Common Threads: Mathematics and Textiles

Common Threads: Mathematics and TextilesAuthor(s): Mary HarrisSource: Mathematics in School, Vol. 17, No. 4 (Sep., 1988), pp. 24-28Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30214514 .

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COMMON HREADS

mathe and tex

by Mary Harris University of London Institute of Education

For some years now, a project called Maths in Work (formerly part of the Mathematics Advisory Team of the ILEA, now part of the Department of Mathematics, Stat- istics and Computing at the University of London Institute of Education) has been working in the field that its name suggests and battling against stereotyping and prejudice. At the below-graduate level at which it works, industry's view of mathematics tends to be depressingly narrow and many of the learning materials produced both by education and industry share the same limited focus. The mathematics-and-its-applications approach which ad- vocates teaching some mathematics and then showing examples of it in use is a justifiable approach for 'A' and graduate levels and engineering in particular can supply many good examples. At levels below these however, the applications approach is less successful. Examples tend to be contrived and because of the widespread assumption that mathematics is arithmetic, the learning materials tend to appear as glorified sum books.

Maths in Work has tried to take a more analytical approach, to take ordinary daily situations and analyse from them mathematical thinking and doing that is going on or, in the hands of a teacher could go on.

Previous work with the design of learning materials had suggested that a simple description in mathematical terms of such a situation can indeed bring its mathematics poten- tial sharply into focus. A knitted polo-necked-sweater may be seen as just that but if it is seen as the four interconnect- ing cylinders it also is, (two intersections and an extension) more mathematical questions than "How?" start coming.

The current project of Maths in Work is to examine textiles as a resource for learning mathematics. Those who work with textiles, at home or in industry, on their construction, decoration and use, know how mathematical the whole field is. For some time Maths in Work has been wanting to produce a pack of materials that would help place this often homely and familiar part of the environment on an equal footing with the more dominating mechanical conception of it. Thanks to funding from the DES, work on the materials was able to go ahead. As the work progressed and more and more mathematically rich cloths were collec- ted, the suggestion arose that a good way of sharing them more widely would be to stage an exhibition. Thus came about "Common Threads - Mathematics and Textiles" held at the Institute of Education at the beginning of December 1987.

The main purpose of Common Threads was not so much to counter the prejudice against textiles as a serious mathematics topic but to offer a range of textiles and textile

activities in such a way as to demonstrate the range and depth of mathematics that does or could go on in and with them. The exhibits would be textiles and the captions mathematical. The aim would be two-fold: to demonstrate to those interested in mathematics the richness of textiles as a mathematical resource and to remind textile workers of how much mathematics there is at their fingertips.

A survey of the draft teaching materials already in preparation suggested a reasonably even spread across a matrix with "craft" and "industry" orthogonal to "manu-

facture", "design" and "use". All six areas would need to be represented in a way that would show various aspects of mathematical thinking and doing. An exhibition seriously concerned with mathematics and aimed at both specialists and non-specialists of all ages would have to show mathematical development in its own right as well as the applications and analytical approaches to its uses.

Five themes eventually satisfied both the self-imposed textiles and mathematics criteria and the physical properties of the gallery. The themes chosen were Symmetry, Number, Creativity, Information Handling and Problem Solving. It was decided to make Symmetry the most prominent and developmental theme for two main reasons. The first was the mainly defensive one of trying to counter- act the narrow public perspective of mathematics as arithmetic. The second was to display a mathematical idea, familiar to most people as a daily visual phenomenon, in such a way as to explore and exploit it mathematically at all levels of education while at the same time showing the fruitfulness of the theme for continuity up a curriculum and unity across it. Symmetry is perhaps the perfect Common Thread. It was decided early on however to stick to plane symmetry. There would be quite enough mathematics on the flat without entering a third dimension and 3D geome- try would be represented anyway in the problem solving section.

The first exhibit in the Symmetry section and thus in the whole exhibition was a piece of cross stitch embroidery from Jugoslavia, a representative of the rich cross-stitch tradition of the Balkans. A motif from the piece was re- embroidered in stages in the way an embroiderer would work, to show how the symmetries could be built up and how the embroiderer uses the rectangular grid of the cloth as orthogonal axes. The content of the captions was a conversation with an embroiderer about what she was doing and demonstrated her intuitive and practical mathematical knowledge. Two samples of cross stitch made by Mien women refugees now in Thailand, and kindly lent by Oxfam Trading, demonstrated their technique of working the

24 Mathematics in School, September 1988



Fairisle sweater kindly donated by the Shetland Fairisle Knitwear Association.

An example of the first few centimetres of a Fairisle sweater.

designs from the back, something they would not have been able to do unless they understood how they were construc- ted. The captions of these first exhibits formed an introduction to the first burst of written mathematics, an attempt to define terms and demonstrate the usefulness of symmetry as an underlying theme for much mathematical content, ter- minology and technique.

Definition of the four isometric transformations followed, using baby socks as exemplars of three non-colinear points instead of the usual triangles or other abstract mathematical symbols. A generous gift from Baby Boots allowed the baby sock idea to continue in an illustration of the seven frieze patterns. Viewers were then invited to identify some of the patterns on some ribbons bought in a local haberdashery department, on a Fair Isle sweater kindly donated by the Shetland Fairisle Knitwear Association and a piece of weaving from Bangladesh. The sweater gave an opportunity to explore the construction of the whole garment; the use of the principle of ratio, how to fit a set of different sym- metrical designs into the same counted space and what happens when the garment is made in the traditional way, as a helix, not on a plane.

