Re: Good Textbook for First Geometry Course for Talented Students?

From: maky m. (mmanch01_at_my-deja.com)
Date: 01/03/05 

Date: 3 Jan 2005 08:56:12 -0800

Herman Rubin wrote:
> ... maky m. <mmanch01@my-deja.com> wrote:
> >Karl M. Bunday wrote:
> >> Hi, everyone,
> >
> >> I wonder what you would suggest as a best textbook for a first
> >> high-school-level geometry course for talented students?
> >
> >maybe you should ask the school's principal.
>
> Unless the principal believes in much better education for
> bright students than most schools even have any provision
> for, this is not likely to get any good results. But in
> that case, how likely is he to be a principal?

don't principals have to approve titles to be used in public school
classrooms?

the answer is subtle, i do not blame you if you fail to realise that it
is affirmative.

> >> I'm trying to gather information to make a suggestion to a local
> >> mathematics program. I am aware of one program that formerly used
> >> Gene Murrow and Serge Lang's textbook Geometry (Springer-Verlag)
> >> and in recent years has used Michael Serra's textbook Discovering
> >> Geometry (Key Curriculum Press).
> >
> >is serra's that glitzy book with one million undeveloped topics and
no
> >skill content?
>
> What do you mean by "skill content"? If you mean being able
> to compute answers to standard type problems, YOU are a big
> part of the problem.

perhaps you haven't seen the textbook mentioned above.

anyways, your concept of "problem" with the mediocre state of
geometry/math education seems naive at best. a big part of the problem
is not those who view skill as an integral part of the learning
process, but rather those who profess any one-dimensional pedagogic
style such as displayed in the textbook mentioned above.

> A good geometry course will have very little computation in it.

do you have an example of such book?

...

> >> What do you think? If you were recommending a textbook for a
> >> class of students selected for high math ability taking a first
> >> secondary-level geometry course, what would you recommend? What
> >> do you like about your preferred textbook?
> >
> >i would probably not worry about recommending a geometry book but
> >rather a geometry teacher instead.
>
> If the course is one tied to algebra and computing answers,
> it is effectively useless. There were good results from
> the old "Euclid" books,

who said or implied anything about a geometry course having to be "tied
to algebra and computing answers?" you, not me.

> even if taught by those with little understanding.

practically nothing (read again PRACTICALLY NOTHING) taught by clueless
people yields good results. examples abound in most american public
schools colleges and universities.

> One of the better modern variations would be even better.

example?

> As for a geometry teacher, get one who believes in teaching abstract
> concepts, and who understands them as such, not merely abstractions
> of the concrete,

this is a nice ideal - it will clash with reality as soon as one
discovers that for most people, learning is accomplished best from the
basic to the complex and not the other way around.

> and has had background in them.

agreed. perhaps the state of mathematics education in america would be
in better shape if the trillion and one mathematically deficient
"educators" were competent in the subjects they teach and not
manipulated by bureaucrats and/or managers.

> --
> This address is for information only. I do not claim that these
views
> are those of the Statistics Department or of Purdue University.
> Herman Rubin, Department of Statistics, Purdue University
> hrubin@stat.purdue.edu Phone: (765)494-6054 FAX:
(765)494-0558

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