In article <4829b84f$0$302$b45e6eb0@[EMAIL PROTECTED]
>,
Beth Kevles <kevles@[EMAIL PROTECTED]
> wrote:
>Citing "The Bell Curve" makes me suspect everything else in those
>posts... "The Bell Curve" is really NOT good science. It's based on
>ideas that lost respect after World War II (and for good reason)!
Whether or not you accept any racial conclusions from
that book, which IS better science than that of its
detractors who keep making unwarranted assumptions,
the distribution of ability is such that the upper
5% outclass the average, and the average outcl*****
the lower 5%. Our miseducational system tries to
teach all the same.
>My guess would be that, with the advent of the algebra requirement,
>schools are pu****ng kids faster than they can learn. Kids who don't
>develop a deep sense of numeracy, who move from math unit to math unit
>at too quick a pace, never develop the basic mathematical foundations
>upon which algebra is built.
If you are trying to build algebra on that basis, you
do not understand any form of mathematics. There are
excellent mathematicians whose arithmetic is poor. I
happen to have excellent ability there, enough to know
that it is useful, but NOT basic. Learning how to do
arithmetic does not develop a sense of anything except
how to act like a machine.
In any branch of mathematics, computation is the LAST
step, and in practical problems, computers will have to
do it. Here is most of high school algebra:
Variables are tem****ary names for anything.
Use as many as you want.
The same operation performed on equal entities
gets equal results.
Now practice using these.
*The first of those should be taught with beginning
reading; variables are not just for "mathematical"
entities. The second should be taught early.
And honestly, there are a lot of excellent
>teachers out there who have the same problem, and so don't teach math
>verhy well at the elementary level (where teachers are expected to teach
>ALL subjects, not just the ones they understand well).
How many teachers, all of whom passed high school algebra,
can understand the above concepts and use them? How many
understand the integers? Right now, nobody is teaching key
mathematical concepts, except for the "Euclid" geometry
course, which most do not take.
One cannot understand the integers without understanding
induction. Teaching calculation does not do anything
else, and even interferes with learning concepts. The
im****tant part is not how, but why.
>I see no evidence that kids are innately too dumb or unmotivated to
>learn algebra. I see (anecdotally, from personal experience) that kids
>are taught ineffectively in the earlier years. And often its the
>system, not the classroom teacher, at fault!
The system should be abolished. Large homogeneous cl*****
can work well; small heterogeneous ones cannot.
>Where I live there's a big push to have most students take algebra in
>eighth grade. This means pu****ng kids through the earlier curricula
>very quickly, and it's come to the point where the classroom teacher has
>no control over the speed at which the curriculum is taught, even at the
>week to week level.
Not using what I now think is the right approach, my
son, admittedly exceptional, essentially learned high
school algebra from a reasonable text before he was
six. The book did not meet my first principle above,
nor did it mention the second explicitly. I myself
learned algebra in less than 5 minutes just before
entering high school, and proceeded to test out of it.
But few college students understand the first statement
above, which is the key to formulating a real world
problem so that the power of mathematics can be used.
One teacher was very frustrated because his 7th
>graders were having trouble understanding negative numbers. He was
>making progress with manipulatives and the number line, and one by one
>his students were starting to get it. But then the day came for the
>county-required unit *****sment, so he had to cover up the number line
>and give his kids the test. He thought that with another two weeks he'd
>have been able to fill in the gap in their earlier math education for
>this topic, and they would have been able to do well. But that wasn't
>allowed, and so the kids did poorly and went on to the next math unit,
>where they probably did poorly as well.
The current method of teaching mathematics is poor, and
the multiple choice *****sments should be totally abandoned.
See if understanding is present, which cannot be done by
multiple choice or short answer questions, and teach it.
And use "mathematical notation", which is merely precise
language, from day 1.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@[EMAIL PROTECTED]
Phone: (765)494-6054 FAX: (765)494-0558
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