Preschoolers' understanding of subtraction-related principles

Little research has focused on an informal understanding of subtractive negation (e.g., 3- 3 = 0) and subtractive identity (e.g., 3- 0 = 3). Previous research indicates that preschoolers may have a fragile (i.e., unreliable or localized) understanding of the addition-subtraction inverse principle (e.g., 2 + 1- 1 = 2). Recognition of a small collection's cardinal value and computational experience, particularly with subtractive negation, may play a key role in the construction of an understanding of inversion. Testing with eighty 3 to 7 year olds revealed that most children demonstrated a reliable and general understanding of subtractive negation and identity at 4 years of age. In contrast, such an understanding of the inverse principle was not achieved by most children until 6 years of age and was preceded by recognition of two and three and an understanding of subtractive negation and identity.