Algebra and its Grammar: Philosophical and Educational Eeflections

Abstract

In this theoretical essay, I intend to reflect on the philosophical foundations of algebra and its teaching possibility from the Epistemology of the use of Arley Moreno, debtor of Wittgenstein's philosophical therapy. Initially I bring up a discussion of how Wittgenstein changes his thinking, abandoning an idea of a rationale for understanding a grammar based on human praxis. I then discuss the linguistic nature of algebra, where I argue that it is a language game that has a grammar, in the Wittgensteinian mold, and point out consequences in teaching based on this understanding. From the idea that meaning is in use, I argue that language should be given greater prominence in teaching, as the use of algebraic language is what allows meaning to be obtained, and this is possible when the student takes possession of grammar immersed in the algebraic language game.