IOWME Newsletter Volume 20, No. 2

IOWME Newsletter Volume 20, No. 2

IOWME NEWSLETTER

VOLUME 20, NUMBER 2, July 2006

The image above is reprinted with kind permission of the UK Resource Centre for Women in Science Engineering and Technology, see the article inside

Convenor of IOWME: Hilary Povey, UK

Newsletter Editor: Heather Mendick, UK

http://extra.shu.ac.uk/iowme/

International Organisation of Women and Mathematics Education

An affiliate of the International Commission on Mathematical Instruction

Welcome to the Second IOWME Newsletter of 2006

I am delighted to be introducing another newsletter. This newsletter is as diverse as ever containing critique and protest, celebration and commemoration.

There was some interest in the idea of having a future newsletter based around the theme of mixed and single-sex educational settings and so we will feature material on this in November. I hope that lots of you who are working in this area and have views and news will send in material to me.

My contact information is:

E-mail addresses: or

Postal addresses: Institute for Policy Studies in Education, London Metropolitan University, 166-220 Holloway Road, London N7 8DB, England

The November issue will also contain a consultation on the format of the next IOWME conference in Monterrey, Mexico, in 2008. I have included a beautiful picture below of the scenery there. In the meantime, if you have any thoughts on this that you’d like to share then get in touch with Hilary Povey, the IOWME convenor.

Her contact information is:

E-mail address:

Postal address: Mathematics Education Centre, Faculty of Development and Society, Sheffield Hallam University, 25 Broomgrove Road, Sheffield S10 2NA

Best wishes,

Heather

P.S. I’ve found more literary quotes on women and maths and scattered them throughout the newsletter (thanks again to Sally Lipsey for sending me one to get me started).

Contents

Welcome to the Second IOWME Newsletter of 2006 2

Contents 2

Essentialism and mathematical agency: a critique of Simon Baron-Cohen’s book ‘The Essential Difference’ 2

UK Celebrating Women Achievers 2

IN MEMORIUM: Claudia Zaslavsky 2

News 2

Book reviews 2

National Coordinators 2

From Letters of Thomas Mann, 1889-1955 (Translated by Richard and Clara Winston. NY: Vintage Books, Random House, 1975, p.30-31)

"I also wholly approve of your not giving too much attention to your tomes
on mathematics and physics. For though I usually don't like to admit it, I
will confess to you just this once that underneath I am a little jealous of
the sciences and secretly experience a diabolic joy when you thoroughly
neglect them. That is old-fashioned, sentimental, and base, I know, and I
promise that I'll never again voice such feelings ... "

This letter was written in April 1904 and sent to Katia Pringsheim who
became Mann's wife in 1905. The daughter of a professor of mathematics at the University of Munich, she was educated at home as there was no
humanistic secondary school for girls. She studied math, however, under
her father and also under Ferdinand Lindemann (renowned for his proof that pi is transcendental). Prof. Wilhelm Roentgen (famous for the discovery of x-rays) was her instructor in physics! The "noted suffragette", Hedwig Dohm, was her grandmother. Katia and Thomas Mann had 6 children and I have not found any information about whether Katia continued to study math and whether any of her children studied more than elementary math.

Sent in by Sally Lipsey ()

Essentialism and mathematical agency: a critique of Simon Baron-Cohen’s book ‘The Essential Difference’

In this paper I draw attention to a recent popular non-fiction book, The essential difference: the truth about the male and female brain (Baron-Cohen 2003), that positions males and females as “essentially different”. The ‘differences’ hinge on the personality traits of ‘empathizing’ and of ‘systemizing’. Systemizing is a trait that is related to mathematical activity and Simon Baron-Cohen associates systemizing with ‘male brains’. This association could be detrimental to female participation in mathematics.

Introduction

Mathematics education is influenced by many social and cultural forces and mathematics educators are wise to be alert to emerging ideas outside maths education. This paper focuses on one such emergent idea as expressed in the recent book The essential difference: the truth about the male and female brain (Baron-Cohen 2003), which I shall refer to as TED for short. This popularised book offers theorisation on two particular ways of thinking, ‘empathizing’ and ‘systemizing’, and claims that “the female brain is predominantly hard wired for empathy and the male brain is predominantly hard wired for understanding and building systems” (p.1). This claim is a challenge to inclusive mathematics education as it distances those who are female-identified from systemizing processes intrinsic to mathematics. Furthermore, the rhetoric of the book associates systemizing with autism and autism with deficiencies in empathy, thus by association, it positions systemisers as lacking in empathy. It is important for those of us with interests in gender and mathematics to understand what Simon Baron-Cohen’s influential claims mean in the particular context of women and mathematics – and this includes females’ identities, participation and agency with regard to mathematics.

