Still another difficulty with the ordinary examination is the tendency among teachers to derive their standards of achievement from the group itself, rather than from any objective standard by which all are measured.  It is possible, for example, for children in English composition to write very poorly for their grade and still to find the teacher giving relatively high marks to those who happen to belong to the upper group in the class.  As a result of the establishment of such a standard, the teacher may not be conscious of the fact that children should be spurred to greater effort, and that possibly he himself should seek to improve his methods of work.

Out of the situation described above, which includes on the one hand the necessity for measurement as a means of testing the success of our theories and of our practice, and on the other hand of having objective standards, has grown the movement for measurement by means of standard tests and scales.  A standard test which has been given to some thousands of children classified by grades or by ages, if given to another group of children of the same grade or age group will enable the teacher to compare the achievement of his children with that which is found elsewhere.  For example, the Courtis tests in arithmetic, which consist of series of problems of equal difficulty in addition, subtraction, multiplication, and division may be used to discover how far facility in these fields has been accomplished by children of any particular group as compared with the achievements of children in other school systems throughout the country.  In these tests each of the problems is of equal difficulty.  The measure is made by discovering how many of these separate problems can be solved in a given number of minutes.[20]

A scale for measuring the achievements of children in the fundamental operations of addition, subtraction, multiplication, and division has been derived by Dr. Clifford Woody,[21] which differs from the Courtis tests in that it affords opportunity to discover what children can achieve from the simplest problem in each of these fields to a problem which is in each case approximately twice as difficult as the problems appearing on the Courtis tests.  The great value of this type of test is in discovering to teachers and to pupils, as well, their particular difficulties.  A pupil must be able to do fairly acceptable work in addition before he can solve one problem on the Courtis tests.  Considerable facility can be measured on the Woody tests before an ability sufficient to be registered on the Courtis tests has been acquired.  In his monograph on the derivation of these tests Mr. Woody gives results which will enable the teacher to compare his class with children already tested in other school systems.  In the case of all of these standard tests, school surveys and superintendents’ reports are available which will make it possible to institute comparisons among different classes and different school systems.  One form of the Woody tests is as follows: