FROM CURRICULAR EXPECTATIONS TO PRACTICE: A PROPOSAL TO INCORPORATE MATHEMATICAL PROOF AND JUSTIFICATION PRACTICES INTO EVERYDAY CLASSROOM TEACHING

Abstract

This article presents a proposal to guide the incorporation of mathematical proof and justification practices into everyday classroom teaching. In the context of Basic Education, the Brazilian National Common Core Curriculum (BNCC) includes reasoning, argumentation, conjecture formulation, deduction of properties, and simple proofs. Research in Mathematics Education, in turn, offers contributions concerning discovery, forms of validation, conceptions of proof, functions of proof, teacher mediation, and discussion of arguments. The challenge addressed in this study is to bring these contributions together so that they can inform concrete teaching decisions and foster a more frequent presence of justification and proof in the development of mathematical content. Based on an interpretive theoretical synthesis, four aspects to be considered in the proposal and five guidelines for practice are presented, along with considerations on activity organization, teacher action, the gradual incorporation of these practices, and possible monitoring indicators. The proposal seeks to reconcile exploration, student participation, and mathematical rigor, avoiding both premature formalization and exploratory activities that end without discussion of the validity of statements. Two examples illustrate its application: the proof of the sum of the interior angles of a triangle and the derivation of the formula for the sum of the first natural numbers. The study is theoretical-propositional in nature, and its effects still need to be investigated empirically.