It may be said at the outset that oral, written, and inner presentations of initial situations, oral, written, and inner announcements of final responses, and oral, written, and inner management of intermediate processes have varying degrees of merit according to the particular arithmetical exercise, pupil, and context. Devotion to oralness or mentalness as such is simply fanatical. Various combinations, such as the written presentation of the situation with inner management of the intermediate responses and oral announcement of the final response have their special merits for particular cases. These merits the reader can evaluate for himself for any given sort of work for a given class by considering: (1) The amount of practice received by the class per hour spent; (2) the ease of correction of the work; (3) the ease of understanding the tasks; (4) the prevention of cheating; (5) the cheerfulness and sociability of the work; (6) the freedom from eyestrain, and other less important desiderata. It should be noted that the stock schemes A, B, C, and D below are only a few of the many that are possible and that schemes E, F, G, and H have special merits. PRESENTATION OF MANAGEMENT OF ANNOUNCEMENT OF INITIAL SITUATION INTERMEDIATE PROCESSES FINAL RESPONSE A. Printed or written Written Written B. " " Inner Oral by one pupil, inner by the rest C. Oral (by teacher) Written Written D. " " Inner Oral by one pupil, inner by the rest E. As in A or C A mixture, the pupil As in A or B or H writing what he needs F. The real situation As in E As in A or B or H itself, in part at least G. Both read by the pupil As in E As in A or B or H and put orally by the teacher H. As in A or C or G As in E Written by all pupils, announced orally by one pupil