
Re: Fractals
Posted:
May 9, 1995 10:14 AM


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 > 7033561920(w) EMail: kmichal@pen.k12.va.us > Fax: (703) 7909712 or KarenDM@aol.com > >

