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Jaime Escalante and NCTM Standards
"Mr. Escalante has been, and continues to be, highly critical of the
NCTM Standards. He is quoted by Charles Sykes in, "Why American
Children Feel Good about Themselves but Can't Read, Write, or Add,"
as saying, "Whoever wrote [the NCTM math standards] must be a
physical education teacher." Mr. Escalante's endorsement of
Professor Allen's Proposal is a significant acknowledgment of the
failure of the NCTM Standards and the need for clear alternatives."
http://mathforum.org/kb/message.jspa?messageID=1126151&tstart=7485
While doing a search to find out what one famous classroom teacher said about NCTM standards, I found some really interesting stuff. Quite honestly, I was worried I might have found Mr. Escalante endorsing them.
For those of you unfamiliar with Jaime Escalante, he was the subject of the movie "Stand and Deliver" which showed him taking a class of pathetic students and transforming them into powerful mathematicians. What happened to Jaime after his success is indicative of the problems in the field of education where success is pushed out the door as it threatens those that want to develop new fads or really have no desire for changing the status quo (tailspinning) of our intellectual capital in America. For Jaime's full story including "the rest of the story", visit this link:
http://reason.com/0207/fe.jj.stand.shtml
In finding the site Jaime is quoted on above, I followed the conversation that was taking place in the comments as supports and opponents of NCTM standards weighed in on the quote. One person, a supporter of NCTM standards, repeated the same poor excuses we hear in Alpine District from our officials. You can read his full letter here:
http://mathforum.org/kb/message.jspa?messageID=1126159&tstart=7485
In this supporter's letter you'll read:
The traditional mathematics classroom does not
allow for the success of ALL students who are enrolled...
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...
In my mathematics classroom today, students are unable to relate the
mathematics done in class and for homework to the real world...
... although rote learning is
NOT eliminated by the Standards, it is just deemphasized in favor of more
thoughtprovoking, mental exercises which accomplish the same end, but with
many additional benefits!!
The page you MUST read is this one from a brilliant Brazilian named Alberto. Honestly, this page is chock full of great stuff. You can read my clips below but they are only a sampling of what's on the full page.
http://mathforum.org/kb/message.jspa?messageID=1126160&tstart=7485
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...
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 reallife things my father, myself, and some
of my friends did or do. How does your scaled down math address my "real life"? ...
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...
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.
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.
Ahh, the sacred cow has never been gored in finer style. It's really amazing to me that district officials and some principals will tell people, "Oak Norton's research is all biased and flawed" and tell them they need to do their own research to know the truth. Then when they do it and arrive at my same conclusions their research is denounced as biased and flawed. As Dr. Jim Milgram, a member of NASA's advisory panel said, these programs have been around for decades and if they were effective, NASA, IBM and others would be actively looking for high schoolers that went through these programs.
In Utah, our educrats at the state department of education have used the NCTM standards as the basis for Utah's standards. We can do better. We should adopt California's standards which were written by mathematicians that understand the above debate. Just because we want everyone to succeed doesn't mean we should lower our standards to make everyone equally illiterate. We should have high standards and work with quality curriculum to help students achieve those levels of performance. TERC and the host of other NCTM programs won't get us there and should be banned from Utah until new standards are written that promote a foundation for higher education.
Other Resources
Ten Myths About Math Education And Why You Shouldn't Believe Them (excellent point by point analysis with lots of independent research to link to)
http://www.nychold.com/myths050504.html
Testimony to NYC Board of Education Jan 2002
http://www.nychold.com/testimocken020123.html
"In order to offer all children access to rewarding careers, it is critical that no student be forced into a curriculum that precludes the second, more advanced, option. Unfortunately, according to the draft document of the Commission report, the NCTM Standards include neither the rigor nor the formal algebraic skills required by students who will go on to be engineers, scientists, mathematicians, physicians, or educators of mathematics, to which list I would add business persons, architects, psychologists, and many more. I agree completely with that assessment, as do a wide spectrum of mathematicians nationwide and particularly in CUNY. In my own classes alone, over the course of thirty years at CCNY, hundreds of otherwise intelligent students have been forced by their inadequate algebra preparation to change their majors and their career plans.
K12 mathematics curriculum reform is urgently needed. Unfortunately, the use of curricula supported by the proposed vendors is likely to increase significantly the failure rate in college mathematics courses. In particular, the K5 TERC curriculum materials fail utterly to provide the basic experiences of symbol manipulation that are prerequisite to the development of algebra skills."
PBS Documentary "Schools That Work" and TERC Investigations Mathematics March 2005 http://www.nychold.com/letocken050327.html
"The problem with TERC Investigations and similar constructivist curricula is twofold: they are weak in content and they encourage what I would call antimathematical habits of mind. They seem oblivious to the fact that mathematics is a highly layered and complex structure in which working fluently at each new level requires automatic and cumulative mastery of facts and procedures from earlier stages. Further, TERC and similar curricula rely excessively on models and pictures while failing to prepare students adequately for the transition to the symbolbased mathematics that lies at the heart of algebra and calculus."
Mathematics Education Reform: Toward a Coherent K12 Curriculum Oct 2005
http://www.nychold.com/talkocken051002.doc
"Let me return to where I began. This is not just about students who take calculus in college. This is about all children. Every single K8 student is entitled to a math program that allows him or her to enjoy the option, later in high school and college, to take advanced mathematics courses needed for science, engineering, finance, architecture, medicine, secondary math education, and other mathrelated careers."
Do NCTM StandardsBased Programs Prepare Students For Calculus? June 2001http://www.nychold.com/forum01ocken.html
"Perhaps the most puzzling feature of mathematics curriculum reform has been the absence of meaningful participation by the community of academic mathematicians. It is imperative that children who are preparing for college mathematics study curricula that have been devised in meaningful cooperation with college mathematics and science teachers. This has not been the case. Indeed, the deemphasis on symbol manipulation skills in most if not all NCTM Standardsbased curricula poses a clear and present danger, both to American children and to the future American technology. To help children succeed in mathematics, we need to have curriculum development and revision that focus on improving the study and development of algebraic skills rather than throwing them away."
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