bluuebunny/crossref_metadata_2025 huggingface dataset:
Pic-Jour Math: Pictorial Journal Writing in Mathematics
Authors: Stix Andi
Published: October 2020

Come every fall, teachers of mathematics are confronted with oversized classes filled with students who vary in both their learning style and their way of communicating what they have learned. Teachers are challenged to recognize and exploit those differences—or risk bored or confused students who lack any true mathematical understanding and may end up manipulating numerical symbols and equations by rote.
Teaching Mathematics with Technology: Mining Mathematics on the Internet
Authors: Kelly M. G. (Peggy) , Wiebe James H.
Published: October 2020

Throughout the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) the notion of students and teachers as critical thinkers, information seekers, and problem solvers is a priority. The Internet, an electronic highway connected by gateways from one computer network to another, furnishes a telecommunications link around the world. The Internet enables students and teachers to access authentic, real-time data for critical analysis. With access to such Internet service providers as a university computer network or a commercial service like Compuserve, Prodigy, or Applelink, students and teachers become active information seekers.
Implementing the Professional Standards For Teaching Mathematics: Planning for Instruction: Barriers to Mathematics Discussion
Authors: Vacc Nancy Nesbitt
Published: October 2020

Soon-Li had picked a buttercup flower and was showing it to her friend Misa. They had been studying circles earlier in the day, and Soon-Li excitedly indicated that each petal was a circle. Misa responded with, “Well, they do look like circles, but look at this one and this one. They are a little wiggly out here, and this one here is not really round like.” Having overheard this exchange, which took place on the playground after lunch, the teacher began the afternoon activities by putting Soon-Li's flower on the overhead projector, displaying it on the screen so that all the students could see its pattern, and stating, “Soon-Li indicated that each of these petals is a circle, but Misa noticed that the edges of some are wiggly, and one is not really round. Therefore, she's unsure if they are circles. Let's hear what the rest of the class thinks about their shape.”
Research into Practice: Number Sense-Making
Authors: Sowder Judith , Schappelle Bonnie , Lambdin Diana
Published: October 2020

In Everybody Counts, a document from the National Research Council (1989), we are told that the major objective of elementary school mathematics should be to develop number sense. This strong statement, if taken seriously, can change the way many—but not all—teachers teach mathematics in elementary school.
Calendar Mathematics
Authors: Porter Jeanna , Chancellor Dinah
Published: October 2020

The calendar is designed to speak directly to students, giving them open-ended questions intended to engage their intellect through their interests. Students are encouraged to work on the activities individually, in pairs, or in small groups. No answers are provided for the calendar questions to encourage students to look to themselves as the mathematical authority, to develop the confidence and critical-thinking skills necessary to validate their thinking.
AT Classic: The Role of Experience in the Learning of Mathematics
Authors: Biggs Edith E. , Hartung Maurice L.
Published: October 2020

Learning mathematics, like learning language and the aesthetic subjects, is an active process and should call into play our imaginative and creative powers so that the subject is a delight to pupils of all ages. Investigations of every aspect of mathematics—number knowledge itself and written calculations, as well as measures, shapes, and representations of all kinds—are included. In the title of this article, the word experience could very well be changed to investigations. Investigations, to me, cover a wider range of activities than experiences, which are often thought of as practical experiences.
A Tribute to the “Arithmetic Teacher”
Authors: Tunis Harry B.
Published: October 2020

The Arithmetic Teacher will cease publication with this issue. Better to serve NCTM's members, the Council is creating two new journals to give wider coverage to issues in mathematics education for prekindergarten through grade 9. So, at age 40, the Arithmetic Teacher becomes part of the history of NCTM's efforts to support members in facing the numerous challenges of the profession.
Slide Rules for the Upper Elementary Grades
Authors: Gramlich Jay J.
Published: October 2020

THE PUBLIC PRESSURE to produce more scientists will quicken the interest in mathematics. The publicity given to sputnik, the shot truly heard around the world, will resound from the kindergarten through the university. The resulting changes which will undoubtedly occur in the curriculum will have to be evaluated by educators at some future date. But to one who has taught in both public schools and teacher education institutions, it seems apparent that much good will obtain from greater emphasis on mathematics and science. Certainly educators have taken a great deal of criticism (justly given) from lay critics about our mathematically illiterate graduates from both high school and college. In fact, if they are deficient in mathematics on leaving high school, the colleges contribute to this deficiency rather than lessen it. This may happen in one of two ways. First, if they are forced into required college mathematics for which they are unprepared they fail or muddle through thereby increasing their frustrations toward mathematics; or secondly, they avoid mathematics entirely and are four years further removed from it on graduation.
Divisibility and Prime Numbers
Authors: Yearout Paul
Published: October 2020

Being an elementary discussion of some of the useful and interesting properties of numbers which are not often considered in elementary and secondary arithmetic courses.
Dress up Your Graphs
Authors: Janicki George
Published: October 2020

The teaching unit on graphing in junior high school grades is sometimes a source of great inspiration to me.
The Concrete Devices of Structural
Authors: Stern Catherine
Published: October 2020

