Learning for exams and learning for yourself are obviously different kinds of activities, even if the level of depth and rigour are similar. For maths-heavy su

Learning for exams and learning for yourself are obviously different kinds of activities, even if the level of depth and rigour are similar. For maths-heavy subjects, I'm not really inclined to believe that traditional exams are the best way to assess a student's knowledge and understanding of the material (especially with regard to rote memorisation). Exams in such subjects haven't changed fundamentally in many many decades, even though we now have lots and lots of new things we could do with them. For instance: do more with computers - like getting the students to solve real-world, many-tentacled, hairy problems by numerical methods, rather than giving them some carefully pruned equation that just happens to have nice analytical solutions. Or introduce more computer-assisted mathematical modelling (e.g. use classical mechanics, to start with). Or on the pure front, teach students to write or at least understand some interesting automated theorem prover. Stuff like that. I suspect that traditional exams have survived simply because they serve their purpose: a percentage of exam-takers fail the exam (which allows the exam-setters to claim that their standards of assessment are rigorous), and a fair percentage will pass the exam, some with flying colours. Whether or not the actual learning goal was achieved has not been determined, since the exam is deemed to be the only instrument that can measure that.