bluuebunny/crossref_metadata_2025 huggingface dataset:
Effect of School Feeding Programme on Pastoralists’ Pupils’ Participation in Regular and Mobile Primary Schools in Turkana County, Kenya
Authors: Ejore Paul Ekeno , Gakunga Daniel Komo , Nungu Musembi
Published: October 2020

Kenya’s Turkana County, being an arid area, is faced with numerous challenges that hinder education programs especially among school going pupils. Therefore, the study sought to establish the effectiveness of the government interventions measures on pastoralists’ pupils’ participation in regular and mobile primary schools in Turkana County. Based on the study, this paper explores the effectiveness of the school feeding programme in promoting access to education among pupils from pastoralist communities in the County. The study utilized both descriptive survey as well as mixed methods. It utilised a sample of 75 head teachers, 225 teachers, 375 pupils, 85 parents, 3 education officers (1 from each sub-county), 1 County Director of Education and 1 County Commissioner. For data collection, the study employed questionnaires, interview schedules and focus group discussions. Quantitative data was coded and keyed into the computer using Statistical Package for Social Science (SPSS). In order to test the effectiveness of the government intervention, regression test an (inferential statistics) was applied. The analysed data was presented using tables. The qualitative data from interview schedules and focused group discussion was organized into major themes as per the research objectives. The results were presented thematically using extensive description and direct quotations. Hypotheses were analysed using regression analysis. The findings of the study showed that the feeding programme influenced many pastoralists’ pupils’ participation in both regular and mobile primary schools. The study recommends that the government should make efforts to ensure that food is supplied to schools in in time. There is also need to enrich the nutritional quality of the food supplied to schools. This paper highlights the major contribution of school feeding interventions in increasing access to quality education among marginalised communities. It will inform future policies aimed at such interventions by governments and education stakeholders.
Syphilis among HIV serodiscordant partners associated with Human Papillomavirus Infection in a bisexual man
Authors: Boldrini Neide Aparecida Tosato , Caldas João Victor Jacomele , Almeida Susana Lamara Pedras , Ferreira Dennis de Carvalho , Silva Alexandre Marques Paes da , Tapias Bianca Nunes Balmas , Santos Maria Carmen Lopes Ferreira Silva , Reis Helena Lucia Barroso dos
Published: October 2020

Introduction: Syphilis and HIV infections are sexually transmitted infections whose diagnosis and treatment contribute toward preventing congenital transmission. Objective: To report a case of three sexually transmitted infections detected in a male partner during Couple Consultation and syphilis in the female partner during prenatal care. Case report: A 34-year-old black female G2P1 pregnant woman was referred to an outpatient clinic of sexually transmitted infections in Vitória, Brazil, reporting a 30-day evolution of painless papular lesions in the external genitalia, suggestive of condylomata lata. Nontreponemal tests were positive for syphilis and negative for HIV. The husband reported unprotected receptive anal intercourse and possessed anal condylomatous lesions and perianal condylomata lata. He was positive for both HIV and syphilis. Histopathological findings showed low-grade HPV lesions and the PCR test found 16, 39, and 53 HPV subtypes. Treatment with benzathine penicillin G was successful for both partners. Conclusion: This study emphasizes the need for Couple Consultation during pregnancy to identify and treat possible sexually transmitted infections.
Long-term clinical complications associated with the use of polymethyl methacrylate in spinal stabilization of dogs and cats: case series
Authors: Diamante Gabriel Antonio Covino , Marinho Paulo Vinicius Tertuliano , Dal-Bó Isis dos Santos , Bregadioli Thales , Paes Fernanda , Rego Renato Otaviano do , Monteiro Bianca Fiuza , Galeazzi Viviane Sanchez , Macedo Aline Schafrum , Ferrigno Cássio Ricardo Auada
Published: October 2020

Vertebral and spinal cord trauma are common conditions in small animal practice and often result in vertebral fractures/luxation (VFL) with concomitant spinal cord laceration, concussion, compression, or ischemia. These lesions have several clinical presentations that may vary from moderate to severe pain and partial to total loss of motor, sensory, and visceral functions, which may result in death or euthanasia. Our purpose is to describe five cases (four dogs and one cat) of complications secondary to the use of bone cement for vertebral stabilization. The patients, between five months and four years of age and weighing between 1.4 and 12.2 kg, were referred to the Small Animal Orthopedics and Traumatology Service of the Veterinary Hospital of the College of Veterinary Medicine and Animal Science of the University of São Paulo. They had a history of post-operatory polymethyl methacrylate (PMMA) reactions (such as drainage or cement exposure due to infection or implant failure) in periods from 9 to 18 months after undergoing spinal osteosynthesis. Surgical implant removal occurred in 80% of the patients (4/5). Complete remission was not observed in the patient with residual implants. The association of pins/screws and PMMA is a versatile osteosynthesis technique and is applicable in all spinal regions. However, delayed complications can occur, which could require additional surgical procedures. Despite the small number of cases included in this study, one can infer that complications related to the use of bone cement in spinal surgery can occur in the long term and should be highlighted during the implant choosing process for vertebral osteosynthesis in small animals.
Optimum design of reinforced concrete shear walls
Authors: Hutchison D. L. , Van Geldermalsen T. J.
Published: October 2020

