APOS Theory: A Framework for Research and Curriculum by Ilana Arnon, Jim Cottrill, Ed Dubinsky, Asuman Oktaç,

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 broadly in several scholarly guides, within the layout of textbooks, and in educating perform, there's no unmarried references that comprises all of the correct information regarding its parts, and gives counsel approximately its program. The aim of this publication is to give the most parts of APOS idea. it may be invaluable for researchers who paintings with, or want to research extra approximately, this theoretical technique, those who are 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 instructors.

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APOS theory acknowledges that a student may pursue different learning paths or follow different trajectories, as a student moves from Process to Action and back to Process or from Object to Process and back to Object. Despite individual differences, a genetic decomposition describes the structures a student needs to construct in her or his learning of a concept. When verified empirically, a genetic decomposition can serve as a useful model of cognition, as evidenced by a number of empirical studies that show the efficacy of APOS theory as a tool for describing students’ conceptions and in the design of effective instruction (Weller et al.

1, two examples of genetic decompositions were presented; the goal was to illustrate what a genetic decomposition is and how APOS constructions are involved in describing the mental constructions involved in learning a concept. In Sect. 1 an additional example, involving the concepts of spanning set and span, is introduced in order to show how previous research informs the development of a preliminary genetic decomposition. 1 Genetic Decomposition for Spanning Set and Span (Based on Ku´ et al. 2011) The design of this genetic decomposition was informed by three sources of data: results from the review of literature about the learning of basis and spanning set, a report on students’ difficulties in construction of the concept of basis (Ku´ et al.

Assimilation and accommodation, the mechanisms used by Piaget in his work, and the mechanism of generalization do not appear in Fig. 1. Assimilation of knowledge refers to a mechanism by which a subject can apply a cognitive structure, essentially without change, to include a cognitive object the subject has not previously dealt with. 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.

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