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Many teachers complain that the work of teaching a foreign language is greatly hampered by the lack, of knowledge of the English language which their pupils have at the time of entering a secondary school. This defect is much more serious in Latin than in French, where the inflexions present difficulty from the beginning, but it is evident that a knowledge of the main functions of words and the elements of analysis of sentences would be of considerable benefit to pupils who are endeavouring to learn a foreign language. In some schools too many pupils begin the study of two foreign languages, French and Latin, at the time of their entry on secondary work. The attempt to learn the elements of two languages in addition to the systematic study of the mother-tongue imposes a heavier burden than many pupils are able to bear. It would be much better if only one foreign language were taught in the first year, except in the case of scholarship-holders, who presumably are the cleverest pupils. This would enable the head teacher to decide who were of undoubted linguistic ability, and consequently might begin the study of a second foreign language after the end of the year with a reasonable prospect of success. Mathematics, including arithmetic, reaches a high state of efficiency in some schools, especially where the value of the concrete is recognized in the initial stages. In some instances, however, the study is purely of an abstract character and out of relation to the world of facts. Too much of the pupils' time is taken up in purely mechanical operations in long multiplication, division, &c. If this work w T ere confined to modest dimensions, and problems of a practical character were given, more interest would be aroused and greater progress secured. In geometry the pupils are sometimes taught the strict geometrical proofs without a suitable preparatory course of practical work being gone through. Numerous simple aids should be used to shed light on the abstract side of this subject. In some scho-ols field-work is done with great benefit. The practical work should bo regarded as a suitable introduction to the abstract point of view—Euclid's proofs. " The average boy or girl does not derive benefit from the so-called proofs of these early propositions ; he gets a better hold of the propositions themselves if they are treated more freely as matters of observation and intuition, and he makes a better start with deduction if he begins this process with the application of these propositions to obtain fresh results than if he begins by applying it to prove results which he already accepts. Some seem to think that there is something loose or unsound or dangerous to a boy's intellectual health in letting him thus assume statements which it has been customary to ' prove.' This idea rests on a misunderstanding of the proposals put forward or of the nature of a geometrical system " —memorandum by the English. Board of Education, on the teaching of geometry in secondary schools. This is equally true of arithmetic where a considerable amount of time is spent in working out purely mechanical examples which are of no practical value whatever. The only justification for their retention is the training in accuracy which they afford; but this could be secured without such tedious processes. More might be made of approximations, although in some schools this aspect of arithmetic receives considerable attention. Many of the examples in arithmetic text-books are not sufficiently related to the pupils' experience. If the examples chosen appealed directly to the children's groups of ideas the answers would be viewed as reasonable or otherwise by th: m, and if considered unreasonable the method of solution would be immediately scrutinized with a view to using a fresh method. In a number of cases where pupils were finding discount or present worth they had the haziest ideas of the meaning of a bill of exchange or promissory note. The leading features ought to be explained and a bill of exchange shown them. Formula? are still employed in the solution of problems. One of the chief reasons for teaching mathematics is the value of such studies as a training in consecutive thinking ; if formulae are used this object is defeated. .* In no subject has such thorough change been introduced into the methods of teaching as in the teaching of science, and few schools attempt to deal with any branch of science unless facilities are afforded for individual laboratory practice. But important as the science laboratory is as an adjunct to the teaching, it is in the attitude to the phenomena considered that the greatest change has come. In the best schools tho pupils are investigators, endeavouring to find out by interrogating nature what her secrets really are. Material is dealt with in some definite fashion under the skilled direction of tho teacher, the results are carefully noticed and set down, and inferences are drawn. The results obtained may be unsatisfactory, and the inferences may be crude, but they represent the pupils' own investigations, and so the method is sound. It is the method of inquiry—facts are brought under strict scrutiny, and conclusions are drawn from observation and experiment. The main aim is to cultivate a spirit of inquiry—" the endeavour is made to inculcate the habits of observing accurately, of experimenting exactly, of observing and experimenting with a clearly defined and logical purpose, and of logical reasoning from observation and the results of experimental inquiry." In this connection the following statement by Huxley has a direct bearing on tho subject : " Not only are men trained in mere book-work, ignorant of what observation means, but the habit of learning from books alone begets a disgust of observation. The book-learned student will rather trust to what he sees in a book than to the witness of his own eyes." It is the method of science that is of paramount importance, not the mere acquisition of facts. In most schools this is clearly recognized, as an. inspection of the procedure adopted by the teacher and of the pupils' notebooks would abundantly testify. Two different methods are followed in making notes—for in the best laboratories the notes are made by the pupils, not dictated by the science master —cither they are made in the laboratory in a permanent form, or a rough copy is made at the time and entered up by the pupil at home. In a few cases the notes had not been revised by the teacher. Systematic revision makes fairly large demands on the teacher's spare time, but when the pupils know that their books are regularly scrutinized it acts as a wholesome influence in eliminating careless work. There were isolated instances or too much reliance on the text-books. The pupils verified the statements set out therein and did not attempt to make an inquiry on their own account. It is obvious that this is contrary to the method of science, which is in essence the faculty of observing and of reasoning from observation and experiment. "Be