Construction of Logical Knowledge: Study of Borrowing in Subtraction

This is a study of the extent to which procedurally proficient children construct the part/whole logical structure that underlies the borrowing algorithm in subtraction. Thirty-four children identified as procedurally proficient were questioned about the values that were exchanged during borrowing and the conservation of the minuend for three subtraction problems. Of these children, 35% conserved the minuend, and only half of those also knew the values that were exchanged. This suggests that an understanding of the part/whole logic of number may be necessary to understand place value and borrowing. Future researchers need to examine ways to encourage children to construct the general, logical principles that underlie arithmetical operations.