41

E.—lb

Writing. —l have been very much impressed during the year with the ease and rapidity with which skill in forming letters in Vere Foster's style may be acquired by very young children, and, at least in those schools where Vere Foster's copy books are in use, the infants should from the beginning be taught the special forms and junctions applicable to them. I see little good in teaching in the lower department of a school anything that has to be unlearnt afterwards. I may add that, on a similar principle as applied to the relation of school teaching to the business of life, any style of writing adopted in our schools should, in my opinion, exhibit with reasonable consistency the quality of " continuity," which forms a characteristic of Vere Foster's, and of certain other Irish and such American series as I have seen. Arithmetic. —There is no part of initiatory work in which the teacher of higher classes'has a greater interest than the teaching of arithmetic. If finger counting or any other form of unit counting be encouraged by the methods adopted in the early stages, its eradication—an essential condition of soundness—will be a labour of difficulty. The infant departments of the schools visited are mostly on the track of right method, whatever variety may exist in intelligent application; but it seems to me that something may be done in the way of establishing a better common understanding of the order of development, of the relation of oral and slate arithmetic, and generally of the ground to be covered. I therefore venture, though with some diffidence, to suggest the following scheme : Stages 1 and 2 are meant to give the minimum requirements of infant classes ; Stage 3 goes a little beyond the minimum requirement of the First Standard, but should be regarded as partly infant work and partly the work of Standard I. Stage I. —Analysis of numbers to 9, done by the use of concrete illustrations, such as pencils, marbles, beads, and dots or other marks on blackboard, or picture symmetrically arranged. (The use of the concrete is necessary for comprehension; the symmetrical arrangement will assist the memory, so that when a question is put the visual impression will at once dictate the answer. The immediate perception in a concrete form of the sum, difference, product, or quotient of any two numbers making together not more than 9 is the principal object to be aimed at. The idea of number apart from objects also to be introduced, and the results of analysis as regards addition to be embodied in a table : thus, 7 + 1 = 8, 6+ 2 = 8,5 + 3 = 8, 4+4 = 8, and I+7 =8, 2 + 6 =8, 3+ 5 =8, 4+4 = 8; the additions to be practised in the table and independently. Consecutive counting to be avoided in this and succeeding stages, lest it encourage a habit of unit counting. Constant use of problems, thus : If John has 6 marbles and I give him 3 more, how many marbles will he have ? Out of 9 pennies I spent 4 pennies : how many pennies have I left ? Stage 2. —Extension of analysis to 20 done in a similar way. Similar embodiment of additions in table, and ample practice until the readiest possible association of any two numbers with their sum has been obtained. Constant use of suitable problems illustrating all relations of the numbers concerned. Introduction to notation, including knowledge of 20, 30, 40, &c, to 100, and practice in reading; thus, 43 = four sets of ten and three, wanting seven to make five sets of ten. Application of previously-acquired knowledge of additions to these higher numbers, the unit figure and the increment being kept the same: thus, 5+4 = 9, 15 +4 = 19, 25 + 4=29, 3+5 =8, 13+5 = 18, 23 +5 = 28, &c. Sums on slates of two columns, involving additions for which the oral work has prepared the children. Stage 3. —Extension of notation to thousands, oral addition by 2, 3, 4, 5—9 to 50, and subsequently to 100; the practice to be given first with the aid of Sonnenschein's picture ring until facility is acquired, the starting figure varying and the increment remaining the same: thus, by fours, 3, 7, 11, 15, &c.; 4, 8, 12, 16, &c.; 5, 9, 13, 17, &c. Embodiment of results of like additions in multiplication table. Oral additions from blackboard of numbers already treated with the aid of the picture ring, but with varying increments. Slate sums and multiplications involving knowledge acquired orally, the numbers employed not exceeding hundreds, but the columns in addition to be of any suitable depth. Constant use of problems in which money tables and measures of length are to be introduced. The analysis of numbers, as far, at least, as Stage 2 goes, must be considered the proper work of an infant department, as providing the basis of all mechanical processes, a specialisation in the direction of addition and multiplication being the chief work of the First Standard, and, in the direction of subtraction and division, the chief work of the Second. But specialisation must also proceed a certain length among the infants, and I think it is not too much to seek that the highest class not presented in a standard should approximately include the following portions of Stage 3: Extension of notation to hundreds, oral additions by 2, 3, 4, 5, to 50, with regular and irregular increment; slate additions combining this knowledge with analysis previously done; and corresponding multiplications orally and on slates—that is, practically, to five times. Generally throughout the teaching it is to be understood that the most sparing use of simultaneous practice must be observed, that slate work should always follow, never get ahead of, what has been treated orally, that mechanical proficiency and intelligent application must be equally regarded, and that a smaller programme thoroughly done is of infinitely more value than a wider programme of uncertain results. Buildings, etc. —The buildings are generally good; but the Inspector does not often visit a school without having his attention called to sundry small matters, such as leakages and the need of repairs to spouting, fencing, &c, which one would think ought to be one of the first cares of the local School Committee, or, at any rate, come before the annual supply of prizes, cakes, and tea. "Closets require attention" is a remark which has very commonly to be made in inspection reports on schools in the country. Eegistebs, etc. —The proper keeping of the registers is one of the most important points in our system of school government, and no keeping can be considered a proper keeping which is not perfectly accurate and complete down to the smallest detail. In point of accuracy I have no criticism to make. General accuracy must be conceded. But in point of completeness and strict adherence to rules of more or less importance I do not find it satisfactory to have had in about one-

6—E. Ib.