RESUME OF LECTURES ON EDUCATION, DELIVERED BY C.C. HOWARD, ESQ, F.R.G.S., AT THE NORMAL SCHOOL, CHRISTCHURCH.

Akaroa Mail and Banks Peninsula Advertiser, Volume 2, Issue 170, 5 March 1878, Page 3

RESUME OF LECTURES ON EDUCATION, DELIVERED BY C.C. HOWARD, ESQ, F.R.G.S., AT THE NORMAL SCHOOL, CHRISTCHURCH.

Second Course —Methods of Teaching

and Organization

Lecture X.—Subect—Arithmetic: Preparatory stage ; figures and elementary rules; order of teaching them ; importance of problems; methods of numeration, addition, and subtraction. The importance of mathematics has been insisted upon by all the best teachers in both the past and present time, and the aim of the present lecture would be to place the teaching of the subject on a rational basis. Hitherto it bad been generally very badly taught, as might be seen in the unsatisfactory knowledge of the subject which so many ladies in the present day possess. Arithmetic is held to be the most practical of all studies, excelling even Euclid and Algebra in its usefulness. At an English examination in 1876 the proportion of marks gained were as follows :—For reading, 94 ; writing, 80 ; and arithmetic, 70; but the subject is doubtlessly better taught in public schools than iv private ones, and the lecturer recommended strongly that teachers should pay greater attention to this branch of school work, and teach principles rather than rules. There are really only two fundamental rules in arithmetic—addition and subtraction. Multiplication and division may also be taught with advantage, but are not absolutely necessary, being only shortened methods of doing addition and subtraction, and with these four rules, sup-plemented-by common sense, almost every arithmetical problem may be solved. In the first stage, mental arithmetic only should be used, giving clear notions of number, and of the relation and sequence of numbers. Explain technical words, such as more and less, and demonstrate as often as possible by objects. Go over ground anew continually, and show relation of numbers in different ways, using the ball frame constantly. The different figures in use must be learnt consecutively, and not be classified. Easy exercises in the addition of numbers, both mentally and on slate, should be gradually introduced. In teaching children to represent numbers by figures, explain carefully that numbers have two values, an intrinsic and local value. That numbers in the right hand column always retained their intrinsic value, but if moved to the left had another value, increased tenfold, and that 0 has no value whatever. The earlier exercises should consist of tens only, and should be followed by others combining tens and units, those numbers being first employed which are most easily understood, such as 22 or 31. Explain the meaning of "teen" and "ty"as terminations, and that "eleven" means one left, and "twelve" two left. No cyphers should be employed at first, but the letters H. T. U. placed over the columns should be used in teaching numeration and notation. Afterwards the proper use ot cyphers should be shown, and the letters omitted. Teach numeration

and notation together, and let the results and answers be written on the slates. Teach the thousands and millions periods at once without the detail of H. T. U., the pupils being exercised in transferring readily n gnmn of figures from one period to another. Simple addition should be preceded by exercises in mental arithmetic, and the explanation of .ugns, sum, &c. Problems should be used from the first, ami the same sum -ho'ild be given in a variety of ways. Th : s rule should be Mlowed by subtraction, instead of, as sometimes recommended, compound addition, because the latter rule involves introducing difficulties of a different notation. In subtraction, transposition is preferable to borrowing, or, as more correctly designated, "the method of equal additions." Teachers should insist on three things— accuracy, neatness, and quiclcness, and should, as far as prasticable, keep this branch of instruction in their own hands, rather than entrust it to pupil teachers or less experienced assistants.

Lecture XL—Subject—Arithmetic continued : Multiplication and Division; Mental Arithmetic ; peculiar combinations ; hints on setting exercises ; School Arithmetics.

The stud)* of arithmetic should be made as agreeable as possible, and the multiplication and addition tables might with advantage be learnt by singing them. The children should first see the results embodied in the rules before committing them to memory. In teaching tables, multiplication and division should be taught conjointly, and the examination tests be irregular. As a matter of convenience it is advisable to teach multiplication tables as far as 12 times, because 10, 11, and 12 times are involved in compound rules, otherwise it is not absolutely necessary to learn beyond 9 times. Instead of burdening the children's mind with the extended multiplication table, it would be better by a good course of Mental arithmetic, by easy and expeditious rules, to give them a power of ready calculation which they could apply to any numbers that might be required of them. Before commencing any rule by slate work, plenty of mental work and blackboard explanation should be given, together with viva voce examination tests. In first examples very few figures should be used, and easy numbers should be chosen for multiplication and division. Help pupils to grasp their work, and plenty of exercise should be given to impress the rule on multiplying by tens, that they might be enabled to see how the principle of the process was involved in notation. After 10 times, choose 20, 30, &c, so as to shew the work by multiples of 1.0. 11 should be taught first as a whole then as 10 x 1, and 12 times in a similar riianner. In long multiplication fill up the blank spaces to the right in 10, 100 times, &c, with o's in the first stage, until the process is thoroughly understood. Use mental arithmetic as much as possible, and notice peculiarities in the use of the number 9. Mr Howard pointed . out several amusing instances in the use of this number, as the multiplication of the nine digits arranged in their proper order by different multiples of 9, and gave several useful rules in dealing with such numbers as 21, 31, 41. He ulso strongly recommended plenty of simple problems in multiplication and division as early as possible. The lecturer concluded by a few practical illustrations of how best to deal with factors, and multiples, G.C.M, and L.C.M., and a few useful remarks on remainders, and recommended teaching long division first by one figure worked out previously by the rule for short division.

The following books were recommended :— Fitcbe's " Science of Arithmetic," Tate's '* First principles of Arithmetic," De Morgan's, Hamlyn Smith's, and Piper's for teachers' use. Barnard Smith's in preference to Colenso's.