This yearbook is the final report of the National Council Committee on Arithmetic. Having endorsed the "meaning theory" of arithmetic instruction, an attempt is made to develop a position that might serve as a basis for improvement of the arithmetic program. After a chapter on the function of subject matter in relation to personality and one on curriculum problems, there follows a chapter on each of the early grades, middle grades, and high school. The next two chapters present discussions of the social phase of arithmetic instruction and enrichment activities, respectively. Chapter 9 presents a discussion of the present status of drill, followed by a chapter on evaluation. New trends in learning theory are applied to arithmetic in chapter 11. Chapter 12 poses many questions for introspective examination. The yearbook concludes with a chapter on interpretation of research followed by listings of 100 selected studies and 100 selected references. (LS)