Individual differences in the development of children's arithmetic fluency from grades 2 to 3

Area of Science:

• Cognitive Development
• Educational Psychology
• Mathematics Education

Background:

• Symbolic integration of number associations is crucial for mathematical development.
• Early arithmetic skills, including addition and subtraction, form foundational knowledge.
• Understanding the hierarchical nature of learning arithmetic is essential for educational interventions.

Purpose of the Study:

• To provide empirical evidence for the process of symbolic integration of number associations.
• To investigate the developmental trajectory of addition, subtraction, and multiplication skills.
• To examine the relationship between basic arithmetic fluency and applied mathematics performance.

Main Methods:

• Longitudinal study with Canadian children assessed in Grade 2 and Grade 3 (N=244).
• Assessed general cognitive skills (vocabulary, working memory, reasoning, inhibitory control).
• Administered single-digit addition, subtraction, and multiplication tasks, alongside applied mathematics measures.

Main Results:

• Addition and subtraction skills were reciprocally related, independent of cognitive skills.
• Subtraction fluency in Grade 2 predicted multiplication fluency in Grade 3.
• Both subtraction and multiplication fluency predicted applied mathematics performance, with multiplication mediating the subtraction-applied math relationship.

Conclusions:

• Learning arithmetic associations follows a hierarchical process.
• Developing arithmetic fluency involves integrating novel components into existing associative networks.
• Subtraction and multiplication skills are key predictors of applied mathematics success.