The arithmetic with which the American schoolboy of the twentieth century wrestles differs in many respects from the "cyphering" which was truly a stumbling block to many a child in colonial days. Not only have there been significant changes in the subject matter of arithmetic, but also in the aim of instruction, in the place of arithmetic in the plan of education, and in the methods of teaching the subject. In fact many of the distinguishing characteristics of arithmetic as a twentieth century school subject are products of the nineteenth century. The purpose of this investigation is to trace in some detail the development of arithmetic as a school subject and the methods of teaching it in the United States, and to show the influence of Warren Colburn in stimulating and directing this development. Appended are: (1) Table of contents of Dilworth's "Schoolmaster's Assistant"; (2) Table of contents of "A New and Complete System of Arithmetic" by Nicolas Pike; (3) Table of contents of Warren Colburn's "First Lessons"; and (4) Table of contents of Warren Colburn's "Sequel". A bibliography and an index are included. [Best copy available has been provided.]