Mathematical reading and interpretation of statements: Semantic challenges in problem solving.

desafios semânticos na resolução de problemas

Abstract

This theoretical essay discusses mathematical reading from the perspective of epistemology and cognitive psychology, consolidating it as the central architectural component in problem solving. It dismisses the premise that failures in problem solving stem primarily from operational inabilities, shifting the focus to noise in semantic decoding and register translation. Based on Duval's Theory of Semiotic Representation Registers, the study analyzes the cognitive cost of converting natural language registers into algebraic and figural registers. Toulmin's argumentation model is incorporated to dissect the semantics of proof, showing how warrants and logical backings depend on a rigorous exegesis of quantifiers and statement constraints. We conclude that the development of symbol sense and mastery of mathematical syntax are imperative for overcoming epistemological obstacles, requiring that reading be treated as an act inherent to mathematical modeling itself.