morning classes was ready. The school building was quiet; all the students and most of the faculty were in the gym. where an important basketball game was being played. I decided that I would catch up on some reading. The latest issue of the Arithmetic Teacher had been lying on my desk for quite a while and I felt guilty for having put it aside day after day as more urgent task continued to demand my attention. I had just picked up the journal and made myself comfortable when I heard a knock on the door. Who could it be? It occurred to me that I might let the knock go unanswered, and no one would be the wiser. But it dawned on me that that “this might be a student in need,” and I found myself calling “come in.”
A Problem-solving Component for Junior High School Mathematics
Authors: Day Roger P.
Published: October 2020

While teaching junior high school mathematics at the Stavanger American School in Norway. I sensed the need to challenge the students' perceptions of mathematics. The seventh and eighth graders seemed most concerned with producing correct answers. They saw little need for questioning, evaluating, checking, and comparing. They simply wanted to be shown “how to do it.” I set out to implement a problem-solving component within the structure of the junior high school curriculum that would alter this. “right-wrong-produce an anwer” mind set. This article reports my experience and sets forth ideas that may work for you.
Producing Curved Surfaces in the Octahedron: Enrichment for Junior High School Students
Authors: Pohl Victoria
Published: October 2020

String art on an octahedron provides a viable way to teach and illustrate geometric concepts to junior high school students. This learning experience also furnihes an opportunity to correlate mathematics and art. Furthermore, artistic geometric constructions often stimulate junior high school students, particularly those who do not fare well in other areas of mathematics. After completing the following construction, students and teache rs should agree that learning can be fun.
One Point of View: Mathematical Literacy for Teacher? Of Course!
Authors: Lichtenberg Betty K.
Published: October 2020

Our profession demands no less than mathematical literacy of all its members. The issue seems to center on the question of how we determine the mathematical literacy for all its members. The NCTM's Guidelines for the Preparation of Teachers of Mathematics offers an exemplary set of standards for the preparation of elementary school mathema tics teachers that insures mathematical literacy. It is crucial to the profession that we insist on adherence to these standards.
Problem Stories: A New Twist on Problem Posing
Authors: Bush William S. , Fiala Ann
Published: October 2020

Problem solving has become the focus of the '80s. The Arithmetic Teacher and the Mathematics Teacher are full of article on problem solving; conference for mathematic teacher overflow with essions on problem solving; and more and more teachers of mathematics are jumping on the problem-solving bandwagon. If you are one of these teachers, this article should interest you.
One Point of View: Great Theory; Why Little Impact?
Authors: Gawronski Jane D.
Published: October 2020

Mathematics education research has established itself a a viable, identifiable discipline. Publications in the area are readily available, presentation on mathematic education research are expected to be part of national and regional programs, and mathematic education positions at the university level often include an expectation of efforts in research. Why then doe the en e linger that the research remains great theory, with little or no clas room impact? Perhap the truth is somewhere between this extreme and the ideal of research-driven curriculum and instruction for K-12 mathematics.
Ideas
Authors: Leutzinger Larry P.
Published: October 2020

Ideas this month focuses on the topic of problem solving. Children need to develop strategies to solve process problems as described in the “Problem Solving: Tips for Teachers” sections of the Arithmetic Teacher. They also need to develop skills in reading, comprehending, and solving story problem. This month's activities involve the children in interpreting story problems, drawing their own conclusions, and making guesses.
A Compelling Case for Calculators
Authors: Yvon Bernard R.
Published: October 2020

Calculator can do a great deal for the mathematics classroom. The first part of this article will present six bonuses I have found that students and teacher experienced when using calculators in elementary, middle, and junior high schools. Next is a section on problem solving and creative problem making as well. Practical help for the teacher who wants to try calculators in the classroom appears in the third section, along with a teacher's checklist. The final section offers advice on personalizing the use of calculators for students and recognizing some of their limitations. I hope the reader will agree that the many pluses present a compelling case for calculator use in today's classroom.
Teaching Primary-Grade Mathematics Skills with Calculators
Authors: Spiker Joan , Kurtz Ray
Published: October 2020

When colleagues see calculators in my first-grade classroom they ask, “How will they be used in the first grade?” Professional pride dictates that I come up with the best answer possible. I tell them I am going to teach (1) what calculators are, (2) what calculators do, and (3) how calculator are used. Children should become comfortable using these tools. The goal is to teach and reinforce the objectives currently required in the first-grade curriculum.
Developmental versus Practice Lessons in the Primary Grades
Authors: Sowell Evelyn J.
Published: October 2020

How can teachers increase students' under tanding of mathematics? Good, Grouws, and Ebmeier (1983) found that mathematics achievement improved when teachers helped students acquire mathematics meaningfully. Meaningful acquisition occurs when students' new idea are related logically to previously learned ideas through carefully designed teaching procedures. This article describes such procedures by contrasting the purpose, materials, and role of teacher and students in developmental and practice lessons.
Geometric Figures Make the LCM Obvious
Authors: Edwards Flo McEnery
Published: October 2020

The greatest common factor (GCF) is easily found by comparing the prime factors of a set of numbers and choosing the prime factors they have in common. The least common multiple (LCM) is often more difficult for students to find. The prime factors of the LCM are not necessarily common to a set of numbers, but their product i a common multiple of those numbers. According to Troutman and Lichtenberg (1982, 173), “the least multiple that is common to some set of numbers will have all the factors of those numbers and no other factors.” How, then, is it possible to find these prime factors just by inspection? One way is to write the prime factors of a set of numbers in a list and use geometric figures to find the prime factors of the LCM.
What Lies Behind Measurement?
Authors: Harrison William R.
Published: October 2020

