Other standard tests and scales of measurement have been derived and are being developed. The examples given above will, however, suffice to make clear the distinction between the ordinary type of examination and the more careful study of the achievements of children which may be accomplished by using these measuring sticks. It is important for any one who would attempt to apply these tests to know something of the technique of recording results. In the first place, the measurement of a group is not expressed satisfactorily by giving the average score or rate of achievement of the class. It is true that this is one measure, but it is not one which tells enough, and it is not the one which is most significant for the teacher. It is important whenever we measure children to get as clear a view as we can of the whole situation. For this purpose we want not primarily to know what the average performance is, but, rather, how many children there are at each level of achievement. In arithmetic, for example, we want to know how many there are who can do none of the Courtis problems in addition, or how many there are who can do the first six on the Woody test, how many can do seven, eight, and so on. In penmanship we want to know how many children there are who write quality eight, or nine, or ten, or sixteen, or seventeen, as the case may be. The work of the teacher can never be accomplished economically except as he gives more attention to those who are less proficient, and provides more and harder work for those who are capable, or else relieves the able members of the class from further work in the field. It will be well, therefore, to prepare, for the sake of comparing grades within the same school or school system, or for the sake of preparing the work of a class at two different times during the year, a table which shows just how many children there are in the group who have reached each level of achievement. Such tables for work in composition for a class at two different times, six months apart, appear as follows: DISTRIBUTION OF COMPOSITION SCORES FOR A SEVENTH GRADE ====================================== | NUMBER OF CHILDREN +----------------------- | NOVEMBER | FEBRUARY --------------+-----------+----------- Rated at 0 | 0 | 0 1.83 | 1 | 1 2.60 | 6 | 4 3.69 | 12 | 6 4.74 | 8 | 11 5.85 | 3 | 4 6.75 | 1 | 3 7.72 | 1 | 2 8.38 | 0 | 1 9.37 | 0 | 0 ======================================