> 1. What happens to children's natural curiosity and enthusiasm for > mathematics as they become socialized by school and society? Why?
This is an interesting question because at first glance it seems to imply that all children lose their natural curiosity and enthusiasm for mathematics as they go through school. But really it doesn't ask that, does it? I would have to say then in response to this question that some children do in fact lose their enthusiasm for mathematics, while other students maintain (and increase) theirs. As for why, I feel one must consider such issues as natural inclination--Are some people more interested in literature or history or biology?
> 2. Comment on the following statement: "Teachers teach only what is > in the textbook and students learn only what will be on the test."
I suppose some teachers are more textbook oriented than others. I imagine the better you know your subject, the less dependent you are on the textbook (But either way, hopefully you are able to use a textbook you are fond of). As for students learning only what will be on the test, perhaps this is natural enough and it is up to the teacher to provide comprehensive exams.
> 3. What should be the principal goal of elementary school mathematics? > What should be the principal goal of secondary school mathematics?
The principle goal---mmm, let's see---I imagine the principle goal of elementary school mathematics is building the basic skills so that the student is able to study mathematics on the secondary level. And on the secondary level, I see the principal goal as--well I see two goals that are equally important, so I'll have to list them both. One is making sure the students are actually able to do the mathematics, and the other is fostering a sense of mathemtics as a pure science (and not something that you necessarily have to apply to something concrete in order to give it meaning--and in this way, hopefully cut down on the number of students who say "When am I actually going to use this?")
And while I have your attention, here's something I've been thinking about lately and if anybody has any thoughts on the matter, I'd like to hear them. It seems here in New York State, in an attempt to integrate the mathematics courses, we renamed Algebra, Geometry, and Algebra II/Trig as Sequential Math Course I, Course II, and Course III respectively. Now I believe in the merits of integrating the courses, but I find the new titles fairly sterile. Isn't it more exciting (and meaningful) to take a course called Geometry than Sequential Math Course II?