In the teaching of science it is common practice to use models and devices which make it possible for the pupils to see with their own eyes all those usually “invisible” objects which they want to study. A model of the solar system, for instance, allows the pupils to discover the relative movements of earth, sun, and moon in a simple set-up which shows the structure of the system. Even abstract principles and formulas become clear when they arc illustrated by experiments which the pupils carry out with structura lly correct concrete devices.
The Littlest Mathematician: An Approach Applicable at all Levels
Authors: Baumgartner Margery
Published: October 2020

Does number cover the whole area of mathematics? Does spelling cover the whole area of language arts? Numerical computation is only one part of the study of mathematics. From a functional viewpoint, it is important to broaden the teaching field to include those aspects of mathematics a student will use after graduation—when machines have taken over much of his computation.
Teaching the Number System Inductively
Authors: Hickerson J. Allen
Published: October 2020

I was asked a question at the conclusion of my address at the Cleveland Conference of the National Council of Teachers of Mathematics last April. The question deserved a fuller answer than I was able to give at the time. I shall attempt to answer it here hoping that the questioner and other members of the audience may have opportunity to read this reply.
“Sets” and Elementary School Mathematics
Authors: Lerner Norbert , Sobel Max A.
Published: October 2020

In recent years mathematicians have been talking a good deal about “sets” and some people have been urging the reorganization of arithmetic instruction to include not only sets but also certain other concepts of modern mathematics. It has been urged that the introduction of sets will serve as a unifying concept for the fundamental ideas of arithmetic, algebra, and some forms of geometry and thus make it easier for a student to deal with mathematics as a unified field instead of a collection of several different areas of study.
Conducting a Math Exposition
Authors: Karbal Harold
Published: October 2020

Last year as the culminating activity of the Math Club we decided to hold a math exposition. Actually the spark had come from the Science Fair held in Detroit a short time ago. The club members needed some way to show what they had learned and done. The Math Club was composed of children with high mental ability, decided competence in arithmetic as evidenced on the Iowa tests, and proven interest in the subject, since they needed to be recommended by their teachers. The club members had studied in their weekly meetings number systems with base two and five and were currently learning to usc the slide rule.
Bibliography of Books for Enrichment in Arithmetic
Authors: Hess Adrien L.
Published: October 2020

Writers and illustrators are devoting much time and talent to producing books which can be used for enrichment and for appreciation units in arithmetic, for the upper grades in particular. While many of the books for the lower grades are essentially counting books. an occasional one goes beyond this and introduces arithmetic addition in a clever manner.
Using Teachers' Manuals for Deeper Learning
Authors: Foote Evelyn W.
Published: October 2020

What can be done in the classroom to heighten experiences in arithmetic, to foster sound reasoning, to produce good thinkers, to promote sensible approaches to problem-solving, to develop skills in computation? Much depends upon the interests, desires, and competencies of the teacher, plus her understanding of the processes concomitant to learning and her patience in dealing with the learners themselves.
“But the Teacher Didn't Show Us that Way”
Authors: Sestanovich John A.
Published: October 2020

When did you hear these words last? You are a parent and still have a child of elementary school age; the last time you heard these words was probably last evening when you tried to help with the arithmetic homework. These words are doubtlessly heard in millions of homes every evening. Is there a reason for it? Is the teacher making it easier for himself? Or is he making it easier for the children, because “he didn't show us that way?” Let's see if we can find out.
What about Those ‘Zero Facts’?
Authors: Oesterle Robert A.
Published: October 2020

It is, in a sense, paradoxical that zero, the discovery of which Dantzig1 characterized as “one of the greatest single achievements of the human race,” should provide such fertile ground for controversy in the methodology of teaching arithmetic in the elementary school.
Eliminate “Borrowing” in Subtraction
Authors: Mossil Max N.
Published: October 2020

A new method which I shall call the raised subtrahend method obviates the need of borrowing, a leading cause of subtraction failures. It was tried for the first time this past year with amazing results. The method invokes a principle that equal raises for two numbers do not affect their differences.
Articulation in Arithmetic
Authors: Stearn Peter A.
Published: October 2020

It is popularly misconceived and widely mis-practiced to divide one number into another as opposed to dividing one number by another.
Uses of Styrofoam in Arithmetic
Authors: Hess Adrien L. , Kearby Lillian
Published: October 2020

One of the first rules of teaching is to catch and hold interest, for without interest much of the teaching effort is wasted. If a learning situation can be made a source of fun, something that will catch and hold interest, then one can expect a high degree of permanence of learning.
Council Resources for Arithmetic Teachers
Authors: Fawcett Harold P.
Published: October 2020

Through the columns of this journal I wish to speak to those who teach arithmetic. I welcome this opportunity for it is my considered judgment that the quality of instruction in arithmetic is in large measure responsible for choices made in later years when mathematics becomes an elective. It is in the elementary school that students are first in troduced in an informal manner to mathematical concepts and one of the purposes of the National Council of Teachers of Mathematics is to serve its members in such a manner as to improve the quality of this initial introduction. One measure of the degree to which the Council is achieving this important purpose is the extent to which its facilities are used by those who direct the activities of the arithmetic classroom.
Challenging the Rapid Learner
Authors: Schwartz A. N.
Published: October 2020

