This an abstract of a talk given by me at the Meeting “Mathematical Academic Malpractice in the Modern Age”, Manchester, Monday 21st May 2018.

**Confident students do not cheat: how to build mathematical confidence in our students**

I think it could be useful to address the question which, in my experience, is almost never asked: what pushes problem students to cheat by plagiarising work from their peers and, increasingly, from the Internet? Some answer can be found in Denizhan (2014):

“These students exhibit an inability to evaluate their own performances independent of external measurements.”

Plagiarism is one of the psychological defenses of a student who does not otherwise know whether his/her solution / answer is correct.

Mathematics provides a simple remedy: systematically teach students how they can check their solutions. This will boost their confidence in their answers – and in themselves.

I teach linear algebra; I have at least two dozen undergraduate linear algebra textbooks in my office — none of them provides systematic advice on these matters. The same applies, I think, to any other undergraduate subject.

In my view, the most efficient methods for checking answers in a particular class of problems usually provided by a more advanced point of view. For example,

- all these elementary problems about systems of linear equations can be effectively checked if the concepts of the rank of a matrix is used;
- the correctness of eigenvalues of a matrix can be checked by using the fact that the sum of eigenvalues is the trace of the matrix, and the product is its determinant, etc.

This retrospective reassessment of previous material can give students a chance to see how actually simple it is — and boost their mathematical confidence.

In my talk, I’ll discuss how to incorporate error-correcting aspects of mathematics into course design.

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