On Sat, Jul 12, 2008 at 11:51 AM, Costello, Rob R <<a href="mailto:Costello.Rob.R@edumail.vic.gov.au">Costello.Rob.R@edumail.vic.gov.au</a>> wrote:<br><br>> what should the ""reconstructed mathematics" look like?<br>
<br>I wrote a review of a Papert paper about this in April<br><a href="http://billkerr2.blogspot.com/2008/04/maths-should-evolve-with-computers.html">http://billkerr2.blogspot.com/2008/04/maths-should-evolve-with-computers.html</a><br>
<br>(I describe the Papert paper as very interesting but all over the place in terms of its presentation)<br><br><br><br><div class="gmail_quote">On Sat, Jul 12, 2008 at 11:51 AM, Costello, Rob R <<a href="mailto:Costello.Rob.R@edumail.vic.gov.au">Costello.Rob.R@edumail.vic.gov.au</a>> wrote:<br>
<blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">[impatient developers worried about too much talking and not enough<br>
doing might want to skip this teacher question]<br>
<br>
The relationship of mathematics to programming is of interest<br>
<br>
Brian Harvey has made some of his text books available online and he<br>
says, in the preface to one of them<br>
(<a href="http://www.cs.berkeley.edu/%7Ebh/v1ch0/preface.html" target="_blank">http://www.cs.berkeley.edu/~bh/v1ch0/preface.html</a> ) that :<br>
<br>
"(If you like programming, but you hate mathematics, don't panic. In<br>
that case it's not really mathematics you hate, it's school. The<br>
programming you enjoy is much more like real mathematics than the stuff<br>
you get in most high school math classes.) In these books I try to<br>
encourage this sort of formal thinking by discussing programming in<br>
terms of general rules rather than as a bag of tricks."<br>
<br>
Papert of course had strong views on this - that school maths was too<br>
dry, and that playing with the turtle gave even young students access to<br>
ideas like vector calculus, in a more intuitive way, without the<br>
formalism normally associated with these ideas<br>
<br>
Similarly Alan Kay, ("The real computer revolution hasn't happened yet"<br>
)<br>
<br>
"One of the realizations we had about computers in the 60s was that they<br>
give rise to new and more powerful forms of arguments about many<br>
important issuses via dynamic simulations. That is, instead of making<br>
the fairly dry claims that can be stated in prose and mathematical<br>
equations, the computer could carry out the implications of the claims<br>
to provide a better sense of whether the claims constituted a worthwhile<br>
model of reality.<br>
And, if the general literacy of the future could include the writing of<br>
these new kinds of claims and not just the consumption (reading) of<br>
them, then we would have something like the next 500 year invention<br>
after the printing press that could very likely change human thought for<br>
the better."<br>
<br>
<a href="http://www.vpri.org/pdf/Pisa_RN_2007_007_a.pdf" target="_blank">http://www.vpri.org/pdf/Pisa_RN_2007_007_a.pdf</a><br>
<br>
<br>
these ideas are congenial to me .... tasted something of this in my own<br>
schooling ...<br>
<a href="http://thinkingcurriculum.decenturl.com/corridor" target="_blank">http://thinkingcurriculum.decenturl.com/corridor</a><br>
<br>
as a teacher I've wondered why we don't make more use of the overlap<br>
between maths and programming .... and have tinkered with such<br>
<a href="http://www.thinkingcurriculum.com/thoughts/?s=lineRider" target="_blank">http://www.thinkingcurriculum.com/thoughts/?s=lineRider</a><br>
<br>
But .... I'd also like to round this out with a question / reflection<br>
<br>
Programming, in itself, with variables and functions, is not quite<br>
maths, is it?<br>
<br>
Or ... does not seem to map very directly against traditional curriculum<br>
<br>
<br>
Is the problem traditional curriculum? Papert (Mindstorms):<br>
<br>
Faced with the heritage of school, math education can take two<br>
approaches. The traditional approach accepts school math as a given<br>
