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Topic: Solving Equations Using Backtracking

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Subject:   RE: Solving Equations Using Backtracking
Author: Mathman
Date: Nov 2 2006
On Nov  1 2006, mirani wrote:
> After 25 years of teaching middle school maths, I have found a way
> to teach solving equations using backtracking that seems to get most
> students to a reasonable level quickly.

If any one is interested in more information, please feel
> free to email me

I'm always a little leary of sending my email address to someone I don't know
about something that is not clearly evident.  Would you please add a little more
detail as to what it is you have in mind?

I taught solution to equations and word problems very successfully for over 30
years.  Two points I noted in that time were that (i) those who have truly great
problems with such mathematics will not use it, ever, in several lifetimes, and
owuld be better off gaining some mastery in what it is they have already learned
to some extent,and (ii)  THE big key to success was the students themselves.
They either fed from each other's enthusiasm positively, or negatively, and all
the trial and error in the world served them little.

A prime, but admittedly rare example was a grade 10 general [trades] class of
over 30 students.  Not a single discipline problem from day one.  After some
period of study, each and every one could solve two equations, two variables in
any of four different ways.  A doubtful teacher was invited to the classroom,
and all she could do was shake her head.  The secret was no secret.  It was the
students themselves, and a gentle, but progressive beginning.

That said, it would be interesting to hear of something new and successful that
I could pass along to colleagues.  I gave a method for
factoring binomials with non-singular leading coefficient to a colleague who
had never seen it, and who now uses it constantly.  There's always something new
to glean, yet still nothing new under the sun.


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