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Re: Fractals
Posted:
May 9, 1995 10:14 AM
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Right on Karen Dee!!!! I agree with you on every point -- expecially the
"going on to another topic" observation.
J. Albani
On Mon, 8 May 1995, Karen Dee Michalowicz wrote:
> 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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