[Edu-sig] Re: explaining functions [Possibly OT]

[Toby Donaldson]

I've always thought of the mathematical and programming notions of 
functions to be very different things. The problem with the mathematical 
definition of a function is that it is that it isn't broad enough, e.g. 
it says nothing about side-effects like printing, making a sound, or 
reading/writing a file, etc.

So I think defining functions as "black boxes" or little machines is the 
way to go ... I think it's a mistake to explain Python functions as 
being the same sort of thing as mathematical functions.

My experience is that the average student usually has no trouble 
understanding how to use a function. They grasp the mechanics pretty 
quickly from examples. Issues such as the difference between printing a 
result and returning a result are confusing to some, as are issues such 
as scope. But you don't need to have a perfect understanding of such 
things to use functions effectively.

By far the biggest difficulty I've seen students have is deciding how 
and when to make their own functions. This is exacerbated by the fact 
that in beginning programming you typically only write small programs 
where writing your own functions might not be useful.

Toby

>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
>  
>