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Re: RE: algebra epiphanies
Posted:
Aug 20, 2009 3:38 PM
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Well said!
MaryLiz Pierce
In a message dated 08/20/09 12:25:17 US Mountain Standard Time, JGroves@Kaplan.edu writes:
Robert Hansen wrote:
> I have been watching the comments, and recollecting
> back on every experience I can think of. I will
> agree that there is an "anxiety" in some children
> that goes beyond the norm and is clearly
> disfunctional. I don't however believe that math
> itself or the way that it is taught is the direct
> cause of it. The issue is sophistication.
How can you expect students to understand math if the curricula
and textbooks are themselves junk? Textbooks full of template
examples, disconnected topics, rote procedures, etc. with little
or no reasoning, little or no motivation. No wonder students
can't understand the books they try to read! The books make little
sense to begin with. And teachers teach the same stuff in books
so that students have no idea what is going on because almost all
the reasoning is missing. If what is being taught is junk to
begin with, then it will still be junk--no matter how it is
taught.
Most K-12 schools don't teach real math but phony math that makes
no sense, that is nothing but disconnected facts and formulas
and procedures, that is nothing but cookbooks being disguised
as math books. So math makes little sense to most students because
the "math" that is taught is nothing but nonsense.
Steen makes a good point in his article "Twenty Questions About
Mathematical Reasoning":
"It may seem obvious that anyone suffering even mildly from 'math anxiety'
would not engage in much mathematical reasoning. But this is not at all the
case. Many students (and adults) who fear mathematics are in fact quite capable
of thinking mathematically, and do so quite often--particularly in their
attempts to avoid mathematics! What they really fear is not mathematics
itself, but school mathematics [Cockcroft, 1982]." They fear school
mathematics because it is meaningless junk to them. And it is meaningless
junk because there is little attempt by teachers and books to present
math so that it makes sense.
> Society expects a certain level of sophistication in
> the student's reasoning ability to say that they have
> "learned" math. Math is pretty easily defined,
> especially a topic like algebra. Math has a clear
> goal to find answers and math can find answers. There
> are no fuzzy corners to hide in and "almost algebra"
> simply doesn't make the cut.
If math is this easily defined, then why do so many educators have
trouble seeing that school math is not real math, that it is
actually junk? Education is so corrupted that most of us who work in
education, including me, have been hurt by all the corruption by being
taught to believe in some of or even lots of this junk. Then we get
used to it and later have trouble seeing that it is junk.
> Now, take society's rightful expectation of how much
> math does it take to mean math and add to it this
> message that "everybody does algebra". A message that
> is FALSE according to the current results, the
> previous results or any results. Add those two
> together and what do you expect the kid to do?????
There is no doubt that this adds to the problem. But if schools
taught real math, not this phony stuff, then everyone could learn to
do algebra.
> If you don't understand what I mean then take a good
> look at sports, where the same thing happens.
> Students were left out of sports not because they
> didn't want to play, not because they couldn't play,
> but because they couldn't play well enough to make
> the "cut". I love the alternative sports leagues that
> have opened up and that do not require "trying out"
> for the team. These leagues were a long time coming.
> But you will never see the end of varsity and little
> league.
Ability in math and ability in sports are completely different
kinds of abilities. This comparison doesn't work. However,
what is happening in math classes is happening in sports as well,
but just because it's supposed to work that way in sports doesn't
mean it's supposed to work that way in K-12 math.
> In any event, I think we have to really start looking
> at whether or not, even with something like algebra,
> that seems simple to us, if we are not in fact asking
> for every kid to make the varsity team. If I were to
> draw a pie chart of math by volume used in this
> country, spreadsheet math would account for 95% or
> more of the math. I understand the academic side of
> enlightening everyone. And I don't have a ready
> answer as to how we are supposed to instill reasoning
> without math, though I have seen reasoning without
> algebra, albeit it was not sophisticated enough for
> every job possible. But I think there is much more
> skill left to teach in math even though it starts to
> move laterally instead of forward. Skills that the
> student will use rather than barely struggle through.
I think you're going too far in comparing algebra to a varsity
team. Many more students are capable of learning algebra than
you realize, but algebra is taught like stuff from a cookbook
and without reasoning so that kids don't get it. They don't get
algebra because it's taught as nonsense, not because they are
incapable of learning it.
Jonathan Groves
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