The present work intends to analyze demonstration schemes in student productions in the university subject of Linear Algebra. Specifically, we study the representations of three students, and their transformations, in tasks that involve propositions of Linear Algebra with a logical value of truth, trying to access their mathematical reasoning. The conclusions of the study indicate that the level of academic performance in Mathematics of a student may not translate the level of academic performance of that student in the construction of proofs. They also suggest a possible connection between the contents, and the experience, associated with the students' first contact with the demonstration and the representations they used in the demonstration schemes. Finally, the conclusions clarify the meanings attributed by the students to non-deductive proof schemes. In a broad sense, the results show the need for classroom interventions, based on research, to generate solutions for the teaching and learning challenges of the demonstration in Higher Education.
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