In article <GJWdnXmZ_tO-S-HV4p2dnAA@[EMAIL PROTECTED]
>,
Larry Hewitt <larryhewi@[EMAIL PROTECTED]
> wrote:
>"Herman Rubin" <hrubin@[EMAIL PROTECTED]
> wrote in message
>news:g5gkhi$8imo@[EMAIL PROTECTED]
>> In article <pI-dnXOHJoj97OfVRVn_vwA@[EMAIL PROTECTED]
>,
>> Larry Hewitt <larryhewi@[EMAIL PROTECTED]
> wrote:
>>>"Herman Rubin" <hrubin@[EMAIL PROTECTED]
> wrote in message
>>>news:g5d3av$8bf2@[EMAIL PROTECTED]
>>>> In article <NfWdnUqt8J2EleXVRVn_vwA@[EMAIL PROTECTED]
>,
>>>> Larry Hewitt <larryhewi@[EMAIL PROTECTED]
> wrote:
>>>>>"Herman Rubin" <hrubin@[EMAIL PROTECTED]
> wrote in message
>>>>>news:g58rn5$4gjs@[EMAIL PROTECTED]
>>>>>> 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.
It is, because of the atrocious way it is taught.
The problems set for one variable require the student
to mentally make lots of substitutions. NO word
problem should limit the number of variables used.
>>>>>>>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.
>>>>>Nice in theiry, difficcult to imposssible in real life.
>> Easy in real life, if one concentrates on understanding,
>> and asks steps to be given. Do you remember your geometry
>> course, where you had to give proofs with statements and
>> reasons? If you did not have that course, which is common
>> now, you have probably not had a real mathematics course
>> in high school. The im****tant :
>Yes, I remember.
>And yes, I did have proofs courses in High school.
>And yes, such courses are now part of the advanced high school curriculum
in
>the districts I have detailed knowledge of.
They may or may not be available. It is not unusual for even
good students not to take the proof geometry course. The
more usual course is terminology, and how to compute perimeters
and areas, and maybe a little more. This was the result of the
educationists in NSF around 1960, who did not accept the
excellent book produced by the committee.
>Did you know that also in every district I am aware of --- 4 entire
>states --- that 2 algebra and 1 geometry course, in different orders, are
>all more than 80% of students are required to take to graduate? Public
and
>private.Some require even less, especially private schools.
>And that, as you note, geometry is the "formal" math class, requiring
more
>rigor in answering questions?
I do not trust the contents of ANY of these courses, except
possibly at the best high schools. Most come out not knowing
what a proof is, or even that there is such a thing as a theorem.
>In every one of those states geometry is taught in the 10th grade or
later
>for these 80% (god, I hate block scheduling), who take algebra i in the
9th
>grade.
Does it matter if the course is low?
>This is what society has deigned to be the standard for education. I
agree,
>it is probably not enough. But even this much is more than much of
society
>wants. And this even includes colleges.
>Most colleges require no more than 2 high school credits in math for
>admission. But some require only 1.
And the college courses have mostly sunk. A good student
might not get any of the "standard" upper division mathematics
course, and will not have any way of knowing it.
>You must understand the resistance teachers and HS administrators get
when
>advising college bound students to take more math courses than admission
to
>the college of their choice requires, risking their precious gpa and
>possibly even admission.
>If you want to change high school math education stop blaming high
schools,
>blame colleges, get them to change. Get them to require trig for
admission.
>Get them to require calc II for graduation.
It will not matter. Cookbook calculus is still bad.
>Won't happen. Half their student bodies will flunk out.
At this time, they should. How else is Joe Sixpack going
to understand how poor the education is? I do not consider
more than 1/3 of the college students prepared for college,
and I am not sure what ****tion of the college graduates are
so prepared. There is great pressure not to fail too many.
>Because until then parents are not going to force their kids to take more
>math. When the "authorities" say that rigor is not needed, rigor is not
>provided. When the "authorities" say that trig, analytical geometry,
>calculus, proofs, etc. aren;t needed, then they won't be taught.
>And even this will only influence the college bound kids. ANd, imnsho, it
>will reduce the number of college bound students.
>>>>>How does a teacher determine, for example. whether an error in a
>>>>>computation with negative numbers is lack of understanding, a simple
>>>>>arithemtic error, or a transcription error indropping a sign whe
copying
>>>>>from a work sheet.
>>>> By having the student put down the work, rather than just
>>>> the answer. I am the "czar" of our department's qualifiers,
>>>> and I can assure you that most students make errors on
>>>> most of the type of problems we assign. We give partial
>>>> credit, and once the faculty see how to do this, there is
>>>> not much disagreement on scores.
>>>This is relatively easy to do at the college level, but in 8th grade
>>>forget
>>>it
But if that algebra is done in third or fourth grade?
.................
--
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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