Elementary school teachers have been charged with the problem of further developing the gifted or talented child in arithmetic. This is an area in which many have done something but in which no one has done enough. The following suguestions are not offered as a panacea for the situation but as practical ideas that may be used and from which others may be developed. In this way it is hoped an additional avenue will be opened for creative thinking in this area. It is intended that these suggestions will be beneficial to any teacher who in some way offers differentiated assignments for the more adept in arithmetic. These procedures should be of assistance in programs utilizing homogeneous sectioning, special teachers, sub-grouping, acceleration, or enrichment.
The Abacus—A New Use for an Old Tool
Authors: Nechin Arlene , Brower Robert
Published: October 2020

Are you looking for an interesting appproach to the understanding of number concepts? Does your class completely understand the use of the zero, place value, and what we mean when we say that our number system has a base of ten? How well do you, as a teacher, understand these concepts? How well can you put forth these ideas to your class?
Work-Type Lessons for Grade Six
Authors: Sherwood Violet
Published: October 2020

In the field of mathematics there is less opportunity than in many other fields for students to read widely and to forge ahead as interest is aroused. Those who find arithmetic easy can work ahead in the book perhaps. However, it is to the students' advantage to have a new process presented by the instructor who can teach more meaningfully than can a textbook. The problem then is to supply material which will challenge the interest and ability of good students and also provide concepts of mathematical value in different types of situations.
Report of the Nominating Committee
Authors: Puett Ida Bernhard , Beckmann Milton , Butler Charles , Fehr Howard F. , Henderson Kenneth B. , Karnes Houston T. , Linton Albert , Peters Ann , Schaaf Oscar
Published: October 2020

The Committee on Nominations and Elections presents its slate of nominees for offices to be filled in the 1960 election. The term of office for the president and the two vice-presidents is two years. Three directors are to be elected for terms of three years.
Using Equations with the Number System
Authors: Dubinsky Pauline
Published: October 2020

Equations can be used to deepen understanding of our number system when they are constructed in such a manner as to channel thinking into a left-to-right computation. This is often performed in “Mental Computation” utilizing groups to arrive at sums, remainders, etc; e.g., 49 thought of as 40 and 9, not as 4 tens 9 ones; 236 thought of as 200 and 36, or 230 and 6, or 200 and 30 and 6, not as 2 hundreds, 3 tens, 6 ones. This types of computation differs from the kind of thinking done when standard forms of algorisms are used in operations with whole numbers and fractions.
A Report on the Use of Calculators
Authors: Beck Lois L.
Published: October 2020

Several fourth, fifth, and sixth grade classrooms in the Riverside City Schools are participating in an experimental program guided by Dr. Arden Rudell, Professor of Educa tion, University of California at Riverside and Mr. Lewis Wickens, Director of Elementary Education. The administrators and teachers involved in this experiment are attempting to determine the extent to which use of the calculator may stimulate learning of arithmetic skills by children in the upper elementary grades. This ex periment is being conducted as a part of the National Defense Education Program.
A Mathematics Assembly Program
Authors: Kavett Hyman , Kavett Phyllis F.
Published: October 2020

Even In this Age of Specialization, a teacher of mathematics of grades 6 through 9 may be called upon to favor his school with an “assembly program” to be cast with members of his official class. The authors of the following ‘play’ used their routine assembly program assignment as a means of showing the whole school some of the “fun” aspects of mathematics, as a means of introducing some amusing, though very thought-and-discussion-provoking ‘tricks,’ as one more ‘stone’ cast at the wall of traditional resistance to mathematics.
Arithmetic Books for Elementary Schools
Authors: Burns Paul C.
Published: October 2020

The purpose of this Paper is to summarize an analysis of ten different series of arithmetic textbooks together with their accompanying workbooks and teacher's guide books. General patterns and new developments are described.
Let's Prove It!
Authors: Brown C. Dale
Published: October 2020

In the Past few years educators have been acutely aware of the attempts being made to revise the mathematics curriculum in our schools. The work of the School Math Study Group, Maryland Project and the University of Illinois has produced some extensive work and experimentation to improve, not only, the content but the method as well. If you have not tried some of their ideas in your class may I suggest that you do. The following problems were enjoyed by both seventh and eighth grade students.
Filling a Gap in Subtraction
Authors: Baldwin Olivia H.
Published: October 2020

Several gaps appear in the teaching of concepts at the primary level when there should be continuity and sequential development step by step. These gaps must be filled in, rather than pulled together if concepts are to be meaningfully clear and processes understood and functional. Observations and outcomes in pupil performance point up the fact that our teachings of the substraction concepts lack wholeness.
Basic Considerations in the Improvement of Elementary School Mathematics Programs
Authors: Weaver J. Fred
Published: October 2020

During the past few years the spotlights of attention on mathematics programs have increased in number and intensity and have broadened in focus. The glare of the limelights now covers the elementary school as well as the secondary school. It will continue to do so with increasing brightness for some time to come.
New Devices Elucidate Arithmetic
Authors: Beckmann Milton W.
Published: October 2020

The national defense eoucation act of 1958, briefly referred to as NDEA, authorized something over one billion dollars in Federal aid over a four-year period. “In the swinging sweep of its 10 titles it touches—and returns to touch again—every level of education, public and private, from the elementary school through the graduate school. Its billion dollars, though authorized for a dozen separate programs, have been authorized for a single purpose-that every young person, from the day he first enters school, should have an opportunity to develop his gifts to the fullest.”1 It is quite clear that Congress recognized how exceedingly important is superior instruction at the elementary level as well as in high school and college. The Act concerns itself with the finding and encouraging of talent, the improving of teaching, and with the furthering of knowledge itself. This Act includes the instructor of arithmetic.
Annual Financial Report
Authors: Ahrendt M. H.
Published: October 2020

