The overlapping of grade upon grade should be noted. Of the pupils in grade 6 about 18 percent do better than the average pupil in grade 7, and about 7 percent do better than the average pupil in grade 8. Of the pupils in grade 8 about 33 percent do worse than the average pupil in grade 7 and about 12 percent do worse than the average pupil in grade 6.
TABLE 13
Relative Frequencies of Scores in an Extensive Team of Arithmetical Tests.[23] In Percents
| Score | Grade 6 | Grade 7 | Grade 8 |
|---|---|---|---|
| 70 to 79 | 1.3 | .9 | .4 |
| 80 " 89 | 5.5 | 2.3 | .4 |
| 90 " 99 | 10.6 | 4.3 | 2.9 |
| 100 " 109 | 19.4 | 5.2 | 4.4 |
| 110 " 119 | 19.8 | 18.5 | 5.8 |
| 120 " 129 | 23.5 | 16.2 | 16.8 |
| 130 " 139 | 12.6 | 17.5 | 16.8 |
| 140 " 149 | 4.6 | 13.9 | 22.9 |
| 150 " 159 | 1.7 | 13.6 | 17.1 |
| 160 " 169 | 1.2 | 4.8 | 9.4 |
| 170 " 179 | 2.5 | 3.3 |
DIFFERENCES WITHIN ONE CLASS
The variation within a single class for which a single teacher has to provide is great. Even when teaching is departmental and promotion is by subjects, and when also the school is a large one and classification within a grade is by ability—there may be a wide range for any given special component ability. Under ordinary circumstances the range is so great as to be one of the chief limiting conditions for the teaching of arithmetic. Many methods appropriate to the top quarter of the class will be almost useless for the bottom quarter, and vice versa.
Fig. 67.