Children's understanding of the addition/subtraction complement principle

BackgroundIn the last decades, children's understanding of mathematical principles has become an important research topic. Different from the commutativity and inversion principles, only few studies have focused on children's understanding of the addition/subtraction complement principle (if a-b=c, then c+b=a), mainly relying on verbal techniques. AimThis contribution aimed at deepening our understanding of children's knowledge of the addition/subtraction complement principle, combining verbal and non-verbal techniques. SampleParticipants were 67 third and fourth graders (9- to 10-year-olds). MethodsChildren solved two tasks in which verbal reports as well as accuracy and speed data were collected. These two tasks differed only in the order of the problems and the instructions. In the looking-back task, children were told that sometimes the preceding problem might help to answer the next problem. In the baseline task, no helpful preceding items were offered. The looking-back task included 10 trigger-target problem pairs on the complement relation. ResultsChildren verbally reported looking back on about 40% of all target problems in the looking-back task; the target problems were also solved faster and more accurately than in the baseline task. These results suggest that children used their understanding of the complement principle. The verbal and non-verbal data were highly correlated. DiscussionThis study complements previous work on children's understanding of mathematical principles by highlighting interindividual differences in 9- to 10-year-olds' understanding of the complement principle and indicating the potential of combining verbal and non-verbal techniques to investigate (the acquisition of) this understanding.