There is limited use in teaching the performance of mathematical methods to students who will never use any. If, however, the stress is on teaching the reasons behind the methods - why and how they come about - this happens to be the most effective way to teach multi-staged, purposeful, accurate reasoning, something everyone does need. Discovering that the reasons can be made readily understandable does also reduce the anxiety about the subject and thus could increase the number of mathematics users - something the economy could hardly survive without.

Also for students who will work in mathematics and science, dwelling on the processes that lead to the methods is equally important, but for another reason: Their main task will consist not just of applying already known methods, but of the development of new ones. For this purpose it should be useful to have considered the methods which they were taught from a view point of having had to deduce them on their own.

The colloquium will demonstrate such a reasoning-approach to a wide range of topics - 'from C to C' (counting to calculus…) - where familiar methods are often found to be backed by very little understanding about their "why's".