The failures in the elementary school are caused more frequently by arithmetic than by any other subject in the curriculum. These failures can be traced to three factors: (1) materials (textbooks, practice exercises, special devices); (2) the teacher's methods of instruction or manner of presentation; (3) the methods and mental processes of the pupils. This monograph reports a study of the third factor and presents a detailed analysis of one group of mental processes--those exhibited in dealing with the four fundamental operations in arithmetic.