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That considerably over half of our children in Standards V. and VI. are still unable to do a fair proportion of the questions set is discreditable both to the children and their teachers. Though the errors were sometimes due to inaccurate work (the result of careless grounding in the simple rules), the failures were too often owing to inadequate comprehension of the problem set or failure to grasp the point of the question. All of these faults were painfully apparent in Standard V., where we often found mechanical work, such as simplifying a complex fraction, clumsily set out and full of errors, whilst the problems were seldom attempted. We admit that Standard V. is a difficult stage, requiring at the outset a thorough grasp of simple fractions and of the principles which their working involves, so as to form a basis for all the operations not only of the one year but of the next, and that the questions set were somewhat difficult; but these excuses do not by any means fully account for the miserable results. We fear that too little real teaching is done, its place being frequently taken by supplying examination and test cards, and that our best teaching often degenerates into the mere explanation of rules, the teacher's mind being rarely in sympathy with the minds of the children, so that he may fully realise their difficulties and lead them by inductive reasoning from stage to stage. If they are led in this manner to obtain a grasp of the underlying principles, they will more readily see their way through problems involving those principles, and will find to their delight that arithmetic is not a bundle of rules, but, as a brother Inspector has aptly put it, " merely common-sense expressed in figures." As it is, we fear that the subject is taught almost entirely with a view to passing the examination, whilst one of the greatest benefits which a thorough arithmetical course should confer—the training of the reasoning powers—is completely ignored. Diagrams and concrete illustrations, not even excepting the ball-frame, may be used with great advantage in Standard V. Mental arithmetic is often neglected, and rarely deserves commendation. We have no doubt that all classes would gain in facility and accuracy by the oral practice of even simple exercises in addition and subtraction. Composition. —This important subject now receives more systematic treatment than was formerly the case, most of our teachers devoting a portion of their time to giving model lessons, and this with , the 'best results. It is now at last recognised that composition is an art, and does not, as Dogberry would have said, come by nature. The exercises in the amalgamation of sentences and in paraphrasing of verse were only moderately well done, but now that teachers are better acquainted with the requirements in these matters better work will be looked for. We propose to test the composition of the Fifth and Sixth Classes by asking them to reproduce in their own words the substance of a narrative read out to them by the Inspector. Paraphrasing will also be expected from the Fifth Standard, as provided by the syllabus. Geography. —During the last two years, since geography has been made a pass-subject in all the higher standards, its study has been improving. The Third Standard children usually get up their modest programme really well, but they are often weak in questions relating to their immediate surroundings. The principal features of the district should be studied first, and from the knowledge the child possesses of those that come under his own observation he will be able by comparison to form an idea of those of other parts of the world. En the Fourth, map-drawing should be more systematically taught, and the children should be trained to keep before them a mental map of the country or part of the world with which they are dealing. Places of interest along the principal trade-routes of the world are apparently learnt disjointedly by rote, for a general hotchpotch of them is often served up when a particular route is asked for. In the Fifth and Sixth most improvement is noticeable, but there also weakness was often betrayed in questions requiring a little thought, especially those in mathematical and physical geography. Grammar. —We regret that in this subject no improvement is observable. The papers submitted to us can only be characterized as a farrago of absurdities, and if nothing better than this can be achieved it would be an unmixed benefit if the subject were excised from the syllabus. If the answers to our questions are to be taken as a test of the quality of the instruction given, and if we have no other criterion, the teaching, especially in analysis and parsing, must be sadly wanting in intelligence. We have no reason to think that grammar is neglected because it has been reduced (or elevated) to the rank of a class-subject, since history and science, which hold the same position, are often admirably taught, even in schools which are in no way distinguished for their success in the matter of passes. It is therefore impossible to avoid the conclusion that the methods of teaching are at fault, the children being allowed to trust to memory and guess-work, and to regard the exercises more in the light of a Chinese puzzle than something to be understood by the application of common-sense. It is much to be regretted that this subject should be thus neglected and misunderstood, since it is, with the possible exception of arithmetic, the one which, if properly treated, is the most useful as a means of developing the reasoning powers, thus taking the place which Euclid occupies in a more advanced course. We strongly advise all teachers to read the remarks on this head in the last report of Mr. Petrie, the Chief Inspector of the Auckland District. The shortcomings noted by him are precisely those we meet with everywhere, and we heartily indorse his recommendations as to the remedy to be applied. History is now generally and successfully taught, but in the lower standards dates are sometimes learnt apart from the value and importance of the events with which they are connected, and the list of events often include unimportant and trivial occurrences which outrage one's sense of proportion, whilst their order and arrangement completely ignore the sequence of history. Science is usually as well taught as can be expected considering the difficulties under which most of the schools labour from want of apparatus. From the nature of the course selected for this year —physiology —this want was not felt so much as usual, and consequently excellent work was done in several schools. Object-lessons. — Although we called attention last year to deficiencies in this branch of instruction, object-lessons strictly so called are still rarely given, their place being taken by a few