The report below gives a brief picture of the financial condition of the Council for the fiscal year June 1, 1959 to May 31, 1960. Readers who wish to compare this report with the similar report for the previous fiscal year will be able to make some interesting comparisons.
A Study of the Quantitative Values of Fifth and Sixth Grade Pupils
Authors: Corle Clyde G.
Published: October 2020

Observations Made of children in the fifth and the sixth grades have revealed a weakness in pupil understanding of the quantitative concepts commonly used in these grades. A pupil may solve a verbal problem, report the results, and defend the algorism without really understanding the meaning of the answer. If, for example, his answer is sixteen feet, the child may be unable to demonstrate within reasonable tolerances the distance the results suggest. If the answer is 3! pounds, many pupils cannot differentiate tactually between this weight and some others within several pounds of it. Temperatures, although the pupils hear them announced daily on radio and television stations, may have relatively little meaning to fifth and sixth grade children. Likewise, time and capacity measures often appear to be only words to intermediate grade pupils.
A Good Teacher—
Authors: Hardgrove Clarence Ethel , Cole Mildred , Gustafson Anne
Published: October 2020

A Good teacher of mathematics learns as he teaches. This characteristic distinguishes him from a poor teacher. As a result, his teaching becomes better and better as he learns more and more and acts on his knowledge. As he helps boys and girls learn, he, too, is attempting to learn some answers to this problem: “How can I better help children learn mathematics?”
Mathematics as a cultural heritage
Authors: Schaaf William L.
Published: October 2020

Broadly speaking1 major cultures can be identified, at least in part, by certain outstanding characteristics. Thus, Babylonia and Egypt were steeped in mysticism and sensuality; the Greeks were preoccupied with ideas and ideals; the Romans, with politics, military prowess, and conquest. The culture of Western Europe from 600 A.D. to 1100 A.D. was expressed largely by its theology. From 1200 to 1800 it was the exploration of nature and the beginnings of science that marked the essence of the period. The spirit of the nineteenth and twentieth centuries, unless it is too early to judge in proper perspective, is typified by man's increasing mastery over his physical environment. This is evidenced not only by the general achievements of science and technology, but also by unprecedented industrial production, effective mass communication, and increasing automation. The creative language of the culture of today is science, and mathematics is the alphabet of science.
Experimental projects and research: Analysis of research in the teaching of mathematics: 1957 and 1958
Authors: Fred Weaver J.
Published: October 2020

Readers of THE ARITHMETIC TEACHER will be interested in a recently published report, Analysis of Research in the Teaching of Mathematics: 1957 and 1958, prepared by Kenneth E. Brown and John J. Kinsella.* Dr. Brown is specialist for mathematics, Office of Education, U.S. Department of Health, Education, and Welfare; Prof. Kinsella, of the Department of Science and Mathematics Education of the New York University School of Education, is chairman of the Research Committee of the National Council of Teachers of Mathematics.
In the classroom: Remainders in division and a floor number line
Authors: Deans Edwina
Published: October 2020

Here are a number of ideas to introduce in your own classroom. They should prove both meaningful and thought provoking.
Experiments in mathematics
Authors: Peak Philip
Published: October 2020

The Board of Directors of the National Council of Teachers of Mathematics appointed a committee to gat her information and to analyze experimental mathematics programs. This committee would like your help in identifying such programs. It has limited its analysis to programs that (1) have printed instructional materials other than courses of study, (2) are of at least one semester in duration, and (3) are not sponsored by a commercial publishing firm. The committee will examine all material, ask the experimenter to make a short personal report, and publish as many of the reports as possible.
In the classroom: Arithmetic in science and social studies
Authors: Deans Edwina
Published: October 2020

Dr. W. A. Brownell, speaking at the Conference on Elementary School Mathematics sponsored by the School Mathematics Study Group held in Chicago, 1959, suggested that “We can go too far if concern for the mathematics of arithmetic leads us to disregard other considerations in working out the program. Whatever the mathematical content selected and whatever the sequence of learning experiences decided upon, we must be sure that we do not exceed the ability of children to learn with understanding and with profit to themselves; nor can we afford to forget that the ultimate purpose of arithmetic in the schools is not solely the preparation of mathematicians (though more and better mathematicians should be produced), but more efficient, more intelligent, and richer and happier lives for all who are subjected to arithmetic instruction.” Arithmetic can make a contribution toward achieving this ultimate purpose by increasing the children's understanding of science and social studies. The development of many important concepts in these two fundamental areas of the elementary school is dependent upon understandings gained in arithmetic.
Number systems, fad or foundation?
Authors: Hamilton E. W.
Published: October 2020

Inventing sets of names and symbols for the purpose of exploring number systems and notation by analogy has become quite common. Since there seems to be little or 110 evidence of the effect the use of these sy:stems has on students, the following report is presented to document the effect which can be expected when such material is used on collegiate teacher trainees under the conditions described.
Numbers, sets, and counting
Authors: Botts Truman
Published: October 2020

