An Investigation of Subtraction Algorithms from the 18th and 19th Centuries

Introduction

How do you subtract? What is your algorithm of choice? The most common subtraction algorithm in the United States today is the decomposition algorithm. While other algorithms exist and are possibly utilized, no other algorithm dominates the contemporary curriculum, classrooms, and pencils of children in the U.S. more so than the decomposition algorithm. Subtraction is one of the fundamental building blocks of arithmetic. Looking to the past and exploring the history of subtraction algorithms can help us glean knowledge of the intended and possibly implemented curricula in past eras. In this article, special attention will be given to 18th and 19th century America. The aims of this article are to identify the different algorithms used during this time period and to discuss implications for the modern teacher.