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By Mr. C. Godfrey, Head Master of the Royal Naval
By Mr. Cecil Hawkins, late Senior Mathematical
By Miss E. R. Gwatkin, Head Mistress of the Queen
THE TEACHING OF MATHEMATICS IN LONDON PUBLIC ELEMENTARY SCHOOLS.
Ten years have passed since the Board of Education ceased to prescribe a fixed syllabus of instruction in Arithmetic for elementary schools. During these ten years each school has had freedom to devise its own scheme, conduct its own examinations, and adopt its own methods of instruction. One would therefore naturally expect to find as the years advanced a gradual divergence from the Board's syllabus as a common point of departure, so that at the present day the syllabuses of the various schools would differ widely from one another and from the original common syllabus. As a matter of fact the divergence, with a few noteworthy exceptions, has been very slight. In the bulk of the schools the Board's Scheme B (see Appendix I.), which was the better of the two prescribed courses, still forms the framework of the mathematical curriculum. It has been enlarged by the inclusion of mensuration, and slightly rearranged so as to admit of the earlier introduction of fractions, but rarely has it been drastically altered. This conservatism is partly due to the fact that the Board continued, up till 1905, to publish Scheme B as a standard of proficiency for the labour certificate, and partly to the fact that most of the available text-books for elementary schools are even to this day based upon that scheme. It required therefore a head teacher of some force of character to overcome the inertia of the older system and strike out a line of his own. Some encouragement was given to initiative and experiment by the publication of the Suggestions to Teachers in 1905, for since that date departure from the normal course has been a little more frequent.
TEACHING OF ARITHMETIC IN INFANTS' SCHOOLS.
Instruction in the rudiments of number is given in the infants' school, on the organisation of which a few explanatory words are necessary, Ön account of exigencies of accommodation children who by age and attainments would normally pass into the lowest class of the Senior Department are in the majority of the London Schools retained in the Infants' Department as Standard I. These children are as a rule seven years of age at the middle of the Educational Year. The children of six, five, and under five years of age are known respectively as Grade III, Grade II, and Grade I or babies. The Standard I. children have for many years past been expected to deal with the four simple rules (see Appendix I.). At the end of the