A subject's test performances have little meaning until they have been compared with norms. The norms that have proved most useful are those based upon age. A subject whose score equals that of an average six-year-old is said to have a mental age level of six years; if the score equals that of the average ten-year-old, the mental age is ten years, etc. A particular subject whose actual chronological age is eight years may have a mental age of four, six, eight, ten, twelve, or even fourteen years. Dividing the mental age by the chronological age gives us an index of brightness known as the intelligence quotient, or I.Q. For example, the eight-year-old of six-year mental age has an I.Q. of 75; the eight-year-old of ten-year mental age, an I.Q. of 125.

The educational significance of mental age lies in the fact that it determines what a subject is able to learn, what can be profitably taught him. Children entering school with a mental age of six years can be taught to read; when the mental age is much less than this, their reading progress is slow. On the other hand, a child who enters school at the age of six or seven but with a mental age of nine or ten years is able, if given a chance, to cover all the work of the first three grades in the first school year.

The educational and social significance of the I.Q. lies in the fact that for a given subject it tends to be fairly constant throughout the period of growth. The child whose I.Q. is 75 at the age of six is not found with an I.Q. of 125 or 150 a few years later. Increases, decreases, and fluctuations of I.Q. do occur, but in the large majority of cases they are rather small in amount, rarely more than 15 or 20 points, and on the average not more than 5 or 6 points in a total range among school children from I.Q.'s below 50 to I.Q.'s above 150.

The child below 60 I.Q. is ordinarily classifiable as feeble-minded and is not likely ever to develop beyond the mental age of eight or nine years, as intellectual growth pretty well ceases by the age of fifteen or sixteen years. Subjects in the range between 60 and 80 I.Q. may or may not be able to make their way in the world, depending largely on their emotional, volitional, and other non-intellectual equipment. Those of 75 to 90 I.Q. may be classified as normal but dull, those of 90 to 110 I.Q., as average normal, those of 110 to 130 as superior, and those above 130 as very superior. About ten children in a thousand test as low as 70, and about an equal number as high as 130. On the average four or five in a thousand are above 140 I.Q. About 15 per cent test below 80 I.Q. and about an equal number above 120 I.Q. It is from those above 115 or 120 I.Q. that we get the majority of our college students. Those as low as 90 are rarely able to graduate from high school, and those as low as 80 rarely progress beyond the seventh or eighth grade.

Intelligence tests are widely used in the schools in grouping children for instruction. Teaching can never reach optimum efficiency in classes of extreme heterogeneity. The class range of ability is reduced by division into A and B sections, and still more by a three-fold or five-fold classification. Classification of children into X, Y, and Z groups (corresponding to bright, average, and dull), with special classes for the feeble-minded and for the most highly gifted, has been found to yield the best results. X and Z groups, for example, do not profit maximally from the same type of curriculum or from the same pedagogical procedures. The methods and subject matter of special classes for defectives have little in common with those suited to average children, and much the same can be said of special classes for the highly gifted. The widespread introduction of special classes for the gifted is unquestionably one of the most significant movements in modern education.

Classification of a given child for instruction is not based upon intelligence tests alone, but takes account of health, previous scholarship, and personality factors. Nor is placement looked upon as final; the progress of each child is followed, and classification is changed when it appears desirable. The aim is to fit the school to the child in order that each may profit to the greatest possible extent from the instruction given. This makes it necessary to have objective measurements, not only of intelligence, but also of as many traits of mind and personality as it is possible to secure. The result is that psychologists are busily engaged in devising, validating, and standardizing scales for the measurement of achievement in all the school subjects, others for the measurement of special aptitudes, and still others for various aspects of personality, interests, and attitudes. In most cases the tests of personality traits must be regarded as tentative and experimental, but they are opening important fields of research and will in time give a much more scientific basis for education than we now have.

The most successful tests, other than those designed to measure general intelligence, are the standardized tests of achievement in the school subjects. These are in part replacing the old-fashioned school examinations which were so notoriously unreliable and subjective. The new-type examinations (the standardized test) call for a far larger and fairer sampling of the child's knowledge and yield scores which are not influenced by the bias of the examiner. When they are used in connection with intelligence tests, the promotion and classification of pupils is effectively removed from the realm of guesswork.