[IAEP] reconstructed maths

[Bill Kerr]

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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