bluuebunny/crossref_metadata_2025 huggingface dataset:
Teaching Rational Number Division: A Special Problem
Authors: Trafton Paul R. , Zawojewski Judith S.
Published: October 2020

Division of fractions and division of decimals are particularly troublesome aspects of work with rational numbers. Fundamental problems occur throughout work with fractions and decimals that have roots in inadequate development of initial concepts, models, and language. Although proficiency with division can be improved, the work must build on a stable foundation of concepts and skills.
Teaching Percentage: Ideas and Suggestions
Authors: Glatzer David J.
Published: October 2020

How much of a tip should I leave for this meal? This everyday question is a challenge for many individuals. The lack of an understanding of the concept of percentage is at the heart of this situation. This article offers ideas and suggestions for teaching the concept of percentage, recognition of patterns, percentage as a special ratio, ways of finding percentages, and fractional percentages.
Teacher Education: Preparing Teachers to Teach Rational Numbers
Authors: Lester Frank K.
Published: October 2020

Other articles in this issue present valuable ideas and points of view about learning and teaching concepts and skills involving rational numbers.
Teacher Education: Preservice Elementary Mathematics Education: A Complete Program
Authors: Dossey John A.
Published: October 2020

The concern over the shortage of mathematics and science teachers has once again brought into focus the critical role played by elementary school teachers in the development of children's mathematical abilities. Although many groups making suggestion for improvement lament the mathematical preparation these teachers receive, none have described their conception of a total program of content, method, and the related clinical experience and practicum.
Another Look at the Teaching of Percent
Authors: Dewar Jacqueline M.
Published: October 2020

The traditional approach to percents in the elementary school is to separate the problems into three classes depending on what is unknown. Unfortunately, even after students have learned (memorized?) the three “cases.” they still have trouble recognizing which case applies to a given problem. College-level mathematics textbooks designed for preservice elementary school teachers do
When Students Talk…
Authors: Corbitt Mary Kay
Published: October 2020

When did you last listen to your students talk about mathematics, not just about today's lesson but about the subject in general and their feelings about it? If it has been a while since you've done this. you might be amazed to learn what perception your students hold. You might also be amazed to discover how much a discussion about mathematics feelings about mathematics can do to increase communication about the subject on other levels.
Research Report: Attitudes toward Mathematics
Authors: Suydam Marilyn N.
Published: October 2020

An individual's attitude toward mathematics has many facets, ranging from awarene of the structural beauty of mathematic and of it usefulnes to feeling about the difficulty and challenge oflearnng mathematic, and to interest in a particular type of mathematics or particular method of learning or teaching mathematics. What do we know about the attitude of elementary school pupils toward mathematics?
Mental Computation
Authors: Reys Barbara J.
Published: October 2020

The ability to compute mentally. that is. to calculate exact numerical answers without the aid of any calculating or recording device, varies tremendously among indi vidual s. A quick survey of any elementary or secondary school classroom will document that some students perform mental computation quickly and accurately, whereas others are greatly hampered on even simple arithmetic problems by the withdrawal of paper and pencil. Occasionally history reports a case of an individual who ha developed extraordinary kill in mental computation. These individuals have both fascinated us and made us curious about the development of such skill. One such example wa Zerah Colburn. Born in Vermont in 1804, the son of a farmer, by the age of eight he was touring America and England displaying his exceptional mental calculating ability. He was able to give instantly the product of any two four-digit numbers. Asked to raise 8 to the sixteenth power, he gave the correct answer of 281 474 976 710 656 in a few seconds without the aid of any recording device (Eves 1969).
Research Report: The Role of Review in Mathematics Instruction
Authors: Suydam Marilyn N.
Published: October 2020

You probably know teachers who how little enthusiasm for review, and students often reflect boredom. Yet the word carries a hidden promise of excitement that we seem to miss. Re-view. See from a new perspective. Review helps children synthesize what they've learned and helps them to identify what they haven't learned. It can help them develop confidence in their ability to be successful in mathematics.
A Test for Divisibility by Primes
Authors: Bezuszka Stanley J.
Published: October 2020

Many people a re interested in divisibility rules, particularly since they can be coordinated with calculator activities. For example, young student can use calculator to gather data, examine the data for patterns, and discover some divisibility rules on their own. (See Bitter and Mikesell 1980; Rey et al. 1979.) Generally, calculator afford a quick way to determine if a number is divisible by a certain prime. Divisibility rules are particlarly useful when the number being tested for divisibility is too large for a calculator to handle exactly.
Matching Instruction to Children's Thinking about Division
Authors: Weiland Linnea
Published: October 2020

Jane wa sharing 792 pennies among 8 children. Although base-ten blocks and paper and pencil were available for use, she chose to argue without the upport of concrete materials.
Store-bought Mathematics
Authors: Burkett Leonard , Whitfield Edie L.
Published: October 2020

