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What is "What Not How"

When teaching mathematics the student is encouraged to always concentrate on what they are doing not how to do it.  You would be discouraged saying 32 = 9 rather it is better to say 32 = 3 x 3 and 3 x 3 is three 3's.  Terms that are used describe the action.  You do not simplify a fraction and heaven forbid you do not reduce it.  You can reduce it but then it would be smaller.  What you are really doing is removing common factors.  You can also insert common factors when adding or subtracting fractions to create like terms.

3a is read as three a's; 4 is read as four 1's; -4 is read as four negative 1's; 2+3x5 is read as two ones plus three fives and since you can only add like terms the answer is seventeen ones.  This eliminates the memorization of Order of Operations.  No longer will you have to Please Excuse My Dear Aunt Sally.  Notice when speaking of money no one gets confused when you say; I have two singles and three fives. Everyone knows that is 17 dollars.  However some would believe 2+3x5=25 and I don't blame them.  After all we read from left to right.  You should not have to rely on Aunt Sally to get the problem correct.  When you do things correctly you do not find the answer, the answer finds you.

To get a better idea of the method check out the instructions on the distributive  property (Factoring at 5 years old).  You will need Adobe Acrobat Reader 11.0 to view this document.  There is a link to the website where you can download this free program on the Resource Page.

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 Intellectual Copyright M. A. Londino 2006
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Last updated: 04/12/10.