[Edu-sig] project Euler

[kirby urner]

On Fri, Feb 13, 2009 at 12:33 PM, Edward Cherlin <echerlin at gmail.com> wrote:
> On Fri, Feb 13, 2009 at 12:02 PM, kirby urner <kirby.urner at gmail.com> wrote:
>> 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?
>
> We have lost the context of the discussion. The question was not which
> tools to use in the classroom, but whether "programming" is the
> appropriate term to use for processes that can be done on a calculator
> (physical or virtual), or on pencil and paper.
>

Oh, I thought we were talking about whether the Euler Project was
really cool or not.

> Of course we should use Pippy. And Turtle Art, and Calc, and Etoys and...
>

Although in Oregon, XOs are extremely hard to come by, me being one of
the few who has one (two actually).

So when it comes to on the ground activities, I promote the hell out
of the XO, market it extensively, but then have to fall back on what's
actually available to Oregonians today, i.e. not XOs.

Given XOs are designed for small hands and look like Fisher-Price
toys, I don't push them for teenagers much, and that's the age group I
tend to start with, and above (older).  I am not like Alan Kay or
Seymour Papert or those people who focus on really early math
learning, where I think you're right on with controlling an avatar
(like a turtle).

Kids who have just mastered piloting their own bodies around, have fun
playing with dolls, using puppets.  I basically look at the early math
sequence as working with puppets and polyhedra (shapes), or call them
objects.

>>>>> 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...
>
> Wonderful site. Major professional tool that children can learn from.
>

Yes.

>> 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,
>
> So if we tell the turtle to set v=5, and at every successive step to
> put down a dot, move by v, and set v =. v+a =. 10, we get dots at
>
> 0 5 15 25 35 45 55
>
> Dividing by five, or alternatively using the first interval as a unit, we get
>
> 0 1 3 5 7 9 11
>
> with partial sums
>
> 0 1 4 9 16 25 36
>
> Very good. The next day, take the students outside with XOs and have
> them take videos of someone dropping a ball from the roof. Pick frames
> at some suitable interval and overlay them. Tell students to turn
> their XOs sideways, and ask if they recognize the dot pattern. Thus,
> in two lessons, uniform gravity means constant acceleration. This is
> Alan Kay's favorite demo.

Yes, I've seen those same demos over and over and over and over.

So when I market the XO, which I do, I steer clear of all of that
stuff.  I don't want to be that redundant with what others are doing.
I don't spend any time with Squeak.  That's not my department and
never will be.  When I met with Alan Kay in London, c/o Shuttleworth
Foundation, he kept talking about how Smalltalk was a dead language.
There's lots of stuff in the archive here where I call him a "slayer"
i.e. some Buffy-like character fighting the ghost of Smalltalk.  He
was encouraging JavaScript quite a bit, had written a whole turtle
thing in that language, very impressive.  I would push Python and
Javascript over Smalltalk any day.  I think Squeak is butt ugly, but
don't tell Alan.  I also think it's a work of brilliance, a gem (not
mutually inconsistent views).

>
>> 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).
>
> With 20, you can do a dissection of a tetrahedron into four pieces.

Yes, and each of those break up into six "A modules" if you know
anything about anything <-- <polemical, teacher trick>

> Two consist of four balls in a row. Two consist of six balls in a two
> by three arrangement. Most people have a lot of trouble reassembling
> them.

Oh wait, I think we're talking about different dissections maybe.  Sorry.

>>> 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.
>>

<< SNIP >>

>> 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).
>
> That's why I am pushing for Free digital textbooks, and incidentally
> for virtual calculators. Anything that can't switch between
> parentheses and RPN is rubbish. That gets us out from under the
> hardware vendors and the publishers.

I have no problem with anything you've said you're doing.  You seem to
be very loyal to your "little people" out there and are doing
everything you know how to reach them.  I sense a lot of people in
your (our) camp, doing their level best.  This gives me hope.  In the
meantime, change is threatening and it's no wonder that Kellogg's Corn
Flakes boxes have never featured anything about OLPC, or that most USA
kids don't have a clue about Python.

I look for companies that invest in the future (like O'Reilly, like
Google).  I look for companies with courage.  Hey, I even look to the
military on occasion, since bravery is supposedly part of the job
description.  In my blogs, you'll find a lot of material on what I
call Pentagon Math, ostensibly about Phi and Fibonacci Numbers, but
it's rather thinly veiled, as I have Google views of the Pentagon
itself, keep asking why kids on military bases, their parents asked to
make the ultimate sacrifice, don't get access to decent educations at
least.  Talk about tyranny!

See Chicago slides for more data.

>
>> 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?
>
> Certainly. When I was in college, Foundations of Mathematics, which
> formed much of the basis of CS, was still in the Philosophy
> Department. I don't care about the labels.

Yeah, me either.  But bureaucrats care very deeply.  Just because we
don't care doesn't mean we have the luxury of pretending others don't
care.

Kirby