School Arithmetic Research Articles

The “Steinmetz problem” and school arithmetic

A simple solution for an intriguing problem.

A SURVEY OF MATHEMATICAL EDUCATION

A SURVEY OF MATHEMATICAL EDUCATION

Butler, Charles H. Arithmetic for high schools. Boston: D. C. Heath and Company, 1953. 336 P. $2.40

Butler, Charles H. Arithmetic for high schools. Boston: D. C. Heath and Company, 1953. 336 P. $2.40

Teaching arithmetic in the junior high school

The author points out that the acceptance of a theory of learning which emphasizes meaning and changing promotion policies in the elementary school must have an effect on the curriculum in the junior high school.The author discusses the resulting changes which, he feels, should be made in the junior high school.

Toward Perfect Scores in Arithmetic Fundamentals: A Study in Research

During the period 1928–42, a number of graduate students of Boston University School of Education were checking on the corrective load in the fundamentals of arithmetic in the upper grades and high school, and the possibilities of better scores, possibly perfect scores, in the fundamentals. Several of these students produced masters' theses which are now on file in the library of the School of Education. Some of the details of these studies which are of interest to teachers in junior or senior high schools or colleges are reported herewith.

Concrete Materials for Teaching Percentage

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.

A School Arithmetic. II. By L.E. Lefèvre pp. xv, 123. Without answers, 4s. ; with answers, 4s. 6d. 1952. (A. & C. Black)

A School Arithmetic. II. By L.E. Lefèvre pp. xv, 123. Without answers, 4s. ; with answers, 4s. 6d. 1952. (A. & C. Black)

A School Arithmetic. II. By L.E. Lefèvre pp. xv, 123. Without answers, 4s. ; with answers, 4s. 6d. 1952. (A. & C. Black)

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What Is Wrong with School Arithmetic?

Arithmetic is the science of putting quantities together and taking them apart. Thousands of the children in our schools have never had a chance to find out that school arithmetic has anything to do with quantities. They are taught to juggle figures.

A School Arithmetic. I. By L. E. Lèfevre Pp. xviii 238. 6s. ; with answers, 6s. 6d. 1952. (Black)

A School Arithmetic. I. By L. E. Lèfevre Pp. xviii 238. 6s. ; with answers, 6s. 6d. 1952. (Black)

Don't Call It Science

On the basis of form, non-mathematicians should have picked up the Russell definition and hurled it into the teeth of the mathematical world. The mathematician' s smug self-assurance, his either-it-is-orit-isn't attitude, coupled with the drudgery traditionally associated with elementary mathematics, have planted him on a pedestal of sorts, and to be able to pellet him up there with the words of one of his distinguished colleagues . . . . Ihe obvious explanation of the non-existence of such a devil-quotingscripture situation is that Russell came up with his epigram as a mathematician writing about mathematics and thereby assured its being kept secret from the world at large. The explanation would probably bd valid, were the author any one but Russell, whose writings have an audience far beyond the mathematical world and have made numerous non-mathematicians sample his less technical mathematical work. Furthermore, the definition has been quoted frequently enough for any alert layman looking for missiles to be aware of it. Possibly grammar school arithmetic so frightens children that after they grow up they are afraid to fight back, even with ammunition supplied by the enemy. Or, maybe they suspect some subtle trickery in it all and conclude the smart thing is to have nothing to do with it. Had some layman with a de-bunking urge quoted Russell to a mathematician, the mathematician would probably have replied: Of course, you're taking it out of its context ...e Russell was still pretty young when he wrote that, and over-impressed by some epigrams he had heard in, an Oscar Wilde play B...* Besides, he had his tongue in cheek . . e. * t Actually, however, while mathematicians may concede the definition suggests a painful effort at being clever, they do not dismiss it on that account,Instead, they consider it with all the seriousness they would give to an assortment of x's and y's strung together into an equation. Ihe fact that a flippant definition such as this might be concocted in the twentieth century and taken at face value is in itself a commentary on mathematics. Historically, mathematics is among the oldest fields of intellectual effort. Much of mathematics currently taught below the college level antedates Christianity. Yet, for all its antiquity, an epigrammatic definition of it is taken seriously, even

School arithmetic. By W.P Workman. 4th edition, revised by G. H. R. Newth. Pp. viii, 548. 8s. ; without answers, 7s. 3d. 1951. (University Tutorial Press)

School arithmetic. By W.P Workman. 4th edition, revised by G. H. R. Newth. Pp. viii, 548. 8s. ; without answers, 7s. 3d. 1951. (University Tutorial Press)

The Need for Mathematics in Business and Industry

A. P. Fugill: The main purpose of this session is to correlate more closely the teaching of mathematics in the high school with the use of mathematics in everyday living. It should be recognized at the start that the high schools can and should teach only the fundamentals of mathematics. It is the function of industry to develop special techniques of use and facility in handling mathematics. The usual high school subjects, arithmetic, algebra, geometry, and trigonometry, are useful in varying degrees in the practice of engineering, or for that matter in any industrial and commercial activity. It would be wasteful to bring every student up to the degree of proficiency required in a few specialized fields. The effort in high school teaching, therefore, should be to use mathematics as a means of developing logical reasoning and judgment, rather than as an exercise in memory.

