Thinking linearly?

A few thoughts about teaching the exact sciences at an advanced stage (perhaps even earlier? debatable). I find that in some disciplines (especially maths!) linear and step-by-step teaching is given extreme importance. Writing things down very very logically is considered the correct way when teaching in the class rooms. I think this is actually harmful. Students might get used to such presentations and then when it comes to thinking about a problem, they often try to analyse and think in the same logical and linear fashion. This is highly undesirable! Problems are not solved by thinking linearly! Analysis yes, but not problem solving. One often has to relate to several different concepts and draw intuition from other problems that people have solved. This means that you might be forced to jump from one idea to another, try out bold conjectures based on some intuition and so on. Many of these paths will fail but they will add to your intuition about the problem. And it is this process that one must try to teach students. This is not easy. It means that when the teacher lectures, he/she will not complete arguments, often will not provide all the details in one go and most importantly, may not give the complete picture immediately. The teacher will state the goal clearly and then wander around a bit, experiment with ideas and try to convey why some approach works the way it works. This will entail quite some work on the part of the student. It will also leave you confused till you see the whole picture. A good teacher will do this so that you vaguely see the direction but not so much that you will sit back and watch the teacher do all the thinking instead of you.

The benefits of this process are that albeit hard, it does teach you to think on your own with suitable guidance from the teacher. It also conveys the message that solving your own problems is not going to be anything like just learning a subject from a book.

This also is precisely why we need teachers. Books are good to learn subjects linearly. But they rarely convey the intuition behind the subject. A teacher can show us how to read between the lines in a book.

To conclude, linear presentations are over-rated.

And all just to talk !

I had a theory in mind. Let's see if I can get it across properly in words.

We are all beings with some basic needs like food, money, stability etc. The so called gene-related needs. At the same time, we humans have another need. And I think it is 'to communicate'. Very often it is through words. Sometimes through just being together. At other times by doing some activity together. But in the end always to communicate. For instance, we all watch a movie say, and then the real fun is when we discuss it later. The movie itself is relatively secondary. I cannot imagine watching a movie on a deserted island where I would know that for sure it will not be discussed later. At least in my experience, some of the best/happiest moments in the past have been when I've had a cool discussion or an interesting fight/argument or a spirited game of say badminton, or a calm discussion with complete understanding between the people involved.

One could dispose all this under the statement 'humans are social animals'. But most of human social behaviour stems from gene-related reasons like survival etc. The rest I think is to a large extent about communicating. For some reason we are all made such that 'to communicate' is almost a necessity. I get the feeling that a lot of activities come up amongst people just so that they have a reason to communicate. For example, cooking together is rarely about the food itself!

Welcome note

Dear Groningen gang,

On behalf of the (kicked out) president, Hon. Tauqeer bhai and yours truly, I welcome you all to a new way of sharing our views on trivial (mostly) and non-trivial things (rarely) in the world around us. I hope that each one of us will continue to play the same "roles" they have skilfully donned on Friday evenings during the past two years.

Despite what we would like to think, evolution is purposeless and so is our blog. Who knows what might evolve out of it.

Regards,

Jyothi