[IAEP] reconstructed maths
Karl Ramberg
karlramberg at gmail.com
Sat Jul 12 12:32:33 CEST 2008
Ixo X oxI wrote:
> Growing up with a father with a PhD in theoretical physics with
> background in astronomy, and a mother with a classic 1st generation
> (think early 1960's) programming background. Combined with both a
> 'quirky sense of humor'' to say the least, I had an interesting
> childhood. (Think ... 'Calvin and Hobbes' cartoon strip, and his
> rather strange parents :) )
>
> Here is some my first interactions with a computer...
> http://gallery.myna.ws/1973/img077.jpg (Card Punch)
> http://gallery.myna.ws/1973/1973-10%2017.jpg (IBM 'mainframe',
> notice parent making sure I don't hit the wrong button. :)
>
> ok.. now what was I talking about again... oh yeah... approach to
> Mathematics... :)
>
> Over the years, I was amazed that in math class the teachers were so
> strict on getting the 'right' answer, they completely bypassed/missed
> 'what the numbers really meant' and 'how to make math easier to
> understand'. Kids in the class were totally confused, and resorted to
> 'memorization' of times tables and answers to conversions (remember
> the 'PeeGee's with conversion tables?' :).
>
> My physics background, taught me... the 'exact' answer wasn't
> important... but more of what it meant, and how it was arrived. ....
> and least of all, how to cross-check the answer and logic-behind-it to
> make sure you were going down the right path... "fast and
> approximate-guess-timating" the answer.
>
> For example,
> 12345 x 54321 = hard/takes time to figure out
> 10000 x 55000 = easy ~ 550,000,000 approx.
> 2000 x 55000 = easy ~ 121,000,000 approx.
> 671,000,000 approx.
> (within .06 % ! )
>
> Too many school kids are taught to use/rely on calculators to 'enter
> numbers' and the answer 'pops out'. Not knowing where the answer came
> from, or if it was actually correct. Or even thinking about it if
> actually made any sense... 89.768 degrees is actually completely
> different answer than 8.9876 degrees.. but yet most students crunch
> numbers and right down the answer without thinking about it.
>
> In most physics classes, teachers encourage giving points for 'showing
> the work and logic behind it' vs. 'just an answer'. Showing the work,
> shows that the student really understands what's going on, and the
> logic problem solving. Just an answer shows that you know how to plug
> numbers into a calculator. (How many people do you know, really
> understand trigonometric functions... or can actually figure out the
> function results by hand.... or do they just plug numbers into the
> calculator? )
>
> I don't know if there is currently an 'Math Thinking-Learning
> Activity" already out there, but I think it would be greatly
> beneficial for math learning students to have exposure to 'learning
> how to think about math' and 'how to quickly ballpark the answer'
> versus 'learning math to get the exact answer'.
>
> Well, at least, there's my 2 cents. :)
> -iXo
>
Good points,
also keeping the context of the teaching relative to the students is
very important. Some topics have a much closer context,
like language, while math can easily loose that connection and become
abstract and make it alienating and unimportant for a large part of the
students.
Karl
>
> On Sat, Jul 12, 2008 at 00:28, Bill Kerr <billkerr at gmail.com
> <mailto:billkerr at gmail.com>> wrote:
>
> On Sat, Jul 12, 2008 at 11:51 AM, Costello, Rob R
> <Costello.Rob.R at edumail.vic.gov.au
> <mailto: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
> <mailto: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>
> > Sent: Saturday, 12 July 2008 9:21 AM
> > To: its.an.education.project at tema.lo-res.org
> <mailto: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
> <mailto:Its.an.education.project at lists.lo-res.org>
> >
> http://lists.lo-res.org/mailman/listinfo/its.an.education.project
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