In article <S7KdnaLb2Jyk3eDV4p2dnAA@[EMAIL PROTECTED]
>,
Larry Hewitt <larryhewi@[EMAIL PROTECTED]
> wrote:
>"toto" <scarecrow@[EMAIL PROTECTED]
> wrote in message
>news:vm9q7458hu8s1mc50ecv6kl07pri6c0k9e@[EMAIL PROTECTED]
>> On Tue, 15 Jul 2008 12:53:54 -0400, "Larry Hewitt"
>> <larryhewi@[EMAIL PROTECTED]
> wrote:
>>>And that, as you note, geometry is the "formal" math class, requiring
more
>>>rigor in answering questions?
>> Except that in many schools in order to get kids to pass geometry, the
>> schools are using *informal geometry* without rigorous proofs.
>> See:
>> http://hsfs2.ortn.edu/MYSCHOOL/WJONES/infgeom.htm
>> Informal Geometry is a standards-based, Euclidean geometry course
>> which meets the criteria for the state's geometry curriculum. The
>> major difference between Informal Geometry and Geometry AB is the
>> amount of formal proofs that are written in this curriculum. There
>> are more hands-on activities and more real-life geometry problems
>> versus abstract problem solving.
>> Having taught this course in a Chicago Public High School, I can tell
>> you that it is not a college prep course and that while some of the
>> concepts are taught, much of the course is dumbed down. There were no
>> formal proofs with statements and reasons in our course. There were
>> some informal proofs in paragraph form which in many ways was harder
>> for the students to understand. My dd called this course *geometry
>> for stones* and she called Conceptual Physics (physics without math)
>> *physics for trees.*
>I know of no distrcit where geometry is intended to be a college prep
>course.
The main value of the geometry course is to give an understanding
of proofs. The rest is of much less value than one would think.
In a sense, it was a key college prep course before the dumbing down.
>In my district it is the second of 3 reuried course, between the
algebras.
Which makes it essentially meaningless, with the idea that
all should pass.
>I'll admit calling it rigorous is an overstatement. But it is the first
>class where rigor is required, at tleast tothe point of listing _all_
steps
>and explaining why you did what you did.
This belongs in FIRST grade. One cannot build up to mathematical rigor.
1
>The first college prep class is trig, a far more rigourous course.
Trigonometry is a few definitions, a little geometry, and algebra.
There is no way in which it is a rigorous course in the sense
of mathematical rigor.
>But even most college bound kids do not take it, witing until they reach
>college to take a :college algebra" course to cover the basic conspts.
The current college algebra courses at the universities are
not of much value. The problem is that they are given with
the idea that the students could not get it the first time,
rather than the attitude that they had not seen anything of
even fair value. We can do a reasonable job for those of
ability who are ignorant if we take that approach, but only
if we do not put them in with those who can no longer understand,
or treat them as such.
One cannot build up to rigor, and no non-rigorous mathematics
should be taught. One does not need completeness, which means
all steps presented, but full rigor. The teachers should be
REQUIRED to be able to fill in the steps, and I do not believe
that most of the high school teachers of mathematics can even
learn it.
>At my Alma Mater mor than 90% of incoming freshmen took it, just about
>everyone but he math and hard science majors and about half the comp sci
>majors.
And they came out knowing facts but no understanding.
If one does not understand induction, one does not
understand what makes the integers the integers.
--
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@[EMAIL PROTECTED]
Phone: (765)494-6054 FAX: (765)494-0558
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