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paring the values—by changing the fractions into equivalent ones having the same numerator. The expression " reducing fractions to a common denominator "is one better dropped. Pupils will understand the addition and subtraction of fractions much more clearly if they are taught that they must " change the given fractions to others of equal value, but having the same denominator," before these operations can be carried out. Mr. Grierson remarks that " mental arithmetic is seldom presented in a brisk and attractive manner calculated to excite interest and emulation." He also regrets " the neglect in Standards I. and 11. (and even Standard III.) of rapid mental addition and similar mechanical calculations, the foundation for which has been so laboriously laid in the preparatory class." The other Inspectors do not advert to this special defect, and Ido not think it is of very general occurrence. Practice in the kind of drill Mr. Grierson has in view can be readily given by means of Nelson's " Mental Arithmetic Drill Charts," which are now supplied to all schools on requisition. Both Mr. Crowe and Mr. Purdie note improvement in the teaching of mental arithmetic, and I have often found it good. The time devoted by pupils to arithmetic is almost nowhere less than five hours a week. For a long time I have felt that more than one-fifth of the whole school-time should not be required for a sound training in this subject. The geography of Standard VI. has been better taught this year than in any previous one. Physical geography, from its inherent difficulty, is still considerably inferior to political, more particularly in the smaller schools. In the other standards geography is a class-subject, and the instruction, though narrow and book-bound, has been on the whole satisfactory. It would greatly benefit by a wider and fuller knowledge of the subject among teachers. A good few seem to know little more than is contained in the text-books prepared for the use of the pupils in the schools. In many schools Standards IV., V., and VI. are grouped together in this subject. The plan of teaching Standard VI. by itself and grouping Standards IV. and V. is much more to be commended. The year has seen no general improvement in the teaching of grammar. The work of Standards 111. and IV. is still distinctly better than that of the higher classes. In Standard IV. the inflections of the noun, pronoun, and adjective are seldom thoroughly known. In the higher standards of all the larger schools from a third to a half of the pupils show a satisfactory knowledge of what has been taught, but many of the others cannot so much as tell the parts of speech with any correctness. Even in small schools the proficiency of pupils in the same class is very unequal. I think the exhibition of a simple " parsing table " on the wall before the pupils in Standards V. and VI. would be an important aid to the quick and thorough working-up of parsing, now such a bugbear. In the smaller schools classes might with advantage be more frequently grouped for lessons in grammar, for some in the lower classes would always be equal to dealing with the work taken up for the first time in the upper. The indifference of so many pupils to this subject, and the like indifference about pen-holding in writing, form the most serious blots on the discipline of our schools. The teaching of history on the lines laid down in the syllabus is generally satisfactory. On the whole, steady improvement is taking place in the teaching of science in nearly all the schools that are properly equipped with apparatus. Mr. Purdie notes that in a few of the northern schools " it is really well taught," and the same can be said of a fair number of the larger schools in and around Auckland. In a good many the teaching is still largely dogmatic through the want of appliances for demonstrating experiments. I hope that the new financial arrangements will enable the Board to give more liberal help towards equipping with the more necessary apparatus schools still unprovided with it. Considering how easily object-lessons can be illustrated by objects for examination and comparison, the training in observing, in describing forms and qualities, in noting and comparing points of likeness and difference, and in inferring the more obvious links between cause and effect and quality and use is still somewhat disappointing. In the larger schools these lessons are mainly given by junior teachers, and the lack of power to secure lively attention and of skill in getting clear, full, and connected oral answers makes the lessons relatively ineffective. I have been pleased to note growing familiarity with the names, forms, and uses of the parts of common flowers, matters of almost universal interest. Mr. Grierson considers the object-lesson teaching satisfactory, Mr. Purdie thinks it fairly satisfactory, as does Mr. Goodwin also. Mr. Mulgan is less satisfied with what he has seen in this field during the year, and deplores the way in which the giving of information distorts the teacher's aims in handling object-lessons. In connection with this, teachers would do well to study the ideas explained in Circular 369 of the Education Department, London, printed in Cox and Macdonald's " Practical School Method." All the pupilteachers of the third year teach an object-lesson, for which marks are given in connection with their annual examination. They often try to teach more in one lesson than can be properly handled and impressed, but in most respects the lessons are fairly well given. They take great pains to provide a variety of materials, &c, for illustration, and generally show a praiseworthy desire to avoid telling what can be seen or shown, or easily inferred. In these respects their lessons are ahead of those given by many more experienced teachers. The custom of combining classes P., Standards 1., 11., and 111. for these lessons is not to be commended, and will not hereafter be approved, except in the very smallest schools. It is much better to take Standards 11. and 111. together as a separate and more advanced class. Eecitation of verses is seldom unsatisfactery, and is generally creditable. Drill is good in many of the larger schools, and in general satisfactory elsewhere. Singing, for which, alas ! but little time can be spared in the present onerous course of study, is also satisfactory as class singing where teachers are competent, but the time is insufficient for giving pupils the power of reading melodies even in the tonic sol-fa notation at sight. Practice of singing is still far too much confined to the special lesson for it. Under this head Mr. Grierson