By Ilana Arnon, Jim Cottrill, Ed Dubinsky, Asuman Oktaç, Solange Roa Fuentes, Maria Trigueros, Kirk Weller
In spite of the truth that APOS thought has been used largely in different scholarly guides, within the layout of textbooks, and in educating perform, there isn't any unmarried references that includes all of the suitable information regarding its elements, and offers assistance approximately its program. The aim of this publication is to give the most components of APOS concept. it's going to be worthwhile for researchers who paintings with, or wish to research extra approximately, this theoretical technique, those who are drawn to the way in which which mathematical conceptions are built in accordance with this conception, arithmetic schooling researchers, graduate scholars in arithmetic schooling, and arithmetic instructors.
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Extra info for APOS Theory: A Framework for Research and Curriculum Development in Mathematics Education
Included in the description of a Schema may be an explanation of how the Schema is thematized into an Object. 1 In addition to describing how a concept might be constructed mentally, a genetic decomposition might include a description of prerequisite structures an individual needs to have constructed previously, and it might explain differences in students’ development that may account for variations in mathematical performance. Thus, a genetic decomposition is a model of the epistemology and cognition of a mathematical concept (Roa-Fuentes and Oktac¸ 2010).
The following example illustrates how the analysis of data may lead to a refinement. In an interview in a study of students’ understanding of spanning sets and span (Ku´ et al. 2011), the authors observed that many students did not understand that the vectors that make up a spanning set are elements of the subspace generated by that set. This difficulty was attributed to a mental construction not accounted 2 A diffraction grating is an instrument used to analyze the light coming from stars. It decomposes the incoming light by diffraction to obtain a pattern of colored lines.
Accommodation refers to a mechanism by which a mental structure is reconstructed and modified in order to deal with a new situation. Both mechanisms are related to the APOS idea of generalization. In the rest of this section, each structure and the way it is constructed is described and illustrated with examples. 1 Actions According to Piaget and adopted by APOS Theory, a concept is first conceived as an Action, that is, as an externally directed transformation of a previously conceived Object, or Objects.
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
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