Children often experience difficulty learning mathematics unless it is related to objects or situations that are meaningful to them. Underhill (1981) reports mathema tical research (Brownell and Moser 1949; Gray 1965) indieating that memory is greatest for learners when the material to be remembered has meaning for them. Mathematics often has little meaning for children when these relationships are not formed. It may seem remote and removed from real-world events and experiences. Teachers seeking to improve mathematics teaching and learning may wish to consider creating a supermarket math lab in the school or classroom. The supermarket setting can provide an experiencebased environment for activities and make mathematics a part of the child's world. This project can be adapted to kindergarten and firstgrade activities and can evolve into advanced concepts and problems found in upper elementary school mathematics.
Research Report: Profile of Expertise in Elementary School Mathematics Teaching
Authors: Leinhardt Gaea , Putnam Ralph R.
Published: October 2020

Over the last five years considerable interest and research have been generated about the contrast between novice and expert teachers of elementary school mathematics. Researchers hope that making this contrast will reveal important insights into the nature of expertise—what it means to be an expert mathematics teacher.
One Point of View: Basic Mathematical Skills or School Survival Skills?
Authors: Maier Eugene A.
Published: October 2020

Some lists of “basic mathematical skills” lead me to wonder why certain topics are included. To me the designation of a mathematical skill as “basic” implies the need for that skill in life beyond school. But I see topics on such lists that have nothing to do with pre paring students to function mathematically in the nonschool world. For example, consider paper-and-pencil procedures for computing problems like 136.7 × 56.8 or 7584 ÷ 354. In a half-century of doing mathematics—as a schoolboy, as a college and graduate student, in any number of odd jobs that paid my way through college, as an industrial mathematician, as a university teacher and reearcher, in everyday life, and just for fun—nothing I have done, apart from schoolwork, requires uch procedures today.
Cooperative Learning and Individualized Instruction
Authors: Slavin Robert E.
Published: October 2020

If you have been involved in education since the early 1970s, you have witnessed a dramatic turn of events: the rise and fall of individualized mathematics instruction (Rothrock 1982).
The Problem of Evaluation in Problem Solving: Can We Find Solutions?
Authors: Szetela Walter
Published: October 2020

As the emphasis on problem solving increases, evaluating students' attempts to solve problems will become more challenging because of different interpretations of problems and a wider variety of procedures available to students.
Problem Solving in Action: The Bulletin-Board Dilemma
Authors: Whitin David J.
Published: October 2020

Our school needed some bulletin boards hung in the front hallway. The custodian and I asked some sixthgrade students if they wanted to help us. A group of six offered their assistance. As they began to take measurements of the designated areas, they had many questions for the custodian and me. “How wide do you want these bulletin boards?” asked one.
Origami: Paper Folding—the Algorithmic Way
Authors: Heukerott Pamela Beth
Published: October 2020

Origami, the oriental art of paper folding, is simple, appealing, and economical. I have used this craft successfully to teach upper elementary students concepts and skills in geometry involving polygons, angles, measurement, symmetry, and congruence. This approach also serves as an example of a geometric algorithm, a sequence of steps to get a result, not unlike the rules for adding whole numbers and so on.
Assessing For Learning: Assessing through Questioning
Authors: Lindquist Mary Montgomery
Published: October 2020

You have probably been using questions to make assessments, perhaps without even realizing that you were doing so. Sometimes, a question may only reveal that a student is not paying attention or cannot repeat what was just said. A class response to “any questions?” may signal a transition to another part of the lesson. In rare moments we use questions to probe our students' understanding; this latter use of questions is addressed in this article.
Research into Practice: Subtracting by Counting Up with One-handed Finger Patterns
Authors: Fuson Karen C.
Published: October 2020

Teachers have succcssfully used a conceptually based unit to teach subtraction with minuends to eighteen (e.g., 13–8) to all ability levels of first graders (Fuson 1986a; Fuson and Willis, in press). Children subtracted by counting up from the smaller to the larger number and kept track of how many words they had counted up by using one-handed finger patterns (see fig. 1). Children had already learned the finger patterns and how to use the finger patterns to add single-digit sums to eighteen by counting on; this procedure and directions for teaching counting on with finger patterns are described by Fuson (1987). Subtraction was initially introduced as the operation done in three different situations: equalizing, comparing, and “taking away” (see the section “Teaching Counting Up with One-handed Finger Patterns” and Carpenter and Moser [1983]).
Problem Solving and Mathematical Beliefs
Authors: Frank Martha L.
Published: October 2020

