The cause-effect paradigm

Some people find differential calculus very easy. Others find vector algebra very easy. However, given that our education system is firmly unidirectional for many justifiable reasons, the calculus-folk would have had to suffer vectors before they came across what they liked. This happens to most students. Unfortunately, the process is so rigorous that such students may be driven to lose focus or interest in the subject as a whole. There could be no other way to do it, but that doesn't mean there's no better way to teach such subjects inside classrooms.

From time to time, students and teachers alike need to be reminded that each topic in a subject is weak by itself, and only with the assistance of other topics is anything achieved. Instead of going from specifics to the larger picture, why not come from the larger picture to the specifics? After all, and this is just an (convenient) example, mathematics is a powerful but singular set of tools used to solve problems in the real world: every problem is application driven, including in string theory and loop quantum gravity, where, without the verification of their hypotheses by experiments, each remains just a strongly-defended opinion.

[caption id="" align="aligncenter" width="510" caption="The tools of multilateral thinking can be used within classrooms as well to improve efficiency and productivity."][/caption]

I must concede that some problems are better solved using some tools than others, but keeping in mind why the problem is being solved like that is important. Even if calculus provides a circuitous route to a solution, what's wrong with its being adopted by the calculus-lovers to get there? When they get there, the relationship between the problem and the solution becomes clearer: there is a better cause-effect relationship established than when a student struggles through vectors and is exhausted by the end, reluctant to take it up again.

As far as laying the groundwork is concerned, teaching students everything is the way to go: at some point later, then, they will be better equipped to make a choice - between what they think they ought to stick with and what they think they can afford to avoid. However, in this order of things, the problems solved using tool-set A and tool-set B, even if in different terms, could be the same, or related in some way so that even what seems difficult could be better understood in terms of what seems easy.

These are only musings concerned with the different ways through which students can convert information into knowledge. The point is: as long as we're here to solve problems, let's have fun doing it.