The recently published New Zealand Code of Practice for the Design of Concrete Structures (NZS 3101:1982) and the newly amended Code of Practice for General Structural Design and Design Loadings for Buildings (NZS 4203) permit a variety of possible design approaches for reinforced concrete shear wall structures. A series of wall designs for dimensionally similar four-storey and eight-storey buildings has been carried out and a comparison of construction cost estimates obtained together with an assessment of the relative design effort required for the different design options.
The Dynamic Relationship between FinTech and Social Distancing under COVID-19 Pandemic: Digital Payments Evidence
Authors: Alber Nader , Dabour Mohamed
Published: October 2020

This paper investigats the opportunities of growth under restrictions of social distancing for FinTech. This has been conducted on 10 countries (United States, United Kingdom, Egypt, United Arab Emirates, Saudi Arabia, Japan, South Korea, Italy, India and Nigeria) during the period from March to June 2020. Results indicate that social distancing may affect digital payments. This has been supported for retail and recreation (X1), grocery and pharmacy (X2), transit stations (X4) and workplaces (X5), whithout any evidence about significant effects for parks (X3) and residentials (X6).    
Cause Determination of the Adjustable-Rate Mortgage Market Collapse During the Financial Crisis
Authors: Wang Ryan P.
Published: October 2020

This paper provides insight into what caused the decline of the adjustable-rate mortgage (ARM) market during the 2007–2009 financial crisis. Contrary to common perception, the failure of the ARM market cannot be primarily attributed to predatory lending targeting subprime borrowers from low-credit households. This popular narrative is incomplete and disregards some important factors. I present three key factors that challenge the narrative and point to previously undiscussed sources that may have contributed to the ARM market collapse. First, the accusation of predatory lending does not account for other possible causes of mass ARM defaults. Second, the sole focus on the market’s subprime segment disregards the impact of prime ARMs on the market. Third, the narrative’s citation of subprime ARMs having greater delinquency rates and foreclosure numbers fails to recognize the significant percentage increase in prime ARM failures in the years leading up to the crisis, as well the disparity in typical outstanding balances between subprime and prime ARMs.
Internationale Politik, Kolonien und Militär im Werk Jeremy Benthams
Authors: Wegener Jens
Published: October 2020

The contributions of London philosopher and jurisconsult Jeremy Bentham (1748-1832), known primarily as the founder of secular Utilitarianism, to questions of international politics, colonies, and the military, have heretofore received a superficial treatment, especially in the German scientific debate. Based on the most current research and profiting from the military expertise of its author, the present monography is the first complete, German-language examination of the mentioned aspects of Benthams thought, revealing its surprising topicality.
Dilemmas Confronting the Teachers of Arithmetic
Authors: Grossnickle Foster E.
Published: October 2020

Afrequent criticism directed towards public elementary and secondary schools concerns the fai lure of their students to demonstrate adequate preparation in the fundamental subjects. This particularly holds true in arithmetic. A recent report gave the findings of a survey conducted in New York City concerning the preparation of former high school students in basic subjects. At the time of the investigation, these students were employed in commerce, industry, and the professions.
The How and Why of Discovery in Arithmetic
Authors: Swenson Esther J.
Published: October 2020

The traveler had occasion to drive frequently on the main highway between two large cities. There were very few towns on the 100 miles of highway and he found himself breaking the monotony by noticing highway signs and other details which told him what places were located along the road in each direction.
Arithmetic on the March
Authors: Eads Laura K.
Published: October 2020

Arithmetic is growing in importance at all school levels. This was quite apparent at the April 1954 meeting of the National Council of Teachers of Mathematics in Cincinnati. The theme of the meeting was “Mathematics on the March” but arithmetic was given serious consideration by speakers and panelists representing schools, colleges, and industry.
Don't Let that Inverted Divisor Become Mysterious
Authors: Eagle Edwin
Published: October 2020

BY PUSHlNG STUDENTS TOO RAPIDLY to the level of manipulation with abstract symbols we often make mysterious and meaningless for them many processes which should seem understandable and sensible. Division by a fraction is a classical example of this situation. “Invert and multiply” becomes a mumbo-jumbo that gets answers, sometimes correct ones, but which the pupils often put in somewhat the same category as rabbits pulled out of hats.
Concrete Materials for Teaching Percentage
Authors: Hauck Eldon
Published: October 2020

