Arithmetic Exercise Research Articles

Statistical appendix

Bleasdale & Nelder (1960) refer to several models which have been used in studying the relationship of yield and density in crop plants and indicate that they regard as most satisfactory the equation:where ω = yield/plant, ρ = number of plants/unit area and A and B are constants. The estimation of the constants for any given case is a very unattractive arithmetic exercise requiring a fairly large number of observations and a tedious iterative calculation; Nelder (1961) has discussed the least squares fit with the equation in the formwhich may readily be derived from (1) by the substitutionsThe data in the present case do not justify attempting this process but some progress can be made by the substitutionsby means of which it is easy to derive from (1) that

Arithmetic Ability of Mentally Retarded Children: II. Understanding Arithmetic Processes

An investigation was undertaken to determine the truth or falsity of the assertion that mentally retarded children of a given mental age are not able to understand as well as normal children of the same mental age the processes which should be employed in the solution of simple exercises in arithmetic. A second aspect of the study endeavored to substantiate or deny the observation of teachers of the mentally retarded that, although the child may indicate that problem should be worked in a given way, he, when asked to solve the problem, proceeds along entirely different arith metical lines from that which he indicated. For example, the mentally re tarded child says that he should subtract to find the correct answer in a certain arithmetic problem, but when he is requested to actually solve the problem he has been observed to use a process other than subtraction. Subjects.?Two groups of fifteen boys each were used in the study: the first, a group of mentally retarded boys from the Wayne County Training School, Northville, Michigan, who comprised the experimental group; the second, a group of boys of normal intelligence from the Adams Elementary School, Birmingham, Michigan, who comprised the control group. The ex perimental subjects had a mean C.A. of 14.29; a mean M.A. of 10.06, and a mean I.Q. of 73-33; the control subjects, a mean C.A. of 9.09, a mean M.A. of 9.96, and a mean I.Q. of 110.4. The mean arithmetic age of the experimental group was 9.73; of the control group 9.84. The T-score between mean mental and mean arithmetic ages of the experimental group is 1.169 at a 5 per cent level of significance; for the control group 1.265 at a 30 per cent level of significance, indicating that basic differences do not exist between mental and arithmetic ages. Significant differences do not exist be tween mental ages of the experimental and control groups (T-score 1.195 at 10 per cent level of significance) or between the arithmetic ages of the two groups subjects (T-score 1.120 at 30 per cent level of significance). The 279

Exercises in Practical Business Arithmetic. By H.F. Hemstock. Pp. 96. 2s. 6d. 1944. (Harrap)

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Exercise in Practical Business Arithmetic. By H.F. Hemstock. Pp. 96. 2s. 6d. 1944. (Harrap)

Exercise in Practical Business Arithmetic. By H.F. Hemstock. Pp. 96. 2s. 6d. 1944. (Harrap)

Exercises in Arithmetic for Middle and Upper Forms. By R. Walker. Pp. 328. With answers, 3s. 6d. Without answers, 2s. 9d. 1932. (Harrap)

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Exercises in Arithmetic. By E. R. Pigrome. Parts I.-III., 1s. each, with Answers. 1926-1928. (Humphrey Milford, Oxf. Univ. Press.)

Exercises in Arithmetic. By E. R. Pigrome. Parts I.-III., 1s. each, with Answers. 1926-1928. (Humphrey Milford, Oxf. Univ. Press.)

Book Review: Teaching and Practice Exercises in Arithmetic

Book Review: Teaching and Practice Exercises in Arithmetic

Can Observation Be Trained in School Children?

General plan of the experiment.?The second experiment to be described was also carried out on the same general plan in the spring and summer of 1910. A whole class of boys (Standards VI and VII), under one teacher, was divided into two equal and parallel groups on the basis of the work done in three preliminary tests in observation. Then one group worked six practice exercises in arithmetic, whilst the other had six practice exercises in obser vation. The two groups again worked together in three final tests in observation. Some important differences, in the standard, age, and sex of the children and in the conduct of the practice exercises, will be noted as the description of the experiment proceeds. The children who did the work.?This experiment was carried out with the first class of a medium-sized boys' school, in the inner ring of the southeastern suburbs of London. The school was the one really poor school in a fairly good district and was not in a high condition pedagogically. But the first class, consisting of Stand ards VI and VII, was a good one and was taught by a very able man who had had some experience in the methods of experimental pedagogy. In considering this work in relation to that of the girls previously described, it must be remembered that it was done by children who were further advanced in their standards, were a year or more older, and was that of boys, who are not naturally so proficient as girls in observational work. But they were in structed and corrected in the course of both sets of their practice exercises, arithmetical and observational, which the girls had not been. They were shown the errors in their arithmetical and in their observational work, both collectively and individually. Another important difference, also, they were, in their tests, allowed a fixed time for the writing up of their observations, namely, forty-five minutes. They were told before every fresh test and exercise the exact marks they had scored in the previous test, the marks for arithmetic being so arranged that they were numerically of the same apparent value as those obtained in the practice tests in ob servation. First-rate work carried approximately the same marks 314

Book Review: Exercises in Business Arithmetic

Book Review: Exercises in Business Arithmetic

Effective drill exercises in arithmetic.

Effective drill exercises in arithmetic.

