Individual differences in algebraic cognition: Relation to the approximate number and semantic memory systems.

Area of Science:

• Cognitive Psychology
• Mathematics Education
• Neuroscience

Background:

• Algebraic competence relies on various cognitive skills.
• The approximate number system (ANS) and memory for arithmetic facts are foundational numerical abilities.
• Understanding the interplay between these foundational skills and algebra is crucial for effective pedagogy.

Purpose of the Study:

• To investigate the relationship between approximate number system (ANS) acuity and algebraic cognition.
• To examine the role of memory for addition facts in algebraic learning.
• To control for potential confounding variables such as intelligence and working memory.

Main Methods:

• 171 ninth-grade students completed tasks assessing ANS acuity, algebraic performance (coordinate plane accuracy, expression evaluation, schema memory), and addition fact retrieval.
• Statistical analyses controlled for parental education, sex, reading achievement, numeral processing speed, symbolic number fluency, intelligence, and central executive working memory.

Main Results:

• ANS acuity correlated with accuracy in coordinate plane tasks and expression evaluation, but not with schema memory for algebra.
• Higher frequency of addition fact retrieval errors was linked to poorer schema memory for algebra, but not to coordinate plane or expression evaluation accuracy.

Conclusions:

• The ANS may support spatial-numerical and numerical-only quantity judgments within algebraic contexts.
• Difficulties in recalling basic addition facts may impede the formation of long-term memories for algebraic structures.
• Learning different facets of algebraic competence engages distinct cognitive and neural systems, even when controlling for general abilities.