A frequently asked question in the decade since problem solving has become a popular topic in mathematics education is “How can we get students to become better problem solvers?” Answers to this question have focused on such in structional techniques as the introduction of problem-problemsolving strategies (“heuristics”), Polya's four-step method, or even the teaching of computer programming languages such as Logo or BASIC.
Mathematics from Children's Literature
Authors: Tischler Rosamond Welchman
Published: October 2020

The mathematics curriculum for young children can grow from children's literature. The following examples encourage children to use a variety of thinking skills—classifying, forming hypotheses, selecting strategies, and creating problems. As a result, they offer more depth and breadth in mathematics than most curriculum guides or texts currently suggest. At the same time, the examples build on children's interests and involve them in an informal, active, and creative way. ln particular, they offer the manipulative experiences that are necessary at this age.
Using Writing Activities to Reinforce Mathematics Instruction
Authors: Davison David M. , Pearce Daniel L.
Published: October 2020

The traditional view has been that students learn to write in English classes and to compute in mathematics classes and “never the twain shall meet.” Certainly little thought has been given to the idea that teachers of various subject areas, especially mathematics, should seek to have students engage in writing activities as part of their study of that area. In recent years, however, this position has been changing, and different authors have recommended increased writing about mathematics by students as a useful and valuable aspect of mathematics instruction (Burton 1985; Greenius 1983; Johnson 1983; Shaw 1983; Watson 1980).
One Point of View: NCTM's Curriculum and Evaluation Standards: What They Are and Why They Are Needed
Authors: Romberg Thomas A.
Published: October 2020

During this past year, NCTM has produced a working draft of a set of curriculum and evaluation Standard for school mathematics (Commission on Standards for School Mathematics of the National Council of Teachers of Mathematic 1987). As chair of the Commission, I have been asked to respond to four questiona.
Teaching Mathematics with Technology: Estimating Numbers and Measurements
Authors: Bright George W.
Published: October 2020

Estimation skills are an important part of mathematics, and even simple technology can be useful in teaching these skills. Estimation skills-both estimation of numerical computations and estimation of measurements—help students become flexible at applying mathematics in everyday situations. By becoming more flexible, students ought to become better problem solvers.
Research into Practice: Developing Understanding of Computational Estimation
Authors: Sowder Judith
Published: October 2020

Many recent documents call for a renewed emphasis on computational estimation in the classroom. However, researchers are only now giving attention to how students learn computational estimation. The research described here focused on how children develop the ability to estimate computations. We begin with a brief description of the theory on which the research was based, describe the research study itself, and finally discuss the study's implications and extensions into the classroom.
The Struggle to Link Written Symbols with Understandings: An Update
Authors: Hiebert James
Published: October 2020

Two of the most striking and informative results from recent research on children's mathematics learning are the following. On the one hand, many children possess a surprising degree of competence with mathematical situations outside of school. For example, before beginning school, most young children can solve simple addition and subtraction stories, such as “Mary has 8 pennies. She gives 3 pennies to Roger. How many does she have left?” (Carpenter and Moser 1984; DeCorte and Verschaffel 1987; Riley, Greeno, and Heller 1983). In other words, before children have been taught how to add and subtract, they can solve addition and s ubtraction problems. Similarly, older children, as well as adults, can solve a variety of real-world problems using strategies that they have not learned directly in school (Carraher, Carraher, and Schliemann 1987; Lave, Murtaugh, and de Ia Rocha 1984; Scdbner 1984).
Research into Practice: Issues in Problem-solving Instruction
Authors: Grouws Douglas A. , Good Thomas L.
Published: October 2020

Research on problem solving can assist teachers by raising issues to consider as instructional decisions are made. Research that focuses on the study of current classroom practice is one good way of identifying such is sues. This article first characterizes some results from our recent research on classroom teaching of problem solving and then summarizes the related issues that teacher should conider as they plan and teach problem-solving lessons.
Developing Preschool Mathematical Concepts
Authors: Maxim George W.
Published: October 2020

Little Jeffrey places one block on top of two others as he busily constructs an elaborate block city. Although he is only two-and-one-half years old. Jeffrey understands that he has just made a “bigger” building by adding one block to two others. He understands this idea even though he does not yet know how to use the terms one. two, and three. But, by acting on his environment. Jeffrey is encountering the basic ideas that will gradually evolve into more sophisticated mathematics concepts. Only after repeated experiences of this type can Jeffrey develop the logical thinking skills necessary to express in words what has happened to his block structure.
What Myths About Mathematics are Held and Conveyed by Teachers?
Authors: Frank Martha L.
Published: October 2020

As teachers of mathematics, we want to help our students to develop a solid understanding of mathematical concepts and to become good problem solvers who are confident of their ability to do mathematics. Research on students' beliefs about mathematics reveals a set of mathematical beliefs, “math myths,” that can be counterproductive to achieving these goals. This article is a report on math myths believed by a group of preservice teachers. However. as you read, you might want to ask yourself these questions: Which of these myths do I believe? Which of them could my teaching methods convey to my students?
Implementing the Standards: Mathematics as Reasoning
Authors: Garofalo Joe , Kufakwami Mtetwa David
Published: October 2020

