mewssjsw@man.ac.uk writes:
>I suppose most teachers speak some kind of 'school maths' and maybe
>'street maths' and maybe some other dialects and genres. Maybe we can
>say it would be helpful to pedagogy if we as teachers have a better
>understanding of our pupils 'street maths' and 'school maths'.... and
>the relations between the two which might help joint articulation
>
>well? what do you think?
First , to express my personal interest here. I am in the middle of
writing several grant proposals which revolve around "key skills for the
digital age" and looking at potential directions for curriculum renewal.
CHAT is an enabling tool for me in that it helps formulate my understading
of why particular curriculae were the way they were and it allows me to
look back on my own education (maths from school and a 60's engineering
degree), and into comparative studies of maths such as Horton's study of
the Kapelle peoples and their Peace Corps visitors to see how the
interaction of different cultural artifacts have come tgether to impose
different ways of looking at problems. The invention of the caculator
cleared swathes of base 10 logarithms from the syllabus, powerful computer
doing finite element analysis by numeric methods rid some engineering
disciplines of less approximate models based on the calculus. With
relatively superficial cultural historic analysis it is possible to see
shifts in school mathematics and the rules/community systems that have
driven them.
With street maths the changes are more subtle and harder to detect. An
interesting case study would be the change to to the Euro accross western
Europe in January when relatively large denomination currencies like the
lire will merge with smaller denominations like the DM, and people will
start thinking differently about magnitudes of money and its relative
exchange value.
The geometry of skateparks present different experiences of designing
space to those involved in agrarian activities. The geometries of
skateparks belong to the digital age, the masses and forms we see in
buildings by Liebskind or Gehrey are only possible because of the
mathematics of our age. Only now can these shapes can be brought into
existence ( my colleague from Manchester has a fantastic example under
construction nearby).
The digital age provides new opportunities to enage in discourse about
quantitative relationships and pattern that are different than before. I
have no feel for how children of the digital age, who come into less
contact with not only the physical reality volumetric and mass but also
any discourse about these things. Do they need an answer to "how do you
visualise a tonne?"? We have a need to envision quantity somehow(or do
we?). If our relationships with quantity become increasingly
technologically mediated , what does that do for the maths curriculum?
We have new tools to have scaffold discourse about mathematics. Elsewhere
I have written at my dismay at seeing the spreadsheet enshrined in the
curriculum, but it is a genre for representing the quantitative and
relations between quantities. I suppose Schwarz's work allowed new
discourses on high school maths, and LOGO still remains a significant
achievement. But I feel there must be other genres there and waiting to be
invented. What do I have to experience to master the genre? What other
genres are available? How do we come to know them?
I have the hunch that Diennes structuralist approach to maths may have
validity that transcends genre.... No I don't.... Diennes presented a
genre of Mathematics that seems to be at a level of abstraction that we
can see patterns emerge more easily than in some other genre, and the
scaffolding to acquire the patterns through games and the use of physical
apparatus. Is there a way that this genre can be translated into a genre
of mathematics in the "digital age"?
or should I look to Spencer Brown?:
"It may be helpful at this stage to realize that the primary form of
mathematical communication is not description, but injunction. In this
respect it is comparable with practical art forms like cookery, in which
the taste of a cake, although literally indescribable, can be conveyed to
a reader in the form of a set of injunctions called a recipe. Music is a
similar art form, the composer does not even attempt to describe a set of
sounds he has in mind, much less the set of feeling occasioned through
them, but writes down a set of commands which, if they are obeyed by the
reader, can result in a reproduction, to the reader of the composer's
original experience."
Most maths writing is about math now (or maths then) and not about math
changing. Can people tell me if I should read the mathematics work in the
fields of situated cognition? Should I go a dig Von Glazerfeld out of the
half read books pile?
Martin Owen
Labordy Dysgu- Learning Lab
Prifysgol Cymru Bangor- University of Wales, Bangor
"How do you explain school to a higher intelligence?"
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