🚀 go-pugleaf

In article <lv1jv0p4bv1hbsbm7jip4vai04pl9ipdcu@4ax.com>,
 <racqueteer@killspamverizon.net> wrote:
>On Thu, 27 Jan 2005 12:09:42 -0800, Jay Kadis <jay@ccrma.stanford.edu>
>wrote:

>>In article <ctbd3h$1j8c@odds.stat.purdue.edu>,
>> hrubin@odds.stat.purdue.edu (Herman Rubin) wrote:

>>> In article <jay-0EC958.09290427012005@news.stanford.edu>,
>>> Jay Kadis  <jay@ccrma.stanford.edu> wrote:
>>> >In article <ctb6i3$1stu@odds.stat.purdue.edu>,
>>> > hrubin@odds.stat.purdue.edu (Herman Rubin) wrote:

 [snip]


>>> >> Even this is not enough, as few teachers understand the
>>> >> basics of their subjects, but proceed by rote.  
>>>  -- 

>>> >OK, got some statistics on this?

>>> How would one get statistics on this?  Let the subject matter
>>> scholars question the teachers on their knowledge of the basics,
>>> and you will find few in mathematics or science who would 
>>> challenge this statement.  But there is no way that you would
>>> get the establishment to agree to this test.  

>>That is pure speculation on your part.

>Yes it is, but for Herman, opinion IS fact.

>> There are examinations that all teachers 
>>must pass to become certified.  It isn't the case that anyone can walk in off 
>>the street and start teaching mathematics.  Perhaps teachers are not at the same 
>>level as cutting-edge researchers in the field, but that does not mean they are 
>>incapable of understanding the material they teach.  I have found that teaching 
>>is the best route to full understanding of the subject matter at hand.

>>> I have taught a few prospective teachers, and my late wife 
>>> taught many of them.  Often coming home after a day of
>>> teaching these, she complained of illness from that.  Not
>>> all of them were bad in the advanced classes, but the one
>>> time she taught prospective elementary teachers in a required
>>> class, it was miserable.

>>Until teachers are respected and paid at a level commensurate with their value 
>>to society you will not get the best of the best to pursue such a career.  
>>Districts with limited funds are forced to accept teachers with limited 
>>abilities.  But that does not reflect the entire educational system.

I have pointed out that the "best and brightest" are not
the ones to teach the same thing over and over, and that to
keep being "good and bright" they have to spend time doing
research and other such activities.  Put them teaching in a
small college, with its higher teaching load, and in a few
years, they are no longer in a good position to continue as
scholars.

			................

>Oh man..  Jay, you have to understand the nature of the man you're
>talking to.  Herman's concept of "understanding" goes FAR beyond that
>of any normal person, and it will not surprise me (though it may you)
>when he comes back and tells you that those degrees are probably
>meaningless, especially if they weren't gained 50-80 years ago - You
>know, in "the good old days"?

It does not go beyond what a "normal" person can do, provided
the normal person is taught the concepts, preferably early,
in WHATEVER field.  One does not learn a concept by learning
definitions or facts or skills; it is learning structure, and
what is behind the structure.  The most important part of
algebra is that a "variable" is a linguistic entity which
can represent anything, and that as long as certain specific
rules of construction are followed, the grammatical form is
correct.  Variables do not have to stand only for numbers,
and it is a mistake, as is now done, to teach them that way.

Similarly, one needs to understand the concepts to translate
relations in other areas into mathematical expressions.  A
mathematician needs to be able to carry out derivations, and
to be able to get solutions to the problems; the user of 
mathematics needs only to be able to get to the level of
using declarative sentences, not to produce works of literature.

>>The problem in math and science education is directly linked to the economic 
>>level of the community.  Communities with high average incomes demand good 
>>schools and get them.  Communities lacking the resources get far less.  This is 
>>the crux of the problem and must be addressed if we want excellence throughout 
>>the educational system.  We cannot afford to let this division of society become 
>>entrenched and further the separation of the haves from the have-nots.  It is 
>>not solely the fault of teachers when education fails to meet our expectations.

This is nonsense.  As long as the public schools teach facts
and formulas, it does not matter.  When the public schools
were teaching reading by the whole word method, any child
who learned in the schools was likely to end up a poor reader,
regardless of the amount spent.  The greatest Biblical scholars,
teaching biology according to Scripture, are not going to 
produce people with any knowledge of modern biology.  And if
they teach it by rote, subsequent learning is deterred.

>Herman doesn't care about that.  He wants all math teachers to
>"understand mathematics", which to him means that they are
>mathematicians first and teachers second.

Someone who is tone deaf is unlikely to be a reasonable
music teacher.  Someone with no grammatical ability, and
these people exist, is not going to be able to present
the structure of a language.  Someone who does not 
understand statistics can teach the various statistical
procedures and formulas, but not what it means.  I could
drill you in the vocabulary of a language, and if you do
not get the grammar from elsewhere, understanding will
not be present.  In this case, there is enough similarity
that a bright person is very likely to get it; mathematical
concepts, which can be often taught in minutes, too many
centuries until someone found them.

My son learned the structure of mathematics and some of
the concepts before first grade, and was at the point
where he could look for them.  My daughter, who is not
a mathematician and not as bright, age nine, and she did
not want to learn too much not being done in school.

The Spanish priests could not imagine a non-alphabetic
language, and destroyed much because they tried to 
force the idea of alphabetic writing on Aztec and Mayan.

Understanding scales does not make one a musician.
-- 
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@stat.purdue.edu         Phone: (765)494-6054   FAX: (765)494-0558