Numbers and counting have been used by mankind and have formed part of his elementary education for many centuries. Sets, that is, collections of things, have been with us for just as long. As a matter of fact, the first use we learn to make of numbers and counting is in determining the size of a set or collection of objects, that is, how many objects the set has as members.
Mental arithmetic
Authors: Koenker Robert H.
Published: October 2020

The majority of arithmetic problems olved by adults and by children in their out-of-school life are solved mentally without the benefit of paper and pencil. In sp ite of the need for and the usefulness of mental arithmetic in daily living, most teachers devote litt le, if any, time to this valuable part of the arithmetic program. Some teachers still rely heavily on rigorous oral drill periods for mastering the basic arithmetical facts, but such instruction is better referred to as “mental gymnastics” than mental arithmetic.
Minutes of the Annual Business Meeting
Authors: Karnes Houston T.
Published: October 2020

This year a change in procedure of the Annual Business Meeting was instituted. The Annual Business Meeting was scheduled to follow immediately after a general session at which time the President presented a paper entitled “Crystal Gazing.” In this paper, President Philip S. Jones gave a fine survey of the work of the Council during the past year and discussed the projects for the future. Past-President E. H. C. Hildebrandt presided at this general session.
Annual financial report
Authors: Ahrendt M.H.
Published: October 2020

The report that follows gives a summary of the receipts and expenses of The National Council of Teachers of Mathematics for the fiscal year ending May 31, 1961. The increases in both receipts and expenditures were approximately proportional to our increase in membership during the year.
Some basic geometric ideas for the elementary teacher
Authors: Rutland Leon , Hosier Max
Published: October 2020

More and more we speak of the mathematics program instead of the arithmetic program of the elementary school. We do this because the content of the program places emphases not only on arithmet ic but also on geometric understandings and skills. Thus, just as teachers need to be more familiar with the present-day approaches to arithmetic content, so it is that they need to be familiar with presentday approaches to geometric content. Yet, not only the approach to arithmetic but also the approach to geometry is differeut today than it was some years ago. More specifically, today we believe it helpful to think of basic geometric ideas in terms of sets of points. What does this mean? It is the intent of this article to show how bas ic geometric ideas are interpreted from this point of view.
A device for practice with common denominators and addition of unlike fractions
Authors: Hammond Robert C.
Published: October 2020

The square in the accompanying figure and the numbers 1–9 have often been used to form a “magic square” in which the numbers in all rows, columns, and diagonals can be arranged to add to 15. This magic square can be adapted so that it becomes a device or game which provides practice in forming common denominators and adding unlike fractions (fractions having different denominators).
Intra-class grouping for arithmetic instruction: critique and criteria
Authors: Lerch Harold H.
Published: October 2020

Attempts to meet the problem of adjusting arithmetic instruction to pupil differences frequently involve the organization of instructional groups of pupils witilln the classroom. The major purpose of subgrouping in arithmetic classes is to provide for individual differences by bringing pupils of like arithmetical backgrounds, skills, understandings, and concepts together into small groups so that they can study and work effectively at rates and levels that are closer to their own abilities and characteristics. Closely related to the possibility of adjusting instruction to pupil differences are other reasons why intra-class grouping for arithmetic instruction could increase the efficiency of the learning situation or increase the productivity per man-hour of teaching and learning. These reasons generally pertain to the interactions and communications witilln the class or to the desirability and effects of pupils succeeding at their own levels.
A digression on 80 square inches
Authors: Glenn Bon
Published: October 2020

Determination of Truth, “democratically” … Teacher. Let us consider 80 square inches.
Modern mathematics begins in the elementary school
Authors: Félix Lucienne , Kavett Hyman , Flyer Kavett Phyllis
Published: October 2020

An understanding of the relation of equivalence and the meaning of equivalence classes is so basic that these ideas must first be introduced to the kindergarten child and refreshed continually thereafter. Because these notions are so fundamental, they are used without conscious thought and appear to be new when studied in more advanced work. Before considering these ideas as part of the curriculum, let us recall their meaning.
Experimental projects and research: Improving elementary-school mathematics programs in American schools
Authors: Fred Weaver J.
Published: October 2020

Efforts to improve elementary-school mathematics programs are many and varied. Some of these efforts focus major attention on teacher education.
Editorial comments: As we read
Authors: Hamilton E. W.
Published: October 2020

It is common knowledge that many of us fail to communicate mathematical ideas to elementary students. We fail for lots of reasons, many of which have been documented from time to time in this journal. One of the main reasons for the publishing of such journals is to provide material and stimulation for improvement. In this spirit, then, and with no particular reference to the articles included in this issue except as they serve as a point of departure, let us examine a few of our shortcomings.
Breaking the lock step in arithmetic
Authors: Echternacht Charles , Gordon Virginia
Published: October 2020

The tremendous scientific developments of recent years have aroused a strong feeling of dissatisfaction with arithmetic teaching not only among educators, but also among parents and the general public.
Division by a fraction—a new method
Authors: McMeen George H.
Published: October 2020

Great progress has been made in the past decade in making the various operations of arithmetic intelligible for the learner. However, a few arithmetic operations continue to challenge our best efforts in this direction. Of these more challenging operations, I can think of none more difficult to rationalize than the operation of division by a fraction in which we “invert the divisor and multiply.” My experiences with hundreds of college education majors have led me to observe that very few of these students come to college understanding the rationale of the operation. This is understandable when we consider the mechanical way in which the operation has been presented in most elementary schools.
Arithmetic achievement of left-handed children
Authors: Groff Patrick
Published: October 2020

