[Edu-sig] explaining functions [Possibly OT]

[Brian van den Broek]

Hi all,

This might be a bit tangential to the topic; if so, my apologies. (I've 
been reading this list for a while, but have never posted before.)

I'm a Python hobbyist, and am not involved in CS education, except 
peripherally. I am also a grad student in Philosophy who has, for a few 
years now, been teaching Introduction to Formal Logic to audiences 
largely composed of Philosophy and Linguistics undergrads with a small 
contingent of Computer Science undergraduates, too.

I have found it difficult to get some of the humanities undergraduates 
to see the understand the general mathematical concept of a function. 
Occasionally, even some of the CS students (who, when I see them, have 
just begun) stumble with the concept, too.

The best I have managed to come up with is to tell them that a function 
is like a 'black box' to which you feed some ordered input of the 
appropriate sort, and it gives you an output determined entirely by that 
input.

I have found that, at least for the humanities students, getting them to 
understand some of the material is largely a matter of finding a useful 
metaphor (and, convincing them that the metaphor is an aid, not the 
thing in itself). That's been the only way to get the ones bothered by 
the mathematician's use of "if ... then ..." to accept it. (They don't 
like that "If 2 + 2 = 97 then I am King of the moon" and "If grass is 
green then sky is blue" are taken to be true.)

So, I am wondering if others on the list have had difficulty getting 
students (particularly students not primarily studying Math or CS) to 
get the idea of a function? If so, I'd be very interested in what 
techniques were of use.

Thanks, and I do apologize if this query is received as too peripherally 
related to the topic of the list. Best to all,

Brian vdB