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In Standard IV. improvement was quite as marked as in Standard VI., and at many schools very fine work was done. Feilding School is especially deserving of mention, for of 40 pupils examined in the standard, 34, or 85 per cent., worked all the sums correctly, o pupils had only one sum wrong, and 1 pupil had two sums wrong; or, to put the result in another way, out of a possible 200 sums correct, only 7 were wrong. This is a very fine performance ; and when it is remembered that all the members of a class of the same number of pupils might have passed with 120 sums right (110 sums right, supposing half the class to have been girls), and that this class had 293 sums right, it will be seen how fallacious a mere percentage of passes is for estimating the comparative quality of the work of different classes or schools. A margin of 73 sums in 200 would point to a vast difference in the efficiency of the teaching of the two classes, yet percentages of passes alone would show 100 per cent, in each class. Bills of parcels this year we were pleased to find worked more accurately than usual. In Standard 111. the work varied very much. At a few schools, notably Feilding, it was excellent; at a few it ranged from bad to inferior ; and at quite a large number there were far too many pupils who just worked correctly only the bare limit of sums to qualify for a pass. But a better record than this might well have been expected, especially considering the simplicity of the questions set by the department. We are of opinion that the examination-cards were too easy to be a fair test of the requirements of the syllabus for this standard ; and hence we were the more disappointed with the quality of the work received. For instance, although the course of instruction is supposed to cover advanced numeration and notation, simple long multiplication, simple long division, and the four money rules, on many of the cards a pupil could gain by the regulations a limit pass in arithmetic without attempting a money sum. Now, there can be no doubt that it is especially desirable that passes in arithmetic in this standard should be particularly strong, considering the amount of new work that has to be overtaken in Standard IV., and so we think the test set should be a searching one. But the strange part of it is that though the tests set by the department during the past few yea,rs for this particular standard have been much easier than those set by us when the work was in the hands of the Inspectors (the tests in Standard V. have always been more difficult, and also those in Standard VI. until this last year), the quality of the arithmetic in this standard has undoubtedly very much deteriorated. The question then arises, Why is this so? Well, perhaps, the "If you wish to hit high you must aim high " theory has something to do with it. The very simplicity of the questions often seemed to be the cause of bringing pupils to grief, though this should not have been so had the teaching been thorough. But undoubtedly the chief reason for the falling-off lies in this : that many teachers, since the classification of the pupils in the two lowest standards was placed in their hands, have promoted Standard 11. pupils who failed badly in arithmetic to Standard III.; while when the classification rested with the Inspectors we invariably refused a pass to a Standard 11. candidate if he failed to obtain 40 per cent, of the possible marks in arithmetic. At the last examinations some pupils in Standard 11. who failed with us in every sum out of six, and several who were correct in only one sum, were promoted to Standard 111. by the teachers. Now it is surely evident that such pupils cannot do credit to Standard 111. at their next examination. It is this leniency on the part of the teachers in passing pupils in Standard 11. that accounts for Standard 111. having for the past few years the highest rollnumber, for those that should not have been promoted almost invariably spend two years in Standard 111. Teachers might note that over one-third of the pupils examined failed in numeration and notation. Now, these should be kept up almost daily, as by invariably requiring pupils to read and write their answers in words, and to put down in figures numbers dictated in words. Then, again, problems in the simple rules generally brought to light wrong methods. Thus, in " What must • be multiplied by to produce ?" multiplication was employed; and in "What must be divided by to produce ?" division was employed. But we think that it is only natural, however sound the teaching, that such young pupils as are in Standard 111. should make mistakes like these, especially considering the prominence of the words " multiplied " a.nd " divided." Furthermore, we are of opinion that a teacher's time would be better employed in obtaining quick and accurate working in purely mechanical sums of reasonable length in addition, multiplication, &c, rather than in getting such young pupils as are found in .Standard 111. to grasp the rationale of such problems as these mentioned, even though they involve only a few figures. No doubt some will say, if multiplication or division has been intelligently taught, it is as easy to find one term as another. This, no doubt, sounds very nice, and is all very well in theory ; but ask the practical teacher how much time he has to give to such work before he can obtain any compensating results, and see what he will say. Children are only children after all; and perhaps the fact that sums of a similar description are not considered beneath the intelligence of a candidate for a teacher's certificate may speak in their favour. It appears to us that Standard 111. is above all the standard in which accuracy should be aimed at, if a teacher is to have any success or comfort in treating the advanced rules with his upper standards ; hence we would respectfully suggest that in future the test set for this standard should involve more purely mechanical work of some length. In Standard 11. the work on the whole was good, though the quality of the passes, and the style of the figuring and setting-out, varied considerably. It is worthy of note that schools with an average of, say, fifty to eighty pupils generally did superior work to the largest schools. In the former it was quite a common experience to find the majority of pupils, and sometimes all the pupils, working every sum correctly. At many schools pupils readily proved their sums, and in proving multiplication by factors showed a sound knowledge of Standard 111. long multiplication. Subtraction generally was the weakest rule, and inability to recognise whether multiplication or division should be used in sums expressed on the cards in words was again in evidence. In Standard I. the majority of the schools did fine work. At many schools the pupils showed considerable skill in setting-out in logical style little problems ; at some the explanatory writing in such sums, which we invariably require, was omitted. Failure was, as usual, most frequent in numeration and notation.