Discussion:  Roundtable 
Topic:  Teaching the Concept of Functions 
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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 textfor each xcoordinate
> there is exactly one corresponding ycoordinate, 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 fatherof(person) (which is a
function  every person has exactly one father), and parentof(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
socialsecuritynumber(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 fatherof()
or parentof(), except in special cases).
> What about composition of functions
The same way: It's pretty easy to see what's going on with
socialsecuritynumberof(fatherof(person))
Ian
 
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