Fostering fluency with basic addition and subtraction facts

The present study involved investigating knowledge and use of the addition-subtraction complement principle (if a + b = c, then c – b = a or c – a = b) by pupils in grades kindergarten to 3. Eighty-one children from three public schools serving a mid-western community participated in the study. Participants were assigned randomly to one of the three conditions: (a) structured training on the complement principle, (b) unstructured subtraction practice, and (c) structured training on a different topic (9 + 7 = ? can be answered knowing 10 + 7 = 17). A computational shortcut task was used to gauge participants’ understanding of the complement principle and their reliable use of the principle. The rationale for the task was that children who know a mathematical relation will use this knowledge to eliminate or minimize computational effort. The task entailed first presenting a “helper item,” such as 7 + 7 = 14 (or a “non-helper” item, such as 8 + 5 = 13), and then leaving it in view when a target problem such as 14 – 7 = ? was presented. Quantitative analyses revealed that the structured-subtraction group outperformed the comparison groups on knowledge of the complement principle and the efficient, appropriate, and adaptive use of the principle as a computational shortcut.Ope