AKAROA AND WAINUI ROAD BOARD. 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 171, 8 March 1878, Page 3

AKAROA AND WAINUI ROAD BOARD. 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 Xll.—Subject—Arithmetic continued ; order of teaching rules more advanced ; " first principles ;" arithmetical equations; model examples. In commencing, Mr Howard contended that as a matter of theory, the study of fractions should immediately follow that of integers, as until children had a knowledge of fractions they could not obtain perfectly accurate results, but were compelled to be content with mere approximations. Another advantage of a knowledge of fractions before commencing the study of compound rules was, that children obtained a far more inteligent idea of the processes involved in them, such as addition of fractional parts, calculation of the odd ounces, &c:, in bills of parcels, the ■working with 5£ and 30£ in long and square measures, and with 365£ in time. This was the order that should be followed by every compiler of a school arithmetic, although it was seldom found so in most books. He, the lecturer, admitted that, owing to the early age children are often removed from school, teachers were frequently obliged to hurry their pupils on through money rules and weights and measures, to fit them for the varied duties of after-life in workshop, office, or behind the counter. So far as money rules were concerned, there was less objection to this, since farthings were really as much wholes as pence or shillings, and might as well be. written similarly under the letter q. It was very desirable that a decimal system, applicable to money and weights and measures should be introduced, as thus a great deal of labor would be spared. The avoirdupois weights were by far the most useful, and the most difficult. The old plan of teaching troy weight early should be continued, as the notation is closely allied to that of the money rules already familiar. Apothecaries weight, being similar in its structure, should follow troy weight. Long and square measures, although difficult to teach, were, nevertheless, of the utmost importance. Every child ought to be, able to measure the carpet required for a room, or the paper required for the walls. Reduction and Bills of Parcels should be taught in connection with each rule. Specimen examples of the methods of working vulgar fractions were then given. The lecturer insisted strongly on the importance of a correct knowledge of the intimate relations between fractions and proportion. Rule of three and Practice were two rules of great practical utility. But teachers should not bind their pupils too closely to the exact routine of the rule, but try to give them facility in calculation. First principles were a means to an end. Mr Howard illustrated his remarks by giving several examples to show that a correct result might often be obtained in a simpler manner than often prescribed by certain rules. The law that the product of the means=product of the extremes, and a method of teaching compound proportion, sometimes called " the method of cause and effect," were illustrated and recommended. The commercial rules were often found very difficult. This arose greatly from the fact that percentage was very imperfectly understood. The principles of equations should be taught as a branch of arithmetic, as well as of algebra, as they often afforded a ready means of solving otherwise very difficult problems. Before concluding, Mr Howard gave several model solutions, by arithmetic, of problems which had been most clumsily solved by an algebraical process in the key of Barnard Smith's arithmetic, in every case more concisely and simply.