Many problems and difficulties in elementary school arithmetic can be resolved through: (1) better instructional methods, (2) more instructional materials (3) better instructional materials, (4) concrete materials for each basic phase of the subject, and most important (5) the know how in using materials in the classroom. Concrete materials for teaching and learning should have: (1) the property of being handled in such a way as to conduct a learning situation to the handler or observer, (2) the inherent structure to present to the learner a sequential pattern leading to the abstract, and (3) a specific relation and application to the subject being treated which, at the same time, gives an immediate experience into reality. Concrete materials will enable the child to participate in discovery and develop organization and insight.
The Boy Who Did Not Like Arithmetic
Authors: Wittenberg Clarice
Published: October 2020

The eight-year-olds in the University of Wyoming Elementary School were making plans on the first day of the fall term for the year ahead. When one of the group protested at the thought of studying arithmetic, the other children were dumbfounded. From all sides they began to tell him, in no uncertain terms, just what would happen to him if he knew absolutely nothing about numbers.
The Seattle Meeting
Authors: Roudebush Elizabeth
Published: October 2020

Teachers of arithmetic and mathematics gathered at Seattle in August to discuss their mutual problems. This was the fourteenth summer meeting of the National Council of Teachers of Mathematics with the Puget Sound Council of Teachers of Mathematics as hosts. Several interesting papers in the field of arithmetic were presented and may become available for publication. Two discusions are reported below.
Editorial comments: As we read
Authors: Hamilton E. W.
Published: October 2020

Besides recording, informing and encouraging, we believe that as a professional magazine, THE ARITHMETIC TEACHER should stimulate reaction on the part of its readers. Some of the ideas presented should be controversial.
Diagnosis and correction of arithmetic underachievement
Authors: Ross Ramon
Published: October 2020

For most children the development of competencies in a quantitative world proceeds at an orderly pace. For a few, howover, growth does not occur in a normal fashion. Various studies have revealed that roughly 15 percent of sixth-grade pupils, for example, are one or more yeats below grade level in arithmetic as measured by standardized tests [4].* While the mentally deficient would account for a portion of this percent, there still remains a sizable portion of the school population who experience difficulty in one or more of the basic processes. These children require remediation, but prerequisite to that remediation is adequate diagnosis.
Student teachers look at the teaching of arithmetic
Authors: Brydegaard Marguerite
Published: October 2020

The student teachers of today Who are embarking upon their journey are one of the strongest determiners of how mathematics Will be taught tomorrow. The way they “look at arithmetic” determines how they will teach it. Each student teacher needs inspired, scholarly, released thinking that leads him to grow continuously in his understanding of mathematics.
Focal point: The training of elementary school mathematics teachers
Authors: Fred Weaver J.
Published: October 2020

Appropriate training for elementary school teachers who provide instruction in mathematics has been a concern of long standing. This concern has been in creased in recent years as various exploratory programs have begun to exert an influence on the content of the elementary school mathematics curriculum.
Editorial comments: As we read
Authors: Hamilton E. W.
Published: October 2020

The first article this month is a heavy one. Professor Dienes presents mathematical structure in a novel way and discusses at considerable length the psychological problem of dealing with its development in children's minds. Don't skip over this article after reading a page or a paragraph, and don't placate yourself with the promise to read the entire article at some other time. Take the trouble to follow the examples through. This may be easier to do if you did your homework based on a couple of last month's articles. But no matter; there is more homework in Dienes' bibliography, homework of a kind that should be obligatory upon any up-todate teacher.
Automatic addition
Authors: Hohn Franz E.
Published: October 2020

Computers and related machines employ devices such as switches, electron tubes, transistors, magnetic cores, magnetic tape, and so on to do their work of storing, processing, and computing numbers. Since a switch is either open or closed, a tube or transistor is either conducting electricity or not conducting electricity, and a magnetic core or a spot on a magnetic tape is magnetized either “positively” or “negatively,” that is, since one of two opposite conditions is always present, it is natural that the internal operation of such machines should be based on the binary number system, which counts by twos. One of the two conditions is used to represent the number 1, the other to represent the number 0.
Mathematics in the second grade
Authors: Howard Hildebrand Francis , Johnson Nellie
Published: October 2020

In the field of mathematics education, there is a great deal of concern about what currently constitutes the elementary school arithmetic program. Interest is evident from many sources including the CUPM Annual Report for 1961-62.
In the classroom: Out of yesterday: A playlet for sixth grade
Authors: Deans Edwina , Baker Betty
Published: October 2020

SETTING: The patio of the home of Jeffrey Lord. Summer furniture is scattered about. A low brick wall forms one end of the terrace, right stage. The entrance door is rear left. A phone is on the table.
Use of manipulative devices in teaching mathematics
Authors: Bernstein Allen L.
Published: October 2020

The use of manipulative and pictorial material in the teaching of mathematics has been an accepted procedure for many years. The modern teacher is surrounded with methods books discussing how to make these devices, and with commercial catalogs offering a tremendous variety of these materials. How does one navigate this maze and make wise decisions conceming the expenditure of professional time and energy and of school funds? We believe that from the experience of the profession certain principles regarding the selection and use of such material have evolved.
The role of the notebook in a mathematics class
Authors: Mehl William G.
Published: October 2020

