How do we recognize when an answer is "right"?
This is a question that has bedevilled the use of computer systems in
mathematics (as opposed to arithmetic) ever since their introduction. A
computer system can certainly say that some answers are definitely
wrong, in the sense that they are provably not an answer to the question
posed. However, an answer can be mathematically right without being
pedagogically right. Here we explore the differences in the context of
computer marking of traditional homework and show that, despite the
apparent distinction, it is possible to make many of the differences
amenable to formal treatment, by asking "under which congruence is the
pupil's answer equal to the teacher's?".
