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Discussion: Traffic Jam Applet tool
Topic: Teaching the Concept of Functions
Related Item: http://mathforum.org/mathtools/tool/10/


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Subject:   RE: Teaching the Concept of Functions
Author: Ian
Date: Sep 23 2004

Hi Susan,

> 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've had some success using analogies like father-of(person) (which is a
function - every person has exactly one father), and parent-of(person) (which
is not a function - every person has two parents) to help explain the
distinction between functions and other mappings.  I also use the analogy of
social-security-number(person) to provide an example of a function that
isn't defined everywhere in the 'domain' (some people don't have SSNs), and of a
function that can be inverted (given a person's SSN, you can - in theory at
least - recover the identity of the person; this doesn't work for father-of()
or parent-of(), except in special cases).  

> What about composition of functions--

The same way:  It's pretty easy to see what's going on with

  social-security-number-of(father-of(person))

-Ian

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