Tests given in Minnesota. Summary: (a) Rapid performers are most accurate; (b) Slower pupils tend to become fixed in the group; (c) The brighter are retarded by the slower; (d) Best retainers are also the most rapid workers; (e) The poorer derive no advantage from being with brighter. Proposes: (1) Letting more capable carry extra work; (2) Excusing more capable from examinations; (3) Organizing classes for repeaters; (4) Giving supplementary work; (5) Letting brighter pupils finish earlier; (6) Individual help to poorer pupils; (7) Having textbooks for minimum and maximum work. 512. Thorndike, E. L. An experiment in grading problems. Mathematics Teacher, vol. 6 (March, 1914), pp. 123-134. A test of problems with directions for grading and the results obtained. 513. Relation between speed and accuracy in addition. See No. 171. 514. Watson, E. E. The college freshman and mathematics. Journal of Educational Psychology, vol. 7 (1916), pp. 223226; pp. 607-609. Describes an attempt to test the mathematical efficiency of college freshmen at Parsons College, Fairfield, Iowa, in 1914, and as far as possible to test their growth during two years. The uniformity of the average record of the different sections was striking. Two sections, of thirty students each, selected at random, showed practically the same ability on series A and B Courtis standard tests. Different texts were studied by each section, and results compared at the end of the year. 515. Werremeyer, D. W. Reliability of grades of testpapers in mathematics. School Science and Mathematics, vol. 14 (1914), pp. 422-429. A report of an investigation in which six teachers graded test papers in geometry, algebra and arithmetic. The tests show that teachers differ greatly as to the value that is placed upon geometry, algebra and arithmetic papers and that they do not place the same value upon the same paper twice. Describes conditions necessary to improvement. 516. Young, J. W. A. Concerning psychological tests in the army and their meaning for the teacher. School Science and Mathematics, vol. 19 (1919), pp. 544-548. Shows that familiarity with the most elementary notations of the mathematical subjects in elementary and high school increases the probability of high rating in general intelligence. XVIII. Disciplinary Values. Psychology 517. Asker, William. Mathematics and efficieny in secondary school work (a reply). School Science and Mathematics, vol. 17 (1917), pp. 147-150. A reply to Professor Moritz' article, vol. 16, p. 233; see No. 32. 518. Davis, Alfred and committee of the Chicago Mathematics Club. The status of mathematics in secondary schools. School and Society, vol. 6 (Nov. 17, 1919), pp. 576-582. Consists of answers to a questionnaire as to the value of mathematics and the deductions therefrom as follows. Value lies in (1) Utility— increasing use of graphs, formula, etc. (2) Culture. (3) Makes one face facts, attack problems, carry on to end. (4) Mental training,— develops reasoning; analytic, logical and abstract thinking; concentration; speed; accuracy. All of these are invaluable in directing modern business which is becoming very complex. 519. Grove, C. C. A note on formal discipline and mathematics. Journal of Education, vol. 84 (Nov. 9, 1916), p. 459. A plea for the existence of "transfer" in the habits of mind which the study of mathematics develops. 520. Harvey, N. A. The doctrine of formal discipline. School Science and Mathematics, vol. 18 (June, 1918), pp. 536-538. An answer to some of the statements made by Professor Young in his article in the January and February numbers of School Science and Mathematics 1918 "concerning experiments to test the transfer of training". 521. Kruse, P. J. A strategic retreat. School and Society, vol. 7 (May 4, 1918), pp. 531-532. A discussion of Professor Moritz' paper "Mathematics as a test of mental efficiency" (School and Society, vol. 7). 522. Mathematics and Psychology. Mathematics Teacher, vol. 8 (June, 1916), pp. 182; vol. 8 (Sept., 1916), pp. 3-10; vol. 9 (Dec., 1916), pp. 103-124. Indicates an attitude towards attacks upon disciplinary value of mathematics, and the proper reaction of teachers of mathematics to those attacks. Deals with "mental measurement", and criticizes the use made of statistics and statistical theory by psychologists. 523. Moore, C. N. Disciplinary values. Educational Review, vol. 54 (Oct., 1917), pp. 245-255. The paper undertakes to show the fallacies in the arguments raised against formal discipline and the errors in the psychological experiments 524. 525. 526. 527. and the results deduced therefrom. It then shows that mathematics is a subject "par excellence" for furnishing a training in logical reasoning and logical organization. Mathematics in secondary schools. School and Society, vol. 7 (Jan. 12, 1918), pp. 54-55. Upholds the methods of investigation and conclusions drawn by the Committee of the Chicago Mathematics Club and attacks the psychology, pedagogy and scientific spirit of certain educational theorists as shown by Dr. Snedden in School and Society, vol. 6, p. 651. On correlation and disciplinary values. School and Society, vol. 2 (Sept. 11, 1915), pp. 378-385. Considers the significance of the literature on correlation between abilities in different school subjects. Final conclusions are not yet justified, but that such work as has been done furnishes considerable support for the contentions in favor of disciplinary values. On the disciplinary and applied values of mathematical study. Education, vol. 39 (Dec., 1918), pp. 209-216. Gives results of a careful examination of the literature of the controversy on formal discipline. Takes a position advocating the high value of the study of mathematics as training in deductive reasoning, and in inculcating scientific ideals and respect for truth. The disciplinary value of the study of mathematics. School and Society, vol. 7 (March 9, 1918), pp. 290-294. Replies to the arguments advanced in certain preceding papers. 