Arithmetic was the first mathematical subject to enter the school curriculum in the United States in a formalized manner. Until the first quarter of the nineteenth century, the prevailing pedagogy of this subject revolved around the tenets of mental discipline theory and the rules method of teaching, which valued memorization and repetitive drill of procedures. This continued until pedagogical alternatives to this approach were offered by innovative textbook writers, most notably William Colburn and his 1825 text "First Lessons in Arithmetic on the Plan of Pestalozzi." In this article, the teaching of arithmetic in the early United States and the influence of Colburn's text is discussed and is later contextualized through their influence on modern mathematics education practice.