[Edu-sig] explaining functions [Possibly OT]

[Brian van den Broek]

Nicholas Wheeler said unto the world upon 2004-12-05 18:28:
> Isn't a math function the same as a computer-science function? You
> give the math function an x, and it returns a y. ie: f(x) = 2*(4x)^x
> -or- def f(x): print 2*((4*x)**x). Most people should be able to grasp
> that, if they've been through highschool algebra.

Hi Nicholas, and all,

I'd agree with you if experience hadn't taught me otherwise. I do see 
the CS and math notions of functions are tightly related (with the 
difference that math functions don't have side effects). But the idea 
that those with highschool algebra should be just fine has proven incorrect.

Many Linguistics and Philosophy students in these classes "hate math" 
and have worked out that writing things like:

    (A -> (B & C)) v (B <-> C)

looks suspiciously like math. They seem to have a mindset that "they 
cannot do it". Which is a shame, and I try like the dickens to make them 
understand the mathematical induction proof of the completeness of the 
deductive system for predicate logic by the time we are done. (I don't 
think they like me much ;-)

My own inclination is to say something like "a function is a set of 
pairs, where the first member of each pair is an n-tuple of inputs, and 
the second member is the m-tuple that is output, and for each input 
n-tuple, there is a exactly one output m-tuple to which it is mapped."

And, right after that, they'd all drop the class ;-)

I think I like the pizza analogy (thanks Kent). My first impulse is to 
say "that isn't mathematical enough!" But, when I consider the 
difficulty that some students have had, and the obvious unhelpfulness to 
the target audience of my above quoted inclination, I think that means 
it might just be perfect ;-)

I'll try it out on Tuesday -- I'm not teaching the course this semester, 
but I do have 12 hours of tutoring lined up before the course final on 
Wed. We will see if it works.

Thanks to all who've responded.

Brian vdB

<SNIP>

>>Brian van den Broek wrote:
>>
>>>Hi all,

<SNIP>

>>>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.

<SNIP>

>>>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