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Topic: Teaching the Concept of Functions

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Subject:   RE: Teaching the Concept of Functions
Author: Mathman
Date: Sep 26 2004
On Sep 23 2004, Susan wrote:
> Every year, I try to get the students not to say, "Oh, you just
> cross out f(x) and write y...what's the big deal."  They can recite
> the definition of a function from their text--for each x-coordinate
> there is exactly one corresponding y-coordinate, but they have no
> idea what this means or how it applies in the real world.  What are
> some ways that you teach this with meaning?  Do you have an analogy
> that really works for kids?

I don't know what grade level you are referring to, but try the old one of
"Think of a number.  Double it ...." and you, of course give the number they
were thinking of.  A function is simply a Rule; you would develop the function
expression from the process of doubling etc until the function emerges [such
usually use "n" not "x", but what's in a name?].  It tells you what to do with
something that can change.  Develop the function as an expression, so that they
see several examples of function expressions.  But write ONLY the expression,
not f(x)=, or y=.

Then find something to do with that expression.  Tell them you are tired of
writing all that stuff down, so you are going to call it simply f(x), "A
function of x."  Now, instead of writing down x^3 + 3x^2 - 5x + 6, you can write
f(x), meaning the same thing understood.  Then find another and go through the
same process, to produce a different function of x.  Call that one F(x).
....well, you get the picture.  It's not just a matter of automatically writing
f(x) = something.  It's a matter of knowing that something is a function of x;
that was x changes in value, so does the entire function value. F(x) is simply a
convenient notation.

It's not as simple as I've described; it takes time and development and example
and discussion.

I hope that helps?


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