Extended computationalism and algorithmic skills

Classic computationalism considers cognition as the result of purely internal processes, i.e. rule-based transformation of internal (mental) symbols that represent the external world. I present two theoretical approaches to computationalism (Wilson's wide cornputationalism and Well's ecological functionalism) that, on the contrary, conceive the possibility to design computational models of cognition that extend beyond the boundaries of the organism to include environmental factors. In this theoretical framework, I propose an extended cognitive model of what I call algorithmic skills, namely, all the cognitive skills involved in algorithm execution.This model includes the external tools we use in this kind of cognitive activities, such as paper and pencil in written algorithms. Lastly, I discuss in what sense this may be considered as a model of extended cognition and show its potential explanatory power with respect to standard explanations in the field of numerical cognition.