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Sage is open source. A student, or anyone else, can learn how sage computes the answers by reading the source code.

This can even be done interactively, by using the ?? magic. Say you want to learn how the Sylvester matrix of two polynomials is computed. After creating a polynomial object

sage: R.<x> = QQ[]

(x in this case) you can read the source code of sylvester_matrix() like this

sage: x.sylvester_matrix??

Admittedly, this will rarely give you a crystal clear explanation of the algorithm, as most of the time the work is done elsewhere (for example in some C library).