> >Andrei said: I am a mathematician and a teacher of mathematics.
> Aren't we all, Andrei?(depending of course on your definition of mathematics.)
Yes, of course. Simply it seemed to me that some people at this list doubted if I belonged here.
> >I believe that it is my job to teach my students > >the ability whicht may be called `rigorous comprehention'. > > I am not sure what you mean by "rigorous comprehension". I thought our job > was to get students to do, think about, talk about mathematics in whatever > form it may come in.
I coined this phrase `rigorous comprehension' trying to make clear what irritates me about the Standards. According to what I meant, without it, there is no mathematics or teaching it.
> totally lost with this sort of method that Andrei is suggesting. Could > anyone honestly say that you would teach a 12 year old "rigorous comprehension"?
You seem to think that `rigorous comprehension' is something like Drakula. It is just what you have to do with any math problem to start solving it.
> >I need this ability every day when I read mathematical > >books and articles. Without it I could not do research. > >This ability means that when I see a book page covered > >by typographical signs I am trying to build a mental > >model of what these sign describe. > > Ahh, know we get to the reason. YOU need this to do your research. What > about the students? Are they doing research? Do they really NEED this?
This question can be rephrased: do students really need mathematics ? This is a very important question. We can discuss it. The answer is not obvious.
> It is not how you learn mathematics but how your students learn that > counts. Wouldn't you agree? Have you done any research that would > inlighten you as to how students learn mathematics?
It depends on how you define `research'. I have taught a lot. And thought about it. I believe that this is the only thing that matters.
> Maybe you should go back and look at the authors names a little more closely. > To say they have no rigorous comprehension is quite a bold statement.
This argument is below you, Scott. Do you think that names really matter ?
> I will tell you cruelty. Cruelty is a college professor who has no common > sense and insists on subjecting students to his own personal interests and > thoughts that are so far over there heads they get absolutely nothing out > of the subject or the class. And then you wonder why so many people are > turned off by mathematics and avoid it like the plague in college. Pretty > cruel, don't you think Andrei?
Thank you, Scott, for your feeling of humor. We need it at this list very badly. Best regards, Andrei Toom