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Re: Fractals
Posted:
May 8, 1995 10:15 PM
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According to Andrei TOOM:
>
> On Mon, 8 May 1995, Tad Watanabe wrote:
>
> > Andrei:
> >
> > What is such a big deal? Do you seriously think you analogy of
> > cheerleaders is comparable to the discussion of fractals, no matter how
> > informal it may be, in mathematics classroom?
>
> I am sure that in many cases discussion of fractals or something
> `advanced' like that in middle schools actually is a disguise
> for the teacher's inability to teach students to solve
> elementary, but substantial problems.
Andrei, this is not a list for dogmatic comments. Why are you
"sure that any many cases discussion..." Have you been in
middle school frequently over the years to verify your statement. I have been
for 33 year and I will tell you that you are wrong. Could you
please tell us your experience with middle school education?
I also suggest you read some of Dr. A. Schoenfeld's work on problem
solving. He is considered an expert in the area. He will tell
you that he has changed him mind since his initial research.
Gee, it's refreshing to see someone admit that one can, with
additional knowledge and research, change ones mind.
>
> > You know, I would be much more concerned if students thought arithmetic
> > was "mathematics."
>
> I do not agree with you, and this is important.
> Arithmetics IS mathematics, or, more exactly, can be.
> There are very good arithmetical problems and every human being
> in this century MUST go through an experience of SOLVING
> (rather than just DISCUSSING) them.
> Too many of my (college) students have not had enough of
> this experience and this seems to be the main root of
> their further difficulties.
> Andrei
>
>
I may be wrong but I think George Polya was to have said that
arithmetic was to mathematics as typing is to writing a
manuscript. Arithmetic is indeed mathematics. However,
mathematics is much, much, much more than arithmetic. When I
figure out gaming strategies I use mathematical thinking and
don't necessarily need arithmetic. When I figure out how I am
going to place my students in my classroom to create the best
class environment, I use global reasoning and spatial sense,
but don't use arithmentic. I suspect that your college
students have not experienced any of the changes in mathematics
that the Standards guide us to today. If they had started
DISCUSSING problem solving and strategies in middle school or
earlier, maybe they would be good problem solvers. Also,
math anxiety plays a big role in problem solving. Students
that are anxious need to be in groups where they can identify
students (or teachers, I problem solve with my students) as
role models.
You can believe anything you want about fractals. I'll
continue to be successful with my students using many diverse
activities, not because I don't know how to guide my students
in problem solving, but because I know happy, excited students
are good math students.
I think its time to go to another topic.
>
>
--
Cheers!
Karen Dee
1994 Presidential Awardee Mathematics
Math History Lives!
Karen Dee Michalowicz VQUEST Math Lead Teacher/Trainer
Upper School Mathematics Chair Virginia Quality Education
The Langley School in Sciences and Technology
1411 Balls Hill Rd, McLean, VA
22012 USA
703-356-1920(w) E-Mail: kmichal@pen.k12.va.us
Fax: (703) 790-9712 --or-- KarenDM@aol.com
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