Why is mathematics a regular part of standard elementary and middle school curricula? What do we believe, assume, or at least hope that students get out of the years of mathematics instruction that they are required to take? We often pose these basic questions to teachers at workshops. and after they get over their initial nervousness and uncertainty, most give one or both of the following responses: (1) mathematics is useful for people—as workers, as consumers, and as educated citizens: and (2) the study of mathematics helps people develop the ability to reason, and thus it helps them to become better problem solvers. These responses are not surprising, since both Dudley (1987) and Smith (1989) list them as two of the reasons traditionally given for the required study of mathematics.
By Way of Introduction
Authors: Shaw Jean M.
Published: October 2020

“Spatial understandings are necessary for interpreting, understanding, and appreciating our inherently geometric world.” With these words, authors of the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989, 48) offer challenging and intriguing tasks for mathematics educators. The tasks include formulating or expanding adult understanding of spatial sense, considering its impact on the curriculum, and implementing a variety of sound, participatory activities with learners. The Editorial Panel has developed this focus issue on spatial sense to help educators gain insights into the nature of this important topic and to present means of developing spatial sense in learners.
One Point Of View: Spatial Sense and Mathematics Learning
Authors: Wheatley Grayson H.
Published: October 2020

Areview of United States school mathematics reveals that rules, procedures, and analytic reasoning dominate the curriculum, whereas little attention is given to spatial visualization. What should be the roles of imagery and spatial visualization in school mathematics? How does spatial visualization relate to the learning of mathematics?
IDEAS
Authors: Silverman Helene
Published: October 2020

The IDEAS section for this month presents techniques for developing spatial visualization while dealing with concepts of area, proportion, and symmetry as design is explored. A sheet is included for parents. Be sure to send a copy of the tangram-pattern sheet on page 33 with it.
IDEAS
Authors: Silverman Helene , Weiss Mikki
Published: October 2020

The IDEAS section for this month focuses on the mathematical patterns and relations that can be developed from the exploration of balance, mass, the length of the mass arm, and the position of the fulcrum.
The Mathematics Textbook: How Can It Serve The Standards?
Authors: Rosemary Schmalz S. P.
Published: October 2020

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

The National Council of Teachers of Mathematics's Curriculum and Evaluation Standards for School Mathematics (1989) and Professional Srandards for Teaching Mathematics (1989) endorse the view that assessment should be made an integral part of teaching. Although many of the student outcomes described in the Srandards cannot properly be assessed using paper-and-pencil tests, such tests remain the primary assessment tools in today's classroom.
Reaching Young Pupils With Technology
Authors: Schielack Jane F.
Published: October 2020

Recommendations in such current publications as NCTM's Curriculum and Evaluation Standards for School Mathematics (Standards) (1989) and the National Research Council's Everybody Counts (1989) emphasize the full use of technology in the classroom at all grade levels. But what is the role of technology in the early grades? How can computers best be used to support primary-level mathematics instruction? Where does the use of the calculator fit into the primary-level pupil's development of mathematical concepts? How can we justify the abstract nature of calculator activities in a primary-level mathematics curriculum built on the needs of young pupils to experience concrete representations of mathematical concepts?
Implementing The “Standards”: Number Representations and Relationships
Authors: Rathmell Edward C. , Rowan Thomas E.
Published: October 2020

Using numbers meaningfully and flexibly is addressed in three of the NCTM's curriculum standards for K–4 and 5–8 mathematics (NCTM 1989, 38, 87, 9 1). The intent in this article is to give activities that are in the spirit of the Curriculum and Evaluation Standards and involve number relationships and representations of numbers.
A Basketball Simulation
Authors: Noone E. T.
Published: October 2020

Basketball, a popular game that practically everyone has played, presents an excellent mean of teaching elementary probability concepts and percents using a computer simulation. In particular, a free-throw shooting contest can be simulated quite easily with a BASIC program. Program 1 replicates the free-throw accuracy of the great stars of college and professional basketball. Program 2 allows the student actually to compete with such stars as Earvin (Magic) Johnson, Michael Jordan, and Isaiah Thomas.
Evaluation: Be More Than a Scorekeeper
Authors: Clark H. Clifford , Nelson Marvin N.
Published: October 2020

