The conflict of studies, and other essays on subjects connected with education

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Macmilla and Company, 1873 - 242 pages
 

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Page 66 - Admission to its sanctuary, and to the privileges and feelings of a votary, is only to be gained by one means, — sound and sufficient knowledge of mathematics, the great instrument of all exact inquiry, without which no man can ever make such advances in this or any olher of the higher departments of science as can entitle him to form an independent opinion on any subject of discussion within their range.
Page 168 - ... study, even by men of feeble ability, were most decided. In comparing the performance in Euclid with that in Arithmetic and Algebra there could be no doubt that the Euclid had made the deepest and most beneficial impression : in fact it might be asserted that this constituted by far the most valuable part of the whole training to which such persons were subjected. Even the modes of expression in Euclid, which have been theoretically condemned as long and wearisome, seemed to be in practice well...
Page 17 - It may be said that a boy takes more interest in the matter by seeing for himself, or by performing for himself, that is by working the handle of the air-pump: this we admit, while we continue to doubt the educational value of the transaction. The boy would also probably take much more interest in foot-ball than in Latin grammar; but the measure of his interest is not identical with that of the importance of the subjects.
Page 224 - ... there shall be introduced examples and questions, by way of illustration or explanation, arising directly out of the Propositions themselves ; but this rule shall not be understood to sanction the introduction of problems into parts of the Examination which are not exclusively devoted thereto.
Page 160 - ... for original research. It is naturally humiliating to an American when a foreign mathematician like Todhunter, well known for the fairness and candor of his views, pronounces a judgment on Americans like the following: "I have no wish to depreciate their labors ; I know that they possess able mathematicians, and that in the department of astronomy they have produced meritorious works ; but I maintain that as against us their utmost distinction almost vanishes.
Page 238 - There appear to be three distinct functions which are recognized as pertaining to the university : one is that of examination, one that of teaching, one that of fostering original research. The first of these three has practically been as yet most regarded ; and many of us hope that it will in future decline either absolutely or relatively by the increased development of the other two.
Page 11 - Another great and special excellence of mathematics is that it demands earnest voluntary exertion. It is simply impossible for a person to become a good mathematician by the happy accident of having been sent to a good school; this may give him a preparation and a start, but by his own continued efforts alone can he reach an eminent position. The rough processes by which prizes are awarded to the possessors of knowledge regard only the results offered for inspection, and overlook the finer gradations...
Page 177 - Cyclodes." accepted as aids to geometry — the mind of the student quickened and elevated and his faith awakened by early initiation into the ruling ideas of polarity, continuity, infinity, and familiarization with the doctrine of the...
Page 17 - It may be said that the fact makes a stronger impression on the boy through the medium of his sight, that he believes it the more confidently. I say that this ought not to be the case. If he does not believe the statements of his tutor— probably a clergyman of mature knowledge, recognized ability, and blameless character— his suspicion is irrational, and manifests a want of the power of appreciating evidence, a want fatal to his success in that branch of science which he is supposed to be cultivating.

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