AWM Book Review:

Common Threads: Women, Mathematics, and Work

by Mary Harris, Trentham Books Limited, Stoke-on-Trent, England 1997. xii+213. ISBN 1-85856-015-2 (paper).

From: AWM Newsletter, January/February 1998.

Reviewed by: Claudia Zaslavsky, 45 Fairview Avenue, #13-I, New York NY 10040.

In September 1989 I participated in the 'POP Maths' meeting in Leeds, England. This event, more formally called 'The Popularization of Mathematics,' had been organized by the International Commission on Mathematical Instruction to deal with the negative public image of mathematics and world-wide problems in mathematics teaching at all levels. The call was for "a major gathering of those interested...accompanied by a nationally-organized, yet international 'event' comprising a major exhibition, films, videos, lectures."

An outstanding feature of the meeting was the POP Maths Roadshow, an interactive exhibition designed to demonstrate that mathematics is both worthwhile and fun. From Leeds the exhibition was to travel to various sites in England and Wales during the following year. The displays were as varied as one may imagine: chaos, number and form in nature, artwork based on the structure of knots, a tile maze, symmetry, mathematics in different cultures, and much more. Groups of schoolchildren, bused in from surrounding communities, enjoyed playing a range of mathematical games from many lands.

One of the most fascinating exhibits was Common Threads, the brainchild of Mary Harris and her Maths in Work Project at the University of London Institute of Education. As the title suggests, the exhibit consisted entirely of textiles, with captions indicating the various aspects of mathematics that went into their design and production. To cite one example, Harris listed the three main variables involved in knitting a sweater: needle sizes, yarn thicknesses, and pattern sizes. She then discussed the Cartesian product of the three variables and their possible combinations. The Aran sweater in the exhibit introduced another variable in the form of traditional symmetric designs incorporated into the knitting process. Included was a photograph of an Aran sweater with a design based on random numbers!

A display of weaving was accompanied by a discussion of the Jacquard mechanism, which "stores infomration in binary form about which threads are to be lifted," and the role of the Jacquard system of punched cards in Charles Babbage's design of his Analytical Engine. Harris quoted Ada Lovelace: "The Analytical Engine weaves algebraical patterns just as the Jacquard loom weaves flowers and leaves."

The exhibit was based on the following themes: symmetry, number, creativity, information handling, and problem-solving. One of the most popular displays was a demonstration of the seven strip or frieze patterns -- the different ways to repeat a pattern in one dimension -- by using a baby sock as the motif. The thirty-four required socks were donated by Baby Boots. Another display focused on the solution of the problems inherent in turning the heel of a knitted sock, as compared with bending a cylindrical pipe into a right angle. The latter is considered 'real maths,' while knitting socks is just mindless 'women's work.'

The Common Threads exhibit wore out in the course of its two-year tour of England. In response to widespread demand, the British Council created two similar exhibits that eventually visited twenty-three countries between 1991 and 1994 before they were retired. Although the final destination for one of these tours was Vancouver, British Columbia, Common Threads never made it to the United States.

The book under review tells about the exhibit --- and much, much more. As Harris states in her introduction,

This book tries to place Common Threads and its influence within the historical context of the development and spread of mathematics education in England and beyond, while tracing the history of the education of girls and women and the effects of their work with textiles on their school curricula. (p. viii)

She is particularly concerned with the negative effects on the majority of the population, especially women, of the kind of mathematics education -- or lack of education -- to which they have been subjected. With the Common Threads exhibition, she challenged the stereotype, associated with feminine activity, that needlework is devoid of mathematical content.

The first two chapters describe the 2000-year history of "how needlework and mathematics came to be stereotypes in polar opposition." The medieval guilds in Europe came to control the output of textiles, and with the introduction of large looms in production workshops and later in factories, women's work was downgraded. Working class women held factory jobs at low pay and under terrible conditions, or resorted to the practice of "sweating" (work at home or in sweatshops) in order to earn a meager income. [The practice continues to this day on a worldwide scale. I have a petition addressed to President Clinton for the abolition of sweatshop abuses in both the United States and abroad.]

