>Mr. Hanson, > >I must say that Pat Robertson and the Christian Coalition would be very happy >with the way you have stood up for their platform.
I'm no right winger nor a member of the Christian Coalition. And I don't agree with either of you.
>However, as much as I respect Jaime Escalante, I believe that he is VERY wrong >about the NCTM Standards.
I don't care for sacred cows, either way. I'm not going to discuss persons here, but points.
>The traditional mathematics classroom does not >allow for the success of ALL students who are enrolled.
Much less today's NCTM classroom. Indeed, I doubt that it allows for the success of ANY student; it seems to me that the very definition of "success" has been mangled.
>Traditionally, classes >with diverse social, economic, and ethnic make-ups have seen only the brightest >students from the upper-middle class strata excel.
The "ethnic" word insults me. I'm a brown skinned Brazilian, not at all "upper-middle" class. My father went from being a poor Amazon River fisherman to a successful electrical engineer on his own wits, and he wasn't a WASP either.
Your equating "traditional teaching" with race is, in my view, one of the great reasons why minorities are so trodden upon in this country. There is no difference between a brown skinned person and a white one as far as intelligence or competence are concerned. If education is failing in this country, it isn't because minority citizens are somehow "less capable" of taking a serious course and being successful at it; in my opinion, it is rather that there's so many people interested in keeping minorities down and "different" and "oppressed" that they don't take real steps towards real equality.
There'll only be EQUALITY - real one - when minority people are demanded the same performance and delivery level as anybody else.
>The attempt of the NCTM Standards is to level the playing field in the >mathematics classroom by encouraging equal opportunities for all students >involved to build their own foundations on which to place basic and advanced >mathematical concepts.
This is the party line, and far from the truth. What you call "equal" opportunity is rather diluting content and demand so much that anyone can get through it without any effort, and consequently without any real learning. The only "equal opportunity" here is the opportunity not to learn and to claim one did. If you equate this with "helping disadvantaged minorities", you're rather slapping us in the face.
>In my mathematics classroom today, students are unable to relate the >mathematics done in class and for homework to the real world.
I live in the real world. I depend on real world mathematics to make my living. And the sort of math I need day to day is very far away from what you - or the NCTM - call "real life". Have you ever designed a computer ? Wrote a complex 3D graphics program ? Simulated a crystal ? Translated computer programs into binary ? Built a wind tunnel ? A hydroelectric power station ? Sent a satellite into space ? These are some of the real-life things my father, myself, and some of my friends did or do. How does your scaled down math address my "real life" ?
If any of your students wants to follow my path - and I'm a well paid computer developer and architect - he'll need to know a lot more math than what the NCTM teaches. Let me give you a hint: set theory, logic, algebraic structures, measure theory, topology, analysis, integration, multivariate calculus, tensors, matrices, linear algebra, graph theory, computer algorithms, lambda calculus, discrete math, fourier transforms.
I could go on; this is MY real life, and the real life of many a professional. The real life of the people who invent, design and build the things you take for granted and the buzzwords that feed your learning. Because THAT is why we teach mathematics, so that some of our students can go on carrying that torch.
Is your teaching up to this challenge ?
>The Standards >attempt to encourage teachers to focus more on the applications of mathematics >and the appreciation of mathematics (connections, connections, connections!!).
Applications of mathematics can only be seriously tackled after the student has a fairly comprehensive grasp of a number of concepts. But if by "application" you mean trivial money or marble problems, these are irrelevant to real mathematical knowledge, and they should have no place in the classroom.
As for appreciation, I've studied math for most of my life and I'm still not in a position to "appreciate" it. I find this concept tremendously conceited, that young students can somehow "appreciate" mathematics or decide on their own whether or not this or that has "connections" with real life, or that they're competent to "critically think" about mathematics.
And in the end, learning mathematics isn't about connections: it's about learning mathematics.
>By encouraging teachers to do this, the NCTM has also established the direction >that textbook publishers should be taking in order to help more students achieve >success in the mathematics classroom.
"Success" here is such a misleading word. Just listen to the freshman and sophomore college teachers in this group, and you'll find out that, much contrarywise, we're doing an incredible poor job in teaching math to our HS students today. And part of the credit must necessarily go to NCTM style methods.
>I cannot take anything away from Mr. Escalante; he succeeded with a group of >students that everyone had given up on. However, I think that is the point of >his success. His classes primarily consisted (at least in the beginning) of >students >from the same socioeconomic background: there was no diversity in his >classroom. Further, he motivated these students by challenging them and >convincing them that he KNEW they could do the mathematics--a strong >underlying tone of the NCTM Standards, as well.
Excuses, excuses. Every individual is different, every class has a personality. It is the responsibility of the teacher to find it and to create a level of interpersonal chemistry that helps students to learn. But even in this particular case, I have my serious doubts: to me, the SAT means nothing, and success in mathematical standardized tests cannot be taken as a serious measurement of mathematical "success". An exam that tests REAL mathematical knowledge cannot have more than five or six problems for a 4-hour time limit; it must be open book and open notes, to weed out trivialities - each problem require more than one non-trivial insight to be solved.
Because THAT is the way mathematics appears in real life. REAL real life, you see; not the party-line watered-down version of it.
>I believe that too many people have short-changed the Standards by taking >what they are attempting to promote much too lightly. The basis behind them >lies much deeper than just elimination of rote learning, although rote learning is >NOT eliminated by the Standards, it is just de-emphasized in favor of more >thought-provoking, mental exercises which accomplish the same end, but with >many additional benefits!!
The very fact that you use the word "rote" shows that you're in the wrong path. There's a lot of exercising and skill acquiring to be done in any serious math course, and that cannot be avoided. Just like a soccer player or a concert violinist, learning mathematics requires an extensive amount of preparation and exercising over years and years. THERE IS NO WAY OUT OF THIS, and the more we avoid holding this bull by the horns, the more it'll gore us and turn otherwise healthy students into mathematical morons.
There are no "mental" exercises in mathematics that don't involve a lot of mathematical knowledge and manipulation. Mathematics isn't just a set of facts that must be memorized or analyzed or "critically" understood; it involves a skill that must be continously honed, a capability of thinking precisely, a continous banging against intellectual walls so that the individual's capacity to handle complexity increases steadily over the years.
Sorry, the NCTM standard, as far as I see it, is far from this ideal.
>Lastly, I'll leave you with the perfect description of what a math teacher >should be. This quote comes from the book _The Dancing Wu Li Masters_ by >Gary Zukav. It is the description of a t'ai chi master:
>He begins from the center and not from the fringe. He imparts an understanding >of the basic principles of the art before going on to the meticulous details, and he >refuses to break down the t'ai chi movements into a one-two-three drill so as to >make the student into a robot. The traditional way...is to teach by rote, and to >give the impression that long periods of boredom are the most essential part of >training. In that way a student may go on for years and years without ever >getting the feel of what he is doing.
Oh, Please. Whatever this is, it isn't mathematics. Even the dialetics you use is totally out of place. I suggest you go to places where mathematics is used in real life, talk to professionals that need it, go to colleges, talk to math, physics, chemistry, statistics, astronomy teachers; find out what real life REALLY is, as far as using mathematics is concerned.