entity and struggles to find ways to teach it. Some educators use<br>
computers for this purpose. Thus, paradoxically, the most common<br>
use of the computer in education has become force-feeding indigestible<br>
material left over from the precomputer epoch. In Turtle<br>
geometry the computer has a totally different use. There the computer<br>
is used as a mathematically expressive medium, one that<br>
frees us to design personally meaningful and intellectually coherent<br>
and easily learnable mathematical topics for children. Instead of<br>
posing the educational problem as "how to teach the existing<br>
school math," we pose it as "reconstructing mathematics," or more<br>
generally, as reconstructing knowledge in such a way that no great<br>
effort is needed to teach it.<br>
<br>
<br>
If is so - what should the ""reconstructed mathematics" look like?<br>
<br>
Much more modelling?<br>
<br>
What sort / style of programming helps?<br>
<br>
What sort of thinking involved in mapping programming / modelling onto<br>
maths, generally?<br>
<br>
Do we have to convince educational authorities to respect recursive<br>
experiments in Scratch/Logo (which my year 8 students enjoyed) for<br>
example, as what maths thinking "really is" ...<br>
<br>
Alan Kay talks of wrestling with creating suitable models that span<br>
teacher and kid skills, allow some learning from both, and get at deep<br>
maths .... j<br>
<br>
Assessment systems in the western world are also not very tailored to<br>
this - we don't assess these models - which impedes the take up of the<br>
ideas ... whereas I could legitimately program in the final year of<br>
secondary maths course in 1985, I don't think it would fit in today;<br>
relegated outside the maths curriculum<br>
<br>
But how isomorphic are the domains of maths and programming - and how<br>
accessible to most kids... questions I wonder about ...<br>
<div class="Ih2E3d"><br>
<br>
<br>
<br>
> -----Original Message-----<br>
> From: <a href="mailto:its.an.education.project-bounces@lists.lo-res.org">its.an.education.project-bounces@lists.lo-res.org</a><br>
> [mailto:<a href="mailto:its.an.education.project-bounces@lists.lo-res.org">its.an.education.project-bounces@lists.lo-res.org</a>] On Behalf<br>
Of<br>
> David Farning<br>
> Sent: Saturday, 12 July 2008 9:21 AM<br>
> To: <a href="mailto:its.an.education.project@tema.lo-res.org">its.an.education.project@tema.lo-res.org</a><br>
</div><div class="Ih2E3d">> Subject: [IAEP] Sugar Labs, LOGO and Brian Harvey<br>
><br>
</div><div><div></div><div class="Wj3C7c">> What is the status of LOGO for sugar? Is it a high priority item?<br>
><br>
> As much as LOGO I would like to bring Brian Harvey, the original<br>
author<br>
> of BL, into the project.<br>
><br>
> He has a wealth of personal experience teaching people how to program,<br>
> he has a strong interest in LOGO, and is a good guy.<br>
><br>
> Brian's page is at <a href="http://www.cs.berkeley.edu/%7Ebh/" target="_blank">http://www.cs.berkeley.edu/~bh/</a> .<br>
><br>
> ucbLOGO's page is at <a href="http://sourceforge.net/projects/ucblogo/" target="_blank">http://sourceforge.net/projects/ucblogo/</a> .<br>
><br>
> If Sugarizing logo is a priority we could do much worse then point new<br>
> contributors to Brian's group to get their feet wet before diving into<br>
> Sugar.<br>
><br>
> I know neither the value of bringing LOGO into OLPC nor the cost of<br>
> Sugarizing it to make a valid cost benefit analysis. If some one<br>
could<br>
> do that analysis and it seems like a good idea it will try to get the<br>
> collaboration started.<br>
><br>
> In my role as 'wiki watcher' I see quite a few people register, ask<br>
how<br>
> they can help, and disappear when no one responds.<br>
><br>
> thanks<br>
> dfarning<br>
><br>
> _______________________________________________<br>
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