Book Review: Drill Exercises and Problems in Arithmetic

Book Review: Drill Exercises and Problems in Arithmetic

(1) Constructive Arithmetical Exercises. By R.W.M. Gibbs. Part I. Pp. vii+244+(Answers)44. 3s. 6d. net. 1922. Part II. Pp. 245-482 + (Answers) 45-76 + two-page logarithmic table. 3s. 6d. net. 1922. (Blackie & Son.) - (2) A General Text-book of Elementary Algebra. By E. H. E. H. Chapman. Part II. Pp. 144-256 +(Answers) xxiii-xxxviii. 7s.6d.net. 1922. (Blackie & Son.) - (3)

(1) Constructive Arithmetical Exercises. By R.W.M. Gibbs. Part I. Pp. vii+244+(Answers)44. 3s. 6d. net. 1922. Part II. Pp. 245-482 + (Answers) 45-76 + two-page logarithmic table. 3s. 6d. net. 1922. (Blackie & Son.) - (2) A General Text-book of Elementary Algebra. By E. H. E. H. Chapman. Part II. Pp. 144-256 +(Answers) xxiii-xxxviii. 7s.6d.net. 1922. (Blackie & Son.) - (3)

Pure Mathematics in a Secondary School Advanced Course

Much has been said about the danger of dividing the various branches of pure mathematics into “water-tight compartments,” and books have been written with a view to breaking down from the very beginning the barriers between the different subjects.I feel, however, that to the average boy who has not yet reached Matriculation standard, the division of Mathematics into Arithmetic, Algebra and Geometry is very real and most helpful. A straight-forward question in mensuration, the study of the identity (a+b)2=a2+2ab+b2, and the theorem that the square on a line is equal to the sum of the squares on its two segments together with twice the rectangle contained by them, for example, will and should appear as separate questions—the first being linked with other similar exercises in Arithmetic, the second depending on algebraical multiplication and being a study in form rather than in area, and the third turning on a geometrical construction. Only after each has been treated in the appropriate way should we show the pupil the cross-connections existing in the three problems.

Exercises in Arithmetic. Arranged in Two Courses. By A. E. LayngM.A. Pp. x+230 + 31. 3s. 6d.; with Answers, 4s. 1920. (Mr. Murray.)

Exercises in Arithmetic. Arranged in Two Courses. By A. E. LayngM.A. Pp. x+230 + 31. 3s. 6d.; with Answers, 4s. 1920. (Mr. Murray.)

The Results of Three Types of Drill on the Fundamentals of Arithmetic

The purpose of this paper is to report a study made of three methods of drill on the fundamental operations of arithmetic. The work was done under the direction of Miss Mary Schenk, now a member of the faculty of the University of Wyoming. All the material was obtained from the schools of Lawrence, Kansas. Three buildings for grades iv, v, and vi and the Central Building for grades vu and vin were used. The study was planned and carried out with the cooperation and under the supervision of Raymond A. Kent, Superintendent of the Lawrence Schools and Professor of Education in the University of Kansas. The teachers were in hearty sympathy with the undertaking since it had been preceded by a series of tests revealing a low achievement in the city as a whole in the fundamental operations with numbers. One series of classes, representing grades v to vni, used the Courtis Standard Practice Tests in Arithmetic; another, repre senting grades iv to vni used the Studebaker Economy Practice Exercises in Arithmetic; and a third, representing grades rv to vni used the best methods of drill which the teachers could devise, without the use of any special material. The Courtis and Stude baker exercises were used according to the directions furnished with them. The number of children of each grade who participated in each kind of drill is exhibited in Table I. Practically all teachers who used either type of practice material had had experience with it the year before. For those of whom this was not true, a demonstration of the proper use of the material was made by Miss Schenk before the trial period began. Furthermore, a statement of the achievements of each child in the fundamental operations as revealed by the Courtis Standard Research Test in Arithmetic, Series B was given to

The Jack Straw Primer. M. W. ArleighAutomatic Exercises in Arithmetic. M. W. Arleigh

Previous articleNext article FreeEducational WritingsThe Jack Straw Primer. M. W. Arleigh Automatic Exercises in Arithmetic. M. W. Arleigh PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by The Elementary School Journal Volume 20, Number 10Jun., 1920 Article DOIhttps://doi.org/10.1086/454868 Views: 71 PDF download Crossref reports no articles citing this article.

BOOK REVIEWS

Book reviewed in this article:Third‐Year Mathematics for Secondary Schools, by Ernst R. Breslich, Head of the Department of Mathematics in the University High School, The University of Chicago.Logarithmic and Trigonometric Tables.Automatic Exercises in Arithmetic, by Mrs. M. W. Arleigh, Supervisor of Arithmetic, San Francisco State Normal.How to Study, by George F. Swain, L.L.D., Gordon McKay, Professor of Civil Engineering in Harvard University and Massachusetts Institute of Technology.Plane and Solid Geometry, by Marquis J. Newell, Instructor in Mathematics, High School, Evanston, Ill., and George A. Harper, Instructor in Mathematics, High School, Kenilworth, Ill.

(1) Longman's Modern Mathematical Series Exercises in Algebra (including Trigonometry) (2) Workshop Arithmetic (3) Plane Trigonometry (4) Numerical Trigonometry (5) Longman's Modern Mathematical Series Exercises in Arithmetic and Mensuration

(1) PROF. NUNN'S three volumes form a unique treatise on the study of algebra. Beginning from the first notions in the subject he.separates the educational grain from the educational chaff, and gives us the grain. So much is found fit for discarding as chaff that the author finds space for treating trigonometry, Cartesian geometry, and the calculus, in addition to a discussion of such recent work as that on the complete number-scale.

Exercises in Arithmetic and Mensuration. By P AbbottM.A. Pp. 524 + 86. Answers. 4s. 6d. 1915. (Longmans.)

Exercises in Arithmetic and Mensuration. By P AbbottM.A. Pp. 524 + 86. Answers. 4s. 6d. 1915. (Longmans.)

Book Review: Exercises in Arithmetic

Book Review: Exercises in Arithmetic