Learning and solving algebra word problems: The roles of relational skills, arithmetic, and executive functioning

Area of Science:

• Cognitive Psychology
• Educational Psychology
• Developmental Psychology

Background:

• Algebra is crucial for advanced mathematics, yet foundational skills are understudied.
• Few studies explore the mathematical and cognitive factors influencing algebra word problem-solving.
• Understanding developmental trajectories of these skills is essential.

Purpose of the Study:

• To examine the relationship between mathematical and cognitive capabilities and algebra word problem-solving skills.
• To investigate how these relationships change across development, from second to ninth grade.
• To identify key predictors of algebra performance over time.

Main Methods:

• Cross-sequential design over 4 years with 3 age cohorts (mean ages 7.85, 10.05, 12.32).
• Annual assessments of algebra word problems, mathematical relational tasks, arithmetic word problems, and cognitive functions (working memory, updating, inhibition, task switching, performance intelligence).
• Cross-sectional analyses and longitudinal autoregressive cross-lagged modeling with structured residuals.

Main Results:

• Cross-sectionally, mathematical relational problem-solving strongly predicted algebra word problem performance.
• Working memory and updating abilities explained variance in relational tasks but not directly in algebra problems.
• Longitudinally, relational and arithmetic skills independently predicted subsequent algebra performance across grades.
• The strength of these predictive relationships remained consistent throughout the studied grades.

Conclusions:

• Developing mathematical relational problem-solving skills is a critical intervention point for enhancing algebra performance.
• Both relational and arithmetic skills are vital, independent longitudinal predictors of algebra success.
• Cognitive factors like working memory play a role in foundational mathematical abilities but may not directly predict algebra performance in this context.