# [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
>
> 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
>
> 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?
>
>     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
>         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
>         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
>         > they can help, and disappear when no one responds.
>         >
>         > thanks
>         > dfarning
>         >
>         > _______________________________________________
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