Math Thinker

I’ve been reviewing  the concept of functions for some work I’m doing now. Much of this post is just me regurgitating my thought process for writing about math.

In my own rough-shot words… a function is:

An equation sometimes written as f(x)=x. “x” is a variable that can have multiple values. f(x) which can also be considered in some cases “y” or the “y” value, is the result of completing the side of the equation with “x.”  If you know the value of either y or x you can solve for the unknown (variable).

Here are some other defintions of functions

A function is an equation (this is where most definitions use one of the words given above) if any x that can be plugged into the equation will yield exactly one y out of the equation. (from Paul’s Online Notes)

Here’s wikipedia’s definition:

The mathematical concept of a function expresses dependence between two quantities, one of which is known and the other which is produced. (from Wikipedia)

I think it’s probably a good idea before you’re teaching any math concept, process or definition to look up how others have defined them or done it. When I took my first Algebra class, I think not understanding the common vocabulary for terms such as variable, value, operation, etc. actually threw me for a loop. Up to this time my math education consisted only of doing ‘problems’ in a book. Nothing was explained about how you did them. You just did. Sad isn’t it, but I suspect that even today many future teachers still aren’t prepared properly for even high-school level mathematics courses.

I feel sometimes that I’m learning about these math concepts very late in the game as an adult. Shame is a sad and unnecessary reaction many of us adults have when we encounter things we don’t know (and feel that we are expected to know). As I get older I’m beginning to think this is one of the more detrimental reactions we have to learning as adults, and It’s really time to chuck it out the window along with that pesky emotion called regret.

I created a very quick simple animation that briefly demonstrates my own exploration of the concept of functions.  You can click the image below to view an animated slide show. The Flash/Captivate presentation will open up in a new window.