528. Moore, E. C. Does the study of mathematics train the mind specifically or universally? School and Society, vol. 6 (Oct., 27, 1917), pp. 481-491. 529. Argues that universal training is negligible in amount and that "we must build upon the solid rock of specific education". Does the study of mathematics train the mind specifically or universally? (Sept., 1917). pp. 1-18. Education is a conscious process and a purposive undertaking. Three reasons verify the need of study; namely, (1) because we reverence certain subjects; (2) because we can not get along without them; (3) to perfect or improve the mind. 530. 531. Does the the study of mathematics train the mind specifically or universally? A reply to a reply. School and Society, vol. 7 (June 29, 1918), pp. 754-764. An extended refutation of an article by R. E. Moritz (School and Society, vol. 6, p. 481). Mathematics and formal discipline-again. School and Society, vol. 7 (Feb. 2, 1918), pp. 137-140. Discusses certain preceding papers and letters. Concludes: "the contention that particular studies have special and greatly to be preferred formal disciplinary effects has not been proven". 532. Moritz, R. E. Does the study of mathematics train the mind specifically or universally? A reply. 533. 534. vol. 7 (April 27, 1918), pp. 485-492. School and Society, A refutation of the arguments made by E. C. Moore in an article with the same title (School and Society, vol. 6, p. 481). Mathematics as a test of mental efficiency. School and Society, vol. 7 (Jan. 12, 1918), pp. 59-60. The opinions of certain psychologists and critics in regard to specific discipline, mental transfer and intrinsic value of mathematics to the contrary notwithstanding, facts prove: (1) "Efficiency in mathematics is a concomitant of strong intellects; conversely inability to master mathematics is indicative of low general mentality", (2) "No other study takes the place of mathematics since it has to do with time, space, matter and motion which are the ultimate terms in our three-dimensional world". The disciplinary value of mathematics. and Society, vol. 7 (June 22, 1918), pp. 739-740. School A letter in reply to P. J. Krause article "A strategic retreat". Maintains his position and claims that casual relation and concomitancy are not only compatible but that the former concept implies the latter. 535. Rogers, Agnes L. Established results of the new psychology as it bears upon the teaching of mathematics. Mathematics Teacher, vol. 9 (Dec., 1916), pp. 85-93. The new psychology is based upon experiment and measurement; the old phychology was based upon introspection and observation. Little has been done in algebra and geometry except by Thorndike, Monroe, and Rugg. Outcome to date: (1) High correlation exists between efficiency in mathematics and efficiency in other subjects. (2) There is transfer the amount varies with the degree of difference between the functions in question. (3) Suggestions for transfer: proper attitudes obtained first, focus attention upon the art of learning and upon the methods of procedure; direct attention upon related ideas; keep attention at high level. 536. The bearing of the new psychology upon the teaching of mathematics. Teachers College Record, vol. 17 (Sept., 1916), pp. 344-352. A discussion of the experimental work that has been done in recent years to determine the relation of mathematics ability to other ability and to determine the amount of transfer of learning, concluding with the four general factors that the author found in such transfer. These are attitudes, ideals, concepts of method, and a high level of attention. 537. Snedden, David. Mathematics in secondary schools. School and Society, vol. 6 (Dec. 1, 1917), pp. 651-652. Criticism of a preceding paper. What say the "life failures" who studied the same mathematics. 538. Starch, Daniel. Transfer of training in arithmetical operation. Journal of Educational Psychology, vol. 2 (1911), pp. 306-310. Eight observers practiced for fourteen days on mental multiplication. Before and after the practice they were given six tests in arithmetical operations, and two in auditory memory span. For comparison, seven other observers were given the preliminary and final tests without the practice series. The practiced observers showed from twenty to forty percent more improvement in the arithmetical tests than the unpracticed observers. There was little change in memory span for either group. 539. Young, J. W. A. Concerning experiments to test the transfer of training. School Science and Mathematics, vol. 18 (Jan. and Feb., 1918), pp. 1-19; 130-138. In the first paper is presented a brief sketch of the experiments listed in Rugg's Monograph (The experimental determination of mental disci-pline in school studies; Warwick and York, Baltimore, Maryland, 1916). The second paper is given up to the author's own theories on the disciplinary value of studies, especially of mathematics. XIX. Historical Material 540. Ball, W. W. R. A school course in mathematics in the seventeenth century. Mathematical Gazette, vol. 5, Part I (Feb., 1910), No. 84, p. 202. Discusses mathematical teaching at Christ's Hospital, London, in the seventeenth century. Used a book which contained sections on arithmetic, algebra, practical geometry, together with the substance of Euclid's Elements I-VI, XI, XII, plane and spherical trigonometry, cosmography, navigation, the sphere, astronomical and logical tables and geography. |