Children's understanding of the addition/subtraction complement principle

Area of Science:

• Cognitive Psychology
• Mathematics Education

Background:

• Research on children's mathematical understanding has increased, yet the addition/subtraction complement principle (if a - b = c, then c + b = a) is understudied.
• Previous research primarily utilized verbal techniques, limiting a comprehensive understanding of children's grasp of this principle.

Purpose of the Study:

• To investigate children's knowledge of the addition/subtraction complement principle.
• To explore the effectiveness of combining verbal and non-verbal methods in assessing this understanding.

Main Methods:

• Sixty-seven 9- to 10-year-old children participated.
• Two tasks were administered: a baseline task and a 'looking-back' task, collecting verbal reports, accuracy, and speed data.
• The 'looking-back' task encouraged children to consider how previous problems might aid current solutions.

Main Results:

• Children in the 'looking-back' task reported using the complement principle for approximately 40% of problems.
• Target problems were solved with greater accuracy and speed in the 'looking-back' task compared to the baseline.
• Verbal and non-verbal data showed a strong correlation, supporting the principle's application.

Conclusions:

• This study highlights interindividual differences in 9- to 10-year-olds' understanding of the addition/subtraction complement principle.
• Combining verbal and non-verbal techniques offers a promising approach to study the acquisition of mathematical principles.
• Findings contribute to a deeper understanding of children's mathematical cognition.