🚀 go-pugleaf

In article <jay-7E1D5F.12094227012005@news.stanford.edu>,
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.  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.

This POSSIBLY might be true in the case of developing
skills, which has NOTHING to do with understanding.  It
might also be the case that teaching concepts and their
development may increase the understanding, but it cannot
bring the person to understanding in the first place.

A good test is one which someone who understands the 
concepts, but has forgotten even most of the details,
can be done given sufficient time, but one who has
memorized the textbook and all the procedures will 
fail miserably.  No basic concepts are taught by
learning the mechanics of the arithmetic operations,
and they can be taught without having facility with
those operations.

>> 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.  

The "best of the best" in mental ability and grasp
of concepts will not last long as teachers; their
minds are not the kind who can do the same kind of
job for years on end.  They can be professors at
research universities, where they are not expected
to teach the same thing over and over.  And even
these will not understand the concepts if they are
presented too late, with losts of computation and
other rote first.

>Districts with limited funds are forced to accept teachers with limited 
>abilities.  But that does not reflect the entire educational system.

It does.  The present requirements are of those
things which weaken education.

>> The best piece of clear evidence we have is the "new math"
>> debacle of more than 40 years ago.  The teachers could not
>> handle the texts which had been tested on tens of thousands
>> of children.  There was a massive program to teach the teachers
>> of this and of high school mathematics, which ended in failure.
>> The university where I was in 1959 had a summer school for 
>> high school teachers who were supposedly the good ones; I
>> did not myself teach in that.   One of those who did stated
>> that at best 10% could learn the basic undergraduate abstract
>> mathematics courses, which should be needed to teach even
>> middle school mathematics.  Unfortunately, in the years since
>> then, those courses have declined under the pressure of 
>> giving degrees to weak students.

>When I see gross generalizations like you made, it causes me to suspect they are 
>made without the requisite background knowledge.  My wife is a  public 
>high-school math teacher and is pursuing a graduate degree in her field.  In her 
>department, there are two teachers with Doctorates and several more with 
>Master's degrees.  Do you think they are incapable of understanding mathematics?

A master's degree in mathematics is rarely meaningful.  And
it is possible to get doctorates, and even do research, in
many areas without adequate basics.

I have been involved in evaluating candidates for faculty
positions for almost a half century now, and I know how bad
it can be.  It is MUCH worse now than 30 years ago; a large
part of the problem is Federal pressures.

>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.

The basic mathematics education, which now baffles most
of the teachers if one attempts to get the concepts across
to them, can be taught in elementary school, but only by
those who understand the concepts.  This includes the
complete use of variables, first-order logic, the various
basic concepts of the integers, rational numbers, and real
numbers, and how these can be used to develop the various
computational methods.  I would expect a high school teacher
to also understands the basic concepts of abstract algebra
and analysis, set algebra and its use in general probability
(NOT computing games of chance), which gives a background
to understanding statistics.  Above all, a sufficient 
understanding of the difference between basic concepts and
means of solving problems is needed that the teacher knows
that teaching how to solve specific types of problems 
without understanding the concepts can prevent even much
later understanding to occur.

-- 
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