E.—lb

46

until the preceding numbers are thoroughly mastered. Same numbers in. the abstract: no figures to be used. Application to easy oral problems. (b.) Meaning of the figures 1, 2, 3, 4, 5, 6, 7, 8, 9. Eecapitulation of (a), with use of figures and increased stress on abstract questions — e.g., How many twos, threes, in six ? Half of six? (c.) Numbers nine to fifteen, treated as in (a), in the concrete, abstract, and in problems, but without using figures. Grouping of eleven, twelve, .... fifteen into a set of ten and one, two, three, four, or five more. Same repeated with ball frame. (d.) Show with the ball frame one ten, two tens, three tens, .... up to, say, twelve tens. Names of these—ten, twenty, thirty .... to ninety ; not of intermediate numbers, [in (o and (d) the gaining of familiarity with groups of ten is an essential feature.] (c.) Figures for numbers ten to fifteen, based on latter part of (c). Eecapitulation of (c), with use of figures. (/.) Treatment of numbers fifteen to twenty as in (a) and (c). [Ball frame or cubes.] Notation of these numbers. (g.) Extension of (a,) to numbers above twenty, thus—Two tens and one to be known as twentyone ; three tens and one, thirty-one .... nine tens and one, ninety-one ; two tens and two, twenty-two; and so on. [On ball frame, followed by notation.] This will give notation of all numbers to ninety-nine. Also additions within these limits— e.g., 23 ands=two tens and three and five = two tens and eight, or 28. (/;.) Extension of (c) and (/) to numbers above twenty — e.g., 9 and 5 = 14, that is, one ten and 4; 19 ands=ten and 9 and 5 = ten and 14 = two tens and 4, or 24; 29 and 5 = 34; and so on. (Ball frame.) [Grouping into tens and units the prominent feature throughout.] (i.) Eegular series of additions by 2, 3, 4, 5 ("counting" proper)— e.g., I+4 =5, 5+4 =9, 9+ 4 = 13, &c; 2+4 =6, 6+ 4 = 10, &c.; 3+4 =7, 7+ 4 = 11, &c.; 4 + 4=B, 8+ 4 = 12, &c. Tables of addition, and perhaps of subtraction, to correspond; tables of multiplication based upon the additions. (/.) Irregular additions, separate numbers not exceeding 9, and total not exceeding 99— e.g., 9+B = 17, 17 + 5 = 22, &c. (k.) Ten tens = one hundred. Extension of notation to 999 or even to 1,999. [Hundreds above 900 may be known at first as ten hundred, eleven hundred, and so on.] N.B.—The ball frame is not a suitable instrument for the first lessons. The most appropriate objects are cubes of wood (all the better if painted in various bright colours), because of the facility with which they can be placed on the teacher's table in view of the children, and arranged in rows, piles, or groups as required. The cubes might be supplemented by counters, pencils, nuts, dots, stars, circles, squares, drawn upon the blackboard, &c. There should be constant revision of earlier work ; the grouping of acquired facts at any stage to form tables, especially of addition and multiplication ; easy oral problems and sums on the blackboard and on slates, based upon the knowledge gained, but not going beyond it. I would warmly recommend to infant mistresses " Numbers Illustrated" (Appleton, New York), a book in which ideas somewhat similar to the above are admirably set forth in concrete form.

SUMMARIES OF RESULTS FOR THE WHOLE DISTRICT. Table A. —Pass Subjects.

Number Number absent, 'excepted. Proportion presented per Cent, of Total School Roll. Proportion passed per Cent, of Total School Roll —" Percentage of Passes." Average Age of those that passed. Classes. Number presented. Number failed. Number passed. Number of Schools presenting Yrs. mos. S7 S6 S5 S4 S3 S2 SI P 84 483 1,140 2,110 3,130 3,047 2,894 6,839 20 31 94 160 138 112 8 51 95 152 112 58 105 383 562 838 379 223 350 675 1,359 1,980 2,418 2,501 0-43 2-45 5-78 10-70 15-87 15-45 14-67 34-67 1-77 3-42 6-89 10-04 12-26 12-68 27 96 129 141 151 156 149 156 14 2 13 2 12 3 11 3 10 2 9 0 Totals for 1888 Correspondingtotals for 1887 19,727 555 476 2,490 9,283 100-00 47-06 156 11 8* 19,447 635 590 2,796 8,353 100-00 42-95 153 11 9* * Mean of avi irage ages,