[Edu-sig] Fwd: Do we "teach computers" when we write code?

[Lloyd Hugh Allen]

I haven't posted in a while -- forgot to reply-to-edu-sig :)


---------- Forwarded message ----------
From: Lloyd Hugh Allen <chandrakirti at gmail.com>
Date: Tue, Apr 7, 2009 at 09:26
Subject: Re: [Edu-sig] Do we "teach computers" when we write code?
To: kirby urner <kirby.urner at gmail.com>


As a math teacher, using the particular example of summing a finite
set of consecutive integers:

To give students a formula, in particular n(1+n)/2, and then have them
do a set of practice problems where they apply that formula, is not
teaching. It might be training.

Instead, consider the case of telling students that: when Gauss was in
elementary school, his teacher needed time to work on some other
matter and so told the students to add all of the numbers from 1 to
100; and that Gauss instantly looked up and said 5050; and the teacher
hadn't actually yet done the problem himself and so denied Gauss'
answer. Gauss, as an ~8 year old, said, no, look, and wrote

1 + 2 + 3 + ... + 100

and then below that wrote

100 + 99 + 98 + ... + 1

and showed that there were 100 columns, and that each column summed to
101. However, he then noted that he had written the series out twice,
and so had to divide that product by two. The 100 columns is the n;
the sum of the first and last number is 1+n; and then divide by two.

And then to have the students try to represent a similar problem, and
to check their answer against the formula, and THEN to have them do a
set of practice problems, that might be teaching.

If the computer were able to understand the story about young Gauss,
then we could teach it. Instead, we can use it to confirm that the
formula seems to work (because computers can add numbers in the
fashion that Gauss' elementary school teacher expected just as fast as
we can apply the formula), and we can show that using the formula is
still faster for the computer than actually summing the list, but no,
we are not teaching the computer.

Perhaps if the computer were then able to, of its own volition, wonder
what we would get if we were to sum consecutive squares, then we could
teach it. As hard as it is to get students to wonder about things,
it's even harder to create that state in computers.

-Lloyd

On Mon, Apr 6, 2009 at 18:05, kirby urner <kirby.urner at gmail.com> wrote:
> I'm wondering what others on this list think of this non-standard use
> of "teaching" when talking about programming a computer.
>
> The authors say we're "teaching" the computer....