Abstract
The aim of this chapter is to explain where APOS Theory came from and when it originated. A discussion of the main components of APOS Theory—the mental stages or structures of Action, Process, Object, and Schema and the mental mechanisms of interiorization, coordination, reversal, encapsulation, and thematization—points to when they first came on the scene and how their meanings developed. The published research of those involved in the development of APOS Theory, which includes some early colleagues and students of Dubinsky as well as those who were members of the Research in Undergraduate Mathematics Education Community (RUMEC), is described. The descriptions in this chapter are very brief and will be expanded in later chapters.
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- 1.
Capitalization is used to differentiate between Piaget’s terminology and Dubinsky’s use of Action, Process, Object, and Schema.
- 2.
As Piaget (1972) acknowledged, subsequent research showed that the age at which various cognitive developments occur could vary as a function of the child’s culture and other factors such as aptitudes and interests.
- 3.
Piaget is using the symbol “+” here, not as addition, but as “and.”
- 4.
Later, SETL was replaced by the interpretive programming language, ISETL, developed by G. Levin.
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Arnon, I. et al. (2014). From Piaget’s Theory to APOS Theory: Reflective Abstraction in Learning Mathematics and the Historical Development of APOS Theory. In: APOS Theory. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7966-6_2
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