Score keeping is a routine that occurs in hundreds of mathematics classrooms throughout the country. Teachers explain assignments, allow a work period, check the answers, then record the scores. Score keeping continues to be a common practice in the name of evaluation. Little attention is given to anything but the score that is recorded in the teacher's record book. Some teachers spend hours each week scoring and recording mathematics papers, but little thought is given to the usefulness of this practice. To many, this procedure has become a ritual rather than a meaningful assessment of students' work.
Teaching Mathematics with Technology: How Big Is a Million?
Authors: Parker Janet , Carroll Widmer Connie
Published: October 2020

Yet despite frequent exposure to such terms, people find it difficult to have any intuition for large numbers. Not until these numbers are put in relative terms do we get a sense of their size, as when we are told that the budget deficit is about $700 for every American. The following activities and guidelines suggest ways to use such relative terms to make large numbers more meaningful to students. Calculators or computers are indispensable aids in facilitating this process.
Cooperative Problem Solving: But what about Grading?
Authors: Kroll Diana Lambdin , Masingila Joanna O. , Mau Sue Tinsley
Published: October 2020

Do your students use cooperative-group work when they are involved in mathematical investigations and problem solving? If you answered yes, you are in good company. More and more teachers these days are finding that working together helps students become better problem solvers.
Systematizing Trial and Error Using Spreadsheets
Authors: Sgroi Richard J.
Published: October 2020

The National Council of Teachers of Mathematics, in its document Curriculum and Evaluation Standards for School Mathematics (1989), places emphasis on the roles of problem solving and technology in the mathematics classroom. The marriage of problem solving and instructional technology in a cooperative-learning setting can be critical to the development of a skilled twenty-first-century work force. Students should be prepared for a future in which the computer is used as an analytical tool rather than merely a vehicle to test the accuracy of programming skills and for solving simplistic problems using long and complicated numerical values.
Word Problems and the Language Connection
Authors: Matz Karl A. , Leier Cynthia
Published: October 2020

Problem solving is generally considered to be one of the essential mathematics skills. The National Council of Supervisors of Mathematics (1989) lists problem solving first among the twelve essential components for mathematical literacy. The National Council of Teachers of Mathematics's Curriculum and Evaluation Standards (1989) recommends that problem solving begin early in the primary grades and that it include a variety of experiences. Word problems offer meaningful quantities and purpose for the calculations students make, but even so, many solvers find them difficult (Smith 1989).
Arithmetic—Friend or Foe?
Authors: Brown Francis R.
Published: October 2020

Widespread concern over the shortage of engineers and technicians has now focused attention on what the Carnegie Corporation of New York calls a national weakness: namely, the mathematical incompetence of the average—and even the above-average—American.
A Bibliography of Mathematics Books for Elementary School Libraries
Authors: Hess Adrien L.
Published: October 2020

Some recent textbooks on the teaching of arithmetic have indicated the existence of a need for a bibliography of mathematics books for elementary school libraries. Spitzer1 states that “there arc many stories in which counting plays an integral part which may be read to children of pre-school and school age.” He lists ten books which would be useful for this purpose. Wilson2 devotes a chapter to “Appreciation Units in Mathematics” in which he discusses some books which would be helpful in developing appreciation for mathematics.
Six Years of Research on Arithmetic Instruction: 1951-1956
Authors: Weaver J. Fred
Published: October 2020

The improvement of instruction in arithmetic is, as in other areas of the curriculum, a function of numerous factors. Without question one of the most important of these is research. The amount, quality and significance of research activity; the extent to which research findings are reported and disseminated; the degree to which the implications of research are implemented in actual classroom situations—all these have a marked influence on the amount of instructional improvement we can hope for in the field of arithmetic.
Learning Principles that Characterize Developmental Mathematics
Authors: Eads Laura K.
Published: October 2020

Developmental mathematics denotes a point of view with respect to pupil learning in the curriculum in mathematics or arithmetic. Some of the characteristics of Developmental Mathematics as this applies to pupil learning are described below.
New Tools, Methods for their Use, and a New Curriculum in Arithmetic
Authors: Schott Andrew F.
Published: October 2020

The arithmetic children learn depends upon the structured learning situations which are a part of their school life and the vicarious learning experiences which occur outside the school. If participation in a structured arithmetic learning situation results in mental frustration or in sheer boredom with the experience future participation in such experiences is either avoided or the learnings resulting from the learning situation are minimal. Motivation is then also absent or minimal. Measurement of learnings in arithmetic appears to be a direct measurement of motivation, not the opposite, as is often supposed. Children who do not learn arithmetic in structured learning situations often report that they “hate” arithmetic. There is an abundance of evidence that learning experiences in arithmetic in school, almost universally, are fearfully frustrating to the majority, and to the gifted, extremely boresome.
Implementing the Professional Standards for Teaching Mathematics: Doing Mathematics Together: Creating a Mathematical Culture
Authors: Corwin Rebecca B.
Published: October 2020

