[Edu-sig] On the front page

[Kirby Urner]

>You can find this article at 
>http://www.nytimes.com/library/national/regional/042700ny-math-edu.html

Yes, I've read it too.  Good overview, with a NY focus (I'm
more used to reading about CA, but the situations are parallel).

<<SNIP>>

>I think there should be an immense initiative to train instructors in
>story telling, and give them access to great stories to tell.  There
>should be summer story workshops for them.  Let a good quarter of
>their time be spent telling stories, another part in constructing math
>labs, and math contests, I bet you would see an incredible increase in
>the math abilities of our children.

I completely agree re storytelling as an important aspect of 
math teaching/learning.  Here are some earlier paragraphs of 
mine to this list, from February:

  I think what's more challenging and interesting is to see 
  math as Keith Devlin does, as a discipline which "makes 
  the invisible visible".  In this sense, a math teacher's 
  job should be about deobfuscating, demystifying, helping 
  students to flesh out their understanding of systems and 
  infrastructure that runs "behind the scenes" in the real 
  world.  In this sense, the teacher is more a storyteller, 
  weaving interesting narratives which interlace history, 
  world affairs, technological innovations.

  But in order to tell these stories from a math-literate 
  point of view, you have to impart numeracy and, as we get 
  closer to talking about our own time, computer literacy.

  So in the course of your storytelling, you'll want to 
  toss out a lot of connected "artifacts" which point beyond 
  themselves to how the world works (sometimes I call them 
  "cave paintings" -- because they're rather sketchy, 
  schematic, idealized).  Patches of notation, snippets of 
  working code, flow charts, diagrams, graphical displays...  
  always trying to up the comfort level, the confidance 
  level, around working with "technical communications" 
  in their many forms.

[http://www.python.org/pipermail/edu-sig/2000-February/000074.html]

>You want children to learn programming, learn to tell programming
>stories.  Give them good programming tools and tutorials and set them
>loose to create their own projects.  Have open source style
>competitions.  Have them work not just in the schools, but in the real
>world too.  If it is going to be a common literacy, it has to be very
>visible, and the benefits of knowing it have to be obvious, everything
>around us should remind us of those benefits.  If not, it will remain
>a minority interest.
>
>Stephen

I agree with this too.  

And we should acknowledge that "gray area" between "programming" 
and simply writing out some algorithms.  Like, in a math context, 
we maybe only need a very few lines of code to implement something.  
You don't have to get into writing these large, gnarly programs 
with hundreds of lines (you can, but you don't have to).  

For example, consider number sequences, series.  The Python can 
be as simple as:

def tri(n):
    # triangular num n = sum of n consecutive counting nos
    if n<=1: return n
    else: return n + tri(n-1)

And the story in this context is not about a computer programmer,
but a 7 year old mathematician, JCF Gauss, who derived a method
for computing the sum of the first N consecutive numbers: 
1+2+3+4...N, which is also the number of spheres packed in a 
triangle:
  
          *        1
         * *     + 2
        * * *    + 3
       * * * *   + 4
      ...        + ...

His answer: N(N+1)/2 e.g. 1+2+3+4 = 4(5)/2 = 10

Visual proof:

  Let S be the sought-for sum of 1 thru N.  Then:

               
                *     * * * *    * * * * *
          *      *     * * *     * * * * *
         * *  +   *  +  * *  =   * * * * *
        * * *      *     *       * * * * *
       * * * *      *            * * * * *

          S        N+1   S        (N+1)^2

Solve for S in terms of N:

         2S + (N+1) = (N+1)^2 
         2S + N + 1 = N^2 + 2N + 1
                 2S = N^2 +  N 
                  S = N(N+1)/2

Even works for N = 1:

            *   *  = * *
         *   *       * *
         S  N+1 S   (N+1)^2

Kirby

See: http://www.inetarena.com/~pdx4d/ocn/numeracy0.html