Relationships between handeduess and arithmetic achievement in the elementary school have not been the subject of intensive research such as that carried on between band preference and reading. In the latter area several comprehensive studies have been made. In general, these investigations of reading achievement and handedness have indicated a lack of significant relationship between these two variables.
Helping children learn multiplication facts
Authors: Careccio John
Published: October 2020

When children get into the fifth, sixth and seventh grades and do not know their multiplication facts, there are a number of ways a teacher can help to give them practice so that they can learn these basic facts. Boredom engulfs students when they have to multiply endless examples. Teachers realize that students need this practice to reinforce what they do know and to give opportunities to use combinations they don't know. There are ways to give this practice and, at the same time, teach new material.
Shall we change our arithmetic program?
Authors: Miller G. H.
Published: October 2020

In making or considering any curriculum revisions, all proponents, administrators, and interested laymen should be aware of certain facts about the arithmetic learning potentialities of children. These facts have been revealed by numerous studies comparing (1) the level of arithmetic ability of children entering the first grade with the required curriculum for that grade, (2) the time allotments for the first six years of arithmetic instruction in the United States with time allotments of other nations, and (3) the comparison of arithmetic achievements of American children with children of other nations.
In the classroom: Mathematical vignettes—ideas from here and there
Authors: Deans Edwina
Published: October 2020

The class discussion centered around the multiplication tables with which the children were having difficulty.
As we read
Authors: Hamilton E. W.
Published: October 2020

Many of the things we read now, be it in the professional journals, the methods books, or the manuals for textbooks, put pressure on teachers to upgrade and modernize their instruction. They are admonished to do things in ways they have never seen in operation. They must learn to recognize ways of thinking foreign to their own experience in the grades and frequently foreign to their adult experience as well. And, in particular, they must learn to recognize patterns and make generalizations, some of which never before occurred to them, and try to transmit some of this to their students.
Taxicab geometry, rabbits, and Pascal's triangle—discoveries in a sixth-grade classroom
Authors: Clarkson David M.
Published: October 2020

Two aspects of the current experimentation with our elementary-grades mathematics instruction have been perhaps underemphasized. One is the opportunity a teacher has to take advantage of the imagination and initiative of her pupils released by the freer approach to the curriculum, and the other is the effect on the teacher herself when the pursuit of a topic new to elementary school leads her to discover a rich vein of mathematics on her own. The following article is an account of the discovery of triangular numbers by a sixth grader, and its consequence, the pursuit of an important mathematical idea by both the class and the teacher. The project took three forty-five minute class periods and the student remarks quoted were taken from a tape recording of the sessions.
Individualized practice in arithmetic—a pilot study
Authors: Moench Laurel
Published: October 2020

In an article entitled “Meeting Individual Differences in Arithmetic,” Frances Flournoy stated that, “At this time we have no significant published research in the field of Arithmetic which aids a school faculty or a teacher in the decision as to what variations to make, how, and how much (in providing for individual differences in the regular classroom with heterogeneously composed groups of children).” 1
Experimental projects and research: The School Mathematics Study Group project on elementary school mathematics, Grades K–3
Authors: Weaver J. Fred
Published: October 2020

Two previous issues of The Arithmetic Teacher presented reports pertaining to the School Mathematics Study Group (SMSG) project on elementary school mathematics, Grades 4–6.1 In this issue we (1) very briefly bring our readers up to date on the project for Grades 4–6, and (2) present an initial report on the project's downward extension to embrace Grades K–3.
INVISIBLE SOUNDS FOR CALVINO’S INVISIBLE CITIES: COLLABORATION IN A CREATIVE PROCESS
Authors:   Unicamp, Manzolli Jônatas , Marinho Helena ,   Universidade de Aveiro, INET-md
Published: October 2020

Inspirados no romance Le città invisibili (1972), de Italo Calvino, que apresenta a descrição de Marco Polo de várias cidades invisíveis e fictícias, os autoresembarcaram numa viagem imaginária para criar sons invisíveis com a sutileza do pianoforte. Num processo semelhante ao romance de Calvino, o artigo apresenta a troca de ideias entre o compositor e a intérprete, separados fisicamente, no Brasil e em Portugal, comunicando-se através de videoconferências e e-mails. À medida que o processo evoluiu, aspectos técnicos do pianoforte e seus sons peculiares foram entrelaçados com os ajustes na escrita criativa do compositor. A estrutura combinatória da obra de Calvino ancorou a troca de materiais musicais entre os quatro movimentos da obra. Este projeto de pesquisa artística teve início em abril de 2014 e culminou na gravação de Sons Invisíveis, incluída no CD Música Nova para Instrumentos Antigos II em 2016. Para descrever esse processo, este artigo aborda procedimentos de composição para instrumentos históricos, particularmente o pianoforte, a natureza combinatória da escrita de Calvino e a sua estrutura correspondente na obra musical final, expressando o caráter inefável da obra-prima de Calvino por meio de sons invisíveis.
Sleep is Inversely Associated with Sedentary Time among Youth with Obesity
Authors: Schroeder Krista , Kubik Martha Y. , Sirard John R. , Lee Jiwoo , Fulkerson Jayne A.
Published: October 2020

