> You probably intended this as a game of analogies > between two adults already blessed with a sophisticated > understanding of points, lines and infinity. The > following is directed at using such accidental > analogies in teaching?
Actually, I don't have a sophisticated understanding of points and lines, for if I would, why should I have started this very discussion? I only want to understand.
> How does this help a student? I can?t see how this in > any way leads to any understanding, sophisticated or > not, of points, lines and infinity. When I reach such > silliness in my own pedagogy I STOP. You are beyond > the student?s thinking.
Then I will try to explain to you how this can lead to any understanding, and you can agree or refuse what I'm going to say: Well, first of all, I dare say, and you will agree, that when you want to learn something, and have understanding in that, you first ought to start from the bases of the subject you're going to study, and analyze the bases very carefully, spending a lot of time in their contemplation, for if you misunderstand the bases totally or partially, when you proceed in further inquiries of the subject, you will reach a lot of false conclusions, based on your misunderstandings of the bases. But to properly understand the bases, you need to understand why they are as they are and not different, and to understand this you need rational arguments. My meaning is that he who wants to learn well anything, with proper understanding of the matter, has to understand everything he does in the process of learning, at least having reason in what he does, for if not, if he accepts anything as a doctrine, without the understanding of why that thing is as it is, by reason that he's lazy or by any other reason, I dare say, he will never properly understand the subject, 'cause his knowledge is based on things that he accepted as "doctrines", and he didn't try to understand why they are as they are with rational arguments, and therefore his very knowledge will be a fake knowledge. Would you not agree with me?
> You are beyond the student?s thinking.
Actually I am myself a student, and I don't think this to be beyond my thinking, of course, if I want to have a rational thinking.
> Just stick with the mechanical definitions of open and > closed segments of real numbers.
What you mean, if I'm not mistaken, is to stick with the mechanical definitions without the understanding of them? That is to say, take this definitions as doctrines, and accept them without any problem? But don't you see that your future knowledge will be based on doctrines? On something you don't understand, for you only accepted the definitions as true and therefore you don't know why they are as they are and not different.
> They will get the sophistication in time, and with use.
Of course they will. But don't you agree that with the use and time they will learn to do everything mechanically, and their wonder of why the definitions they have accepted are true will vanish with time.
> Also, would a young student even understand the > meaning or the source of the meaning for male and > female plugs?:) > > Bob Hansen
Maybe not, but we need something simple to start with.