Mathematical Proof
Discourse Genre and Logical Connexions from a Linguistic Perspective
DOI:
https://doi.org/10.17851/2237-2083.32.3.%25pKeywords:
Mathematics, genre, logical relations, connexion, Systemic functional linguisticsAbstract
One of the main tasks faced by those studying Calculus, Algebra or Geometry at tertiary level is writing the text known as ‘mathematical proof’. The purpose of a proof is to prove that an initial statement is true by deductive reasoning, through the alternation of mathematical symbolism and natural language. Beyond the solving of the problem itself, writing this kind of multisemiotic discourse involves particular difficulties; one of them is to establish logical relationships, through natural language, that make sense of relations along the proof. The aim of this study is to offer an initial description of the proof as a genre as well as of the patterns of connexion that are relevant to it. Based on an interdisciplinary work between linguists and mathematicians, a set of proofs constructed by Mathematics professors at a Chilean university are described. This characterization is grounded on Systemic Functional Linguistics, with focus on ideational discourse semantics, connexion in Spanish and mathematical discourse. The paper proposes three stages for the proof: Point of the proof ^ Mathematical reasoning ^ Confirmation. The paper also shows that mathematical proof, like genres from other disciplines, displays predominantly external causal connexions realised congruently and incongruently, and internal connexions realised congruently. The analysis shows that connexions are crucial for the ideational formulation of propositions and for threading together the different stages of the mathematical proof genre.
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