A Comparison of Equality in Computer Algebra and Correctness in Mathematical Pedagogy (II)

摘要

A perennial problem in computer-aided assessment is that "a right answer", pedagogically speaking, is not the same thing as "a mathematically correct expression", as verified by a computer algebra system, or indeed other techniques such as random evaluation. Paper I in this series considered the difference in cases where there was "the right answer", typically calculus questions. Here we look at some other cases, notably in linear algebra, where there can be many "right answers", but still there can be answers that are mathematically right but pedagogically wrong. We reformulate the problem in terms of articulating the sought-after properties, which may include both mathematical equivalence and algebraic form.