In “Building a Metric City or Town” Alec (1980) states, “The mathematical skills prerequisite to learning to measure the length of an object are minimal. The major skill a student needs to have is to be able to read a numeral.” In other words, measuring the length of an object consists of lining up one end of the ruler with an end of the object and reading off the numeral that corresponds to the other end. If a child can perform this task, we conclude that he or she knows how to measure. No wonder most students have such a superficial understanding of measurement; we do not teach basic measurement concepts.
Patterns, Thinking, and Problem Solving
Authors: Van de Walle John A. , Holbrook Helen
Published: October 2020

To get young children to think on their own is most difficult. By third grade, they seem to be well into the pattern of waiting to be told exactly how to do something. Then they copy the procedure routinely. This “copy what I've been told” syndrome, which appear in virtually every subject area, is counterproductive to the development of problem-solving skills. By it very nature, to solve a problem means one must think about the problem; choose. try, and test strategies for solving it; and finally find an answer. To be told how to solve a problem immediately reduces it to an exercise.
Let's Do It: Fun with Primary Math Centers
Authors: Chapman Carol
Published: October 2020

Mathematics centers in primary school classrooms can help pupils learn and have fun at the same time. These centers can be used for both enrichment and reinforcement. In my experience with second- and thirdgrade classes, the centers also give me more time to work with c hildren having difficulty with their daily lesson.
Do You Think You Might Be Wrong? Confirmation Bias in Problem Solving
Authors: Johnson James E.
Published: October 2020

This article focuses on a particular cognitive process involved in problem solving, namely, the ability to create hypotheses and the ability to relinquish hypotheses (Wason 1960). This process is illustrated with activities suitable for children and adults—activities that illustrate how to stres the importance of producing and evaluating new ideas while solving a problem.
Triangular Tiles for Your Patio?
Authors: Willcutt Bob
Published: October 2020

In the problem that follows, students are asked to find different possible tiles that could be manufactured by the make-believe Universal Tile Company and to show how a particular tile can be used to cover a floor. Students are led from a simple beginning to levels that will challenge their spatial problem-solving abilities and encourage their creativity. The challenges involve working with rotations and reflections and deciding if two tiles are really the same or are different. The students have a chance to be creative when they are asked to make up their own designs, including coloring and other artwork, to show customers how a particular tile will look when installed as a floor. This activity is one that you will find mathematically rich and rewarding for your students.
Computer Corner
Authors: Ryoti Don E.
Published: October 2020

Students need to count objects and to group objects for an understanding of the number system. Students also need to learn the sequence of names for the counting numbers. The computer can be used to illustrate how the digits change. The following programs print the successive counting numbers from 1 through a number that the user enters.
The World of Alphanumerics
Authors: Bain Donnie
Published: October 2020

Mathematics teachers are always on the lookout for problems and activities that include the manipulation of numbers and problem-solving techniques. I found such a problem in a contest offered by the magazine Games entitled “Millionaire.”
Reflections and Symmetrya–a Second-Grade Miniunit
Authors: Woodward Ernest , Buckner Patsy G.
Published: October 2020

At Marshall Elementary School, Fort Campbell, Kentucky, students are assigned to small groups for instruction on specific mathematics topics. Assignments to these groups are made on the basis of when students are “ready” for a particular topic. The five-day mini unit described in this article was taught to a group of seven second graders and one third grader. The second graders were slightly above grade level and the third grader was slightly below grade level.
Research into Practice: Children's Strategies in Ordering Rational Numbers
Authors: Post Thomas , Lappan Glenda , Cramer Kathleen
Published: October 2020

Our comments here are based on interviews from two teaching experiments with fourth and fifth-grade chil dren. The students were taught many aspects of fractions using a variety of manipulative materials including circular and rect angular piece. Cuisenaire rods number lines, and chips. Each student had his or her own materials. Each worked independently, in small groups, and as a whole cl ass, spending much time talking about and performing a wide vari ety of fraction- related tasks.
Coordinate Graphing: Shaping a Sticky Situation
Authors: Vissa Jeanne M.
Published: October 2020

The topic of coordinate graphing is often introduced as an isolated textbook topic for students in the third grade. Children's current fascination with stickers can be incorporated into an inte resting approach to graphing in the middle elementary grade. The following activities were organized to meet the need for experience in graphing skills, as well a to integrate practice in symmetry and the recognition of shape. A sugge ted enrichment activity concern the need for three coordinates to locate points in physical spaces.
Assessing For Learning: The Interview Method
Authors: Labinowicz Ed
Published: October 2020

Holding interviews with individual children on mathematical topic can reveal both unsuspected weaknesses and surprising strengths in their mathematical thinking. Provocative findings are likely outcome when the conversations extend beyond the structured format of workbook exercises and paper-and-pencil tests. Despit e similar written responses on work heets and test from many children in your class, interviews with several individuals will uncover a wide range of understanding or methods used. For example. some children will get right answer for computational task while having basic misunderstanding of the concepts underlying the procedure used. Other children will reveal original procedures that have not been taught in class. In addition, children making computational error may reveal a better conceptual understanding of the procedure than many who compute accurately. Such provocative findings—currently masked by an overdependence on paper-and-pencil evidence of learning—are likely to challenge your classroom practice. What you learn from children in a few interview can have a dramatic effect on what you teach, when you teach it. how you teach, and how you evaluate children's progress.