A good video

I just saw a good video on understanding and teaching. It's even funny in places.
The first is here
I think the take-home message is that the teacher needs to say what the teacher is trying to explain, and get all students to actively engage in solving problems and thus prepare the student for the exam.
That's a very superficial assessment, and I might rewrite this blog.

So you think you have explained something?

I was just reading the description by a computer scientist of how his programming language executes.
I could not help thinking that the description was very incomplete, and yet the author was probably convinced that he had explained it well enough.

This is somewhat troubling:
  Are our minds geared to thinking that we have explained something well enough when this is in fact wrong?

I cannot help to think of how we fall for logical traps.

It seemed to me that the author had gone through the following strategy: he wrote down what came to mind when thinking about the execution of the subject. Yet, because the community in that field is tiny and because there is supposed to be a reference to that subject anyway it seemed to him that he had done enough. This is illustrative of what goes on in a small community of researchers: if you don't understand them then you should go and work with them for a certain time and it will sink in.

But there is another aspect: this being a programming language that is available, one can always go and try it out and it will sink in that way.

One of the things that I am trying to point out is that the explanation must be understood in the context of
what resources there are in the community for further explanation.

Concepts that take a long time to get

In my life I have on occasions found concepts that seemed hard to understand.
In retrospect I think that I had not assimilated the background to prepare myself, but whatever the reason
I'll put commit some of these of these to my blog, because I know that it is going to be hard to ask other people for such concepts. Teachers are the ones who have the biggest collection of concepts that are hard to get because they meet these in their students all the time.

One concept I found very hard to figure out was the notion of datum in geography.

Another concept I had trouble was with Universal Element in Birkhoff and Maclane's book on Algebra.
It was very hard to remember even if the definition was very short, whats more it seems to mix ideas
from different levels that should not be there: an element of a set and category theoretic ideas which I thought should have existed at another level.

The various kinds of joins in SQL were rather hard to get at first. I felt I should "get back to those later".


I also remember a friend having a lot of difficulty explaining what he meant by the "time value of money".
I think it was also because I refused to accept his conceptual starting point.



I do know that a lot of people have trouble with pointers in the C language.

I have been told that students have many problems with the notion of limits in Calculus. I never had problems here.

I have seen peole have huge problems with how loops could work in computer "functional languages".