APOS Theory

In mathematics education, APOS Theory is a model of how mathematical concepts are learned. AOPS Theory was developed by Ed Dubinsky and others and is based on Jean Piaget's notion of reflective abstraction. AOPS stands for Actions, Processes, Objects, Schemas, the four main mental structures involved in the theory. APOS Theory takes a constructivist view towards mathematical learning. Implementations of APOS Theory in classrooms typically use the ACE Teaching Cycle, a pedagogical strategy with three chronological components: activities, classroom discussion, and exercises. Implementations also often use mathematical programming languages, most commonly ISETL.

See also

• Mathematics education
• Constructivism (philosophy of education)
• Reflective abstraction
• Jean Piaget

References

• Arnon, Ilana; Cottrill, Jim; Dubinsky, Ed; Oktaç, Asuman; Fuentes, Solange; Trigueros, Maria; Weller, Kirk (2014). APOS Theory. New York: Springer New York. doi:10.1007/978-1-4614-7966-6. ISBN 978-1-4899-9825-5.
• Oktaç, Asuman; Trigueros, María; Romo, Avenilde (March 2019). "APOS THEORY: CONNECTING RESEARCH AND TEACHING". For the Learning of Mathematics. 39 (1): 33–37.
• Tall, David (1999). Reflections on APOS theory in Elementary and Advanced Mathematical Thinking (PDF). International Group for the Psychology of Mathematics Education.