APOS Theory

APOS Theory is a framework that explains how people develop mathematical understanding through four interconnected stages: Acting (performing actions), Planning (thinking about those actions), Observing (watching the outcomes), and Symbolizing (using symbols to represent ideas). As students move through these stages, their comprehension deepens, enabling them to perform more abstract and sophisticated mathematical thinking. The theory emphasizes that understanding is a dynamic process, built through interaction with methods, reflections, and symbolic representations, helping learners develop a more complete and flexible grasp of mathematical concepts.