Any attempt to measure the achievements of children should result in a discovery of the progress which is being made from week to week, or month to month, or year to year.  It would often be found quite advantageous to note the deficiencies as well as the achievements at one period as compared with the work done two or three months later.  It will always be profitable to get as clearly in mind as is possible the variation among members of the same class, and for those who are interested in the supervision of schools, the variation from class to class, from school to school, or from school system to school system.  For the teacher a study of the variability in achievement among the members of his own class ought to result in special attention to those who need special help, especially a kind of teaching which will remove particular difficulties.  There should also be offered unusual opportunity and more than the ordinary demand be made of those who show themselves to be more capable than the ordinary pupils.

The type of measurement which we wish to discuss is something more than the ordinary examination.  The difficulties with examinations, as we have commonly organized them, has* been their unreliability, either from the standpoint of discovering to us the deficiencies of children, or their achievements.  Of ten problems in arithmetic or of twenty words in spelling given in the ordinary examination, there are very great differences in difficulty.  We do not have an adequate measure of the achievements of children when we assign to each of the problems or words a value of ten or of five per cent and proceed to determine the mark to be given on the examination paper.  If we are wise in setting our examinations, we usually give one problem or one word which we expect practically everybody to be able to get right.  On the other hand, if we really measure the achievements of children, we must give some problems or some words that are too hard for any one to get right.  Otherwise, we do not know the limit or extent of ability possessed by the abler pupils.  It is safe to say that in many examinations one question may actually be four or five times as hard as some other to which an equal value is assigned.

Another difficulty that we have to meet in the ordinary examination is the variability among teachers in marking papers.  We do not commonly assign the same values to the same result.  Indeed, if a set of papers is given to a group of capable teachers and marked as conscientiously as may be by each of them, it is not uncommon to find a variation among the marks assigned to the same paper which may be as great as twenty-five per cent of the highest mark given.  Even more interesting is the fact that upon re-marking these same papers individual teachers will vary from their own first mark by almost as great an amount.