"Herman Rubin" <hrubin@[EMAIL PROTECTED]
> wrote in message
news:g5ktm1$ff6@[EMAIL PROTECTED]
> 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.
>
Nope.
The main value of secondary geometry is to get students to hink spacially.
Look, this will go nowhere.
Here's achallenge for you.
Got into a 9th grade calssroom.
Teach the kids.
Try to get the averaage 15 yr old to understadn and comply with the rules
of formal proofs.
Try to get a 16 yr old to understand number theory.
Or, if you'ld rather, pick a lower grade and start them off "right".
Let us know how it went.
Larry
> 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
|
