James Davenport
Visiting Full Professor, University of Waterloo, Canada
Hebron & Medlock Professor of Information Technology and Chairman, Powerful Computing WP, University of Bath, UK
Joint work with Russell Bradford (Bath) and Chris Sangwin (Birmingham)

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?".