Re: Is there really that big of a change in high school geometry teaching in the past 15 years?
- From: "Dave L. Renfro" <renfr1dl@xxxxxxxxx>
- Date: Sat, 8 Nov 2008 05:28:33 -0800 (PST)
rabbits77 wrote:
I recently started to tutor a HS sophmore taking Geometry.
I have not looked at HS geometry since I myself was in HS
well over 15 years ago. I remember pretty much classic
Euclidean geometry, let's call it "postulates and proofs".
What is interesting is that I went to a very bad public HS
in another state and would have expected something more
rigorous from this course since he is going to a prominent
public high school in a prestigious community.
What this student showed me is a very far cry from those days!
While I remember a text that more or less mirrored Euclid's
Elements this student didn't even have a text but a series
of photocopied course materials that seemed to break the
material down to a very very fine grain. That is, a whole
chapter on SSS, a whole chapter on SAS, etc. I guess I can't
say that this is bad...I would not have minded such a treatment
of the material back when I was in HS but does this represent
a real shift in how the subject is taught(for better or worse?)
or just particular to this school?
As someone who has spent many years browsing through every
volume of quite a few journals in university libraries
(Bull. AMS, all MAA journals, Math. Gazette, Mathesis,
and many more), this sentiment has been coming up since
at least the 1870s, when an organization was formed in
England in order to revise the geometry curriculum (the
organization later started a journal, now known as The
Mathematical Gazette). Another major reform took place
around the turn of the century (1900) that was spearheaded
by John Perry, and many more reforms followed over the years.
When you read the literature from all these various eras
(things like book reviews, commentaries on math education, etc.),
it's amazing how all the critics seem to be making the same
criticisms, despite the fact that what they're criticizing
winds up being _exactly_ the material the next generation's
critics hold up as being the golden standard of excellence.
In recent years, with the rise of discussion groups (and later,
the rise of the internet), we can even find the same phenomenon
being played out there, as the following post from roughly your
HS era shows.
------------------------------------------------------------------
"How Prevalent is Students' Proving Theorems in Plane Geometry???"
sci.math (1 December 1994)
http://groups.google.com/group/geometry.pre-college/msg/7dd3b7d5abdebc37
I have been largely out of touch with high school mathematics
since, well, high school (class of '64).
So it came as quite a surprise when a friend recently informed
me that it is no longer automatic that a high school course in
Plane Geometry have a strong emphasis on students' proving
theorems from axioms.
My question to those of you who are high school math teachers is,
How prevalent in Plane Geometry courses these days is the
inclusion of a strong emphasis on students' proving theorems?
I'd like, if possible, a ball-park figure: Is it closer to 5%,
or 25%, or 50%, or 75% or 90% or (you name it) of all high school
Plane Geometry courses that strongly emphasize students' proving
theorems?
Thanks,
Dan Asimov
------------------------------------------------------------------
Dave L. Renfro
.
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