Why

My former AP told  us to never to use the word "why" in class.  He didn't believe it had a place in a math lesson.  He felt "how" was all that was necessary, especially with weak students.  He felt many were incapable of understanding the reasoning and  we should just concentrate on getting them "to do" so they would pass the regents.

When I went to school a zillion years ago, no one ever explained "why" either.  We memorized the rules and "did".  I never understood the reasoning behind choosing the proper signs when I factored or why the "a" in a quadratic equation could not equal zero or much of anything else.  But, I was a good student.  I studied, memorized the rules and did well.  It wasn't until I had to teach someone how to factor that I grasped the "why" of the signs and understood the implications of "a" not equal to zero or even why I could not divide by zero.  It suddenly became crystal clear and the factoring which I had previously been able to do with much trial and error was easy.  Now, when I teach the topic, I make sure to make sure my students understand "why" each time.

My students do not all get this.  I would be kidding myself if I believed I reached them all but I know I have succeeded with many.  I love watching their faces as they look at examples, analyze the problem and successfully arrive at an answer they know is correct because they fully understand "why" they did what they did.

The math they learn in my classroom will probably be long forgotten by the time they graduate and go on to careers in their chosen areas (unless of course it is an area that requires math) but I am convinced the "why" will be a lesson never lost.  Understanding reasoning is the first step in solving problems in any area, whether it be academics or life.