Last summer one of my former students approached me and said, “Mr. Mehl, you know those notebooks which we had in our math class? Well, I still have mine and I've found good use for it even in the eleventh grade!” The student had at one time been in my eighth-grade mathematics class.
Using the subtraction method in dividing decimal fractions
Authors: Broussard Vernon
Published: October 2020

There are two ways in which the teacher may introduce the decimal notation. First, he may consider decimals as a special form of common fractions having denominators of 10 or some power of 10; second, he may treat decimals as an integral part of our decimal system of numbers. Regardless of the method used, the pupil must see the relationship between the two ways of writing a decimal fraction.
In the classroom: Binary can be F-U-N
Authors: Ochsenhirt Marion E. , Wedemeyer Mary M.
Published: October 2020

The seventh-grade students of the North Hills Joint Schools have found that there is fun as well as educational value in using the binary system. As all teachers of modern mathematics know, one of the main reasons for teaching the binary system is that the pattern for place value in this system is identical to that of the traditional decimal system. Developing the pattern in an entirely new situation gives the student a better understanding of the decimal system.
National Council of Teachers of Mathematics: The Council's drive to improve school mathematics
Authors: Allen Frank B.
Published: October 2020

According to our Articles of Incorporation, the object of the National Council of Teachers of Mathematics is “To assist in promoting the interest of mathematics in America, especially in the elementary and secondary fields, by holding meetings for the presentation and discussion of papers, by conducting investigations for the purpose of improving the teaching of mathematics, by the publication of papers, journals, books, and reports: thus, to vitalize and coordinate the work of many local organizations of teachers of mathematics and to bring the interest of mathematics to the attention and consideration of the educational world.” I believe that any impartial review of our accomplishments will support the conclusion that we have achieved a high degree of success in the attainment of this objective.
The 1963-64 budget
Authors: Karnes Houston T.
Published: October 2020

The Committee on Financial Policies, Budgeting, and Auditing for 1963 was composed of Julius H. Hlavaty, Harold Fawcett (substituting for Clifford Bell), Button W. Jones, Chairman, and Myrl H. Ahrendt, ex officio.
Sets and numbers
Authors: Paul Jan S.
Published: October 2020

Two plus 5 equals 1 plus x. What does x equal? Simple? Of course, but then you aren't a first-grader. Nor are problems confined to number-letter substitutions. Another example might deal with oranges or candy. Try this one: Jean and Jennifer have seven oranges together. Jean has 3 more than Jennifer. How many oranges does Jean have? Don't know the answer? Don't be surprised if a first- or secondgrader can give you a straight, fast answer using sets of objects and numbers associated with those sets of objects.
Illustrating cardial and ordinal numbers
Authors: McLean Robert C.
Published: October 2020

Puzzles are sometimes useful for illustrating differences which may be difficult for some students to understand. There is a routine often used by a well-known team of comedians which well illustrates the pitfalls of confusing ordinal and cardinal numbers. It also underlines the contribution set language can make to clarity of expression.
In the classroom: The role of games, puzzles, and riddles in elementary mathematics
Authors: Dohler Dora
Published: October 2020

What can we do to make math more inviting for our students? How can we lead them into the interesting experiences which are so much a part of mathematics?
The effects of instruction on the stage placement of children in Piaget's seriation experiments
Authors: Coxford Arthur F.
Published: October 2020

In his book, The Child's Conceplion of Number, Jean Piaget 1 stated that the concept of number has three basic aspects: cardinal number, ordinal number, and unit. He has given criteria for determining when a child understands each of the basic concepts. A child understands cardinal number when he is able' to construct a one-to-one correspondence between two sets of objects and to conserve this corrspondcnce when it is no longer perceptually obvious.
Kindergarten mathematics
Authors: Fitzsimons Lucille
Published: October 2020

In our eagerness to develop mathematics concepts for today's five- and six-year olds, are we mixing up our number ideas and merely confusing the children, or are we preparing thoughtful programs which help to develop number concepts at this particular age level? Clarity in planning and identifying activities which develop specific mathemat ics understandings is essential.
In the Classroom: Fun, fact, and fancy
Authors: Parrish Cada R.
Published: October 2020

There is much said and written about the slOw-learner. “How are they identified? What are their characteristics? Why are they slow?” All of these questions are important, but to us, as classroom teachers, the problem is this: “We have the slowlearners. What can we do with them?”
In the Classroom: Geometric number stories
Authors: Condron Bernadine F.
Published: October 2020

Counting and basic addition facts can be reviewed at the beginning of the second grade through the introduction of a new topic, geometry. Not only would it, serve as a less painful way to review, but it would also open the door for more logical reasoning, thinking, and creating. Many new concepts and new vocabulary will be learned as an incidental part of this type of review.
In the classroom: The twist
Authors: Hughes Marjorie
Published: October 2020

