278
THE NEW ZEALAND GAZETTE.
No. 7

ARITHMETIC.

39. The following shall be the complete course in arithmetic:—

PREPARATORY CLASSES.

The numbers from 1 to 20. The composition of every number up to 20 should be known, and the children should be taught to perform mentally and orally every kind of operation with these numbers that is within the mental powers of children of their age and development, and similarly to apply the power thus acquired to concrete examples and to various easy problems.

Where the preparatory classes have separate teachers, part of the work of Standard I. may be attempted also.

STANDARD I.

The numbers from 1 to 100. The composition of every number up to 100: e.g., 28 would be known (1) as 2 tens and 8 ones or units; (2) as 27 + 1, 26 + 2, 25 + 3, &c.; (3) as 14 + 14, i.e., 7 + 7 + 7 + 7, &c.; (4) as 4 sevens, 7 fours, 14 twos, 2 fourteens. Again, it should be known that ½ of 28 = 14, ¼ of 28 = 7, &c. Also that 28 + 72 = 100: thus, 28 + 2 = 30; 30 + 70 = 100. Also that 28 + 17 = 45: thus, 28 + 7 = 35; 35 + 10 = 45; &c. In short, there should be instruction to secure the power of working orally addition, subtraction, multiplication, and division of the numbers 1 to 100, neither operating numbers nor the result being greater than 100.

Each number should be taught in the first instance by concrete examples, and the composition and the grouping should be similarly taught. Examples should include examples in shillings and pence; yards, feet, and inches, which should be taught by the actual measurement of the length and breadth of books, slates, desks, the class-room, of the height of a desk, of a window-sill, of the mantelpiece, of the children themselves, &c. The written work to be within the same limits.

It is recommended that subtraction should be taught by the method of complementary addition. This method is just as easy to teach as any other method; it is independent of any trick or device, and, inasmuch as the modern contracted methods of division, practice, &c., depend upon it, the children would have nothing to unlearn at a later stage.

Too much emphasis cannot be laid upon the fact that success in teaching arithmetic is proportional to the attention given by the teacher to the oral work at every stage, but most especially in the early stages. This oral work should begin with concrete examples, which should be repeated again and again in various forms until the relationship of the numbers is grasped. When any principle is grasped it should at once be applied to new concrete problems based upon the experience of the children. The chief advantage to be gained from the written work in arithmetic is, probably, that it enables the pupil to have before his eyes the several logical steps by which a given result is obtained. It is no doubt true that many minds cannot deal with large numbers without some visual aid, but it is equally true that greater attention given to oral work would produce a much greater amount of skill in dealing mentally with comparatively large numbers than is usually found in our schools.

STANDARD II.

The numbers up to 1,000.

The composition of every number up to 1,000 should be known: e.g. 100 would be known as 10 tens, 200 as 2 hundreds or 20 tens, &c.; 340 as 3 hundreds and 4 tens, or as 34 tens, or as 10 times 34, &c.; 672 as 6 hundreds, 7 tens, and 2 ones or units, or as 67 tens and 2 units. The composition of these numbers should be taught from the concrete, by the use of cubes, bundles of sticks, bags of shot, &c., or by means of diagrams. The four simple rules, multipliers and divisors being confined to the numbers 1 to 12 and 20. The pupils should understand the meaning of ½, ⅓ … ¹⁄₁₂, ¹⁄₂₀, applied to concrete examples. Reduction of pence to shillings and pence, or of shillings and pence to pence; also of shillings to pounds and shillings, or of pounds and shillings to shillings; but not reduction of pounds shillings and pence to pence, or vice versa. Compound rules (money), multipliers and divisors not to exceed 12, and sums of money in the questions and answers not to exceed £20.

STANDARD III.

The numbers up to 1,000,000. The composition of these numbers should be known in a general way: e.g., 10,000 would be known as 10 thousands, or as 100 hundreds, or as 1,000 tens; 20,000 as 20 thousands, &c.; and so on up to 1,000,000, which would be known as 1,000