The paper starts by giving an introduction to TED and the roots of the central ideas. Then it

· offers a critique of TED’s argument,

· discusses issues specifically related to mathematics, and

· challenges the notion that suggests females are not systemisers,

before rejecting this ‘new biological determinism’ in the conclusion.

The Essential Difference?

The central claim of the book, published for a wide audience, is stated as men and women have fundamentally different brains on average (Baron-Cohen 2003, p.2). The book is written in a ‘folksy’ style and Baron-Cohen is quick to say that his topic is a delicate one and is not intended to be grist for reactionary gender oppression. The outline of the book’s argument is that: every person has ‘empathizing skills’ and ‘systemizing skills’. These skills are assessed by psychological tests that Baron-Cohen and colleagues have developed that assign to an individual a ‘systemizing quotient’, SQ, and an ‘empathizing quotient’, EQ. Results indicate males on average systemize and females empathize (Baron-Cohen 2003, p.62) and thus the ‘difference’ of his title is key to mind and gender.

The roots of these concepts

The author is an academic psychologist whose field is the study of autism and this popular work draws on his research. Autism is defined as a ‘triad’ of abnormalities in behaviour in the domains of “social development, communication, and repetitive behaviour/obsessional interests” ((Baron-Cohen et al. 2002, p.491). Thus someone with autism is ‘untuned’ to the social world and Baron-Cohen and colleagues hypothesise that such social-tuning deficiency is a result of impaired empathising faculties. In a positive turn, Baron-Cohen and colleagues have considered the other aspect of the triad to do with repetition and obsession and constructed the concept ‘systemizing’ which for autistic individuals is “intact or even superior” (Baron-Cohen et al. 2002, p.495). The work has a root in exploring Hans Asperger’s 1944 notion that “autistic personality is an extreme variant of male intelligence” (quoted in translation from original German in Baron-Cohen 2003, p.149). Baron-Cohen’s theory extends Asperger’s notion to position ‘the male brain’ as ‘systemizing’ (one that understands and builds systems). Baron-Cohen then constructs a female counterpart by positioning ‘the female brain’ as ‘empathizing’. These concepts of empathizing and systemizing, together with the attributions ‘male’ and ‘female’, were presented previously in a collection of papers on cognitive development (Baron-Cohen et al. 2002) principally for a professional educational audience. In this paper, the empathising-systemizing theory is explained in terms of agency and intention: that people with empathising skills recognise mental states in others and produce “appropriate emotional response” (p.495); people with systemizing skills “understand and predict the behaviour of non-agentive events” (p.495). And it is more than mere capacity – there is a recognition that capacity is fuelled by the subjects’ own agency, their interests, desires and drive. The link to gender comes later in the paper and is based on Kimura’s work (e.g. Kimura 1999) and work from his own colleagues, together with Asperger’s previously mentioned conjecture. Inasmuch as the systemizing concept comes from the criteria for diagnosing autism, one can see why Baron-Cohen would conceptualise systemizing as oppositional to empathizing (Baron-Cohen et al. 2002, p.495; Baron-Cohen 2003, p.5).

A brief critique

· The concept of empathizing as used in Baron-Cohen (2003) is defined by means of the ‘Empathy Quotient’ questionnaire. In this questionnaire, empathy is construed sometimes to be social skills (“I can sense I am intruding, even if the other person doesn’t tell me”, “I find it hard to know what to do in a social situation”) but also to relate to a personal emotional state (“it upsets me to see an animal in pain”, “seeing people cry doesn’t really upset me”). This begs the question about what empathy is.

· The notion that the concepts of systemizing and empathizing are negatively correlated is suggested but not stated; the nuance cannot be interrogated as the bivarate data are not presented. The book does not claim that systemizers are not empathisers; it is the discourse, rhetoric and style that presents this juxtaposition.