By the end of the nineteenth century a minimum amount of schooling was mandated. For working class girls, the curriculum was based on needlework, the kind of plain sewing that might enable them to sew for their families or obtain jobs. Middle class girls, on the other hand, learned the fancy embroidery by which they would affirm the social status of their future husbands. As for mathematics, "the social classes became defined by the mathematics they were taught, and the mathematics to be taught defined the different gradations of society" (p. 38).

Furthermore, the mathematics that was taught differed for boys and for girls. Even middle class girls were prevented from learning much more than arithmetic and perhaps some algebra. The publication of Herbert Spencer's books in the second half of the nineteenth century furnished 'scientific' proof of women's mental inferiority. Not only would higher education make women physiologically unfit for motherhood, but it would also disincline them from their feminine duties, thus leading to the moral decline of the family, the race, and the empire. Of all subjects, mathematics was thought to put the greatest strain on the learner. In fact, Ada Lovelace's illness was attributed to "too much mathematics" (p. 69). Several decades later, the Headmistress of Manchester High School argued that mathematics "should be kept at a minimum for girls...the subject being useless to them" (p. 77).

Nor have such attitudes disappeared in the twentieth century. In my book Fear of Math: How to Get Over It and Get On with Your Life, I relate the story of Becky, a former elementary teacher and librarian. Her father had told her: "You only need to know up to twelve. No recipe calls for more than twelve," an allusion to her future role as a housewife.

Harris discusses the devastating effects of exclusion from mathematics in contemporary society:

Girls barred from mathematics by expectation, convoluted theory, or the habits of long history, are deprived of input to and status in one of the most powerful parts of their own heritage and culture. (p. 85)

In the 1970s and 1980s, attitudes began to change in the face of the attack on mathematics education as a male, middle class preserve. She cites the role played by researchers in sociology, psychology, and mathematics education in tearing down the hurdles, beginning with work in America.

Harris took a different tack with her Maths in Work project. Her job was to analyze data from a skills survey of workplaces in order to influence curriculum development and improve the available learning materials for school-to-work programs. She was struck by the amount of mathematical thought that had been overlooked in the responses to the survey, and began to conduct her own investigations by going into factories, interviewing people in various fields of production, and carrying out many tasks herself. Eventually she produced

learning materials that would take practical, open-ended problems from workplaces and put them, with the minimum of instruction, into the hands of teachers to use and develop as they willed. (p. 94)

The tasks would be creative and open-ended. She named her pack of activities "Cabbage," a word derived from the French _coupage_, for the practice among garment makers of squeezing out a few extra pieces for their own use while cutting the cloth. (My mother-in-law reported having done this when she was a dressmaker for the nobility in tsarist St. Petersburg.) The twenty-two activities were quite varied, and included _adinkra_ designs from Ghana and baskets with symmetrical patterns from Botswana.

Several chapters describe the Common Threads exhibit and its effect, both in England and in the twenty-three countries that it visited. Harris accompanied it to thirteen of these sites. In Zimbabwe it was housed in the Sheraton Hotel, where it attracted considerable favorable attention. The most effective visit was to Botswana, where educators and the Art Gallery supplied many more items, not merely textiles. In all countries, teachers were involved in workshops. The exhibit was instrumental in shaping new curriculum ideas involving applications to the indigenous cultures and in helping to overcome the devastating effects of the wholesale adoption of 'New Math' in the former colonial countries in the 1960s and 1970s. Harris writes:

As in cultures from which it is transported, mathematics reinforces power structures, labels different levels of social class and effectively filters out whole people through the handy tool of universally recognized results of commercially published examination. (p. 153)

Mary Harris displays an enormous breadth of scholarship and research, citing authorities in the many aspects of women's studies, mathematics education, ethnomathematics, and education in general. She does not mince words in condemning racist, sexist, and classist practices in England or in any other part of the world, past or present. Photographs of several displays -- the baby sock strip patterns, Hungarian embroidery, Botswana baskets -- make up for the reader's inability to view the actual exhibit. The book closes with a photograph of a poster that Harris designed, showing abstract geometric designs in one column and identical designs in patchwork in the other column. The first column is headed "real maths," while the second is labeled "girls' stuff."