Rebecca Corwin is professor of education at Lesley College in Cambridge. Massachusetts. where she teaches courses in mathematics education. curriculum development and computer intergration. She is also codirector of the National Science foundation-funded Talking Mathematics projett at the Technical Education Research Center (TERC) in Cambridge
Making Connections: A Case For Proportionality
Authors: Cramer Kathleen , Post Thomas
Published: October 2020

Proportional reasoning is one form of mathematical reasoning. Many aspects of our world operate according to proportional rules. In the science classroom, proportionality surfaces when density is explored, when balance beams are used, and when any two equivalent rates are compared. ln the mathematics classroom, proportionality surfaces when properties of similar triangles are examined, when scaling problems are investigated, and when trigonometric functions are defined. The importance of proportional reasoning is stressed in the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989, 82).
Hypermedia: a Vehicle for Connections
Authors: Babbitt Beatrice C. , Usnick Virginia
Published: October 2020

In recent years, numerous reports have called for reform in American education in general and mathematics education in particular (e.g., Leitzel[1991]; NCTM [1991]; National Research Council [1989, 1990, 1991]). One suggested reform is revamping the curriculum to include mathematics more relevant to society and student current needs. In addition to changing the curriculum. these report have recommended changes in the method used to teach the curriculum. Among the suggested changes in methodology are an increased use of technology and opponunities for students to connect mathematical ideas.
Creating Story Problems
Authors: Fairbairn Donald M.
Published: October 2020

Much has been written concerning how to teach problem solving, going back to Póya's steps in problem solving (1957). The imponance of problem solving is also well documemed. Problem solving was made the “agenda for the eighties” by the National Council of Teachers of Mathematics (NCTM). The Curriculum and Evaluation Standards (NCTM 1989, 77) indicates that “problem situations can serve as a context for exploring mathematical ideas. Through these situations, students have opportunities to investigate problems, apply their knowledge and skills across a wide range of situations, and develop an appreciation for the power and beauty of mathematics.”
Implementing the Professional Standards for Teaching Mathematics: Teaching and Learning Mathematics through Classroom Discussion
Authors: Vacc Nancy Nesbitt
Published: October 2020

Tien-Tien announced during the news of the day that her grandmother was coming for a visit. Her third-grade teacher later used this news to introduce the mathematics lesson as follows: ‘If Tien-Tien's grandmother leaves China tomorrow morning, how long do you think it will take her to arrive in North Carolina?” The discussion that followed included a variety of important questions and comments. “Is she going to fly or take a boat?” “How fast does a plane fly?” “Will she come this way (pointing to Europe on the map) or that way (Pacific Ocean)?” “Can she sleep on the plane or will she need to land someplace so she can sleep in a bed?” “Where can the plane land on the way here from China?” “How often does a plane need to land for gas?” “I know that my cousin in Chicago is one hour later than we are. If she has to land in Chicago. won't that make a difference in how we figure the time?”
Calendar Mathematics
Authors: Alarid Cherry , Loflin Cathy
Published: October 2020

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

The goal of those who support NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) is to develop the mathematical power of all students. To achieve this goal, teachers in all mathematics classrooms will need materials and professional support to maintain their commitment to the task and their proficiency in accomplishing it. “Teachers are key figure in changing the ways in which mathematics is taught and learned in schools. Such changes require that teachers have long-term support and adequate resources” (NCTM 1991, 2). This focus issue contains a variety of ideas to support classroom teachers as they begin the difficult job of planning for instruction in mathematics that will help all students achieve mathematical power.
Helping and Getting Help—Essential Skills for Effective Group Problem Solving
Authors: Farivar Sydney , Webb Noreen M.
Published: October 2020

Seventh grade teacher: “My students have been working together in groups for a while now. They're getting along fine. But I'm finding that a lot of them still don't understand the work. I tell them to ‘work together’ and that it is all right to help each other. Sometimes I worry that they are only giving each other the answers. How can I get them to focus on problem solving and not just putring down the right answer?”
Drawings for Story Problems: Practices in Japan and the United States
Authors: Shigematsu Keiichi , Sowder Larry
Published: October 2020

The problem-solving strategy “Make a drawing” is used in both the United States and Japan but with different degrees and varying amounts of success in each country. The purposes of this article are to compare what seem to be Japanese and United States practices in promoting the use of drawings in solving story problems and to use that comparison to suggest some teaching approaches.
A Comparison of Achievement in Arithmetic in England and Central California
Authors: Buswell G. T.
Published: October 2020

In May 1955, an arithmetic test containing 100 items was administered to a cross-section sample of schools in England under the direction of the British National Foundation for Educational Research. Through arrangements with the Foundation and the University of California (Berkeley) an adapted form of the same test* was given to a similarly selected sample of schools in Central California in January, 1957. The study was financed by the research fund of the Department of Education of the University of California (Berkeley). This article reports a comparison of the results.
Research on Arithmetic Instruction—1957
Authors: Weaver J. Fred
Published: October 2020

