title: Children's understanding of the addition/subtraction complement principle.
abstract: BACKGROUND
  In 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.
  
  
  OBJECTIVE
  This contribution aimed at deepening our understanding of children's knowledge of the addition/subtraction complement principle, combining verbal and non-verbal techniques.
  
  
  METHODS
  Participants were 67 third and fourth graders (9- to 10-year-olds).
  
  
  METHODS
  Children 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.
  
  
  RESULTS
  Children 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.
  
  
  CONCLUSIONS
  This 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.
authors.affiliation: Centre for Instructional Psychology and Technology, KU Leuven, Belgium.
authors.forename: Joke
authors.initials: J
authors.lastname: Torbeyns
authors.affiliation: Centre for Instructional Psychology and Technology, KU Leuven, Belgium.
authors.forename: Greet
authors.identifier: http://orcid.org/0000-0003-3999-1393
authors.initials: G
authors.lastname: Peters
authors.affiliation: Parenting and Special Education Research Unit, KU Leuven, Belgium.
authors.forename: Bert
authors.initials: B
authors.lastname: De Smedt
authors.affiliation: Parenting and Special Education Research Unit, KU Leuven, Belgium.
authors.forename: Pol
authors.initials: P
authors.lastname: Ghesquière
authors.affiliation: Centre for Instructional Psychology and Technology, KU Leuven, Belgium.
authors.forename: Lieven
authors.initials: L
authors.lastname: Verschaffel
mesh_terms: D002648:Child; D002657:Child Development / Q000502:physiology*; D032882:Comprehension / Q000502:physiology*; D005260:Female; D006801:Humans; D008297:Male; D055641:Mathematical Concepts; D011340:Problem Solving / Q000502:physiology*
keywords: addition/subtraction complement principle; arithmetic; understanding of mathematical principles