Objective: Pathways underlying the sleep-obesity relationship in youth are poorly understood. In this study, we examined associations of sleep with sedentary time and moderate-to-vigorous physical activity (MVPA) among youth, stratified by weight category (obesity versus no obesity).
A sub-aim examined whether controlling for screen time changed the sleep-sedentary time association. Methods: Methods entailed secondary analysis of baseline data collected June-August 2014-2017 during a school-based healthy weight management trial in Minneapolis/St. Paul, Minnesota.
Participants (N = 114) were 8-to-12 years old with BMI ≥ 75th percentile, most of whom were members of racial/ethnic minority groups (57%) or from households receiving economic assistance (55%). Mean nightly sleep duration and daily screen time were measured by survey, MVPA and
sedentary time by accelerometer, and height and weight by research staff. Multivariate linear regression examined associations of sleep with sedentary time and MVPA. Results: Sleep was inversely associated with hours of sedentary time (β = -1.34 [-2.11, -0.58] p = .001) and percent
of time spent sedentary (β = -2.92 [-4.83, -1.01], p = .004), for youth with obesity only. The association was unchanged by screen time. Sleep was not significantly associated with MVPA in total sample or stratified models. Conclusions: Associations among sleep, activity levels,
and obesity may differ based upon movement type (sedentary time vs MVPA) and weight category (obesity vs no obesity).
Kronik
Authors: Philipson Lotte
Published: October 2020

Indhold: Nyt musikfund - messe fra 1500-tallet!; Erhvervelser; Besøg; Udkån til udstillinger; Personalia
Kronik
Authors: Philipson Lotte
Published: October 2020

Indhold: København - Porten til Europa; Udstilling på Slotsholmen 31. april - 11. oktober 1996 i anledning af Kulturbyåret; Andre udstillinger; Erhvervelser; Udlån til udstillinger; Besøg, Personalia;
Kronik
Authors: Leergaard Joan
Published: October 2020

Indhold: Musik i "Skåret" - Katalog af Fuzzy; Lyskunst på havnefronten; Biografier - 6 foredrag i Den Sorte Diamant; International resolution om bevaring af digital kulturarv; Udstillinger; Erhvervelser;
Frederik IIs og Christian IVs Foliobibler
Authors: Beckhaug Hans , Raes Peter
Published: October 2020

Med forord af Peter Raes
Kronik
Authors: Leergaard Joan
Published: October 2020

Indhold: Foredrag og seminar; Danmarks besættelse 1940-1945 -formidling af historieforskningens resultater; F uldmåneaftener; Brunch på biblioteket; Vinkler på viden; Gads leksikon om dansk besættelsestid 1940-45; Ny H.C. Andersen-portal; ARKADE, der er en fagpørtal før arkitektur, kunst og design, har set dagens lys; Nye værker i Carl Nielsen Udgaven; Kirkemusik på nettet: Mogens Pedersøn Pratum Spirituale (1620); A.P. Bereereen: Fædrelandske melodier (1840); Dansk Musikfortegnelse 1931-71 i REX; Flere breve til og fra J.P.E. Hartmann; Samarbejde mod bibliotekstyverier; Find rundt på KB; Musikarrangementer; Udstillinger; Livets gang i Lidenlund; Erhvervelser
Kronik
Authors: Leergaard Joan
Published: October 2020

Indhold: Har fortiden en fremtid?; Audiovisuelt foredrag med Heiner Goebbels; Et kig bag kulissen; Latinsk psalter med tilknytning til Roskilde; Sjældne tryk som e-høger; Udvikling i H.C. Andersen-portalen; Brev fra H.C. Andersen til hans moder dukket op; Næstved-kalendariet online; Islandsk håndskrift på nettet; Thomas Laubs samlinger af salmer på nettet; Den musikvidenskabelige database RILM i online-version; Musikhistorisk Museum og Carl Claudius"' Samling kan nu søges i REX; NORDINFO-penge til nordisk netarkiv-projekt; Udenlandske Ældre Samling på nettet; Udstillinger; Erhvervelser
Kronik
Authors: Leergaard Joan
Published: October 2020

Indhold: Bøger og bibliotek; Evaluering af Det Kongelige Biblioteks forskning 1998-2002; Langsigtet plan for museer og kulturbevaring; Bevar Bogen - et stort sponsorprojekt; H.C. Andersens dagbøger på nettet; H.C. Andersens eventyrmanuskripter på Det Kongelige Bibliotek nu på nettet; Frederik V's Adas på nettet; Den danske Rimkrønike online; Korthistorisk Selskab er stiftet; Georg Philipp Telemanns kantate til Frederik V nu online; Tilføjelser til basen med dansk teatermusik online; Teksterne til sommerrevyer er katalogiseret; Dansk kammermusik trykt før 1900 er nu online; Online node - Sperontes: Slugende Muse an der Pieisse; Frederik Schybergs og Jens Kistrup arkiver kan søges på nettet; Anselm, Malachias, Bernhard & Basilius - nu på nettet; Klassikerhåndskrifter fra tre renæssancer; Tilvækst i registrering af Udenlandske Ældre Samling på nettet; Foredrag; Besættelsen og erhvervslivet; Litteraturforsker og professor Anne-Marie Mai modtog i efteråret 2003 G.E.C. Gads og Det Kongelige Biblioteks forskningsformidlingspris, H.O. Lange-prisen; Det store bogtyveri; Udstillinger; Indiske dage; Danske bogbindere; Udstillinger i Oktogonen; Musikarrangementer; Erhvervelser
Arvids dagbog fra Finland foråret 1940
Authors: Petersen Arvid E.
Published: October 2020

