CHAPTER XIV.

METHOD OF TEACHING-ARITHMETIC.

Increase in Study of Arithmetic since 1833-Its objects Intellectual and Mechanical-Too much of blind following of Rules in some Schools-Habits of Indolence-Teachers urged to improve this Department-Too few Arithmeticians in some Schools.

IN 1833, the number of Arithmeticians was 3,022 out of 10,108 pupils enrolled. In 1842, there were 5,542 out of 13,291. The increase is from 1 in 3 to 1 in 23.

"Instruction in Arithmetic," says Director Spilleke,"has two objects,-1. To assist in forming the pupils' powers of thought; and, 2. To give him practical expertness in the transactions of ordinary life. Formerly the latter object alone was pursued by most Teachers, (for here too there were honourable exceptions,) and it cannot be denied, that the Schools in this way turned out excellent calculating machines, who could not, however, make any great pretension to powers of thinking, judging, and drawing conclusions. A

desire for the same result is, perhaps, the causeapart from the convenience with which the business jogs on in the old method--why Teachers are still found, who will not shake themselves free from this indolent, spiritless, and spirit-quenching mechanism, although they have ocular demonstration how children are roused, when, in their early lessons, instead of being subjected to mechanical drudgery, their intellectual powers are sought to be developed." After expressing regret that parents find it necessary to shorten the period of their children's attendance at school, he concludes, -"If they can allow time they will find that their children will not only reckon accounts accurately, but further, (and which is not to be despised,) that they will, by and bye, become observant, intelligent, and reflecting men."

It is much to be apprehended, that the proportion of schools within the range of the Bequest, to which the censures above quoted are applicable, in respect of Arithmetic being taught by a mere blind following of rules, is not small. The subjoined extracts will show, that in a few schools it is well and rationally taught; but in others it is equally evident that this part of the business is merely mechanical. The following remarks contained in last Report, have still far too wide an application :

"The degree of proficiency in Arithmetic, generally corresponds with the extent to which the intellectual methods of instruction have been adopted. And, indeed, it is obvious that a boy

who has been taught to exercise his reason, will nowhere find that power more beneficial than in this branch. The absence, indeed, of habits of reflection and active mental operation is the obvious and direct cause of the striking deficiency which is very frequently met with in arithmetical instruction. That deficiency is exhibited,-1. In the pupil's acquirement of formal and mechanical rules, without reference to the rationale or principles; and, 2. In his consequent inability to work questions, for the solution of which the rules acquired by him would suffice, if he knew how to apply them. When the question is stated precisely in the terms set down in the book, he can apply the particular rule readily enough, but is reduced to a state of helplessness if it is stated in such a manner that the applicability of the rule is not manifest in the terms of the question —if, in short, there is wanting to the calculation anything beyond mechanical dexterity."

To the preceding causes should be added the prevalence of habits of extreme mental indolence in performing the operations, which ought not to be tolerated. The memory is trusted with nothing, not even with the carrying of 1. A condition of mental repose, not dreamt of under the very tropics, is countenanced; and, in the indulgence of that, short division is performed the long way to save the mind the labour of carrying remainders. In adding, the remainders are always written down. The easiest process in simple division cannot be confided to the feeble powers.

of evanescent thought, but must be carefully wrought out by operation on the slate. The extracts will show that these statements do not, in any respect, exceed the truth. Surely there is no occasion for such mental inertness? Surely it is not worthy of any Teacher to countenance or permit habits so inimical to mental activity and promptitude?

The Reporter desires anxiously to press upon the Teachers a serious consideration of the condition of this branch of instruction, in their respective schools. It nearly concerns their credit and their usefulness, to place it generally upon a more intelligent and more efficient footing, than for the most part it at present occupies. For their assistance and direction, he is enabled, on high authority, to recommend the study of the treatises of Professor de Morgan and Dr. Lardner; and the well-informed Schoolmaster's own reflections, addressed in earnest to the subject, cannot fail to suggest the necessary amendments.

It has elsewhere been remarked, that the study of Arithmetic is, in some cases, limited to far too small a proportion of the pupils; and this is a point which will require, in future, to have more weight assigned to it than heretofore in the distribution of the revenue.

(92.)

"Arithmetic. 11 exercised together solved questions in multiplication, addition, and practice, in first-rate style, combining expedition with accuracy, and working by such different methods, as to show excellent intelligence."

(93.)

"Arithmetic satisfactory. The pupils performed the operations required, and were better able than usual to explain and justify them."

(94.)

"One boy, who has gone through a course of Book-keeping showed, when questioned very closely upon it, a perfect knowledge of the details and principles, and of the use of the different books."

(95.)

"On entering the school, I found two classes at work under the charge of monitors, and a third with the master, at Arithmetic. He exercises the arithmeticians mentally, giving them six or seven figures in succession, of which they give the sum without using their slates. Thus, the Master gave orally the numbers 4, 5, 8, 3, 2, 6, and the pupil retaining these in his memory, and without writing them down, gave the sum 28. This must be a useful exercise for teaching habits of close attention, and of promptness in mental operations."

(96.)

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Pupils, professing to have advanced much further, do not know how to set about multiplying a sum by 31; and when shown the way, all brought out wrong answers."

(97.)

"

"In Arithmetic there is a sad want of expertness, all simple operations being worked out on the slate, e. g., 15 divided by 4. Thus they are very slow, though ultimately correct. A question of interest was, however, done better, and, by one boy, with good intelligence."