Abstract

BEITES, Patrícia Damas; BRANCO, Maria Luísa Frazão Rodrigues  and  COSTA, Maria Cecília Rosas Pereira Peixoto da. Proof Schemes for Propositions of Linear Algebra with Logical Value True. Relime [online]. 2020, vol.23, n.1, pp.37-78.  Epub May 28, 2021. ISSN 2007-6819.  https://doi.org/10.12802/relime.20.2312.

The purpose of the present work is to analyse proof schemes in students’ productions in a curricular unit of Linear Algebra in Higher Education. Concretely, we study the representations of three students, and their transformations, in tasks that contain propositions of Linear Algebra with logical value true, trying to access their mathematical reasoning. The conclusions of the study indicate that the level of performance in Mathematics of a student may not translate the level of performance of that student in the construction of proofs. They also suggest a possible connection between the contents, and the experience, associated to the first contact of the students with proof and the representations used by them in the proof schemes. Last but not least, the conclusions shed light on the meanings for the students of proof schemes which are not deductive. In a broad sense, the findings show the need for research-based interventions in the classroom to address the challenges of the teaching and the learning of proof in Higher Education.

Keywords : Proof in mathematics; Proof schemes; Mathematical reasoning; Representations; Linear Algebra.

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