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
======================================

A study of such a distribution would show not only that the average
performance of the class has been raised, but also that those in the
lower levels have, in considerable measure, been brought up; that is,
that the teacher has been working with those who showed less ability,
and not simply pushing ahead a few who had more than ordinary capacity.
It would be possible to increase the average performance by working
wholly with the upper half of the class while neglecting those who
showed less ability. From a complete distribution, as has been given
above, it has become evident that this has not been the method of the
teacher. He has sought apparently to do everything that he could to
improve the quality of work upon the part of all of the children in the
class.

It is very interesting to note, when such complete distributions are
given, how the achievement of children in various classes over