Why?

When you were a kid, you wanted to know the answer to this question for almost every situation… “Why is the sky blue?”…. “Why are there Braille keypads on the drive-up ATM machines?”  …. “Why is this snake bite all puffy and red?”  Many times our parents placated us with an answer so we left them alone.   

Mother:  “Jimmy, sit down!” 

Jimmy:  “Why?” 

Mother:  “Because I said so!”

 But as we grew older, this question took on a more profound meaning as we began to explore the world around us at a more intimate level.  We began to ask questions of ourselves, of our faith, and of the nature of the universe itself.

As a Geometry teacher, I find that my students detest Geometric proofs with a hatred that can only be rivaled by the fires of a thousand suns.  But what students fail to realize is the importance of answering the question:  “Why?”

In a Geometric proof, as in many things in life, you are required to make a statement and then back it up with some kind of supporting evidence.  In order to understand the thought process that goes into a Geometric proof, imagine somebody sitting with you, constantly asking “Why?”

I am certain that at some point in your life, you have done something silly and someone asked you:  “Why did you do that?”  Now your brain is whirring, trying to think of an answer to that question that you think they will buy.  If you’re like me, you come up with something that is plausible that you think this person wants to hear, when deep down inside, you know you did not have a reason, you were just being silly. 

Mother:  “Why did you stick those tweezers in that light socket?”

Son:  “Um….. because I wanted to see if I could get my nose to light up like Rudolph’s.”

In a Geometric proof, you have to make a statement and then provide a logical reason as to why or how you know what you said is true.  For instance, if I know that a certain point is a midpoint of a line segment, then I know that the line segment is broken up into two parts that have the same measure; but the question still remains… “Why?”  We know that the segment is broken up into two congruent parts because we know what the definition of a midpoint is.  So the answer to the question “Why?” is because of the definition of a midpoint.

The point I’m trying to make is that many students feel as if proofs are pointless, extraneous, and trite; that they provide no benefit whatsoever.  However, what they actually do is allow you to practice answering the question, “Why?”  They teach you to critically examine the world around you and look for answers.  They teach you to be self-reliant.  I would go as far as to say that proofs teach you be skeptical of statements without reason, or belief without question.  They teach you to challenge your beliefs.  Some may be fearful of such power to challenge beliefs, but I posit this statement to you:  You should always challenge your beliefs….

Why?

Because if you don’t challenge your beliefs, they will never get any stronger.