[IAEP] reconstructed maths

Sat Jul 12 10:03:19 CEST 2008

Thanks Bill 

Love that paper 

http://www.papert.org/articles/AnExplorationintheSpaceofMathematicsEduca
tions.html

But it does tell me that all this is still pretty speculative and early
days 

not much in the education system that builds this thinking it seems 

hopefully sugar / olpc might give a boost to this, be a catalyst for
these approaches 

________________________________

From: Bill Kerr [mailto:billkerr at gmail.com] 
Sent: Saturday, 12 July 2008 5:28 PM
To: Costello, Rob R
Cc: dfarning at sugarlabs.org; its.an.education.project at tema.lo-res.org
Subject: reconstructed maths

On Sat, Jul 12, 2008 at 11:51 AM, Costello, Rob R
<Costello.Rob.R at edumail.vic.gov.au> wrote:

> what should the ""reconstructed mathematics" look like?

I wrote a review of a Papert paper about this in April
http://billkerr2.blogspot.com/2008/04/maths-should-evolve-with-computers
.html

(I describe the Papert paper as very interesting but all over the place
in terms of its presentation)

On Sat, Jul 12, 2008 at 11:51 AM, Costello, Rob R
<Costello.Rob.R at edumail.vic.gov.au> wrote:

[impatient developers worried about too much talking and not enough
doing might want to skip this teacher question]

The relationship of mathematics to programming is of interest

Brian Harvey has made some of his text books available online and he
says, in the preface to one of them
(http://www.cs.berkeley.edu/~bh/v1ch0/preface.html
<http://www.cs.berkeley.edu/%7Ebh/v1ch0/preface.html>  ) that :

"(If you like programming, but you hate mathematics, don't panic. In
that case it's not really mathematics you hate, it's school. The
programming you enjoy is much more like real mathematics than the stuff
you get in most high school math classes.) In these books I try to
encourage this sort of formal thinking by discussing programming in
terms of general rules rather than as a bag of tricks."

Papert of course had strong views on this - that school maths was too
dry, and that playing with the turtle gave even young students access to
ideas like vector calculus, in a more intuitive way, without the
formalism normally associated with these ideas

Similarly Alan Kay, ("The real computer revolution hasn't happened yet"
)

"One of the realizations we had about computers in the 60s was that they
give rise to new and more powerful forms of arguments about many
important issuses via dynamic simulations. That is, instead of making
the fairly dry claims that can be stated in prose and mathematical
equations, the computer could carry out the implications of the claims
to provide a better sense of whether the claims constituted a worthwhile
model of reality.
And, if the general literacy of the future could include the writing of
these new kinds of claims and not just the consumption (reading) of
them, then we would have something like the next 500 year invention
after the printing press that could very likely change human thought for
the better."

http://www.vpri.org/pdf/Pisa_RN_2007_007_a.pdf

these ideas are congenial to me .... tasted something of this in my own
schooling ...
http://thinkingcurriculum.decenturl.com/corridor

as a teacher I've wondered why we don't make more use of the overlap
between maths and programming .... and have tinkered with such
http://www.thinkingcurriculum.com/thoughts/?s=lineRider

But .... I'd also like to round this out with a question / reflection

Programming, in itself, with variables and functions, is not quite
maths, is it?

Or ... does not seem to map very directly against traditional curriculum

Is the problem traditional curriculum? Papert (Mindstorms):

Faced with the heritage of school, math education can take two
approaches. The traditional approach accepts school math as a given
entity and struggles to find ways to teach it. Some educators use
computers for this purpose. Thus, paradoxically, the most common
use of the computer in education has become force-feeding indigestible
material left over from the precomputer epoch. In Turtle
geometry the computer has a totally different use. There the computer
is used as a mathematically expressive medium, one that
frees us to design personally meaningful and intellectually coherent
and easily learnable mathematical topics for children. Instead of
posing the educational problem as "how to teach the existing
school math," we pose it as "reconstructing mathematics," or more
generally, as reconstructing knowledge in such a way that no great
effort is needed to teach it.

If is so - what should the ""reconstructed mathematics" look like?

Much more modelling?

What sort / style of programming helps?

What sort of thinking involved in mapping programming / modelling onto
maths, generally?

Do we have to convince educational authorities to respect recursive
experiments in Scratch/Logo (which my year 8 students enjoyed) for
example, as what maths thinking "really is" ...

Alan Kay talks of wrestling with creating suitable models that span
teacher and kid skills, allow some learning from both, and get at deep
maths .... j

Assessment systems in the western world are also not very tailored to
this - we don't assess these models - which impedes the take up of the
ideas ... whereas I could legitimately program in the final year of
secondary maths course in 1985, I don't think it would fit in today;
relegated outside the maths curriculum

But how isomorphic are the domains of maths and programming - and how
accessible to most kids...  questions I wonder about ...

> -----Original Message-----
> From: its.an.education.project-bounces at lists.lo-res.org
> [mailto:its.an.education.project-bounces at lists.lo-res.org] On Behalf
Of
> David Farning
> Sent: Saturday, 12 July 2008 9:21 AM
> To: its.an.education.project at tema.lo-res.org

> Subject: [IAEP] Sugar Labs, LOGO and Brian Harvey
>

> What is the status of LOGO for sugar?  Is it a high priority item?
>
> As much as LOGO I would like to bring Brian Harvey, the original
author
> of BL, into the project.
>
> He has a wealth of personal experience teaching people how to program,
> he has a strong interest in LOGO, and is a good guy.
>
> Brian's page is at http://www.cs.berkeley.edu/~bh/
<http://www.cs.berkeley.edu/%7Ebh/>  .
>
> ucbLOGO's page is at  http://sourceforge.net/projects/ucblogo/ .
>
> If Sugarizing logo is a priority we could do much worse then point new
> contributors to Brian's group to get their feet wet before diving into
> Sugar.
>
> I know neither the value of bringing LOGO into OLPC nor the cost of
> Sugarizing it to make a valid cost benefit analysis.  If some one
could
> do that analysis and it seems like a good idea it will try to get the
> collaboration started.
>
> In my role as 'wiki watcher' I see quite a few people register, ask
how
> they can help, and disappear when no one responds.
>
> thanks
> dfarning
>
> _______________________________________________
> Its.an.education.project mailing list
> Its.an.education.project at lists.lo-res.org
> http://lists.lo-res.org/mailman/listinfo/its.an.education.project

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