The complexity of the relationships involving the human mathematics, the phenomena and the noumenal mathematics: suggestions for epistemological approaches in the classroom
DOI:
https://doi.org/10.5007/1981-1322.2023.e93064Keywords:
Complexity, Construction x discovery, Languages, Mathematics, ClassroomAbstract
Languages consist of foundations composed of signs, demanding a speaking mass to transform them into social realities. They are classified into: (i) historical languages (idioms) and (ii) artificial (referring, the latter, to specific techniques, such as Mathematics). The languages, including Mathematics, are simplistic and reductionist, remaining in a lower position than the complexity of the phenomenal and noumenal worlds. The investigation described in this text was of a theoretical nature, based on Morin's philosophy of complexity. It is assumed that languages are chronological constructions in charge of both individuals and societies. Not getting confused with the respective thoughts, the languages, however, walk pari passu with them. Notwithstanding the aforementioned discrimination, in this article, for didactic purposes: (i) idiomatic signs and the cognitive activities related to them are called, without distinction, languages; (ii) mathematical signs and the cognitive actions concerning them are called, indifferently, Mathematics. The hypothesis whose coherence we tried to show in this scientific communication is that Mathematics (as a symbolic structure and as technical thinking) is elaborated over time with a view to achieving increasingly accurate understandings, explanations and consensus on (among other things) phenomena and noumena. In other words: Mathematics is human, and with it we move towards so-called noumenal Mathematics. The pedagogical contribution of this work consisted of the argumentative foundation of the proposal that, in Mathematics classes, there should be discussions, debates, reflections and/or meditations about what knowledge is, particularly mathematical knowledge, with emphasis, in such classes, to ideas based on the philosophical system of complexity.
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