Stanley Smith Cook 1875-1952

Stanley Smith Cook was born at Canterbury on 25 January 1875, and was the second of three sons of William Henry Cook and his wife, Martha Marsh Smith, both well-known residents of Canterbury. As a boy he was educated, primarily, at a Church School in Canterbury, and in 1889, at the age of fourteen and three-quarters, proved his ability by winning in competition a scholarship which enabled him to enter the King’s School of that city. In his first year he won a Form Prize and the Lower School Arithmetic Prize, and was consistently at or near the top of his form all through his school career. He was made a Senior King’s Scholar in July 1890, and reached the Sixth Form in the following year being then only sixteen years of age. While he did well in French and at times in classics, he made mathematics and chemistry his principal studies, and on more than one occasion scored full marks in mathematics in his examinations. In his last term he won the Mitchinson Prize for mathematics, the School’s premier award in that subject. On the result of examinations held in December 1892, he was awarded an Open Minor Scholarship in Mathematics at St John’s College, Cambridge, and went into residence in the Michaelmas Term, 1893, to read for the Mathematical Tripos. In June 1895, on the results of College Examinations, he was elected into a Foundation Mathematical Scholarship, and was also awarded the College Herschel Prize for Astronomy. Cook had hoped ultimately to be appointed a professor of mathematics, but while sitting for his Mathematical Tripos in 1896 he became ill, and was unable to complete his papers. He still, however, came out as Seventh Wrangler and graduated.

Factors Related to Over-Achievement and Under-Achievement in School

Previous articleNext article No AccessFactors Related to Over-Achievement and Under-Achievement in SchoolJohn J. Kurtz and Esther J. SwensonJohn J. Kurtz Search for more articles by this author and Esther J. Swenson Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by Volume 59, Number 8Nov., 1951 Article DOIhttps://doi.org/10.1086/441844 Views: 6Total views on this site Citations: 25Citations are reported from Crossref Journal History This article was published in The School Review (1893-1979), which is continued by the American Journal of Education (1979-present). Copyright 1951 The University of ChicagoPDF download Crossref reports the following articles citing this article:Satish S. Salunkhe, Yashwant Joshi, Ashok Deshpande Optimal Academic Ranking of Students in a Fuzzy Environment: A Case Study, (May 2018): 453–462.https://doi.org/10.1007/978-3-319-75408-6_35Albert Ziegler, Albert Ziegler, Heidrun Stoeger Shortcomings of the IQ-Based Construct of Underachievement, Roeper Review 34, no.22 (Apr 2012): 123–132.https://doi.org/10.1080/02783193.2012.660726Heidrun Stoeger The History of Giftedness Research, (Jan 2009): 17–38.https://doi.org/10.1007/978-1-4020-6162-2_2Robert Arthur Schultz Understanding Giftedness and Underachievement: At the Edge of Possibility, Gifted Child Quarterly 46, no.33 (Sep 2016): 193–208.https://doi.org/10.1177/001698620204600304Robert Arthur Schultz Illuminating realities: A phenomenological view from two underachieving gifted learners, Roeper Review 24, no.44 (Jun 2002): 203–212.https://doi.org/10.1080/02783190209554181Nurit Bar-Eli, Amiram Raviv Underachievers as Tutors, The Journal of Educational Research 75, no.33 (Dec 2014): 139–143.https://doi.org/10.1080/00220671.1982.10885370Charlotte E. Malone, William J. Moonan Behavioral Identification of Gifted Children, Gifted Child Quarterly 19, no.44 (Jul 2016): 301–306.https://doi.org/10.1177/001698627501900408Charles A. Asbury Selected Factors Influencing Over- and Under-Achievement in Young School-Age Children, Review of Educational Research 44, no.44 (Jun 2016): 409–428.https://doi.org/10.3102/00346543044004409Kenneth R. Mitchell, Olga E. Piatkowska Characteristics associated with underachievement: Targets for treatment, Australian Psychologist 9, no.33 (Sep 2007): 19–41.https://doi.org/10.1080/00050067408256522Charlotte Elaine Malone Early Childhood Education of Gifted Children, Gifted Child Quarterly 18, no.33 (Jul 2016): 188–190.https://doi.org/10.1177/001698627401800316Morris D. Caplin The Relationship between Self Concept and Academic Achievement, The Journal of Experimental Education 37, no.33 (Jan 2015): 13–16.https://doi.org/10.1080/00220973.1969.11011123Arthur J. O'Shea Peer Relationships and Male Academic Achievement: A Review and Suggested Clarification, The Personnel and Guidance Journal 47, no.55 (Dec 2011): 417–423.https://doi.org/10.1002/j.2164-4918.1969.tb05165.xDorothy Rubin Mother and Father Schemata of Achievers and Underachievers in Primary School Arithmetic, Psychological Reports 23, no.3_suppl3_suppl (Sep 2016): 1215–1221.https://doi.org/10.2466/pr0.1968.23.3f.1215Robert M. Jackson In Support of the Concept of Underachievement, The Personnel and Guidance Journal 47, no.11 (Dec 2011): 56–62.https://doi.org/10.1002/j.2164-4918.1968.tb02868.xRussell L. Adams, Beeman N. Phillips Factors associated with under- and over-achievement among socio-economically and racial-ethnically different elementary school children, Psychology in the Schools 5, no.22 (Feb 2006): 170–174.https://doi.org/10.1002/1520-6807(196804)5:2<170::AID-PITS2310050216>3.0.CO;2-YMark H. Thelen, Charles S. Harris Personality of College Under-Achievers Who Improve with Group Psychotherapy, The Personnel and Guidance Journal 46, no.66 (Dec 2011): 561–566.https://doi.org/10.1002/j.2164-4918.1968.tb03229.xRobert R. Weatherford, John E. Horrocks Peer Acceptance and Under- and Over-Achievement in School, The Journal of Psychology 66, no.22 (Jul 1967): 215–220.https://doi.org/10.1080/00223980.1967.10544898John J. Teigland, Ronald C. Winkler, Paul F. Munger, Gerald D. Kranzler Some Concomitants of Underachievement at the Elementary School Level, The Personnel and Guidance Journal 44, no.99 (Jan 2012): 950–955.https://doi.org/10.1002/j.2164-4918.1966.tb03618.xWILLIAM W. FARQUHAR, DAVID A. PAYNE A Classification and Comparison of Techniques Used in Selecting Under- and Over-Achievers, The Personnel and Guidance Journal 42, no.99 (Jan 2012): 874–884.https://doi.org/10.1002/j.2164-4918.1964.tb04746.xAnn G. Skillman Verbal communication between mothers and sons in learning problem families 1, Smith College Studies in Social Work 34, no.22 (Feb 1964): 140–160.https://doi.org/10.1080/00377316409517323F. N. Cox A Second Study of Academic and Social Adjustment in 4th and 5th Grade Children, Australian Journal of Education 7, no.33 (Oct 1963): 213–219.https://doi.org/10.1177/000494416300700310Merle B. Karnes, George F. McCoy, Richard Reid Zehrbach, Janet P. Wollersheim, Harvey F. Clarizio, Lela Costin, Lola S. Stanley Factors Associated with Underachievement and Overachievement of Intellectually Gifted Children, Exceptional Children 28, no.44 (Dec 1961): 167–175.https://doi.org/10.1177/001440296102800401F. N. Cox Academic and Social Adjustment in 5th Grade Boys, Australian Journal of Education 5, no.33 (Nov 1961): 185–192.https://doi.org/10.1177/000494416100500307 Thomas R. Ford Social Factors Affecting Academic Performance: Further Evidence, The School Review 65, no.44 (Oct 2015): 415–422.https://doi.org/10.1086/442410Charles A. Ullmann Chapter IV: The Socially Maladjusted, Review of Educational Research 23, no.55 (Jul 2016): 432–452.https://doi.org/10.3102/00346543023005432