I heartily recommend it, whether you're facing your first math class, sweetly suggesting, ”Now keep your columns straight,” or if you're a veteran of 40 or 50 years, still insisting, “KEEP YOUR COLUMNS STRAIGHT.” Now if someone told you that with a simple twist you could banish three-fourths of all your difficulties in long division, in hard multiplication, in addition of uneven decimals, and probably in comprehension of borrowing and carrying, wouldn't you at least give it a try? Unorthodox? Yes, but EFFECTIVE.
In the classroom: Nimble numbers
Authors: Margolin Sandra
Published: October 2020

In the summer, 1963, viewers young and old were taken on a magic-carpet journey into the fascinating world of mathematics throught he medium of television. The program was called “Jimble Numbers” and was produced by the Dade County Board of Public I nstruction on the ETV station, WTHS-TV, Channel 2.
Focal Point: The Cambridge Conference on School Mathematics
Authors: Weaver J. Fred
Published: October 2020

Within the past year a potentially significant influence on the mathematics curriculum and on mathematics education has become the subject of much interest and discussion. We refer to that which is known simply as “The Cambridge Conference on School Mathematics.”
Comments on ancient Egyptian multiplication
Authors: Stern Catherine , Stern Margaret B.
Published: October 2020

In recent issues of The Arithmetic Teacher there have been short reports on a method of multiplication credited to the ancient Egyptians.1 In these articles this interesting procedure is presented without an explanation of why it works. In the April, 1963, issue, in a letter to the editor, Carl A. Wirth discusses the process and transcribes the figures used into the binary system of notation. However, as he himself states, this explanation “may be too advanced for the elementary grades.”
In the classroom: Algebraic approaches to developmental work with the operations
Authors: Deans Edwina
Published: October 2020

In some of the newer programs in elementary school mathematics there is an attempt to close what has previously been quite a gap between arithmetic and algebra; to use algebra as a way of bringing adventurous thinking to the mathematics content of the grades. It may be that algebraic approaches to some of our elementary school mathematics will help children grasp generalizations and build concepts more adequately. Why? Because under the guidance of a skillful teacher they have the opportunity to try out and test variation after variation while keeping constant the basic concept which is being developed.
An illustration of the unrecognized assumption
Authors: Todd Robert M.
Published: October 2020

Some students, parents, and teachers are puzzled by the emphasis on explicitly stated assumptions and precise definitions that mark the “new math.” “Is all this nitpicking necessary?” asked one frustrated School Mathematics Study Group teacher. Maybe it is. Unrecognized assumptions have led to false conclusions and even tragedy—engineers can think of several bridge failures and similar disasters traced to an unrecognized assumption that was false.
Mathematics for summer fun
Authors: Rosenthal Morris , Sitts Marvin
Published: October 2020

Modern educational theory stresses the importance of letting a child develop at his own rate. This theory too often conflicts with practice in regular school with its passing dates, deadlines, and standardized testing. Summer has been looked on as a kind of salvation time for youngsters—a time when they can, in truth, do what they please. But doing what they please in this complex world usually requires some organization that can best be provided by thoughtful adults. Based on such reasoning, the Mott Summer Program has been developed in Flint. Schools are open six weeks of the summer and staffed with teachers who are specialists in recreation, a variety of crafts and skills and, more recently, the subject areas sometimes considered less fun—science, arithmetic, language, and reading. This paper will describe the first summer of one of the newest of these programs—a program in arithmetic for upper elementary children.
Number in the western world—a bibliography
Authors: Young Miriam H.
Published: October 2020

Everything is Number,” said Pythagoras more than twenty-five hundred years ago.1 During the nineteenth century, Kronecker expressed the feeling that “God made the integers; all the rest is the work of man.”2 Lobatchewsky and Bolyai, with their non-Euclidean geometries, proved that mathematical axioms were not God-given, self-evident truths.3 Others go even further and say that numbers were invented by man.
Individualizing arithmetic instruction
Authors: Redbird Helen
Published: October 2020

The United States' system of public education is based on individual likenesses — not on individual differences. The idea is that we are alike enough that we can be educated together. Individual likenesses is still a good concept to use in the educational process. It should not be considered as opposed to individual differences, but as another concept in arranging for learning in the classroom. The real question to me, as a teacher, is which one is the better concept for a given learning situation.
In the classroom: Considerations in the selection of learning aids
Authors: Spross Patricia
Published: October 2020

The multiplicity of learning aids for instruction in arithmetic now available for purchase under Title III of the National Defense Education Act is both stimulating and confusing. Some considerations are of prime importance to help teachers employ devices effectively.
Sic transit gloria arithmetica
Authors: Mueller Francis J.
Published: October 2020

If there is a moral to my paper, it might be phrased something like this: He who reads old books is likely to be more politic about the present.
Motivation
Authors: Jackson Humphrey C.
Published: October 2020

I would like to take you on a mathematical safari, an expedition to hunt for evidences of motivation. Motivation is somewhat like the Abominable Snowman. There is evidence that it exists, but it is difficult to capture.
Minutes of the Annual Business Meeting
Authors: Karnes Houston T.
Published: October 2020

