9 × 7 | 10 | 700 | 20,000| 500-2000 7 × 9 | 10 | 700 | 20,000| 500-1750 8 × 6 | 10 | 750 | 20,000| 500-2500 6 × 8 | 9 | 700 | 20,000| 500-2500 | | | | 63 ÷ 9 | 9 | 500 | 4,500| 300-2500 64 ÷ 9 | 9 | 200 | 4,000| 100- 700 65 ÷ 9 | 8 | 200 | 4,000| 100- 600 66 ÷ 9 | 7 | 200 | 4,000| 100- 550 67 ÷ 9 | 7 | 200 | 4,000| 75- 450 68 ÷ 9 | 6 | 200 | 4,000| 87- 575 69 ÷ 9 | 6 | 200 | 4,000| 87- 450 70 ÷ 9 | 5 | 200 | 4,000| 75- 575 71 ÷ 9 | 5 | 200 | 4,000| 75- 700 | | | | _XX_ | 40 | 550 |1,000,000| 300-2000 _XO_ | 20 | 500 | 11,500| 150-2000 _XXX_ | 15 | 450 | 12,000| 100-1000 _XXO_ | 25 | 400 | 15,000| 150-1000 _XOO_ | 15 | 400 | 5,000| 100-1000 _XOX_ | 10 | 400 | 10,000| 100- 975 ====================================================================== Having made his estimates the reader should compare them first with similar estimates made by experienced teachers (shown on page 124 f.), and then with the results of actual counts for representative textbooks in arithmetic (shown on pages 126 to 132). It will be observed in Table 2 that even experienced teachers vary enormously in their estimates of the amount of practice given by an average textbook in arithmetic, and that most of them are in serious error by overestimating the amount of practice. In general it is the fact that we use textbooks in arithmetic with very vague and erroneous ideas of what is in them, and think they give much more practice than they do. The authors of the textbooks as a rule also probably had only very vague and erroneous ideas of what was in them. If they had known, they would almost certainly have revised their books. Surely no author would intentionally provide nearly four times as much practice on 2 + 2 as on 8 + 8, or eight times as much practice on 2 × 2 as on 9 × 8, or eleven times as much practice on 2 - 2 as on 17 - 8, or over forty times as much practice on 2 ÷ 2 as on 75 ÷ 8 and 75 ÷ 9, both together. Surely no author would have provided intentionally only twenty to thirty occurrences each of 16 - 7, 16 - 8, 16 - 9, 17 - 8, 17 - 9, and 18 - 9 for the entire course through grade 6; or have left the practice on 60 ÷ 7, 60 ÷ 8, 60 ÷ 9, 61 ÷ 7, 61 ÷ 8, 61 ÷ 9, and the like to occur only about once a year! TABLE 3