Conceptual understanding of complement principle and its relation with subtraction by addition

Subtraction problems of the type M, S = ? can be mentally solved by means of various strategies, including the subtraction by addition (SBA) strategy in which one determines how much needs to be added to the subtrahend to get to the minuend (e.g., 75−43=? by ‘43+30=73 and 73+2=75, so the answer is 30+2=32’). Several studies have shown that adults use this strategy frequently and efficiently. Children, however, hardly report it. The lack of conceptual knowledge about the addition/subtraction complement principle (i.e., if a−b=c, then c+b=a) has been put forward as a potential source for children’s scarce (reported) use of this strategy. In the present study, we investigated this relation. We administered three tasks to 67 third- and fourth-graders, two of them focusing on the conceptual understanding of the addition/subtraction complement principle and one on the use of the SBA strategy. Both verbal and non-verbal data were collected. Most children showed conceptual understanding of the addition-subtraction complement principle, but hardly any of them also reported the SBA strategy. Moreover, only in fourth grade significant positive correlations were found between the measures of conceptual understanding and the use of SBA. So, it seems that the lack of conceptual knowledge of the complement principle is not a principal explanatory factor for children’s scarce use of the SBA strategy. We will discuss the theoretical, methodological, and instructional implications of these results, and definitely focus on the intriguing differences between the verbal and non-verbal types of data on both types of tasks.status: publishe