[LogoForum] Re: Why teach LOGO
The message below is being cross-posted from LogoForum.
--- In LogoForum@xxxxxxxxxxxxxxx, Cheryl Hughes <hughesgctm@xxxx>
wrote:
Thank you, Juan and Harvey.
I'm giving a workshop in which
I want to try to convince other math teachers of the
validity of teaching LOGO to middle school age children.
I thought Brian made a good point in another post in which
he positied follow-up questions such as teaching Logo
compared to another computer language, teaching programming
and selecting Logo as the particular programming language
to use, etc.
An issue which came to my mind a few years
back had to do with the unlearning of what is learned
via learning Logo if one attempts to learn Scheme/Lisp
(which use a prefix notation) or, say, Forth (which uses
a postfix notation) or mathematical Sigma notation.
My point is basically this: That present-day
mathematical notations (qualifying as `languages'?)
would not have been developed if the Worf-Sapir hypothetical
limitations of so-called `natural' languages weren't
regarded a high-resistence obstacles. So, to whatever extent
my thesis is valid, why not keep mutating and evolving
otherwise static, stagnent mathematical notations to either
minimize or preclude obstacles? As an example I will present
3 notations for representing the addition of 5 numbers.
Logo-style infix notation:
1 + 2 + 3 + 4 + 5
lisp & scheme style prefix notation
(+ 1 2 3 4 5)
postfix notation
(1 2 3 4 5 +)
Which of these educes (as in `education) the best-practice
of summation? Some may prefer to think of a single sum
as a series of sums. I for one would like to think of
a single sum as a SINGLE summation of any number of
numbers. I suspect that *many* children never undo the
`false' or `limited `rightness' of regarding a sumation
of numbers as a tedious process of sticking a plus sign
between each and every blessed number of those they want
to tally up! Moreover, if one were to start with prefix
notation, rather than natural_language-emulative infix,
then there would be a smaller feat to learn `applicative'
programming in which one can easily -- with cognitive,
conceptual ease -- apply any of a broad range of mathematical
functions to our list of numbers thusly:
(define our_numbers (list 1 2 3 4 5))
(apply '+ our_numbers) ;=> 15 <-- closer to Sigma notation
(apply '* our_numbers) ;=> 120 <-- closer to Pi Notation
Please note that we didn't have to do a single extraneous
thing to our list of numbers; we didn't have to glue them
togehter with + to get a sum and we didn't have to glue
them together with * to get a product.
If my hunch is correct, those who don't undo the `superstitious
behavior' <http://www.google.com/search?hl=en&lr=&q=%
22superstitious+behavior%22+psychology> of pasting together
compound sums with plus sign `glue' to `get' or `make'
a sum or total would seek a way to compose lexically orthodox
(for these suffering from `functional fixedness'
<http://www.google.com/search?hl=en&lr=&q=%22functional+fixedness%
22+psychology&btnG=Search>) one-and-only-one `right' way/form
of 1 + 2 + 3 + 4 + 5
So, in closing, another family of questions which might
take the place of `Why teach Logo?' might have to do with
`Why teach ...
infix notation?
Natural language emulative syntactical forms?
dynamic binding?
< etc, ... all the soon-to-become `right', orthodox,
standard, etc. features of Logo>
This is not offered as rhetorical question.
I do believe it is `good' or `educational'
to teach Logo ... especially to young children.
Why? Because they have already been adulterated
by `natural language' thus usually capable of
grasping the natural language_emulative syntax
(moreso than Scheme or Forth, for example).
However, if syntax, structure, or form of
the `natural language known as `English' were
so superior why do mathematics teachers present
these same students with mathematical syntax, structures,
and forms which help them to transcend the limitations
of `English'? If one is qua IS a mathematics teacher
-- intrinsically interested in transcending the limitations
of English and other `natural' languages -- then why would
(s)he want to *only* teach Logo which so heavily relies on
its verbose, decidedly goofy syntax of `two plus two'
thinly veiled as `2 + 2'? Why not teach prefix and postfix
representations of the same cognitive processes as alternate
`lateral thinking' <http://www.google.com/search?hl=en&lr=&q=%
22lateral+thinking%22> ways of representing the same mathematical
problem?
All for this one, Cheryl.
Gene
Thanks for the information and opinions.
Cheryl
earlyfire@xxxx wrote:
Dear Juan,
The way in which people employ logo in educational environments,
serves to make it an outrigger to the direction of standardized
testing and purely materialistic formulations of learning, compressed
down, trivilized, made unsubtle, equated to arsenels and inventories
and skill and knowledge banks of demonstratable, literally
demonstratable assessment criteria.
Logo lives at the intersection of work and play, of labor and
creative envisioning, and because its a holistic activity in which
left and right-brained activity find a marraige, teaching logo is a
way of healing the complacence many identify as a Redneck Rigidity, a
Mental Lockjaw or Fundamentalist Mentality, where the only rewards in
education are equated with what you see is what you get, with what
you can collect and own, and put in a gradebook or a Swiss Bank.
In the communication, in the communion between analytical and
imaginative focus, a connection is made between what is useful and
what is meaningful and inspired. This, to my knowledge, or so I
bravely suggest, is the balance, the TAO which defines the purpose of
learning, where the certainty of expertise and the vulnerability
where courage can arise co-sponsered within both individuals and by
extension community striving and celebration.
So Logo, looked at in this almost homeopathically potentiated
context, turns out actually to be nothing less epic, wondrous in
scale and scope than an illumining path to self-knowledge hiding out,
almost a prisoner within the brutal, brittle, little factories of
education, and offers a redemption of education from an Industrial
Model of Productivity promulgated and loudly hawked at the expense of
Dreaming.
Warm Regards from Tucson, Arizona
Harvey
-----Original Message-----
From: Cheryl Hughes
Sent: Sep 6, 2005 1:21 AM
To: LogoForum@xxxxxxxxxxxxxxx
Subject: Re: [LogoForum] Re: Why teach LOGO
Thanks!
jotape1960 <jotape1960@xxxx> wrote: Well, I think: Why not?
LOGO is a very useful computing language. It let to introduce the
little kids, young and adult people on the computing world. It let to
help with the mathematical world understanding. It let to play and to
talk with a new "friend" (the turtle).
But the most important thing to me is: LOGO forces you to think how to
think to solve a problem. It's so great!!!
LOGO won't make you into an "standard" advanced user (or robot?) of
PCs; LOGO will make you into a programmer!!!
Then, I repeat: if you write: Why teach LOGO?, I write: Why not?
GOD BLESS YOU!!!!!!!
Juan J. Paredes G.
From Curicó, Chile, with love
LogoForum messages are archived at:
http://groups.yahoo.com/group/LogoForum
.
