[Edu-sig] project Euler

[Edward Cherlin]

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.

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

>>>> 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.

> 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.

> 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.
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.

>>>>> 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).

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.

> 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.

>>> 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
>



-- 
Silent Thunder (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) is my name
And Children are my nation.
The Cosmos is my dwelling place, The Truth my destination.
http://wiki.sugarlabs.org/go/User:Mokurai (Ed Cherlin)