The Mental Structures and Mechanisms of APOS Theory
APOS Theory is a theory of mathematical understanding, its nature, and its development. It is an outgrowth of Piaget’s theory of reflective abstraction (Piaget 1971) and, although originally created to apply Piaget’s ideas about children’s learning to postsecondary mathematics, it has been applied to elementary school and high school mathematics as well. The basic tenet of APOS Theory, a constructivist theory, is that an individual’s understanding of a mathematical topic develops through reflecting on problems and their solutions in a social context and constructing or reconstructing certain mental structures and organizing these in schemas to use in dealing with problem situations. The main ideas in APOS Theory were introduced in Dubinsky (1984). The acronym APOS was first used in Cottrill et al. (1996).
The mental structures proposed by APOS Theory are actions, processes, objects, and schemas (and thus the acronym APOS). The...
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References
Arnon I, Cottrill J, Dubinsky E, Oktac A, Roa Fuentes S, Trigueros M, Weller K (in press) APOS Theory: A Framework for Research and Curriculum Develpment in Mathematics Education. Springer.
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Dubinsky, E. (2014). Actions, Processes, Objects, Schemas (APOS) in Mathematics Education. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4978-8_3
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