In article <173d74hoh9ejhv26tari2uq56lv4hekj4r@[EMAIL PROTECTED]
>,
Bob LeChevalier <lojbab@[EMAIL PROTECTED]
> wrote:
>Barbara <mom_2_one@[EMAIL PROTECTED]
> wrote:
>>On Jul 10, 9:41am, hru...@[EMAIL PROTECTED]
(Herman Rubin) wrote:
>>> In article <486f7172.10114...@[EMAIL PROTECTED]
>,
>>> Way Back Jack <Rela...@[EMAIL PROTECTED]
> wrote:
..............
>Herman doesn't consider "basic high school-level algebra" to include
>the "basic mathematical concepts" that he is talking about, which are
>theoretical and abstract. He thinks that "basic high school-level
>algebra" is mostly plug and chug recipes for solving problems, and
>rote memorization of terminology, and he considers neither of these to
>be real "mathematics".
>>> The following includes essentially all of algebra, except
>>> for technical terms not used at the high school level:
>>> A variable is a tem****ary name for something,
>>> which must maintain its meaning in a given context.
>>> The same operation performed on equal entities
>>> yields equal results.
>>I respectfully disagree. For whatever reason, the term *algebra* has
>>taken on some mythical status as something extremely difficult and
>>fear-inducing.
>The reason, as I learned from raising two kids who got that attitude,
>is that *algebra* IS extremely difficult and fear-inducing.
>All other subjects (except the more mathematical sciences) use the
>normal English language, where words have fuzzy meanings that can be
>gleaned from context, and there is some overlap with the methodology
>that they use in solving non-academic problems.
>Mathematical language is first and foremost *precise*. Misspell a
>word and people will understand you. Fail to remember a word in most
>subjects, and you can talk around the word and show that you
>understand. But in mathematics, every step must be followed
>rigorously, and the most minor error means that you are totally and
>irrecoverably wrong, unless you notice the error and start over or
>backtrack. Nothing else in a kid's life works like that. Life allows
>for some amount of sloppiness. Mathematics does not. Teachers don't
>know how to teach this (if they realize that this is the essential
>difference) and kids see it as "difficult" and ultimately not
>kid-like.
Unfortunately, teachers who do not know better grade on the
answer. One should grade on understanding what is to be done,
and as in English, errors should be corrected and pointed out
to the student.
Often, the teacher grades on whether the problem is done as
indicated in the textbook recipe. There may be many ways
about doing the problem; if the second sentence is followed,
other than arithmetic errors or sloppiness, there will be
no mistake made.
This precision in mathematics is also needed in ALL of the
sciences, and alas the public seems unable to understand that
the government cannot just legislate in violation of the laws
of nature, and achieve miracles.
>>Yet without referring to it as *algebra* per se, the
>>aforementioned concepts are introduced in most math curriculums in the
>>4th or 5th grade (5th grade at One's school, which uses a truly awful
>>math curriculum). Discussion at lunch -- One's friend: *your school
>>is so far behind ours! WE'RE learning algebra!* One *We're not even
>>close to algebra. We're learning about variables.*
>>Of course, the answer is not to re-name the subject. Rather, the
>>answer is to show the students that algebra isn't that difficult.
>You can't show what isn't true. Mathematics is difficult unless one
>first learns to appreciate precision and rigor. That may be why
>skilled musicians tend to do well in math - part of becoming skilled
>is learning that precision. But most kids don't stick with music for
>the same reason - hours of practice learning to produce precisely the
>sound you want isn't worth it to them.
Teach the appreciation of precision and rigor in first grade,
and that part of the problem will disappear. We CAN teach
precise mathematical concepts to kids, but it is difficult to
do this with adults. Stop hurting children by avoiding the
rigor which adults seem unable to understand.
--
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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