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. > >
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: firstname.lastname@example.org Fax: (703) 790-9712 --or-- KarenDM@aol.com