SPECIAL REPORTS EDUCATIONAL SUBJECTS. VOLUME 26. THE TEACHING OF MATHEMATICS IN THE UNITED KINGDOM. PART I. Being a series of Papers prepared for the INTERNATIONAL COMMISSION ON THE TEACHING OF bont penre Dieu et mon-drotr LONDON: PUBLISHED BY HIS MAJESTY'S STATIONERY OFFICE. To be purchased, either directly or through any Bookseller, from PRINTED BY EYRE AND SPOTTISWOODE, LTD., EAST HARDING STREET, E.C., PRINTERS TO THE KING'S MOST EXCELLENT MAJESTY. 1912. Price Three Shillings. PREFATORY NOTE TO VOLUME 26 OF SPECIAL REPORTS ON EDUCATIONAL SUBJECTS. The present volume is the result of the action taken by the International Congress of Mathematicians at their meeting in Rome in 1908, when, at the proposal of Dr. David Eugene Smith, Professor of Mathematics in Columbia University, New York, it was resolved to appoint an International Commission on the Teaching of Mathematics. This Commission was entrusted with the task of securing a series of Reports on the state and progress of mathematical instruction in various countries of the world. There were certain difficulties in arranging for the collection of reports in this country, and the Board of Education were approached and asked to give assistance in the matter. The Board were glad to avail themselves of the opportunity which thus presented itself of adding to their series of Special Reports on Educational Subjects a collection of papers dealing with mathematical teaching in this country. In order to assist the Office of Special Inquiries and Reports in the collection of suitable material, the President appointed an Advisory Committee consisting of : Mr. C. E. Ashford. Sir George H. Darwin, K.C.B., F.R.S. Mr. C. Godfrey, M.V.O. Sir George Greenhill, F.R.S. Mr. G. H. Hardy, F.R.S. Professor E. W. Hobson, F.R.S. Sir Joseph Larmor, F.R.S. Professor A. E. H. Love, F.R.S. This Committee acted at the same time as the British SubCommission of the International Commission on the Teaching of Mathematics. The Reports which have been secured through their assistance are therefore intended to serve a double purpose; on the one hand they enrich the series of Special Reports, while on the other they serve as the Report of the British Sub-Commission, which will be submitted to the International Congress of Mathematicians meeting in Cambridge this year. The Board desire to take this opportunity of expressing their cordial thanks to the members of the Committee for the assistance they have rendered, and to the various authors who have contributed papers to this and the accompanying volume. In particular they wish to express their acknowledgment of the A (11)13913 Wt 12931-131 2000 8/12 E&S a 2 invaluable service which has been rendered by Mr. C. S. Jackson, Secretary to the British Sub-Commission, on whom has fallen the main work in connexion with the collection and revision of the papers included in this and the accompanying volume. Mr. Jackson has placed his time and knowledge most freely at the disposal of the Board. The Board's thanks are also due to the authorities of those Colleges at Oxford and Cambridge who have courteously given permission for the reprinting of their Scholarship Examination papers. The Board are also indebted to the Delegates of Local Examinations, University of Oxford; the University of Cambridge Local Examinations and Lectures Syndicate; the Oxford and Cambridge Schools Examination Board; the Senate of the University of London; the Joint Matriculation Board of the Universities of Manchester, Liverpool, Leeds, and Sheffield; the Delegates of the Clarendon Press, Oxford, and the Syndics of the Cambridge University Press, for a similar service. It may be said that the immediate cause which led to the formation of the International Commission was a divergence between mathematical and pedagogic requirements in the schools and Universities. This divergence is well illustrated by the papers which appear in the present volumes. It is hoped that their publication may contribute towards the diminution of this divergence, a task in which all who are interested in mathematical instruction are eager to co-operate. Though the papers are published by the Board on the recommendation of the Committee, it must be clearly understood that neither the Committee nor the Board accept any responsibility for the statements and opinions contained in them. Office of Special Inquiries and Reports, August 1912. CONTENTS. By Mr. P. Ballard, District Inspector of Schools under the London County Council. By Miss Irene Stephens, Lecturer in Mathematics at By Miss Helen Bartram, Head Mistress of the By Mr. W. C. Fletcher, Chief Inspector of Secondary By Mr. E. Kitchener, Head Master of the Golden Course in Mathematics for Municipal Secondary Schools 119 By Mr. George A. Gibson, Professor of Mathematics in the University of Glasgow. By Mr. J. W. Mercer, Head of the Mathematical Department of the Royal Naval College, Dart- mouth, with a Preface by Mr. C. E. Ashford, The Teaching of Arithmetic in Secondary Schools |