math through programming

Jeff Sandys sandysj at
Wed Feb 14 11:48:20 EST 2001

I am cross posting this to comp.lang.logo to expose the 
Logo community to python and "Computer Programming for 
Everyone" (CP4E).

My view of Logo is a mathematical playground.  I still 
believe that it is a better language for young students 
(I like working with 9 year old and above), and it 
embraces different learning styles with a cleaner and 
more forgiving syntax.

The advantage of python is object programming, which 
some Logo languages have, and a skill that can be used 
later.  While the learning processes developed with Logo 
translate to other programming languages and to thinking 
in general, I have never seen any commercial applications 
or job openings for Logo.

What python is missing is a course outline that is age 
appropriate and accommodates different learning styles. 
I am eager to try python on some middle school students 
in an after school programming club, but without a plan 
I will stick to tried and proven Logo.

Jeff Sandys

Kirby Urner wrote:
> [
> below is my most recent post to math-learn, clearly a
> response to something earlier -- but with enough standalone
> content to give the idea.
> Earlier posts in the same thread include Python source
> code for computing Pascal's Triangle and comparing the
> results with balls randomly falling, pachinko-style,
> through a triangulated grid of pins (some of you may have
> seen the well-known science museum demo showing the bell
> curved result).
> Thanks again to Tim Peters for cluing me re 'Concrete
> Mathematics' which I went out and grabbed some months ago
> (if edu-sig had a search feature, I'd go find where he
> first posted about it, as an easier intro than Knuth's
> "telegraphic" 'Art of Computer Programming' -- and indeed,
> that's how this text evolved, from notes around the
> mathematical preliminaries leading into Knuth's magnum
> opus).
> I'm cross-posting this here as a snap-shot of my ongoing
> effort to combine the math learning process with a
> strong programming element, to create a hybrid more
> adapted to life in the 21st century.  The mass-education
> juggernaut has too much inertia to steer in this new
> direction any time soon, but there's always the hope
> that more alert passengers will jump overboard and swim
> for their lives :-D (good to have this alternative more
> seaworthy craft in the vicinity, given the more
> conventional curriculum simply isn't).
> complete thread:
> Kirby
> ]
> Subject:      [math-learn] Re: Intro to Probability
> Author:       pdx4d at
> Date:         Tue, 13 Feb 2001 16:33:03 -0000
> > So the short way to write (n-k+1)! is just n!/(n-k)! as
>                             ^^^^^^^^^^^^^^^^^^^^^^^^^^
> > that cancels all terms except n(n-1)(n-2)..(n-k+1).
> Right, a typo, thanks to a close reader for catching that.  What I
> wanted to express with (n-k+1)! were the k terms in n(n-1)...(n-k+1),
> but of course these aren't equivalent. What I need is notation to
> expressing a "falling factorial" running for k terms, and, indeed,
> such notation is offered in 'Concrete Mathematics' by Graham Knuth
> and Patashnik (Addison-Wesley, 1994), pp 47-48.
> The notation can't easily be written in ascii unfortunately, but
> "n to the m falling" is written [n to the m-underbar].  With "n to
> the m rising" = [n to the m_overbar].  "These functions are also
> called 'falling factorial powers' and 'rising factorial powers',
> since they are closely related to the factorial function n! =
> n(n-1)...(1).  In fact n! = [n to the n-underbar] = [1 to the n-
> overbar]."
> So anyway, what I should have written was [n to the k-underbar].
> This book 'Concrete Mathematics' I've mentioned before on math-teach,
> as exemplary of what I'm aiming for at the college level with my
> K-12 curriculum writing.  It's used for computer science students
> a lot, but it's also just a fine introduction to a lot of concrete
> (not too abstract) mathematics, including discrete probability,
> binomial coefficients and elementary number theory.
> I'm also trying to boost geometry content, by moving 'Beyond
> Flatland' (off the plane) -- which links to a 'Beyond Calculators'
> push as well (as I haven't seen many rotating polyhedra on
> calculator screens -- though maybe these have appeared in Japan
> by this time, a market typically ahead of the USA's in the
> calculator department).
> As I wrote to a math educator recently by email:
>    You may remember from emails past that I'm one of those
>    looking for ways to incorporate more of Bucky Fuller's
>    contributions into early math ed.  I also push a "math
>    through programming" approach, and converge it with the
>    Fuller-informed spatial geometry.  "Beyond Flatland" and
>    "Beyond Calculators" summarize my two pronged strategy
>    to revamp math ed pedagogy.
>    I've just put up a new essay, well-illustrated, which
>    looks at the "Beyond Flatland" approach:
>    And here's a review of my "Beyond Calculators" initiative:
> Kirby

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