>[snipped in several places] >1. What really is "mathematical power" and how do your students get it? > [The definition given in this reform document differs markedly from > those given in the various Standards documents, in my opinion] I believe that "mathematical power" is the power to use mathematical language to articulate relationships, patterns, etc. that one observes in their dealing with the environment. For example: My son (now 18yrs. old) playes a game called Mancala, I'm sure many of you know it. He is unbeatable! All of our family members, electrical engineers included, have made it their mission to beat him at this game and cannot. It does not matter whether he begins the game or plays second. It does not matter the number of stones that the players begin with. When questioned about what he does (thinks) as he plays he cannot articulate what he is thinking. If he had "mathematical power" he would be able provide the mathematical explaination as to what he is thinking when he plays. Since he has taken mathematics up through pre-calc. It is particularly discouraging to find that with all that math he cannot use the language to articulate his thinking. I see his math knowledge to be as useless as his knowledge of spanish. He has memorized "dialogues" and does not have the power to generate "sentences" of his own. In otherwords he has never been taken to the application/synthesis level in math.
People with "math power" can create their own "sentences" about the world and its relationships.
>3. Comment on the statement: "As computers become more powerful, the > need for mathematics will decline."
I would rather say, as computers become more powerful the need for arithmetic will decline, the need for mathematics will increase.
>4. Why is it that mathematics education in the United States resists > change in spite of the many forces that are revolutionizing the nature > and role of mathematics itself? Our reliance on "sub standard" standardized tests!
>5. Why do you suppose that 50% of school teachers leave the profession > every seven years?
Cut backs in funding are eliminating 2.5 million from our school district budget for next year. 90% of these cuts will be staff.