From Concrete To Abstract...

The other day i was attending a lecture. The professor said an interesting thing. There is one method of learning which is first giving a concrete idea and then making it abstract. So that people identify with the solution or the problem before they can actually relate to the generalized solution. Though its pretty straight forward and basically a solid concept as to how it applies to the different subjects that we study. If we take Discrete mathematics, the subject itself is based on abstract ideas. It deals with abstract ideas before actually putting them into practice. Though it could be done the other way round, it would not be as interesting and in some cases may not even serve the purpose that the subject seeks to achieve. i.e. make us think about situations in a generic manner instead of looking at numbers explicitly.

On the other hand there are programming courses which themselves abstract. From the beginning to the end. A program is itself an endeavor to conceal the underlying structure and simplify the workings for the user of the system. In that sense it increases the concrete nature for the user, but creates a layer of abstraction for the programmer which he must handle. But then to start and end with abstract things may not always be easy. Thus it is best for the student to start from concrete things. But in most of the cases the concepts required for the understanding is not imbibed beforehand. Anyway,.. Lets not get into how courses are designed. But then again, I liked the concept. From concrete to Abstract,... From Abstract to concrete... :-) ...