E.—lB

10

finished off. In the upper classes there was a falling-off in the quality of the freehand drawing. Geometrical drawing was generally fair, and scale-drawing was very fair. In the lower classes the teacher should draw on the blackboard the figure which is to be copied by the pupils, and should show how it is built up, which lines are drawn first and how they are drawn, and so on. After the copies have been drawn lightly they should be passed by the teacher before being lined in. In Standard IV. the geometrical drawing, and in Standard Y. the earlier lessons in scale-drawing, should be taught in the same way. Model-drawing and solid geometry in Standard VI. require a free use of the blackboards. By means of the guiding sketches shown in the books the pupils in Standards IV., V., and VI. should be able to undertake much of the freehand with very little assistance from the teacher. Arithmetic. —Except for Standard I. and Standard 11., the test-cards in arithmetic are now issued by the Education Department, and therefore, as far as possible, the examinations in arithmetic are uniform throughout the colony. In Standard I. the work was generally good, but in Standard 11. there was much inferior work. In many cases failure arose from a want of thoroughness in the instruction, numeration and notation in particular being poorly prepared. Problems were very indifferently done. In Standard 111. the work was fair, but the marks were not so high as I should like to have seen them, for in this subject it is not sufficient that pupils should merely "scrape" through; they should have such a knowledge as will enable them to cope easily with the work of Standard IV., which is relatively much harder than that of Standard 111. In Standard IV., Standard V., and Standard VI., the work was fairly accurate. Some of the teachers adopt " rule-of-thumb " or cram methods in teaching the arithmetic of Standard V. and Standard VI. This is especially the case with interest and its modifications in Standard V., where formulas and arbitrary methods are generally used, with the result that the pupils are quite at a loss when the wording of a question varies in the slightest from what they have been accustomed to. Arithmetic retains its prominent position in the curriculum chiefly on account of its value as a means of mental training, but by such devices as the above its value is nullified. In introducing new rules teachers are often at fault in taking their pupils at once into the more difficult problems of the rule, or in taking only such introductory oral work as is to be found in the small text-books in use. New processes should always be preceded by sufficient oral instruction and simple graduated examples to give the pupils a good apprehension of what is required by the new exercise. For this the "oral work" in the books is insufficient, serving to show only the lines that should be followed in the introductory lessons. By taking small and manageable numbers, by varying the exercises on them, and by leading the pupils to recognise the underlying principle in all the different forms of the question, the teacher prepares his pupils for dealing with numbers of greater magnitude. Again, pupils will frequently say they cannot do a certain sum which may involve working with numbers up to hundreds of thousands or millions. The teacher works the sum on the blackboard and expects his pupils to remember how to work other sums of the same kind. He shows how that sum has to be worked, but it does not follow that he shows how similar sums have to be worked. "Take an easy example," is the maxim in such cases, and lead the pupils to see for themselves how the larger and more complex operations are to be performed. Moreover, pupils should be trained when puzzled to substitute easy numbers in a question. In such a sum as this : " What number must 8,963 be multiplied by to produce 5,869,763 ? " if a pupil says to himself, " What number must 3 be multiplied by to produce 18 ? " he knows that the answer is 6, and to get 6 from 18 and 3 he must divide, consequently the problem has to be worked by division. In time he comes to recognise this particular kind of sum, and is able to proceed at once without any substitution. In profit and loss sums this method of substitution is particularly efficacious. I should like to impress upon teachers the necessity for a thorough preparation of the addition, multiplication, and division tables, as very many errors occurred through these being imperfectly taught in the preparatory and lower classes. Pupils in Standard I. are not required to multiply by numbers exceeding 5, and consequently the tables beyond " 5 times " are not generally taught; but a teacher who displays foresight will require his P3 to know the tables to " 5 times "at least. In Standard I. the whole of the tables should be thoroughly committed to memory. In fact, P3, Standard 1., and Standard 11. should be well beyond their own requirements in arithmetic when they come up for examination. Mental arithmetic is weak in many of the schools, and is not sufficiently used in the ordinary class arithmetic, the pupils performing laboriously on the slate simple operations which should be mentally performed. Mental arithmetic might be more used for recapitulating principles already taught, short examples being given. Some of the papers received by me at the examinations contained very neat work, all the steps being carefully explained in a way that showed that the pupils had thoroughly grasped the principles involved. In these cases I always made considerable allowance for any error that was obviously merely mechanical, and such not infrequently made all the difference between passing and failing. I should, however, like to see the ordinary work on the slates set out more neatly, especially in the lower classes. Composition. —After leaving school few pupils have occasion to remember the capital of Turkestan, to find the present worth of a bill, or to remember the date of the Magna Charta, but all have to give expression to their thoughts and ideas, and all, in a greater or less degree, must put their thoughts on paper. If, then, for the practical purposes of life any one subject should receive great attention, it is composition; but here I do not limit the application of the term to the mere writing of essays and letters, but use it as embracing any part of any subject where the synthesis of sentences is needed. Composition should therefore be taught as early as possible, and this is where the majority of teachers fall into error. They presume—or the methods they adopt take it for granted—that the pupils know the English language, whereas their vocabulary is extremely