The Annual Business Meeting was scheduled to follow immediately after the 8:30 A.M. general session during which President Frank B. Allen presented a paper entitled “The Council's Drive to Improve School Mathematics—a Progress Report.”* Contained in this paper was a fine survey of the work of the Council during the past year and indications for important projects to be done in the future. Burton W. Jones presided at this general session.
Plane polygons
Authors: Sandling Dolores C.
Published: October 2020

My sixth-grade class of academically able pupils took a side trip into geometry one day as a result of a discussion of angles. We named the types of angles and checked the clock at various times during the day to determine the angle formed by the hands of the clock at these hours.1
Lewis Carroll: author and mathematician
Authors: Stright Robert L.
Published: October 2020

Millions of children and adults are acquainted with the book, Alice in Wonderland, and its author, Lewis Carroll (Charles Lutwidge Dodgson). It is also a fairly well-known fact that Carroll was some sort of a mathematician. Few people realize, however, the amount of mathematics contained in this seemingly simple book and others like it. Nor do most people realize the effect of Carroll's mathematical mind upon his work. “Alice in Wonder land owes its unique place in our literature to the fact that it was the work of a genius, that of a mathematician and logician who was also a humorist and a poet.”1 In fact, the “Alice” books (Alice in Wonderland and Through the Looking Glass) have been described as the “original work of a mathematician and logician, interested in the precise meaning of words, who was at the same time a genius of invention and poetic imagination with a love for children and a gift for entertaining them.”2
In the classroom: Improving the teaching of place value
Authors: Wholey Nonie McGrath
Published: October 2020

One of the main reasons for teaching computation in bases other than ten in elementary schools is to teach the children the meaning of our own decimal, or base ten, place value system. Though teachers have always taught the meaning of place value and have pointed out that our numeration system is based on groups of ten, we do not realize how superficial the pupils' understanding is until we ask them to apply the principles of place value to numerals with bases other than ten, i.e., binary, tertiary, etc. What should be a fairly simple procedure (for instance, counting in base three) is difficult because the pupil is uncertain about the basic principles of our own familiar decimal system, and he must now apply these principles to a nondeciroal system.
Discovery in mathematics
Authors: Ranucci Ernest R.
Published: October 2020

Many interesting facts may be discovered by elementary school students who observe things right around them.
Computation skills: results of acceleration
Authors: Ivey John O.
Published: October 2020

In a recent news article, “Project Mathematics,” published in The Arithmetic Teacher, Mr. Fred C. Beyer1 reported on the new program of mathematics in California. The project by the County Superintendents' Association to develop a scope and sequence for mathematics is another step toward more effective articulation from one grade to the next and from the elementary to the secondary schools. Other organizations, as well as research programs, curriculum studies, and new textbooks, have influenced the modernization of the elementary arithmetic program.
Mathematical understanding of seventh- and eighth-grade pupils, 1948 and 1963
Authors: Thurlow Virginia
Published: October 2020

The importance of understanding basic concepts in the learning of arithmetic has received much attention in recent years. Interest has been evident from many sources, as reflected in the professional literature, the work of cmriculum planning groups, revisions of basic textbooks, inservice programs, and new mathematics programs such as the School Mathematics Study Group and the Greater Cleveland Mathematics Program. It would be reasonable to assume that arithmetic instruction has improved as a result of this recent, intense emphasis on understanding.
Quantitative thinking of preschool children
Authors: Josephina Sister
Published: October 2020

The kindergarten organization within the United States is in the second century of its establishment. Yet the program, more than any other segment of the school, has been characterized by diversity of practice. With a steady increase of attendance in kindergartens (in 1960 the Bureau of Census reported 58.8 percent of all fiveyear- old children enrolled in public and private kindergartens) arise the problems of what should constitute the scholastic diet of these children and, more importantly, how they should be educated.
In-service education–modern arithmetic and good pedagogy
Authors: Gurley Allan W. , Hicks Randall C. , Lott Jurelle G. , Reeves M. Louise
Published: October 2020

This is a report of a systemwide in-service program which utilized three University of Georgia faculty members in a team-teaching approach. Used in the program were lectures, questions and discussions, professional books, students' textbooks and accompanying teachers' manuals, films, filmstrips, programmed materials, recent experimental studies and research, various teaching aids and devices, consultants and specialists, and a wide variety of written materials especially prepared to meet the needs of the individuals and the grade level groups.
Easy construction of magic squares for classroom use
Authors: Cappon John
Published: October 2020

In the December, 1963, issue of The Arithmetic Teacher Bryce E. Adkins gave six rules for construction of odd-cell magic squares.1
An ordered pair approach to addition of rational numbers in second grade
Authors: Hildebrand Francis Howard , Johnson Nellie
Published: October 2020

The purpose of this paper is to demonstrate a method used to develop a binary operator for addition of rational numbers at the second-grade level.
Modern mathematics—go or no go?
Authors: Hipwood Stanley J.
Published: October 2020