One year ago THE ARITHMETIC TEACHER contained a summary of research on arithmetic instruction published during the six calendar years, 1951 through 1956.1 The present summary represents a continuation of the previous one and brings it up-to-date through the calendar year of 1957.
Thought Processes in Grade Six Problems
Authors: Corle Clyde G.
Published: October 2020

Arithmetic, the “third r” of the elementary school curriculum, is receiving a generous share of attention, both from professional education groups and from laymen as well. Educational leaders vary in their feelings toward the subject. Some show a determination to improve the subject; others are openly critical; and still others seem indifferent to the kind of teaching that is being done. Laymen are often outspoken in their criticism, supporting these opinions by random observation, previous personal school experiences, and hearsay. Standardized tests, teacher-made tests, and performance of textbook tasks serve almost entirely as criteria for judgment, both by professional and lay evaluators.
Glen Rock Scores on a Canadian Test
Authors: Kreismer Clifford R.
Published: October 2020

Interest in the achievement of Our school children is at an all time high. Few would dispute that. Never before has the man on the street been so concerned, not only with his child's achievement compared with Tommy's next door, but with his country's children compared with another nation's youngsters. Nowadays it is not considered an irrelevant question when a parent at a P.T.A. meeting asks the principal how the hometown school district stacks up with the U.S.S.R.
80,000 Children's Reactions to Meanings in Arithmetic
Authors: Stokes C. Newton
Published: October 2020

We have been faced with the problem of improving learning in arithmetic for a long time. Many of us have given considerable attention to its solution. For the past quarter of a century the consensus among us has been that the meanings approach in teaching and learning was the means of a solution.
An Experimental Study in Teaching Percentage
Authors: Kenney Russell A. , Stockton Jesse D.
Published: October 2020

Many students are troubled with percentage. The difficulty may lie in the way in which it is presented. Survey tests in Kern County and elsewhere have inclicated a lack of achievement in this particular field. Many teachers have indicated their awareness of the problem in teaching clear concepts in the field of percentage. Supervisors and consultants have observed that many teachers and pupils have difficulties in this field. In order to study the problem at some length and determine if possible, remedial measures, the following study was undertaken.
Thinking Afresh about Arithmetic
Authors: Gattegno Caleb
Published: October 2020

When so many people have already been engaged in examining the basis of our knowledge of number, there seems to be little chance of finding something new to say on that venerable subject. Still it is my contention that we have barely started examining that field and that at least one generation of research workers will be needed to clear the ground that I shall survey in this article.
Arithmetic for the Gifted
Authors: Parsons Cynthia
Published: October 2020

The teacher of a group of 25 or more active and interested elementary pupils finds herself faced constantly with the problem of what to do with the ones who get through quickly, while she employs her talents and patience with those who need closer supervision.
A Comparison of Achievement in Arithmetic in England, California, and St. Paul
Authors: Bogut Thomas L.
Published: October 2020

For the convenience of the reader, the format and much of the information published in Dr. Buswell's presentation has been incorporated in the following article.
The Growth of Pre-school Children's Familiarity with Measurement
Authors: Davis O. L. , Carper Barbara , Crigler Carolyn
Published: October 2020

Concepts of number and measurement are essential elements of mathematical and scientific thinking. Growth in understanding of number ideas has been studied by several investigators (1; 2; 3; 4; 8; 9). A number of studies have investigated children's understandings of certain kinds of measures (1; 3; 5; 6; 7; 8; 10; 11). Development of ideas of measurement seem to progress in a manner similar to concepts of number. Some studies have dealt with an investigation of the ideas of measurement in pre-school children (1; 5; 6; 7; 8; 10; 11), and some have investigated the growth of single measurement ideas (6; 11). MacLatchy developed an interview test for the pre-school child's familiarity with measurement (7).
A Comparison of Test Results: North Carolina, California and England
Authors: Tracy Neal H.
Published: October 2020

“The Arithmetic Teacher” for February, 1958, earned an arttcle on comparison of arithmetic achievement in English and California schools by G. T. Buswell.1 The reported results were viewed with alarm by some and raised a number of questions regarding arithmetic achievement in the United States. Some of these questions were related to the training of teachers who are to teach arithmetic and others were related to achievement of students at the point of terminal training. It was decided that a study, centered in selected North Carolina chools, might provide some clues regarding the answers to these questions.
Similarities Between Teaching Language and Arithmetic
Authors: Hickerson J. Allen
Published: October 2020

During the last 30 years we have discovered a great deal about how children learn language communication. As a consequence, instructional programs in oral and written expression, listening, reading, and grammar have improved considerably in recent years.
Blocks to Arithmetical Understanding
Authors: Collier Calhoun C.
Published: October 2020

