"Herman Rubin" <hrubin@[EMAIL PROTECTED]
> wrote in message
news:g5j9cu$6iqa@[EMAIL PROTECTED]
> 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.
>
>
No, it is becaue of scoietal attitudes created in large part from attempts
to make intor math rigorous.
I had parents in PTOassemblies talk about how hard math was, how boring it
was, and how a reward for meeting fund raising goasl was a pass to ditch
math.
In college I had fellow students in other disciplies ooh and ahh about me
being a math major --- it was just "so hard".
I had parents debate the need for math with me when I called them in
becauee
theur kid slept through first period.
>>>>>>>>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.
>
Not around here.
The proof aren;t as riorous as the grad level geometry course. but they
are
proofs.
An they learn far more than simple area and perimiter ccalcs for tri- and
quadrilaterals.
About half the course is proofs of the angle theorems and extensions of
these theorems into the larger multilaterals.
Even this is betyond many students --- ther eis a high failure rate. A
dirty
little secret is thattwo failures puts you into a "math for dummies"
section
open to seniors on;y who ar ein jeopardy of mot graduating if they don;t
pass geometry and algebra ii/.
>>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.
>
So you say.
Truth is, there are very few texts in circulation, most texts are very
simialr, and courses tend to look alike.
>>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?
>
I do not understand.
>>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.
>
Thye willnot take it because they do not need it.
A journalist does not need topology.
A registered dietician doe snot need a linear algebra course.
A lawyer deos not need differential equations.
>>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.
>
So ther eis no hoep.
All you want to do is complain?
>>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.
>
That is your whine.
But hte people paying the bills are satsdisfied.
AS I said vefore, who am I to tell others how to think?
Larry
>
>>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
|
