In article <DJKdnTbdRZZdv-PV4p2dnAA@[EMAIL PROTECTED]
>,
Larry Hewitt <larryhewi@[EMAIL PROTECTED]
> wrote:
>"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.
Knowing teachers and students, the amount of formal proofs goes
down to almost nothing, and the amount of it learned by students
is likely to be absolute zero even if it is there.
>>>> 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.*
And I must strongly accuse the college admissions offices,
in their rush to get more students, being willing to accept
geometry for stones and physics for trees. These students,
if the term can be used for such, lower the standards of the
college courses, as good student evaluations are now needed
for tenure, and often even for promotion of a tenured associate
professor to full professor.
>>>I know of no distrcit where geometry is intended to be a college prep
>>>course.
It was before WWII, and it should be now. This includes for
those not going into mathematical subjects; it is unfortunate
that our politicians and judges have no idea what a formal
proof is, and what an inductive proof (NOT a proof by induction)
is; the latter is what is used in decisions where the facts are
in dispute.
>> 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.
This does not occur by giving names and formulas.
>Look, this will go nowhere.
>Here's achallenge for you.
>Got into a 9th grade calssroom.
>Teach the kids.
If they understand English, it might still be possible.
>Try to get the averaage 15 yr old to understadn and comply with the
rules
>of formal proofs.
Average, average, average. Students of different ability
MUST be taught differently; not accepting this is denying
the well-established fact that people are different.
>Try to get a 16 yr old to understand number theory.
This might be much easier.
>Or, if you'ld rather, pick a lower grade and start them off "right".
I have posted here, many times, that the time to teach about
variables is when they can read a little and make symbols.
It is part of language; restricted to mathematics, it loses
its simplicity.
>Let us know how it went.
Do you think the educationists would let me try?
--
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
|
