Mimicry of proofs with computers: The case of linear algebra

This article examines the idea of ‘following the flow of a proof with an example ’ in order to assist the learner in the challenging task of understanding mathematical proofs. This strategy is termed ‘mimicry of a proof’. However, such mimicry can be impractical or unreasonably demanding when the mathematical objects in the proof are difficult to manipulate without technological enhancement. This is the case with many proofs in Linear Algebra, in which the manipulated objects are vectors or matrices. Therefore, the article focuses on the idea of proof mimicry with a computer algebra system (CAS). As examples, this strategy is applied to the proofs of two theorems: the basis theorem and the orthogonalization theorem. In addition, pedagogical guidelines to be followed in constructing a set of computer activities for students are presented and examined. 1