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are what I have most frequently to complain of in the arithmetic. For instance, in working such a sum in Standard IV. as " If 800 horses cost £11,400, what did each cost on an average?" more pupils would multiply than divide. Thus, boys in the habit of riding horses since they were able to toddle would gravely inform me that the price of a horse was several thousand pounds. Again, in Standard V. I have found whole classes puzzled at the term " £2 15/- per cent." simply because it was not written "2f ft," and interest has been made far more than principal. All this is what I call the result of " cram." If pupils were trained to write down their premisses as they proceed, the work would be more intelligent. An example may be of advantage. A Sixth-Standard pupil being required to find the cost of carpeting a room, the length and width of the floor, the breadth of the carpet, and the price per lineal yard, being given, the left-hand half of his slate would present the following: Area of floor = . . . . ; width of carpet = . . . ; .•. length of carpet = . . . . Cost of carpet per yard = . . . ; .-. total cost of carpet =.. . . The statements would of course be under each other. In such a sum fractions should be employed—not, as I almost invariably found, reduction; and no multiplication should be used till after the cancelling in the last fraction. And here I may say it appears to me a pity that fractions are not introduced earlier into the syllabus than at present. Ido not think a boy thrown on the world without any acquaintance with fractions —and many boys leave school after passing the Fourth Standard —can turn his knowledge of arithmetic to much practical account. From what I saw, both on visits of inspection and examination, I have no doubt that bad results in arithmetic are often due to the constant copying during the year. There is no subject which offers more opportunities for copying and prompting than arithmetic —for a word or glance is sufficient—and none in which it is more difficult to detect them. The only effectual way to stop these faults is to make them impossible. But many teachers take no notice of them. Prompting in spelling, deliberately done before me without any idea that it was wrong, was an every-day occurrence. Again, at one large school, where the arithmetic in Standard I. was very bad, one boy calmly left his place and went some distance away to a class-fellow. On being asked what he was doing, he replied indignantly, " I am only showing him how to do it," What a tale of bad training throughout the year this tells! And yet the headmaster of that school was surprised at the bad results in arithmetic. I found mental arithmetic in general very poor. Grammar and Composition. —ln Standards 111. and IV. the parts of speech required were generally recognised, provided only no thought was required to note the function of the word. In the latter class ability to distinguish inflections of nouns and pronouns was absent from nearly all schools. Surely pupils who write down on their papers that such words as " children," "■ horses," and "our," are singular number are incorrigibly thoughtless, and have received no educative training. In Standard V. parsing was bad, a mood outside the indicative, subjects, and objects being seldom recognised. The work was fair in Standard VI., except analysis, which in few schools showed effective treatment. Composition in Standard 111. was very weak, few pupils giving me anything sensible except when they remembered word for word a previous lesson; while the forming of a simple sentence containing a word on the card was either neglected as too difficult or misunderstood. At a few schools, indeed, complete statements and" paragraphs w Tcre made, with due attention to punctuation and capitals. In Standards IV. and V. I was glad to find a general improvement in writing letters. In Standard VI. the subjects ought to have been better handled. I again impress upon teachers the importance of beginning with the sentence in teaching English grammar and composition (vide last report). When a child can construct a sentence he feels that he is doing something. Parsing should be subservient to logical analysis. But how thoughtless rote-work may creep in even here was shown at the pupil-teachers, scholarships, and standards examinations, when candidates, after analysing sentences correctly, parsed subjects as objects, and vice versa. As has been well said, the custom of teaching the English language to children by first drilling them in the parts of speech and their functions is about as reasonable as prefacing the art of walking by a course of lessons on the bones, muscles, and nerves. At three schools where I received excellent composition I found that the subject was taught in connection with analysis. The almost universal habit of allowing pupils to jerk out disconnected words in answer to questions is ruinous to good composition. Pupils should always be required to make distinct statements. And in this connection I may say that a great deal of ignorance is due to teachers being satisfied with an approach to a correct, or partially correct, oral answer from one pupil, and failing to impress upon the whole class what is required to be made known. Geography. —ln Standard 11. I examined some excellent classes, and those taught by rote were evidently in the minority. At the best schools pupils in this standard could travel in their mind's eye over the world, noting continents, oceans, &c. The slate-work in Standard 111. was generally neater than in the previous year, and the viva voce answering was fair. In Standards IV., V., and VI. pupils were most successful in locating places, but they often failed to trace a voyage from one country to another. New Zealand geography was generally weak, and mapping in Standard V., outside of New Zealand, was invariably bad. In physical geography pupils often ignored the questions, or they failed to apply their knowledge. Political geography should wait on physical. History. —This subject was on the whole fairly known except in Standard 111., where a searching oral examination often disclosed a great lack of intelligent teaching. Lists of battles generally comprised the whole stock of the children's information ; but as to what nation these battles were between, whence the Saxons or Normans came, in what period Great Britain was first ruled by one sovereign, whether Wellington was a French or English general, and Waterloo situated in England, Belgium, or New Zealand, they were generally quite in the dark. The aim in teaching history should be, to give facts that will help the children t6 see how the nation has grown and organized itself—not mere biographies of monarchs and lists of battles. History and geography should be taught hand in hand. Education is always advanced by the gathering of suitable associations around the subject of study.