SCARVES AND JACKETS
The HPM Meeting held in Taipei in August 2000, sparked off a train of events
for me that I am pleased to be able to share through the newsletter.
At the Taipei Meeting I wanted to emphasis a particular set of
points from my research on mathematically gifted young people in New Zealand,
that seemed to me to be important in showing ways in which more of us could
develop our instincts to express ourselves mathematically. These young people
had different senses of the aesthetic, different aptitudes and skills, different
understandings of which areas of mathematics were interesting, and different
school experiences. They paid attention to detail and they used all their senses
to notice, understand, appreciate, teach, know, use, experiment, think, learn,
and apply their mathematical thinking not only in mathematics but in all their
other pursuits as well. They made things that reflected their skills and aesthetic
senses rather than always depending on writing as their method for expressing
the theories, conjectures and calculations that interested them.
The more I thought about how to emphasis these points effectively,
the less conventional overheads seemed appropriate. And the more I became reluctant
to prepare conventional overheads, the more a different set of stories came
to mind. Generally they were stories that reminded me first, that some patterns
that would be hard to write down in conventional notation are there nonetheless
all around world in three dimensions, achieved and able to be appreciated; and
second, that many of us have told stories in conference presentations that show
that students who were bored with mathematics and its ‘secret’ formulae,
came alive when they began themselves to make examples and models.
This gave me the idea of making ‘substitute overheads’.
I realised that what I was saying could be said through the making of garments
that valued patterns and colours and enabled a visual exposition to accompany
the verbal. I set myself a problem to answer, "Take any garment and a bundle
of scraps and make something that describes a mathematical idea and leads to
a discussion of its history", and went to Taipei with eight purpose-created
jackets and scarves folded in among my notes. I was genuinely impressed by the
response to my ‘substitute overheads’ of those who came to my presentation,
and I could not resist saying this to several people when I came home.
One of these people happened to tell the story to a local art
dealer and, intrigued, he suggested I might like to show him what I had done.
My ensuing visit ended with his offering me a two-week "solo artist’s
exhibition" at his gallery. So eight months after the Taipei Meeting, the
original collection of eight scarves and jackets had been expanded to thirty,
and I had developed a way of writing about each item so that verbal explanation
and visual image could hang in the Gallery side by side. The exhibition attracted
over 350 visitors in the fortnight. Adults who claimed to have no knowledge
of mathematics found themselves working out number sequences, thinking through
theorems, talking about whether or not mathematics was a philosophy and art
rather than the set of skills and rules they had previously assumed it to be.
There were reviews in both a local and a national newspaper. Later in the year
a ten-minute slot on my ‘maths-art’ and me was included in a nationally
shown TV arts programme, and that gave me the opportunity to organise another
exhibition.
While I am, of course, personally delighted that a conference presentation can
turn so easily into art and exhibitions, I am even more delighted to have stumbled
upon another way of interesting people in basic mathematics, its history, its
usefulness for thinking, writing and visualizing as well as for calculating,
estimating and understanding, and its ability to cross cultural boundaries and
educational limitations. I make no apology for mixing colours, observed details,
logical processing, whimsical illusions, natural interconnections, and historical
and cultural understandings for it seems to capture people’s imagination
in a way very similar to that described in many papers given at HPM Meetings,
and it enables brief hints to be given of mathematical ideas that can be followed
up as chosen by individuals. There is nothing particularly complex in the mathematics
that I am able to portray by this method of presentation, but neither is there
anything particularly complex in the mathematics that large numbers of school
children (and therefore, presumably, adults) are unable to understand, according
to many reports.
Computer graphics have reminded us of the advantages of using
colour and shape and change and fluidity to capture the imagination, illuminate
problems, and improve the learning processes through a ‘hands-on’
approach to understanding basic mathematical ideas. It would be sad not to use
the knowledge we have gained from modern technology as a reason for revitalising
the use of old creative skills and technologies as well as the new. Thus, I
plan to continue to have exhibitions and sell the scarves-and-their-stories
whenever I can, so that they go to places where they will encourage people to
acclaim the ideas that underpinned the attitudes of the students in my original
research, namely, that basic mathematical concepts are fun to use and talk about,
that lots of mathematical information is present in the world around us, and
that ideas inspired by mathematical thinking are easily made a part of many
sociable conversations.
Concerning the scarf above: the unfurling fern that finds
expression in New Zealand in the koru
is a symbol used in many places in the world to express ideas of continuity,
new life and replacement.
A symbol similar to that of the koru can be seen in artwork of the descendants
of the earliest settlers in Taiwan.
By the time I arrived home from the conference in Taiwan in August, thoughts
of the unfurling fern frond, the conference discussions on ways in which concepts
and symbols of infinity turn up in cultures all around the world, and the orange
and green colours of the flight attendants' uniforms on EvaAir (the national
airline of Taiwan) were all strong in my mind.
Here they are mixed together to suggest as many antipodal links as you can see,
for example, a Fibonacci number sequence, EvaAir, ferns and koru: all concepts
that link people and their cultures around the world.
There will be an exhibition at the 2nd International Conference
on the Teaching of Mathematics in Crete in the first week of July. Since the
time of the Taipei Meeting, a small group of us have discussed the possibility
of a book emerging from this whole idea, a book that is a sort of mathematical
anthology for children, parents and teachers, a word-and-picture ‘pleasure
garden’ of associated ideas based on the responses of people who see the
exhibitions or buy a scarf and through that are drawn to tell what appeals to
them about an item, ways they have used that mathematical idea, or what they
know of its history and of similar expressions of relationships used in other
cultures. If anyone is interested, or able, to organise an exhibition in the
northern hemisphere in the weeks following mid July, 2002, I should be pleased
if they were to get in touch with me by email at
cdaniel@maths.otago.ac.nz
Coralie Daniel
Otago, New Zealand
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