_Seventh Sum_ (7 points).--A merchant mixed 25 pints of wine at 2s. a pint with 60 pints at 2s. 6d. a pint; at how much per pint must he sell the mixture in order to gain 55s.? etc.
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 |Average|Children |Average| |Average Children|Points.|in Proper|Points.| All Children in Class-- |Points. of-- | | Class. | | | --------+-------+---------+-------+--------------------------+------- 6 years| 1.45 | 6 years | 1 |Infant | 1.5 7 " | 3.93 | 7 " | 6 |Junior (first year) | 6.5 8 " | 7.00 | 8 " | 7 | " (second year) | 6.83 9 " | 9.65 | 9 " | 14 |Intermediate (first year) |16.00 10 " | 15.47 |10 " | 23 |Intermediate (second year)|22.42 11 " | 21.47 |11 " | 29 |Senior |28.45 12 " | 22.50 | | | | 13 " | 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.