[Edu-sig] project Euler

[kirby urner]

On Fri, Feb 13, 2009 at 11:43 AM, Edward Cherlin <echerlin at gmail.com> wrote:

<< SNIP >>

>
> I mean the Calculator activity in Sugar, or gcalctool.
>

Our use Pippy maybe?

>>> 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584
>>> 2 8 34 144 610 2584
>>> 2 10 44 188 798 3382, ok, 4 more terms...Third grade paper and pencil
>>> arithmetic for the rest.

Recent meeting with Anna Roys, TECC/Alaska (tecc-alaska.org):

Lesson plan:  On-line Dictionary of Integer Sequences, enter 1, 12, 42, 92...

Follow some links, to my page included, even if just for the pictures
(good Virus from Life -- made out of metal nuts it looks like).
Treasure hunt?

We're focused on linking algebraic sequences, generator type stuff, to
visual imagery, imaginary content, like we do later with coordinate
systems (XYZ, spherical...), but "figurate numbers" ("polyhedral
numbers") are a first bridge between algebra and geometry, coordinates
be damned (until later).

Glue four ping pong balls together:  voila, a tetrahedron (your unit
of volume in some curriculum segments, unless your school is some kind
of joke -- Alaska leading the pack here in some ways).

>>>
>>>> I think the word "programming" is misleading in some contexts.
>>>
>>> I don't use the word for anything that can easily be done on a
>>> non-programmable calculator, an abacus, or a half sheet of paper by
>>> one with the skills commonly taught (though not very often learned in
>>> full) for each.
>>
>> I'm not that impressed by "commonly taught skills" i.e. if a kid knows
>> how to use a TI, but not Python, I'm inclined to move on to the next
>> candidate.
>
> EEEE! No! Pencil and paper arithmetic skills, not gadgetry. Multiple
> column addition, subtraction, multiplication.

It's not either/or, but if it's between a TI and Python, then I say Python.

Either way, you'll need paper and pencil skills too.

A quick challenge:

Spheres packing around a nuclear sphere go 1, 12, 42, 92... 10*L*L +
2, where L is the layer number, except where L = 1 we have just the
one ball (the shape is a cuboctahedron).  So how many balls total?
Add up all the layers.  Yes, very easy to do in APL.

In Python:

def cubocta( layer ):
    if layer == 1:  return 1
    return 10 * layer ** 2 + 2

def total_balls( layer ):
    total = 0
    for i in range(1, layer + 1):
        total = total + cubocta( i )
    return total

But isn't there a closed form algebraic expression for total_balls
that doesn't require cumulative adding?  Damn straight.  We'll get to
it.

Don't forget to watch the cartoons!  This isn't Bourbaki.
Visualizations encouraged!  This is MVC.

>
>>>> Using Python as a calculator is what Guido mentions in his tutorial.
>>>>
>>>> Python or TI?
>>>>
>>>> XO or TI?
>>>
>>> Similarly for APL and J.
>>>
>>
>> Yes, as I've mentioned, APL was my first language and I've worked with
>> Iverson himself on a paper about J.  I heard from Roger Hui just the
>> other day.  Part of why I fell in love with Python is because of its
>> orthogonal primitives, feels like APL in some ways.  Plus the whole OO
>> thing is way cool, highly accessible.
>>
>> My oft stated preference is to NOT ever (ever) get stuck in teaching
>> just one language, even if one emphasizes just one in this or that
>> classroom or on-line session.
>
> We have to get away from the notion that "teaching programming" =
> "teaching language syntax". That's why I am working on a set of
> demonstrations of programming and Computer Science ideas in Turtle
> Art, where children can create programs directly as trees, not linear
> texts that a parser turns into a tree for execution.

I'm just interested in teaching math.  I don't give a rip about
Computer Science (just kidding, I care plenty).

But in Oregon, CS is just an elective, the first to go in hard times,
whereas math has a monopoly lock, is in bed with TI, and is controlled
by various text book publishers (not O'Reilly).  Good thing we're
breaking free of that stultifying quagmire in Alaska and places.  XOs
are likewise part of the stimulus package.

Anyway, I just call it math, or gnu math.  I don't call it computer
science, because I don't want to be shoved off to the sidelines, like
my peers have been.  I'm a gnu math teacher, not a computer science
teacher.  Just trying to avoid the kiss of death you understand?

>
>> Per some brain science I've been
>> studying, we really do *not* multitask, even though we appear to, any
>> more than an Intel chip really does (OK, some do, but at one time it
>> was all round robin).
>>
>> Kirby
>

Kirby