By Ilana Arnon, Jim Cottrill, Ed Dubinsky, Asuman Oktaç, Solange Roa Fuentes, Maria Trigueros, Kirk Weller
Despite the fact that APOS idea has been used generally in different scholarly guides, within the layout of textbooks, and in educating perform, there is not any unmarried references that includes the entire suitable information regarding its elements, and offers suggestions approximately its program. The target of this booklet is to offer the most parts of APOS conception. it may be important for researchers who paintings with, or wish to examine extra approximately, this theoretical method, those who are attracted to the best way which mathematical conceptions are developed in accordance with this conception, arithmetic schooling researchers, graduate scholars in arithmetic schooling, and arithmetic teachers.
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Additional resources for APOS Theory: A Framework for Research and Curriculum Development in Mathematics Education
For example, the formation of the disjunction P _ Q can be described as an Action on the statements P; Q. The Action, which goes well beyond simply putting these symbols into a disjunction expression, involves the construction of a mental image of the two statements and the determination of the truth or falsity of the disjunction in various situations. Through interiorization, the Action is transformed into a Process for forming the disjunction of two declarative statements. If nothing further is done after this Action is interiorized, then it will be impossible for the disjunction to be combined with other statements.
Each of the structures that make up APOS Theory is constructed via a mental mechanism: an Action is interiorized into a mental Process, a Process is encapsulated into a cognitive Object, a Process can be reversed to construct another Process, two Processes may be coordinated to form a new Process, and a Schema can be thematized into a cognitive Object. In their study of uncountable infinite Processes, Stenger et al. (2008) describe the terms structure and mechanism and the relation between the two: 26 3 Mental Structures and Mechanisms.
A cognitive path describes a process of learning focused on the mathematical aspects of the concept. Although it may seem that there is some similarity between “cognitive path” and “genetic decomposition,” their focus and content are different. Cognitive paths describe or suggest a linear cognitive progression based on an analysis of the mathematical aspects of the concepts involved. Instead of a linear progression, a genetic decomposition in APOS Theory describes the mental structures and the mechanisms by which those structures are constructed.
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