Ved Elly Bruunshuus Petersen
Kronik og Publikationer
Authors: Philipson Lotte
Published: October 2020

Indhold: Byggeriet KBA 112; Det Kongelige Bibliotek er nu i gang med anden etape af KBA 112, med et nyt universitetsbibliotek for humaniora og med nye magasiner; Eventyrbog til indvandrerfamilier 2005; Udstillinger; Netadgang med egen bærbar pc på alle Det Kongelige Biblioteks betjeningssteder; Fotografi i Diamanten; H. C. Andersen; H. C. Andersen på Arabisk; Foredrag; Koncerter; Musikarrangementer; Erhvervelser; Publikationer; Direktør, professor dr. Dieter Lohmeier Schleswig-Holsteinische Landesbibliothek, Kiel, fratrådte 24. januar 2005; Det Kongelige Bibliotek på nettet; REX; Online lån af musik;
Kronik og Publikationer
Authors: Philipson Lotte
Published: October 2020

Indhold: Det Kongelige Biblioteks udbygning på Amager; Det Kongelige Bibliotek på nettet; Webudgivelsen H.C. Andersen og musikken; Udstillinger; Foredrag; Musikarrangementer; Erhvervelser; Frimærkehandler og jernbanehistoriker Peer Olav Thomassens Fond; Publikationer
Kronik og publikationer
Authors: Philipson Lotte
Published: October 2020

Indhold: Bøger og bibliotek; KUB indgar aftale med IT­ Universitetet og Datalogisk Institut; Det Kongelige Bibliotek på nettet; Udstillinger; Foredrag; Musik; Erhvervelser; Publikationer
Kronik og publikationer
Authors: Philipson Lotte
Published: October 2020

Indhold: Publikationer; Erhvervelser; Musik; Günter Wallraff: Martin Walser; Uwe Tellkamp; Foredarag og debat; Udstilligner; Bøger og bibliotek;
Kronik og publikationer
Authors: Philipson Lotte
Published: October 2020

Indhold: Bøger og bibliotek; Det Kongelige Bibliotek på nettet; Udstillinger; Dronningens ansigt – et blandt mange; Portrætkunsten i dansk bladtegning; Foredrag; International forfatterscene; Ingo Schulze; Herbjørg Wassmo; John Irving; CPH.LITT: De store nordiske; Musik; Erhvervelser; Publikationer;
Kronik og publikationer
Authors: Philipson Lotte
Published: October 2020

Indhold: Bøger og bibliotek; Europæisk digitaliseringsprojekt om første verdenskrig; Det Kongelige Bibliotek på nettet; Udstillinger; Foredrag; International Forfatterscene; Geert Mak; International Kvindeaften; Karl Ove Knausgård; iT.house, Det Humanistiske Fakultetsbibliotek; Musik; Erhvervelser; Publikationer
Kronik og publikationer
Authors: Philipson Lotte
Published: October 2020

Indhold: Bøger og bibliotek; Jyske Lov; Kulturminister Per Stig Møller; Det Kongelige Bibliotek på nettet; Foredrag; Foredragsrækken Carsten Niebuhr; International forfatterscene; Paul Auster og Siri Hustvedt; Beate Grimsrud; Amos Oz; György Dragomán; Et Øieblik – ny scene for litteratur og lyrik; Musik; Erhvervelser; Publikationer
Kronik og publikationer
Authors: Philipson Lotte
Published: October 2020

Indhold: Publikationer; Erhvervelser; Musik; liTHouse; Kulturnat 2011; Brown Bag Lectures; Operaintroduktion; International Forfatterscene; Foredrag; Udstillinger; Bøger og Bibliotek; CENL;
Kronik
Authors: Meile Jakob Kyril
Published: October 2020

Bøger og bibliotek; Werner Bests korrespondance; Bogseminar 2012; Bogforum 2012; Det Kongelige Bibliotek på nettet; Georg Brandes’ dagbøger; Udstillinger; Nazismen i bladtegnerens streg; Det er løgn! Er videnskab til at stole på?; Foredrag; International Forfatterscene; Hans Magnus Enzensberger; Isabel Allende; Orhan Pamuk; Jan Guillou; Students Only; Koncerter; Fyraftenskoncerter; India Today Festival; Kulturnat 2012; Erhvervelser
Til skolebal i nisseland
Authors: Thrane Lotte
Published: October 2020

Om eventyret som tilflugtssted for børn og barnlige sjæle – og om et eventyrligt skoleforsøg på Frederiksberg i begyndelsen af forrige århundrede.
Besættelsesforskningens faser og veje
Authors: Bryld Claus
Published: October 2020

Den store kildeudgave om Werner Bests korrespondance, som Det Kongelige Bibliotek udgav i 2012, affødte en foredragsrække om aktuelle emner i relation til udgaven. Indledningsvist blev banen kridtet op af professor Claus Bryld med et foredrag d. 18. april om besættelsesforskningens udvikling siden 1945. Artiklen her er en bearbejdet udgave af foredraget.