During the twentieth century, major changes occurred in conception of arithmetic as a school subject. These changes resulted from both the study of arithmetic itself and from influences from movements and developments outside the subject matter; and they have affected both the content of arithmetic and the methodology of presenting that content to students. The author discusses the study of content, of learning and of the learner as key components in the changes in mathematics education during the first half of the century, and concludes that in order to be effective, arithmetic has both a mathematical aim and a social aim. Instruction must be meaningful and organized around the ideas and relations inherent in arithmetic as mathematics. However, to be intelligent in quantitative situations, students must see sense and have experience in using the arithmetic they learn in ways that are significant to them at the time of learning. Brownell concludes that both aims are both essential and attainable to a functional curriculum in arithmetic. This article is reprinted from the February 1954 issue of the "Arithmetic Teacher" (also reprinted in the October 1986 issue of the "Arithmetic Teacher" [see EJ341852]).