Martin and others,

I'm not sure myself how well that analogy carries over to mathematics
or in what sense it does.  But Murray Eisenberg is correct in that
we should be careful about reasoning by analogy; if the analogy holds,
we're good.  Otherwise, we commit the logical fallacy that is usually
called "false analogy."  

The comment you had made about lawyers caught my attention since I recall
several famous mathematicians in the past who were also lawyers as well:
Fermat and Cayley.  And our fellow list-member Ralph Raimi does mention
in his article "Why Study Trigonometry?" (which he referred to in his
post in this thread) that his daughter is a lawyer, had taken calculus in
college, and was glad she did.  One of my fellow math faculty members 
has been pondering over the years about going to law school.  He had
especially been pondering that decision quite a bit a number of years ago,
but I don't think he's pondering that decision as much these days as
he used to.  

I remember diagramming sentences in sixth grade, but we didn't go as
far as the textbook did.  And that school year was the only year we did that
and in fact was the last English class that I had that focused on grammar
and mechanics.  The English classes from grades 7 onward focused on 
literature and writing with the assumption that we already knew grammar
and mechanics.  Luckily I did*, and I later observed that schools ending
the study of grammar at around that time is a big mistake and explains why
we see only relatively few people these days who have a strong understanding
of English grammar and mechanics.  And that makes our job difficult when it
comes to helping college students improve their writing skills: Our suggestions
don't make sense to them because they don't understand the terminology
behind grammar.  For instance, telling them that the sentence "Knowing
that fractions are difficult for me to understand, math will always be
tough for me to understand" contains a dangling modifier makes no sense to
most of them since they don't know what a dangling modifier is. 
 
Diagramming sentences might help students with mathematics, but I can't
say for sure.  This is a new idea to me since I haven't heard anyone
else suggest that before.  I do find it worth giving further consideration.
I do agree that diagramming sentences comes a lot closer to mathematics
than other aspects of grammar not only for the reason you had given
but also because diagramming sentences makes it explicit how the parts of
a sentence are related to each other, and mathematics studies relationships
as well as patterns.      
  
I also would not make the claim that mathematicians alone have the key
to good thought and reasoning.  I'm still debating with myself on how well 
math can help one to learn to think.  A key phrase is "can help" since studying
math doesn't guarantee this.  For instance, maintaining a healthy weight
and avoiding too much junk food and too much of a sedentary lifestyle can
help one to live a long, healthy life, but doing all this does not guarantee
that one will live a long, healthy life.  Even if studying math really does
help a lot (assuming math is studied logically and not as a mere collection
of rules and stuff to regurgitate rotely on exams and other assignments),
I wouldn't claim that math alone does this.  For instance, the claim that
physical exercise can help one to remain healthy is true, but exercise is
not the only thing that can help.  


Jonathan Groves    


*N.B. I did in the sense of knowing well what grammar and mechanics were
taught to me in K-12.  But in high school I read a style manual that my
mom had used in college a few years back, and it contained some information
on grammar that I didn't know about.  For instance, I didn't know until
I read this style manual what a dangling modifier is.    



On 5/19/2010 at 6:04 pm, Martin C. Tangora wrote:

> There have been some good points made in this thread,
> and a lot of platitudes.
> 
> Below, I do not know what Murray Eisenberg intended
> by "the specific analogy" --
> there is no analogy evident in the example
> immediately following,
> about whether athletes should warm up; I suppose the
> writer
> intended the analogy between doing math to improve
> reasoning skills,
> and doing tire-stepping to prepare for football.  
> 
> Actually the example immediately following is not
> well stated, 
> because the serious question is not whether one
> should warm up 
> before exercise, but whether one should warm up
> before stretching.  
> I speak as a former college athlete who continues
> to compete in track & field, and to take ballet
> lessons (possibly,
> at its best, the most scientific of all exercise
> programs), and
> currently getting therapy to stretch my fingers.
> If there are serious people arguing against warming
> up
> before exercise, I'd like to see some citations.
> But stretching without first warming up 
> is quite well understood to be dangerous.
> 
> Jonathan Groves and Raymond Greenwell 
> bring up the obvious point that there are different
> kinds
> of thinking, in fact different kinds of intelligence.
> Mathematics surely is usefully related to grammar
> rather more than to literature, and to law 
> rather more than to sociology.
> 
> I worked with a very thoughtful lawyer for several
> years
> (in historic preservation) and we both were struck by
> how similarly our minds worked.
> 
> I gather that to diagram a sentence was not a
> standard
> grammatical exercise in the UK as it used to be in
> the US,
> but it is a way to bring geometrical intuition to
> bear
> on the parsing exercise.  Thus it is even closer to
> mathematics
> than most grammatical work, because it is not only
> a matter of understanding rules and applying them,
> but of displaying patterns in space.
> 
> However, it is just arrogance for mathematicians to
> believe
> that only they have the key to real thinking.  I used
> to
> suffer from that form of arrogance, but later in life
> I had the good fortune to meet many persons of
> striking
> intelligence, who were weak in mathematics, but who
> could
> solve problems of other kinds with infinitely more
> speed,
> skill, and grace than I ever could.
> 
> At 08:01 AM 5/19/2010, Murray Eisenberg wrote:
> >Why?
> >
> >Reasoning by analogy can be treacherous. And the
> specific analogy is dubious (unless there is specific
> evidence to back up the claim).
> >
> >For example, trainers typically insist how important
> it is to warm up, even perhaps stretch, before
> exercise. But lately quite a few doubts have been
> raised about that by medical and exercise scientists.
> >
> >Sometimes common sense and the self-evident is
> correct; often they are  not.
> >
> >On 5/18/2010 5:49 PM, Martin C. Tangora wrote:
> >>(1)  I think that the burden of proof
> >>that learning mathematics *does not* train the mind
> >>belongs with those who make that (negative) claim.
> >>Similarly the claim that learning Latin grammar
> >>*does not* make one a better speaker and writer of
> English
> >>is so dubious that it hardly deserves our
> attention.
> >>
> >>Nobody in the athletics department questions
> >>the value of football players high-stepping through
> >>automobile tires.  It is self-evident that this
> exercise
> >>improves strength and coordination.  The fact that
> >>the tires are removed from the field of play
> >>before the opening kickoff does not detract from
> >>the value of the exercise.
> 
> Martin C. Tangora
> University of Illinois at Chicago
> [log in to unmask]