[IAEP] reconstructed maths

Ixo X oxI ixo at myna.ws
Sat Jul 12 10:36:55 CEST 2008

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.  :)

On Sat, Jul 12, 2008 at 00:28, Bill Kerr <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> 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
>> > 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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