By Ilana Arnon, Jim Cottrill, Ed Dubinsky, Asuman Oktaç, Solange Roa Fuentes, Maria Trigueros, Kirk Weller
Even though APOS concept has been used greatly in different scholarly guides, within the layout of textbooks, and in instructing perform, there is not any unmarried references that comprises all of the suitable information regarding its elements, and gives counsel approximately its software. The aim of this publication is to offer the most components of APOS thought. it may be important for researchers who paintings with, or want to study extra approximately, this theoretical process, those people who are drawn to the best way which mathematical conceptions are built in response to this conception, arithmetic schooling researchers, graduate scholars in arithmetic schooling, and arithmetic teachers.
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Extra resources for APOS Theory: A Framework for Research and Curriculum Development in Mathematics Education
34 4 Genetic Decomposition Trigueros and Martı´nez-Planell (2010) followed this approach in their study of students’ learning of two-variable functions. The authors used observations of student work to develop a preliminary genetic decomposition of two-variable functions. They then conducted interviews with students who had completed the course and used the interview data to refine their preliminary analysis. The design of a genetic decomposition can also be based on the historical development of the concept.
Revision ! data analysis yields a genetic decomposition that reflects very closely the cognition of the concept for many individuals and that can be used in the design of instruction that positively affects student learning. There are several issues to be clarified. When referring to a student in the context of APOS Theory, the researcher is not considering a specific student. Rather, he or she is considering a “generic student,” that is, a representative of the class of students who are learning that concept.
As we have said, this means that some internal construction is made relating to the action. An interiorized action is a process. Interiorization permits one to be conscious of an action, to reflect on it and to combine it with other actions. (Dubinsky 1991, p. 2 Description of Mental Structures and Mechanisms 21 In the same spirit, Dubinsky et al. (2005a) give the following description of a Process and interpret it for the case of functions: As an individual repeats and reflects on an action, it may be interiorized into a mental process.
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