Dividend 60 61 62 63 64 65 Divisor 7 8 9 7 8 9 7 8 9 7 8 9 7 8 9 7 8 9 Number of Occurrences 3 9 1 1 2 5 4 6 1 17 5 9 5 22 0 1 10 1 Dividend 66 67 68 69 70 71 Divisor 7 8 9 7 8 9 7 8 9 7 8 9 8 9 8 9 Number of Occurrences 2 1 4 0 1 1 1 3 2 0 6 1 6 2 1 0 Dividend 72 73 74 75 76 77 78 79 Divisor 8 9 8 9 8 9 8 9 8 9 8 9 8 9 8 9 Number of Occurrences 16 10 7 5 3 3 5 3 3 2 3 0 4 1 0 2 Dividend 80 81 82 83 84 85 86 87 88 89 Divisor 9 9 9 9 9 9 9 9 9 9 Number of Occurrences 4 15 2 4 1 2 0 3 2 7 Tables 3 to 8 show that even gifted authors make instruments for instruction in arithmetic which contain much less practice on certain elementary facts than teachers suppose; and which contain relatively much more practice on the more easily learned facts than on those which are harder to learn. How much practice should be given in arithmetic? How should it be divided among the different bonds to be formed? Below a certain amount there is waste because, as has been shown in Chapter VI, the pupil will need more time to detect and correct his errors than would have been required to give him mastery. Above a certain amount there is waste because of unproductive overlearning. If 668 is just enough for 2 × 2, 82 is not enough for 9 × 8. If 82 is just enough for 9 × 8, 668 is too much for 2 × 2. It is possible to find the answers to these questions for the pupil of median ability (or any stated ability) by suitable experiments. The amount of practice will, of course, vary according to the ability of the pupil. It will also vary according to the interest aroused in him and the satisfaction he feels in progress and mastery. It will also vary according to the amount of practice of other related bonds; 7 + 7 = 14 and 60 ÷ 7 = 8 and 4 remainder will help the formation of 7 + 8 = 15 and 61 ÷ 7 = 8 and 5 remainder. It will also, of course, vary with the general difficulty of the bond, 17 - 8 = 9 being under ordinary conditions of teaching harder to form than 7 - 2 = 5. Until suitable experiments are at hand we may estimate for the fundamental bonds as follows, assuming that by the end of grade 6 a strength of 199 correct out of 200 is to be had, and that the teaching is by an intelligent person working in accord with psychological principles as to both ability and interest.