An increasing number of public schools are introducing mathematics course work which comes under the broad title of modern mathematics. A major curriculum change of this nature inevitably brings about problems, both in the school and in the community. There will always beresistance to change on the part of some faculty members and articulate members of the community. Such resistance is good, as long a it is constructive and honest, for it will help refine the new program and tailor it to local needs.
Method—a function of a modern program as complement to the content
Authors: Glennon Vincent J.
Published: October 2020

The professional domain of the teacher of mathematics on whatever grade level is referred to as mathematics education. Mathematics education can be defined as the intersection set of the psychological foundations, the cultural foundations, and the mathematical foundations.
Algebraic arithmetic for elementary school
Authors: Bradfield Donald L.
Published: October 2020

The mysterious Mr. “X” of algebra is creeping into the elementary school curriculums of the United States. In arithmetic classes throughout the country children are learning enthusiastically the language and symbols of algebra. However, the content of the algebra which should be included in the elementary school arithmetic program has not been examined rigorously. A decision is needed on precisely what algebraic concepts will be taught at the elementary level. Since students in the elementary school find it fascinating to work with both numerals and letters as symbols for numbers, algebraic skills which beginning students in algebra in secondary schools find quite routine can be introduced properly to elementary school students who find them challenging. This article will explore briefly the possibilitie for developing an algebraic arithmetic for elementary school. Those algebraic concepts which should be included in an elementary arithmetic program will be stated precisely.
Addition—not so easy
Authors: Hilaire Paul A.
Published: October 2020

A dictionary define addition as “the uniting of two or more numbers into one sum.” How does one “unite” numbers? One cannot see number. Addition, if so defined, must be a mirage.
In the classroom: Let's add automatically
Authors: Lawlis Frank
Published: October 2020

In preparation for a teaching unit for my seventh-grade students, I created a useful audio-visual device. Actually, the basis for the apparatus is taken from commercial computers, but it served my purposes for illustrating number systems. My students helped design the visual aid.
Editorial comments: How do you as a classroom teacher evaluate new learnings?
Authors: Brydegaard Marguerite
Published: October 2020

Today's program for mathematics includes many ideas that lead to new learnings. What are the basic concepts that underlie these learnings, and which of them are of greatest importance? Are these important concepts identified sharply? Are they included in tests and exercises designed to evaluate learing? How much importance should be attached to pupil behavior as measured by standardized tests? What procedures do you as a classroom teacher use to help you evaluate pupil learning? These are a few of the questions that each teacher must try to resolve.
Three views of the multiplier
Authors: Cunningham George S.
Published: October 2020

In multiplication, which factor is the multiplier? The modern tendency seems to be to avoid the question.
The library program fosters arithmetic learnings
Authors: McClenathan Louise
Published: October 2020

Are you aware that your library program can help you teach arithmetic concepts? I discovered the possibilities as I searched for a meaningful way to introduce fractions. One day my fourth graders and I listed on the board categories of reading interests suggested by members of the class: animals, story collections, biography, history, travel, adventure, science, humor, jokes, games, plays, poetry, riddles.
Machines
Authors: Karlin Marvin
Published: October 2020

Drop some meat into a meat grinder, tum the handle, and out comes hamburger. Drop a number into our number machine, turn the handle, and out comes a number (Fig. 1).
There's sense in nonsense arithmetic
Authors: Olsen Elizabeth P.
Published: October 2020

If you hear “Blub-blub” coming from the fourth-grade room of Middle Grove School, it doesn't mean we're going under for the third time. This is Martian Mathematics, or for you earthlings, 11five. If you hear “Fur-flea” as the answer to a question, don't call the health department; we're just doing Doggy Arithmetic, and fur-flea is Doggy for fifty. These are part of our own class-invented secret numeration systems.
Ambiguities in teaching arithmetic
Authors: Porterfield O. V.
Published: October 2020

In the March, 1956, issue of The Arithmetic Teacher1 Dwight presented a test of thirty items and asked the reader to rationalize his answer to each item in language suitable for elementary grade pupils.
The magic box
Authors: Jennings Thomas J.
Published: October 2020

Among the benefits from the recent reappraisal of elementary school mathematics programs is the increased stress upon the search for patterns. Youngsters are encouraged to discover relationships among seemingly unrelated data. In this way, they develop their ability to think creatively.
Finding the greatest common factor with the number line
Authors: Adkins Bryce E.
Published: October 2020

Finding the greatest common factor of two numbers to “reduce” the terms of a fraction is a source of difficulty for many students and for some teachers of arithmetic. The commonly taught algorism involves finding the prime factors of the terms of the fraction. If the terms have prime factors in common, the GCF is the product of all the common prime factors.
“Signed-digit” subtraction
Authors: Sandel Daniel H.
Published: October 2020

