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The objective of this paper is to introduce, into the English scientific-philosophical literature of Genetic Epistemology, a model called the Model of the System of Schemes of Actions and Operations on Symbols and Signs (MoSSAOSS), and summarize its results, so far. MoSSAOSS articulates some of the principal theoretical and experimental results obtained by Piaget and his coworkers, in a systemic, systematic and synthetic view. Here, the term model means a schematic representation of experience, in which the relation of elements can be explored by means of logic and mathematics in order to deduce properties that correspond to direct observable empirical properties, in a sufficiently accurate form. Through explicit definitions and hypotheses, MoSSAOSS intends to reveal, in an abstract and simplified form, the general structure and functioning of the System of Schemes of Actions and Operations on Symbols and Signs. This system makes explicit the necessary elements for the acquisition of knowledge by the epistemic subject (the knower subject), allowing for the explanation of its developmental stages, as well as the attribution of meaning to objects and situations, and to the subject’s actions and operations. Conceived in 1992 and introduced in Portuguese scientific-philosophical literature in 2014, MoSSAOSS has been used in a research program to study the necessary structures for knowledge acquisition, particularly scientific-philosophical knowledge. Its main results are summarized here.