5S4 



NATURE 



[December 30, 1920 



to jjo by the board, and the admission of a subject 

 to the curriculum must be based upon its value in 

 relation to the conditions of social welfare. Not only 

 mathematics, but all subjects, are to be reviewed and 

 revalued. The psychologist has come upon the scene. 

 The uncritical belief of the past in " mental discipline " 

 is challenged. The general recognition of individual 

 differences and the growing practice of differentiation 

 and adaptation afford additional reasons for a close 

 examination of the usual courses, and side by side 

 with this problem is that of the courses best adapted 

 for average mortals and for those who will proceed 

 to an advanced stage of study. 



As for the method of presentation, the report em- 

 phaticallv condemns the old divorce from reality. 

 The ideas and the interests of the pupils must be 

 utilised as the environment in which the mathe- 

 matical conception is to find its natural setting-. The 

 existence of the conception within the milieu provides 

 the necessary stimulus for its utilisation. The ideas 

 and interests of the pupil provide it with projects 

 and problems to which it desires solutions. _ The 

 instruments for this purpose are to be found in the 

 concepts. The "instrumentally selected content" 

 must be free of all that will destroy potential interest, 

 and will make an end of the watertight compart- 

 ments into which our subject has so long been 

 divided. With this instrumental basis pf selection 

 and procedure it is possible for all to begin together. 

 But the future specialist will already, as he proceeds, 

 be more attracted than the average student by the 

 mathematical relationships, and find pabulum for 

 thought in the mathematical instrument itself and 

 in the assumptions which in the earlier stages he has 

 taken for granted as natural. The place for the fully 

 developed logical system is not here as yet, nor will 

 it be found in the Work of the future engineer, who 

 will be content with the mathematics which is 

 required in the projects and problems of a preliminary 

 engineering course. 



Definition is likewise required of the demarcation 

 between the practical and the cultural or "inter- 

 pretative " use of mathematics, and here must also 

 be defined the groups which require enough to meet 

 their social demands and individual aptitudes. 

 These groups must necessarily overlap. The content 

 of the course in all cases must be decided by a pre- 

 liminary studv of the irreducible minimum, and that 

 is obtained bv the rigid exclusion of all material of 

 which the specific value for the definite purpose can- 

 not be fullv shown. The proposals do not differ in 

 anv very marked degree from the conclusions of, say, 

 the Committee of the Mathematical .\ssociation, which 

 some years ago drew up a tentative course for 

 average students and for future specialists. There 

 is in this bulletin much that is worth quoting. Condi- 

 tions of space limit us to the following passage, 

 which, though it contains nothing new, is neverthe- 

 less very true, and its teaching cannot be too strongly 

 impressed upon the minds of teachers, especially upon 

 those of the young and enthusiastic. 



" Teachers . . . onlv too frequently deceive them- 

 selves as to the place that the presentation of a 

 rigorously logical proof plays in bringing conviction. 

 The worth of a sense of logical cogency can hardly 

 be overestimated ; but we who teach not infrequently 

 overreach ourselves in our zeal for it. The teacher of 

 introductorv mathematics can well take lessons from 

 the laboratory, where careful measurement repeated 

 under many different conditions will bring a convic- 

 tion often otherwise unknown to the puoil who is not 

 sifted in abstract thinking. Probably in most 

 instances an inductivelv reached conviction is the be<;t 



NO. 2670, VOL. 106] 



provocative of an appetite for a yet more thorough- 

 going proof." 



There is one further point that should be noticed : 

 the resentment on the part of American secondary 

 schools at the attempts of the colleges to dictate the 

 contents of their courses. Any restriction placed upon 

 the free play of discussion and experiment is strongly 

 deprecated. 



University and Educational Intelligence. 



London. — .\ lecture on "Some Considerations on 

 Tonus and Reflexes " will be given at the Royal 

 .Society of Medicine (i Wimpole Street, W.i) by Prof. 

 J. K. A. Wertheim Salomonson, professor of neuro- 

 logy in the University of .\msterdam, at 5 p.m. on 

 Monday, January 17. This lecture has been arranged 

 under a scheme for the exchange of lecturers in medi- 

 cine between England and Holland. Five other Dutch 

 lecturers will also give one lecture each, particulars 

 of which will be announced later. A course of eight 

 lectures on "The Physiology of the Embryo, Foetus, 

 and Newly-born " will be given by Prof. M. S. 

 Pembrey in the Physiological Theatre, Guy's Hos- 

 pital, at 4.30 p.m. on Thursdays, January 13, 20. and 

 27, February 3, 10, 17, and 24, and March 3. .Admis- 

 sion to these lectures is free, without ticket. 



Sir r^EON.ARD Rogers has been appointed Stuart 

 Mill lecturer in tropical medicine at the London 

 (Royal Free Hospital) School of Medicine for Women, 

 and Miss Dorotfiy Maughan lecturer in pharmacy. 



In connection with Somerville College, Oxford, a 

 Mary Somerville research fellowship of the value of 

 250J. for three years will be offered in March next. 

 Particulars may be obtained from Miss M. F. Moor, 

 Old Headington, Oxford. 



Api'LICVtions are invited by the Senate of the I'ni- 

 versitv of London for the Graham scholarship in 

 pathologv, value 400/. per annum for two years, and 

 tenable at University College Hospital, Gower Street, 

 W.C.I. Particulars are obtainable personally from 

 the professor of pathology at the college. .Applica- 

 tions for the scholarship must be sent to reach the 

 Principal Officer, University of London, South Ken- 

 sington, S.W.7, by the first post of Monday, January 

 17, 1921, marked "Graham Scholarship." 



On December 20 Mr. J. H. Gardiner, representing 

 Messrs. James Powell and Sons (Whitefriars), Ltd., 

 in company with Mr. P. Annett, divisional organising 

 officer for the Middlesex Education Committee, made 

 a visit to Greenhill, Drill Hall, and Harrow Weald 

 Council Schools, and addressed the boys who, having 

 reached the age of fourteen, were upon the point of 

 leaving school. The object was to interest the boys 

 in the glass industry and to suggest to them the 

 possibilities of good employment in the glassworks 

 that are now being erected at Wealdstone. The boys, 

 having been told the character of the work and the 

 prospects that it holds out to them to learn one of the 

 most important trades in the country, were invited 

 to attend a series of evening continuation classes 

 during the coming term, when a syllabus has been 

 arranged to give them a thorough grounding in Eng- 

 lish, (arithmetic, the metric system, physical mani- 

 pulation (woodwork, etc.), freehand drawing, and 

 elementarv chemistrv and phvsics. .After attending 

 the classes a selection will be made of the most 

 promising boys, who will then pass through a special 

 course of technical lectures in glass, its chemistry 

 and prooerties. .After this they will be drafted into 

 the works, where a special laboratory is being fitted 



