Integrating Higher-Order Thinking Skills, Cognitive Load Theory, and Metacognition in Algebraic Problem-Solving

This study synthesizes 30 years of research (1990–2020) on algebraic problem-solving, integrating Higher-Order Thinking Skills (HOTS), Cognitive Load Theory (CLT), and metacognitive strategies to enhance student outcomes. Utilizing a critical synthesis approach with data from student interviews, problem-solving observations, and longitudinal tracking, the analysis reveals consistent patterns across diverse educational contexts despite limitations and variable factors like teaching styles and cultural differences. Results show a significant increase in problem-solving accuracy from 52% to 78%, with students developing strategic thinking, including problem-type recognition, strategy selection, and self-monitoring. The integrated framework is effective across various algebraic tasks, from basic equations to complex polynomials, addressing core reasoning skills rather than superficial procedures. These findings challenge algebra’s reputation as a barrier, offering educators a robust approach to foster skill development, confidence, and self-responsibility. By emphasizing reflective learning and self-responsibility, this framework makes algebraic reasoning accessible, transforming it into a gateway for mathematical proficiency across diverse student populations.