Chapter Vi Arithmetic in the Junior-Senior High School

Chapter Vi Arithmetic in the Junior-Senior High School

A Selected List of References on Elementary School Arithmetic

With summer school “just around the corner” it would seem advantageous to the elementary-school teacher to have a list of selected references on arithmetic at hand in order to facilitate the study of instructional problems. With this thought in mind a list of books published since 1946, and articles published since 1947, was prepared. Some excellent articles dealing with the frontiers of educational research in arithmetic were not included because the list was compiled to serve teachers interested in suggestions for the improvement of instruction in arithmetic.

CHILDHOOD BEHAVIOR SEQUELAE OF ASPHYXIA IN INFANCY

On the basis of an analysis of the records of 673 children referred for in-patient psychiatric treatment, the majority of those having a history of pertussis in infancy, or asphyxia neonatorum, showed a characteristic behavior syndrome. The behavior syndrome consisted of the six following traits: Unpredictable variability in mood, hypermotility, impulsiveness, short attention span, fluctuant ability to recall material previously learned, and conspicuous difficulty with arithmetic in school. Each of these behavior traits occurred from once and a half to twice as frequently in patients with a history of asphyxia in infancy as in a control group. The syndrome, consisting of at least five of the six traits, occurred more than eight times as frequently in the patients with a history of asphyxia as in a control group. The syndrome occurred significantly more frequently in children with a history of pertussis when the illness occurred in the first three years of life rather than later. Since this behavior syndrome presents a serious handicap to successful social adjustment in later childhood, strenuous therapeutic efforts should be made toward eliminating asphyxia as a complication of illness in infancy.

Shorter School Arithmetic. By G. H. R. Newth. Pp. 248. 1947. 4s. 3d.; with answers, 4s. 9d. (University Tutorial Press)

Shorter School Arithmetic. By G. H. R. Newth. Pp. 248. 1947. 4s. 3d.; with answers, 4s. 9d. (University Tutorial Press)

Remedial Arithmetic in High School

Remedial Arithmetic in High School