Measuring arithmetic: A psychometric approach to understanding formatting effects and domain specificity

Area of Science:

• Cognitive Psychology
• Educational Psychology
• Developmental Psychology

Background:

• Children's arithmetic performance is influenced by various cognitive factors.
• Understanding the interplay between item formatting, cognitive abilities, and arithmetic skills is crucial for effective educational interventions.

Purpose of the Study:

• To investigate the impact of arithmetic item formatting on children's answers.
• To determine if non-arithmetic abilities contribute to performance across different formats.
• To evaluate leading theories of arithmetic cognition, including Triple Code Theory and Encoding Complex Theory.

Main Methods:

• Utilized multitrait, multimethod data and confirmatory factor analysis.
• Examined 1314 3rd-grade students using 11 measures of arithmetic across symbolic and language-based formats.
• Assessed exact and approximate calculation demands and the role of executive attention and language.

Main Results:

• Findings supported Triple Code Theory and Encoding Complex Theory.
• Arithmetic outcomes varied across language, Arabic numeral, and estimation formats, yet remained distinct.
• Executive attention directly predicted all arithmetic outcomes, with language playing a facilitative role.

Conclusions:

• Executive attention is a key predictor of arithmetic performance, irrespective of problem format.
• Language facilitates numerical processing, particularly when executive attention is considered.
• Mathematical problem-solving interventions should target executive attention, language, and their interaction, such as internal speech.