Teacher2Teacher 
Q&A #104 
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From: Jim 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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