"Herman Rubin" <hrubin@[EMAIL PROTECTED]
> wrote in message
news:g5q5un$22ve@[EMAIL PROTECTED]
> In article <DJKdnTbdRZZdv-PV4p2dnAA@[EMAIL PROTECTED]
>,
> Larry Hewitt <larryhewi@[EMAIL PROTECTED]
> wrote:
>
>>"Herman Rubin" <hrubin@[EMAIL PROTECTED]
> wrote in message
>>news:g5ktm1$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?
Set up a lab program in the math department, say on Saturday mornings, for
interested parents to enroll their child in. Such programs are common in
Schools of Music (and in other fine arts areas). Music teachers aren't
trained by education departments, but by music departments, so such
programs
serve multiple purposes. They provide hands-on experience to college
professors, who then are teaching actual children, as opposed to just
hypothesizing about how things will work with children. They provide a
research laboratory to test and try out new programs, which then become
common, and they provide observation and practi*** experiences for
students
who are going through music training, before they ever begin any
significant
training in pedagogy. (Music pedagogy is typically a 5th or even 6th year
program, completed after the music requirements are satisfied. Specialist
training in Orff, Kodaly, or Dalcroze isn't even availble until after a
teacher has a baccalaureate degree in music). My university was the first
to begin Orff-Schelwerk in the USA, in a lab program between the
university
and the local schools. Other similar programs have done the same with
Kodaly and Dalcroze, and Edwin Gordon has taken his research as well. The
result is that all of these tested methodologies have found their place in
the elementary school music curriculum, and, in areas where elementary
school music is actually taught by trained music specialists, the quality
of
music instruction K-12 is much, much higher than it was 30+ years ago
(finances have eliminated or cut back music from so many districts that
unfortunately it is relatively rare for a child to get regular cl***** in
the elementary years-and then, such districts wonder why the secondary
music
programs fall apart). Even when there is no trained music teacher, if a
district actually purchases and uses a music textbook series, which are
designed for classroom teachers, many of the principles which have been
shown to be effective will be applied, and the students will STILL get a
higher quality music education than was available in most schools 30+
years
ago.
There is absolutely no reason why other academic departments couldn't do
likewise. If you want to teach children, train teachers, and change
education, the first step is doing it yourself, locally, in a situation
under your control. Prove what you do works, and eventually, what works
will
be adopted. Given that over half my preschool music students this year
were
enrolled in Kumon math (which is simply drill and memorization, at a very
high price tag), I don't think you'd have any trouble getting students.
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