Without systematic methods of testing, it would be a very difficult task to discover just what connections might be wrongly or inadequately formed, in the case of a given child. The standardized measuring scales and practice exercises, devised during the past fifteen years, furnish a systematic means of exploration. These are constantly being extended and improved, to cover each and every kind of habit that a child must acquire, for achievement in arithmetic. The principle of these scales and tests is to establish by experiment the speed and accuracy of typical school children, grade after grade, in the performance of the various functions separately. It thus becomes possible to discover in the case of a deficient pupil whether he needs correction and drill in every function, or in only one function. By means of the Courtis tests, for example, it may be discovered whether a child’s difficulty is in addition, multiplication, division, in speed or accuracy, or both speed and accuracy, and so forth. The use of existing scales and tests for diagnostic purposes has been described by Courtis, Uhl, Anderson, and others. We may expect great improvement in these methods in the future. At present the standardizations are in terms of school grade norms. A better plan for diagnostic purposes would be to standardize in age norms, giving a percentile distribution for each twelve-month interval of the period of immaturity. VII. NERVOUS INSTABILITY AND SPECIAL DEFICIENCY IN ARITHMETIC Nervously unstable children are, as Burt has pointed out, often deficient in arithmetic, even when in general intelligence they are not deficient. This follows from the same causes of failure as were set forth under discussion of nervous instability and special difficulty in reading. To build up little by little the intricate hierarchy of arithmetical habits, each habit in its essential sequence, is a task uncongenial to the flighty, uncontrolled, or negativistic neurotic. Individual instruction is here, again, the solution of the problem. The neurotic can learn arithmetic within the limits of his intelligence, by means of patient individual instruction, given preferably at rather brief sittings. VIII. ARITHMETICAL PRODIGIES