By Ilana Arnon, Jim Cottrill, Ed Dubinsky, Asuman Oktaç, Solange Roa Fuentes, Maria Trigueros, Kirk Weller
Although APOS concept has been used largely in different scholarly guides, within the layout of textbooks, and in instructing perform, there isn't any unmarried references that includes the entire suitable information regarding its elements, and gives assistance approximately its software. The target of this publication is to offer the most parts of APOS conception. it's going to be worthwhile for researchers who paintings with, or wish to examine extra approximately, this theoretical method, those who find themselves drawn to the way in which which mathematical conceptions are developed based on this thought, arithmetic schooling researchers, graduate scholars in arithmetic schooling, and arithmetic teachers.
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Extra info for APOS Theory: A Framework for Research and Curriculum Development in Mathematics Education
The depth and complexity of an individual’s understanding of a concept depends on her or his ability to establish connections among the mental structures that constitute it. These connections form the basis of a Schema (described in more detail in Sect. 5 and in Chap. 7) whose coherence (described briefly in Sect. 5 and in Chap. 7) is crucial to an individual’s ability to make sense of mathematical situations related to the concept. Assimilation and accommodation, the mechanisms used by Piaget in his work, and the mechanism of generalization do not appear in Fig.
The genetic decomposition may explain discrepancies in performance. The student who succeeds may give evidence of having successfully made one or more of the mental construction(s) called for by the genetic decomposition. The student who shows limited progress may show evidence of having begun to make the construction(s). The student who fails may not have made the construction(s) at all or may give evidence of having been unsuccessful in having made the necessary construction(s). If the differences in student performance cannot be explained by the genetic decomposition, then it may be the case that the genetic decomposition needs revision.
This idea is discussed in detail in Sects. 2. Dubinsky (1997), referring to Piaget’s ideas, wrote that: Objects, once constructed, can be transformed to make higher level actions and then processes, and so on. This can continue indefinitely. Moreover, any action, process, or object can be reconstructed, as a result of experiencing new problem situations on a higher plane, interiorizing more sophisticated actions and encapsulating richer processes. The lower level construction is not lost, but remains as a part of the enriched conception.
APOS Theory: A Framework for Research and Curriculum Development in Mathematics Education by Ilana Arnon, Jim Cottrill, Ed Dubinsky, Asuman Oktaç, Solange Roa Fuentes, Maria Trigueros, Kirk Weller