Subtraction by addition. A most efficient strategy for solving symbolic subtraction problems?

Children in Flanders are traditionally taught to solve symbolic multi-digit subtractions, such as 815 – 668, by directly subtracting the smaller number from the larger one (DS). However, one can also make use of subtraction by addition (SBA), whereby one computes how much there is to be added to 668 to get at 815. Especially for subtractions with a small difference between the two given numbers SBA seems particularly suited (e.g., 903 – 886). Several studies have shown that adults use SBA frequently, efficiently, and adaptively, and some recent studies have also found evidence for frequent, efficient, and adaptive SBA use in children. The current dissertation had three main goals: (1) expanding the existing literature about children’s SBA use, (2) examining the associations between children’s and adults’ executive functions and their selection and execution of SBA, and (3) studying the relations between children’s SBA use and their subtraction-related conceptual knowledge.

Study 1 (Chapter 2) examined SBA use in fourth- to sixth-graders of varying mathematical achievement levels. Results showed that children solved almost half of the subtractions with the untaught SBA strategy and used this strategy more efficiently compared to DS, especially on small difference subtractions. The children adapted their strategy selection to the numerical characteristics of the subtractions and to their individual strategy speed, and the sixth-graders were adaptive for their individual strategy accuracy too. In Study 2 (Chapter 3), third-graders of varying mathematical achievement levels’ SBA use was examined, using two-digit subtractions (e.g., 72 – 64). These children also showed frequent, efficient and adaptive use of SBA, albeit to a lesser extent than the fourth- to sixth-graders of Study 1.

Study 3 (Chapter 4) examined the relation between adults’ executive functions and SBA use. Updating skills were, as expected, related to strategy efficiency, but inhibition and shifting were unexpectedly not related to strategy selection. Study 4 (Chapter 5) examined the relation between executive functions and SBA use in a sample of children. Overall task proficiency was associated with all three executive functions and more detailed analyses showed that strategy selection was associated with updating whereas strategy execution was associated with updating and shifting.

Finally, in Study 5 (Chapter 6), the relations between children’s SBA use and their subtraction-related conceptual knowledge were examined. The occurrence and frequency of SBA were not associated with children’s subtraction-related conceptual knowledge. However, it was found that children’s adaptive use of SBA was associated with their knowledge of the addition/subtraction complement principle (i.e., knowing that if a + b = c, then c – b = a and c – a = b).