SEVERAL INVESTIGATORS have considered problems centering about the teaching of logical or "critical" thinking. Lazar (16) made an analytical and historical study of the terms "converse," "inverse," and "contrapositive" in geometry and their applications in textbooks. He formulated new definitions of these concepts and illustrated them with propositions from plane geometry. Smith (26) published data obtained in 1932 on errors made on a series of diagnostic tests by a group of 114 pupils having a mean IQ (Terman) of 118. He noted the extent to which, under ordinary conditions, students fail to comprehend the "if-then relationship" and the meaning of proof. He also showed how slight changes in the details and complexity of construction exercises increase the number of errors made by pupils. In 1939, with a group of 74 pupils so selected that the mean and the standard deviation of IQ's were the same as those of the 1932 group, the procedure was repeated except that methods of teaching were designed especially to emphasize and facilitate analysis and generalization by the pupils. A comparison of error counts revealed statistically significant reductions. This investigation provided data on the extent to which transfer fails to take place even within a narrow field unless it is facilitated by appropriate instructional methods. Fawcett (9) sought to develop general concepts and abilities related to proof. He emphasized the necessity for clearly defined terms, for assumptions or unproved propositions, and for realizing that no demonstration proves anything beyond the limits set by the assumptions. The majority of his experimental group of 25 pupils was in the eleventh grade, having a median IQ (Otis) of 115. These students were given a course in which the primary features were (a) the development of geometric concepts and principles by individuals and by group discussion, without the aid of a textbook, and with unusual emphasis upon a creative type of logical thinking; and (b) the utilization of nongeometric reasoning situations for introducing, clarifying, and applying logical concepts and abilities. The organization and content of the course accordingly departed markedly from the traditional. Test results indicated that the pupils made a statistically significant gain in the ability to analyze nonmathematical material, while pupils in several other groups used for comparison did not. Fawcett recorded numerous instances of "transfer of training" apart from his tests. Although achievement of geometric knowledge was not the major objective, the median score made by the experimental group