From: jamess@athena.mit.edu (John A Mess)
Subject: Re: Is Math Hard?
Organization: Massachusetts Institute of Technology
Date: Thu, 5 Nov 1992 18:02:44 GMT

     I apologize this is very long, but it is a response to the numerous
postings recently criticizing, unjustly, most high school teachers.  

In article <Bx79Lo.LG1@mentor.cc.purdue.edu> hrubin@pop.stat.purdue.edu (Herman Rubin) writes:
>In article <1992Nov4.044300.15766@cbfsb.cb.att.com> wa2ise@cbnewsb.cb.att.com (robert.f.casey) writes:
>>In 5th grade, we did set theory (at least the simple stuff).  At the time,
>>I couldn't believe that we were doing such easy stuff instead of hard
>>long division and such.  But it seemed that the teacher and the rest of
>>the class had a hard time figuring it out....
>
>From the experiences when people who had an understanding of mathematics
>taught it, most of the children could get some grasp of the subject.  But
>failure of the attempts to teach the teachers was what killed the new math.
>Teachers who can only teach rote can only do harm to those who want more.

     This was a very common problem in the 60's and 70's when public educa-
tors wanted to "modernize" the process.  The idea of teaching reading by
using phonetic symbols, by leaving out words, and other garbage was often
*forced* on public teachers from above.

>>I also had a science teacher who didn't know sh*t about science, and I
>>could tell it then (didn't dare _say_ anything about it).  He was trying
>>to explain about atoms and molecules, "molecules of pencil sharpener"
>>not "atoms of iron and carbon" making up a pencil sharpener.  Wasn't too
>>hard to ask questions he couldn't answer, but he had ways to retaliate
>>for making him look dumb.

     This is a recurrent complaint.  We've all had one or more "incompe-
tent" teachers.  Public teachers must teach the class, a very heterogeneous
group.  If the idea is to sell basic science ideas, it should be presented
simply.  Now before you hit F, let me state clearly:  the teacher must help
the students learn basic ideas which are basically correct (there are few
facts which don't fail as you learn more, be it physical--consider optics
where you begin assuming straight lines and end up considering electromag-
netic waves-- or biological--the failing of the Central Dogma of genetics.)
I do not advocate teaching patently false science as in the above case but
beginning with basic assumptions which can be refined as the student masters
other fields of knowledge.  Relativity is a classic example.

>>But grammer school was mostly based on one's ability to memorize random
>>facts, not on one's ability to figure stuff out.  

     This is the failing of public education.  To teach the gcd of students,
most schools teach facts.  Mastery learning requires that a student must 
master a concept.  This self-paced study doesn't conveniently fall into 
"yearly advance" scheme.  Most of us use this approach, doing outside reading
to come up to speed.  However, teaching facts and using standardized tests
to measure retention is more convenient.  College faculty are no less culp-
able.  Few faculty devote time to helping students learn the concept.  In
mathematics, we teach operations.  It's no wonder when students come to an
advanced class and are told prove this they panic.  Proofs aren't facts or
operations.

>I believe that most of us do not think that such teachers should be in
>the classroom.... The system is broke.  There is no way that we can get 
>enough competent teachers NOW.... That is why there is no hope of getting 
>an adequate public school system.
>Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399

     We often think of public school teachers as having the same curricular
flexibility as college academics which is untrue and unfair.  In a high
school class, a student wishing to take the ACT or an advanced placement
test must have covered certain materials.  School boards often tell the 
teacher you must cover all of this.  Second, when the student enters college,
s/he has had some exposure to the discipline presumably.  I ran up against
this problem trying to explain to a bright middle school student what a nega-
tive number is.  They "knew" that it came before 0 on a number line.  He
wanted a "real" meaning.  Why was it positive when multiplied?  Wouldn't it
be a "bigger" negative number?  Given the number of students of my genera-
tion whose parents couldn't help them with their homework--simple algebra and 
geometry--I question the adequacy of education in the 40's and 50's!
     The increasing education of parents and support of kids will increase
expectations which will have to be met.  The image of the nerd is a cultural
failure of America where studiousness is reviled.  Students need to be reas-
sured that you can be bright and popular.
     I deeply resent all the epithets thrown at public school teachers who
try hard to cope with the drugs, violence, crowded classrooms, and asinine
requirements.  There are some teachers who are incompetent, most are not.  
Most the students here at MIT and around the country do not come from private
schools.  If you are deeply concerned, contact a local high school and offer
to teach for a week.  I promise you, it will challenge you.
     Is the system broke?  I would ask, has it ever worked efficiently?  
Schools are forced financially to choose between hiring a new science teacher
or outfitting a new laboratory taught by a former English teacher who had a
biology course in college.  School boards tend to see facilities as image en-
hancers and one-time capital expenditures, hence favorable.  We don't have a
dearth of competent teachers but a dearth of jobs.  When industry pays more
competitively, you are left with the old, tenured teachers and those whose
abilities don't meet industrial standards.
     When my wife was studying at IU to teach Biology, her advisor told her
to learn a sport to coach so she could supplement her salary.  She was told
to expect starting at $19K.  With coaching, get $22K.  Today she works at
Harvard Medical School as a technician where she earns $26K.  She would still
like to teach, but now it would be a drop in salary, benefits, and extended
hours away from home.
     I've ranted longer than I wanted, but I feel that those who point nebu-
lously at public school teachers do everyone a great disservice.  If a stu-
dent doesn't want to learn, there is nothing that can be taught.  Changing
that attitude can sometimes be done by the teacher, but it requires the sup-
port of the environment--peers, parents, society--as well.  If it is broke,
now is the time to fix it.  If it's not broke, now is the time to make it
better.  
Newsgroups: sci.math