Children's Difficulties in Subtraction: Some Causes and Questions

Abstract

A model of subtraction development and the computing difficulties and research issues suggested by the model are outlined. It is argued that, in order to mentally compute the differences for written, symbolic problems such as 5 − 3 = □, children first use a counting-down procedure because counting down is consistent with their informal concept of subtraction as “take away” and represents a logical extension of their mental procedure for (N − 1) problems. Counting down requires an ability to count backward while keeping track of the number of backward steps. The demands of the simultaneous processes help to explain the difficulty of subtraction relative to addition, the difficulties some children have with informal subtraction, and why—as larger problems are introduced—children tend to supplement counting down with a counting-up procedure.