APOS-SRR Approach: a Result of the Networking of Theories Between APOS Theory and Semiotic Representation Registers

The objective of this research was to formally articulate Action, Process, Object, and Schema (APOS) Theory and Semiotic Representation Registers (SRR) Theory through the Networking of Theories methodology. As a result, we propose an approach denominated APOS-SRR, an explicit relationship between the subject, the mathematical object, and the semiotic representation system. This approach integrates the mental mechanisms of APOS Theory and reconceptualizes its structures as semiocognitive structures. The main methodological contribution of this study is the Semiocognitive Genetic Decomposition, conceived as an analytical tool for structuring the process of conceptual construction and for identifying how semiotic transformations are associated with cognitive constructions in advanced mathematical thinking.