The Bangladeshi weaving was worked by a woman of immense skill and no formal education. A problem to which she was wearing a solution when interviewed, but which was not in the exhibition, is offered here. Given that you have found a worn factory-knitted sweater on a rubbish dump, how can you find out if there is enough yarn in it when unpicked to weave a shawl of reasonable width and length?

A machine knitter made the next exhibit. She took the letter y, and instructed her machine to read it right to left and up and down in both directions. Using these reflections and translations (the machine can't do rotations) she pro-

Weaving by Sarat Mala Cakma of Bangladesh.

duced a sophisticated plane pattern and some interesting motifs on the way to it. The exhibit made a good introduction to the 17 wallpaper patterns which were followed by two examples on cloth kindly donated by John Lewis.

A Turkish Kelim rug gave an opportunity to analyse the construction of a set of plane symmetries under the parti- cularly constrained conditions of working them on borders

Mathematics in School, September 1988 25



Frieze patterns on ribbons bought in a local haberdashery department

and a central panel at the same time, coping with several in one row and within a width prescribed by the number of warp threads.

The symmetry section ended with some rotational symmetries on a Shetland.tammy and some appliqu6e embroidery worked by women from Laos. Some baskets from Botswana, rotational symmetries worked on Archi- medes spirals, formed a bridge into the next section of Common Threads, which was on Number.

The same demonstrative and analytical approach was followed in this and all the subsequent sections. The Number section contained an example of ratio calculations

and the cartesian product of three sets, in the form of a scarf for Dr Who (viewers were invited to identify the stripes using coded clothes pegs); number groupings in the form of designs of and on an Arran sweater; an exhibit on the problems of recording quantities of numerical data when you try and write down a traditional oral craft tradition or a modern machine based technique (the problem of knitting patterns); an exhibit on mathematics and lace and how they are linked closely by the development of accurate graph papers and one on mathematics and crochet, the craft that can theoretically work an infinite number of loops into another loop.

26 MIthematics in School, September 1988



Transformations on the letter Y performed

on a knitting machine

The Creativity section contained quilts together with the comments of the makers many of which showed the feeling very common amongst women that they are useless at mathematics while their work denies their words. The theme of Information Handling was developed through a brief history of the techniques of weaving, starting with a simple handloom where grid patterns were demonstrated, terms defined and the normal graphical methods of the craft shown. A Jacquard mechanism formed an introduction to computers and computer control at domestic and industrial levels of the design, manufacture and dyeing processes.

The final section on Problem Solving was in two parts. The first was on optimising the use of rectangles, how garments are made either from the whole rectangles of cloth a loom produces or by cutting them up in such a way as not to waste any cloth. The second presented two sets of problems in three dimensions, one on angles on curves (the design and construction of umbrellas), the other on the problem of putting a right angled bend in a cylinder while keeping the surface of uniform thickness. Twelve different solutions to the design of sock heels were offered in both knitting and on the ratio graph paper now published for textile workers.

The success of Common Threads can be measured in three ways. The number of school parties wanting to come had to be controlled for safety's sake and many were

01M SA_

disappointed. Many came from very far away and teachers arranged for their children to develop the work in a Museum or Gallery. One school asked the Tate to lay on a lecture on mathematics in art for the party not at Common Threads and then swapped the groups over. Another, a boys school, brought the whole of one year in four batches and one school returned with the same group several times, using the exhibition as the learning resource it was meant to be. Many teachers commented on how pleasant it was to be able to come on a maths outing.

Secondly, the enthusiasm of teachers and members of the public was stated clearly and often. There was a consistent response from craft workers, many of whom are also mathematicians, that such an event was long overdue. Thirdly, so many requests have been received that a catalogue is now being prepared and arrangements are being made to hire out Common Threads to educational bodies.

Although Common Threads obviously made a small dent in it, the problem of prejudice remains strong. The "It's not maths" response is still heard but it comes mainly from people with no experience of textile work. There is a double prejudice too, with first of the notion that needlework is a trivial activity followed by the view that real mathematics does not concern itself with trivia. Then there is the rather jokey and patronising form of prejudice that could have

Rotational symmetries by a Fairisle knitter and Laothian embroiderers. hL

Mathematics in School, September 1988 27



Baskets from Botswana. Rotational symmetries on

Archimedes spirals.

filled the exhibition with knitted kline bottles and such, with the implied message "Here is some real maths you can do with your (trivial) knitting." It is trivial too (and sexist) to dismiss textile activities as simply "girl friendly" and a counter to the dominant mechanical culture. Many problems in textiles are unique to the medium; many men work with textiles, many women do not. Surprisingly common too in view of its demonstrable untruth is the statement that all knitting and stuff is an occupation of middle class women with time and money to spare.

The "It's not maths" response is interesting none-the- less because it forces the respondents into saying what they

think maths is. If mathematics really is the specialist abstract and symbolic system they claim, then much of school maths is not maths either but a collection of steps on the way to a goal many never reach. And if maths is the wholly abstract system it is, why is it necessary to have so many text-book examples of practical maths from the environment? And having chosen practical examples, why are they so often limited to mechanical ones? By choosing to ignore or denigrate half our environment we are blinding ourselves to a very rich mathematical resource, one that is common and natural to all cultures and both sexes. The reasons for this choice are not mathematical.

28 Mathematics in School, September 1988



Common Threads: Mathematics and Textiles

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