This scale enables us to determine by the total number of points obtained the level of the child in arithmetic, and at the same time we find out what sums can be done by the pupils of each age. This is shown in the table.
Results of Arithmetic Tests in an Elementary School in Paris.
| All the Children of— | Average Points. | Children in Proper Class. | Average Points. | All Children in Class— | Average Points. |
| 6 years | 1.45 | 6 years | 1 | Infant | 1.5 |
| 7 years | 3.93 | 7 years | 6 | Junior (first year) | 6.5 |
| 8 years | 7.00 | 8 years | 7 | Junior (second year) | 6.83 |
| 9 years | 9.65 | 9 years | 14 | Intermediate (first year) | 16.00 |
| 10 years | 15.47 | 10 years | 23 | Intermediate (second year) | 22.42 |
| 11 years | 21.47 | 11 years | 29 | Senior | 28.45 |
| 12 years | 22.50 | ||||
| 13 years | 24.75 |
It will be noticed in the table that the averages are a little less when calculated on all the children. We have indicated this difference already, and have explained the reason for it. We have based our scale upon the marks obtained by all the children.
In practice we consider that M. Vaney's system of points is not indispensable. It is sufficient to find out whether or not the pupil can do the sum set. If he can, he is at that level; if not, he must be placed in the grade below. Some examples will show how we use these results. We select them from a class of defectives.
Roger B——, age ten and a half years, is asked orally, for he cannot write: "If I had 19 apples and ate 6, how many would be left?" He replies first 9, then 6. One then tries easier sums. Q. "I have 4 apples, and eat 1?" R. "Three are left." Q. "I have 12 apples, and eat 2?" R. "There are 9 left." Q. "I have 8 apples, and eat 2?" R. "There are 7 left." Evidently this child does not clear even the first step. He has therefore four years and a half of retardation.
In this connection let us remark that as Roger is a child whose attendance has been regular, it follows that in his four and a half years at school he has scarcely learned more than a normal child learns in two months. We recently met with a similar case at Bicêtre. This was a child of twelve, who had begun to learn his letters at the age of four, and who did not yet know how to spell! In presence of such cases one may well ask whether the teacher who has not managed in four and a half years or in eight years to teach a defective child what a normal child learns in a month has not wasted his own time and that of the defective. At this point let us call attention to a defect in the mechanical calculation of retardation. Little Roger, who is ten and a half years, and cannot yet read by syllables, has only four and a half years of retardation, if we apply to him the usual rule. It would therefore appear that he is at the same level of intelligence as a child of thirteen and a half, who belongs to the intermediate course, first year, for the latter has also a retardation of four years and a half. The error of this method of calculation is at once apparent. The real significance of retardation is proportionate to the class and course which the pupil has reached. We shall return presently to the exact estimation of retardation.
Let us quote another example to show the application of the arithmetical test.
Ostrow, twelve and a half years, replies correctly to questions 1, 2, and 3. At the fourth he hesitates and begins by multiplying 7 by 89, and obtains as answer 783, which is doubly inexact, because he ought not to have multiplied, and the multiplication is incorrect. Then he draws back, and tries a division of 89 by 7; he obtains an incorrect answer (11), which does not satisfy him. Finally, he tries a multiplication: says 7 times 10 makes 70. He next adds 7 several times to reach 89, but he becomes confused, and finishes by finding the number 13, which is almost correct. This child is therefore at stage 4; he does not clear it, but he attempts it. Look at the scale. We give him full points for Problems 1, 2, and 3, plus 2 points for Problem 4, or a total of 8, which puts him at the level of children of eight and a half years, which amounts to a retardation of four years.
Spelling.—The test of spelling is a piece of dictation given individually or collectively. The scale contains the first phrases of the dictation. We reproduce them all here, pointing out the grammatical difficulties which they contain, and the scale for marking faults which seemed to us most fair. [We quote the phrases in French, as a translation would not indicate the real difficulties. It will be observed that in many cases correct spelling implies grammatical knowledge.—Tr.]