Within the U. S., conceptual and procedural competence are also highly correlated. Second and third graders who correctly execute the subtraction borrowing procedure also are more accurate in detecting conceptual flaws in a puppet’s subtraction procedures than are children who do not execute the subtraction algorithm consistently corrrectly (Cauley, 1988). Conceptual understanding of multidigit addition and subtraction and the ability to invent effective computational procedures are also positively correlated in first through fourth graders (Hiebert & Wearne, 1996).