It seems reasonable to suggest, at the outset of this address,* that several points be kept in mind.
An Adventure in Topology—Grade 5
Authors: Clancy Jean C.
Published: October 2020

To take an adventure implies the unknown, and that is just what a group of fifth grade children did recently in mathematics. Before such a trip could be taken, the consent of all had to be obtained. In this case the pupils had a desire to learn and the teacher who acted as the guide, wished to stir the imaginations of her pupils.
Prognosis for Studying Algebra
Authors: Dinkel Robert E.
Published: October 2020

Who should study algebra and when should this study begin? With the renewed interest in the study of mathematics and since the program of the ninth grade in many schools continues to be mostly algebra it is pertinent to consider in grades seven and eight the prognosis for success in algebra. This problem was investigated by the writer and the conclusions he found are briefly presented in this article.
Standard Time
Authors: Sanford Vera
Published: October 2020

“The earth, you know, turns round once in every 24 hours, or, in common language, the sun moves round the earth in that time; in what time, then, will the sun travel over 15 degrees? and why? over 1° (degree) of motion? over 1' (minute) of motion? By the foregoing, we see that every degree of motion makes a difference in time of 4 minutes, and every minute of motion a difference of 4 seconds. Now, since longitude is reckoned in degrees round the earth, can you tell me hmv to find the difference in time between one place and another, after knowing their difference in longitude?"* When this book was written, the relation between the difference in longitude of two places and their difference in time was an academic matter. Travel and communications were slow. Local time was sufficient.
The Insatiable Quest: Mathematicking
Authors: Brydegaard Marguerite
Published: October 2020

THE WORDS OF THE TITLE for this paper are freighted with meaning. The first three words, THE INSATIABLE QUEST, describe the basic method of learning; they apply to areas of the curriculum. The last word, MATHEMATICKING, defines the process of achieving efficient and intelligent behavior with regard for size, order, position, and amount. It is the process through which the pupil's CONQUEST of an education of mathematics should evolve.
Arithmetic in the School Camp
Authors: Roossinck Esther P.
Published: October 2020

School camping in the united States is an exploding idea. Over five hundred school systems representing twenty-four states have school camping programs. These programs vary, but there is a general trend toward a one week program for sixth graders. In the type of program this article considers, pupils and teacher together assume direct responsibility for designing, carrying out, and evaluating their plans. These activities are selected by the groups on the basis of being the best way to reach certain educational goals which can be attained better by group living in the outdoors than in a classroom.
Division is Understandable
Authors: Izzo Ruth Kelley
Published: October 2020

Sometimes in our teaching we fail to build upon children's past experiences to make arithmetical concepts meaningful. Most of us accept the fact that the reading of the printed word is successful if a child has a background of experience to bring to word symbols. We know that a word such as mother has meaning for the child. He can call upon his background of experience to give meaning to this abstract symbol because he has a knowledge of, a feeling for, an attitude about a mother. When he reads the word he draws upon his past experiences to gain meaning. As teachers we capitalize upon this understanding and utilize it in helping the child learn to read.
University of Maryland Mathematics Project
Authors: Garstens Helen L. , Keedy M. L. , Mayor John R.
Published: October 2020

In the fall of 1957 the University of Maryland Mathematics Project (Junior High School) was started. The project was undertaken as a cooperative enterprise of the departments of mathematics, education, psychology, and engineering of the University of Maryland and the four major public school systems in the Washington area—Washington, D. C. public schools, Arlington County (Virginia) public schools, and Montgomery and Prince Georges Counties (Maryland). The project has been guided from its beginning by an Advisory Committee which also includes representatives of the Maryland State Department of Education, the Mathematics Section of the Maryland State Teachers Association, and the United States Office of Education, as well as the cooperating university departments and public school systems.
The Use of Class Time in Arithmetic
Authors: Shipp Donald E. , Deer George H.
Published: October 2020

This study* Sought to determine whether varying the per cent of class time spent on developmental activities and on practice work affects achievement as measured by a three-part arithmetic achievement test. It considered the effects on achievement in Understanding Arithmetic, Using Arithmetic Accurately, Solving Problems, and Total Achievement. Also, the effects on the upper, middle, and lower ability groups were compared to determine whether these groups were affected differently by this variation in the use of class time.
A Kit for Arithmetic
Authors: Adkins Julia
Published: October 2020

While teaching a course (Arithmetic Principles and Teaching) for prospective elementary teachers, I wished to acquaint the students with a philosophy of teaching for which the “discovery method” is an expression of the philosophy. I decided that an effective way to achieve this goal would be to use role playing. In doing this I would use with the students techniques that I hoped they would use later with their own students.