Re: ontologic math anxiety

From: Martin Owen (mowen@rem.bangor.ac.uk)
Date: Mon Oct 15 2001 - 02:30:56 PDT


xmca@weber.ucsd.edu writes:
>Jay damn well knows he would get a rise by insinuating students should
>not be
>exposed to sophisticated views of what mathematics is, one problem being
>that
>the withholding makes an intellectual elitism, at least one ideational
>class
>distinction. There is neither any evidence, as far as I know, that
>indicates
>what prior developments are necessary to establish understandings, to
>whatever
>varied degrees, of the ontology of mathematical objects. Nor is there a
>significant theory of the development of mathmatical thinking/action that
>spans
>from counting to incompleteness. And should we make on students' behalf
>the
>decision whether they will like math or not, whether they will take it
>seriously, or not? But I love Jay, and am glad to read his chapterish
>postings, how provocative they are to inquiring minds.
>
>And other communications beckon...
>
>bb

One thing I ask my teacher training students is "how do you see a ton?".
100 years ago there was within most cultures a physical awareness of
ratio, porportion, quantification and rates of change. In some cases this
was tacit but in many cases this was explicit. My early maths education in
the 50's was clearly realted to this culture where volumetric, weight and
monetary based commodity movement was a significant part of life and
walking in any main street in the world there would be direct experience
of this mathematics. Trigonometry was the skill of the colonial.
Understanding the boundaries of land, and the bridges that spanned it was
driven by the economics of ownership, and the potential of military men to
act. ( there is a current popular record from Knopfler and Taylor about
two working emigres called Mason and Dixon).

As a production worker in a glass lens factory on taylorist "measured day
work", I became intimately aware (through conversation with my fellow
workers) of rates of change, constants, multipliers, and the differential
calculus that links production line to order book to labour costs and the
quantity of money in your pocket at the end of the week.

Papert in his forward to Mindstorms, talks about his enagement with gears
and mechanisms in his fathers workshop.

These days fewer westerners work in productive industries where there is a
direct contact with the product. Pre-packaged, fork lifted, bar coded
cultural artifacts have changed our mediation system. "Being digital" is
changing our mathematics. (How?)

In the 70's and 80's I was fortunate to have contact with Zed Diennes. Zed
had a great feeling for structural mathematics: that beneath mathematics
operations there was an essential syntax and to engage with that syntax
would be more effective than engaging in rote presented mathematical
semantics; to look for pattern, the origins of meanings, and to see the
quatitative world from multiple viewpoints. Zed's great gift was the
ability ot see these structures portrayed in ludic experiences where the
abstraction is made accessable. A rush to teach "basics" in the UK seems
have driven us back to teaching superficial arithmetic: we use numeracy
as an excuse to avoid teaching mathematics.

There is undoubtedly a problem. In our primary schools we have too many
teachers who have never had a good experience of mathematics.

Martin Owen
Labordy Dysgu- Learning Lab
Prifysgol Cymru Bangor- University of Wales, Bangor

"How do you explain school to a higher intelligence?"



This archive was generated by hypermail 2b29 : Thu Nov 01 2001 - 01:01:46 PST