The subtraction algorisms that students usually learn can be found in current professional literature. These processes are mainly concerned with cucumvcnting an impasse and facilitating a correct solution as painlessly as possible.
Prompting versus intermittent confirmation in the learning of a mathematical task
Authors: Mcneil John D.
Published: October 2020

There is need for more experimental evidence on whether it is better to present learners with the correct response before asking them to make their own responses (prompting), or whether it is better to require learners to make overt responses before being presented with the correct response (confirmation). Cook and Kendler (1956), for example, found that prompting was superior, but Angell and Lumsdaine (1961) found that a combination of the two practices was more effective than either confirmation or prompting alone.
A multiple view of the Euclidean algorism
Authors: Feldman Leonard
Published: October 2020

The elementary teacher who wishes to explore the woods of mathematical abstractions might rightfully be fearful of getting lost. There is, indeed, an aura of dreadful symbolism that prevents an appreciation of some very nice territory. However, a leisurely pace, with reassuring landmarks, will often enable one to complete a satisfactory exploration. A case in point is the Euclidean algorism for obtaining the greatest common divisor. This is a topic that one first expects to meet in an excursion to the woods of number theory or in the ring of polynomials over a field. Nevertheless, in its basic form it is direct and simple enough to be used and understood by children in a fifth-grade class.
A rationale in working with signed numbers
Authors: Cohen Louis S.
Published: October 2020

In the teaching of signed numbers to children in Grades 4-8, I have used the “Postman Stories” model devised by the Madison Project.
The effects on conventionally taught eighth-grade math following seventh-grade programmed math
Authors: Meadowcroft Bruce A.
Published: October 2020

Often in the utilization of special methods and educational materials a continuous sequence cannot be maintained from one grade level to another. This is sometimes experienced in the area of programmed learning where an excellent course may be had that is suitable for one grade level but has no suitable sequel for the next grade level. Critics have frequently suggested that programmed learning provides low retention and produces superficial learning. Some answers to these suspicions and the efTects of interrupted programs might be had from the following report.
A conference on mathematical learning
Authors: Weaver J. Fred
Published: October 2020

Within the past few years there bas been increased recognition of the need for interdisciplinary approaches to problems associated with the learning of mathematics. Social scicnti ts in general, and psychologi ts in particular, have met with members of the mathematical community in an attempt to identify and attack the e problems on a broader base than either diseipline might do alone.
Teacher competence: what to evaluate and how
Authors: Moody William B.
Published: October 2020

The recent revolution by the modern mathematics movement has resulted in some major changes at the elementary level in curriculum materials and the training of teachers to handle these materials. Universities and colleges are starting to offer and require courses especially designed for elementary teachers at both the pre- and in-service levels.
Report of the Nominating Committee
Authors: Peak Philip , Allen Frank B. , Hawthorne Frank , Hess Adrien L. , Ingraham Mary L. , Jones Phillip S. , Lewis Eunice , Lowry William C. , Lund Jens L.
Published: October 2020

The Committee on Nominations and Elections presents its nominees for offices to be filled in the 1966 election. The vicepresidents are elected for a term of two years, whereas the directors are elected for a term of three years.
Sense and nonsense in a modern school mathematics program
Authors: Fehr Howard F.
Published: October 2020

If there is one phrase today that is prominent in the literature and conversation of all persons, professional and lay, and yet very nebulous, ambiguous, and meaningless in the minds of most of these persons, it is “modern math” or “the new math.” Now Modern Mathematics, as exemplified in such topics as Modern Algebra, Linear Algebra, Point-Set Topology, Algebraic Topology, Finite Mathematical Systems, Set Theory, and the like, is an exceedingly abstract, logical, axiomatic, well-structured system of knowledge. There is no nonsense in these branches of mathematics. They are pursued by students majoring in mathematics and science at the upper university and graduate levels of study. They have no place—no place—in elementary school mathematics. To do any of this mathematics in the elementary school would be more than nonsense—it would be insanity.
Probability and statistics—trial teaching in sixth grade
Authors: Wilkinson Jack D. , Nelson Owen
Published: October 2020

The Cambridge Report1 clearly indicates that the study of chance situations, more formally called probability, is a vital and appropriate part of the mathematics program for the elementary school.
Individualized instruction in a learning laboratory setting
Authors: May Lola
Published: October 2020

In this period of education it would seem the pressure is on to cram more and more into heads in a mad race to produce more and more right answers in shorter and shorter periods of time. It was decided in Winnetka, Illinois, to produce a laboratory setting of Jeaming, a place where children could have searching experiences that would challenge them to use their thinking power, a place where children could make mistakes, leam from them, and thereby build more adequate comprehensive thinking power.
A test to check divisibility by any number
Authors: Lemmon Becky
Published: October 2020

Choose a number; to it add a multiple of seven so that the last digit of the sum will be zero. Next add a multiple of seven to the sum so that the last two digits will be zero. Keep repeating this process adding one more zero each time, until the number can be easily divided by seven. If the remaining number is divisible by seven then the original number was a multiple of seven.