Re: Multiple variable reasoning (Was: Appropriate for Gen Phys? was: comprehending electric/magneticinteractions)

[Jack Uretsky <jlu@HEP.ANL.GOV>]

On Fri, 4 Jul 2003, John Clement wrote:

> Please notice that along with my comment I gave a specific example.  The
> particular lesson is one where they are given a specific statement and
> then are asked to apply it to a variety of situations.  One of the
> difficulties they have is that they use other information instead of the
> given information.
__________________________________________________snip_______________________
        While I agree with the "difficulty" I disagree with John's
assessment of the source of the "difficulty".
        The inability of students to apply lessons learned in one
situation to other situations is, IMO, closely related to their lack of
understanding of the nature of proof in mathematics.  Further, the
recommended curricula for K-12 seems to make little attempt to teach
this.  If you haven't looked at high school math texts in a few decades,
you're in for a treat.
        On April 26 (or thereabouts) I posted a comment from a math
educator who puts the blame on pressure from us "users" of math
teaching.  Here is the quote:

-----------begin quote
In practice, at the lower-division college level, I would
say (from my experience) that there is little emphasis
on proof in such courses as calculus and differential
equations that are primarily service courses.  Math.
depts. generally regret this, but there is a push from
engineering and science depts. to have math. depts. teach
the students to learn to apply formulas and solve problems.
However, the situation is quite different for upper-division
math courses, which are taken mainly by math majors.
Abstract algebra, advanced calculus, and real analysis
(amongst others) require students to prove lots of theorems,
and students' competence is judged primarily by their
ability to prove theorems on their own.  Little emphasis is placed
upon students' regurgitating theorems from textbooks or lectures.

______________________________end quote

        As far as I am concerned, this quote is a smoking-gun example of
grotesque miscommunication.


                                        Regards,
                                                Jack










  "Don't push the river, it flows by itself"
                                Frederick Perls