ABSTRACT
Instruction in the basic arithmetic operations comprises the bulk of mathematics lessons during the elementary school period. The difficulties which this material poses are surprising from two perspectives. Beyond the single-digit combinations, children must learn a handful of procedures for using those combinations in multi-digit calculations—carrying in addition and multiplication, borrowing in subtraction, and the long division algorithm. They also must learn to apply the operations to word problems. One of the intriguing discoveries from recent research on early number development is that knowledge about addition and subtraction can be traced all the way back to infancy. Like other infant research, the data stem from infants’ responses to actual sets of objects. Infant knowledge of addition and subtraction has been of particular interest as a way of differentiating among alternative theories of number development. A fundamental yet powerful way of understanding addition and subtraction is as ways of describing operations that transform quantities.
