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Q&A #104

Teachers' Lounge Discussion: Factoring trinomials

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From: Jim <pacs44@earthlink.net>
To: Teacher2Teacher Public Discussion
Date: 2005112007:58:58
Subject: Re: "illegal moves" -Are we magicians or mathematicians?

I do not consider myself to be the "answer" to all of math.  I am
probably not the best mathematician in my building, but I am bothered
by what my search has uncovered.  I have been teaching for 16 years
and in political terms consider myself a converted moderate.  I used
to be a right wing mathematician accepting only algebraic/graphical
solutions.  The Math A has forced me to the middle.  I am always
looking for new ways to teach students how to do things.  Thus, I
looked on this forum to see if anyone has any ideas (not tricks) on
how to teach factoring a trinomial.  The tic tac toe method seems like
a possible option albiet a little confusing at first, at least it is
justified mathematically.  This "illegal move" bothers me.

We may or may not realize it, but there is no gray in mathematics. 
For instance, each equation solving step could be justified with a
therorem definition, axiom, etc.  When we allow students to multiply
by the constant (> 1) and go from 6x^2 to x^2, we can't justify this
unless we use this "illegal move" theorem.

Understand, we are respoonsible for students understanding how
mathematics works so that they can deal with mathematics at every
level not just in algebra or more specifically factoring.  Don't plant
a seed that we can randomly multiply two numbers in an exPression or
equation and have equivalent expressions.  You may give them a trick
that works today, but sets them up for confusion later!

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