By Ilana Arnon, Jim Cottrill, Ed Dubinsky, Asuman Oktaç, Solange Roa Fuentes, Maria Trigueros, Kirk Weller

ISBN-10: 1461479657

ISBN-13: 9781461479659

Despite the fact that APOS idea has been used largely in several scholarly courses, within the layout of textbooks, and in instructing perform, there is not any unmarried references that includes the entire correct information regarding its elements, and offers suggestions approximately its software. The aim of this ebook is to provide the most parts of APOS conception. it may be invaluable for researchers who paintings with, or want to examine extra approximately, this theoretical method, people who find themselves attracted to the way in which which mathematical conceptions are built in keeping with this thought, arithmetic schooling researchers, graduate scholars in arithmetic schooling, and arithmetic teachers.

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The mental development of a Schema will be discussed in Chap. 7. As research has evolved, there are many genetic decompositions published by authors around the world (see the annotated bibliography in Chap. 12). In general these genetic decompositions have been tested by research and either supported or refined and then used for new research or in the design of teaching activities. Refinements of genetic decompositions will be considered in greater detail in Sect. 5. 3 Role of the Genetic Decomposition in Research Genetic decompositions play a central role in APOS-based research, since a theoretical model is necessary to provide researchers with hypotheses that can serve as the basis for the design of theory-based instruments to obtain and analyze 38 4 Genetic Decomposition data from students.

1. It may be recalled here that the description included in the genetic decomposition is not the same as the mathematical introduction of a concept, as is clearly illustrated by the example on mathematical induction shown in Sect. 1. There are genetic decompositions based on data from observations of students who are learning a mathematical concept. Analysis of observations leads to a description of the cognition of the concept, which can be verified empirically. 34 4 Genetic Decomposition Trigueros and Martı´nez-Planell (2010) followed this approach in their study of students’ learning of two-variable functions.

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.

### 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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