· The book’s essentialising of males as systemizers and females as empathizers based on statistics of the extremes, ‘queers’ the outliers and obscures the fact that the distributions of scores for males and females overlap considerably. Indeed, in another paper (Baron-Cohen et al. 2001) Baron-Cohen’s own data shows that for one characteristic, “having attention to detail”, that is associated with systemizing, the means of scores of ‘control females’ were actually higher than those of ‘control males’ (p.8).

· Early on in the book, Baron-Cohen defines male and female in 5 different ways: (1) genetic, (2) gonadal, (3) genital, (4) ‘brain type’, and (5) ‘sex-typical behaviour’. Definitions (4) and (5) are his own: your brain is ‘female’ if your empathizing is stronger than your systemizing, and vice versa, and sex-typical behaviour “follows from (4) brain type” (Baron-Cohen 2003, p.98). His definitions serve to reify his ‘the essential difference’ slogan. But tagging on to the list (1-3) of far more physically defined concepts of male and female, definitions that are based on the questionnaire he designed, is misleading: it suggests that these concepts are more real than they actually are. The first three are based on bipolar physical states, not on overlapping normal distributions of attributes based on his constructs.

Issues related to mathematics

Mathematics involves systemizing: sorting out structural features of problems; understanding and working with the logic of events, machines or rules; representing ideas symbolically and attributing meaning to these symbols and operating with them creatively and independently. These are mathematical attributes that involve ‘systemizing’. Other questionnaire based work from Baron-Cohen and colleagues, (Baron-Cohen et al. 1998), certainly indicates that autism is more common in mathematically-orientated families. Highly talented Mathematics Olympiad winners surveyed by Baron-Cohen and colleagues had similar scores to an Asperger syndrome group on the ‘attention to detail’ sub-scale. On most other sub-scales they had scores about mid-way between the control and the Asperger group but were similar to the controls’ scores on ‘communication’ (Baron-Cohen et al. 2001).

Empathy is easier with one with whom you co-systematise. And this suggests that communities of systemisers do develop inter-personal bonds that can be interpreted as empathy. It is worth noting that the notion of an ‘appropriate emotional response’ is very much culturally relevant. And so in the mathematics communities, if there is a lack of ostensive personal chat that should not be read as ‘inappropriate emotional response’; quite contrary-wise, silent support of the practice may well be deeply felt, empathetic. Maths students from a recent project (see Rodd and Brown 2004) speak of the importance of their study mates who share their mathematics undergraduate practice. The biographical sketch of Richard Borcherds, a mathematician with an Asperger’s syndrome profile (Baron-Cohen 2003, p.155-70) exemplifies that even strong systemizers who are low empathizers may have their place in the world and be functioning well in their context.

Mathematical minds?

Anyone who’s successful at math seems to me quite obsessive. You have to be obsessive, otherwise you wouldn’t do it. When I’m into something, I’m effectively working all the time - I’m thinking about it when I’m standing in line at the grocery store, and I wake up with ideas.

Professor Jenny Harrison, University of California at Berkeley.

Epitomic characterisation of a mathematical mind was given by Krutetskii (1976) after his investigation of mathematically precocious children. His analysis does suggest that superior systemizing skills, like “grasping the formal structure of a problem” are available to these mathematically exceptional children in his “structure of mathematical abilities” (p.350). Krutetskii’s work includes a discussion of “personality traits needed for success in mathematics” (p.345). These are dominated by affective orientations like having a “positive attitude towards mathematics … a striving and need to study it” (p.345):

joy in creation, a feeling of satisfaction from intense mental work and an emotional enjoyment of this process heighten a person’s mental tone, mobilize his (sic) powers and force him to overcome difficulties … all the gifted children were marked by a profoundly emotional regard for mathematical activity” (p.347)

Thus Krutetskii shows us that feelings are central to being able to engage in deep systematic work and his case studies show a wide range of empathetic orientations in as much as we can glean from descriptions of the subjects’ being interested in other people as well as in maths.

Anecdote: on empathising systemising

Two female maths graduates and educationalists A and B were discussing an education paper, one copy of which had been printed off by B. B passed the paper to A aware, and slightly uncomfortable, that the pages were not in order. She was a tiny bit embarrassed that she was passing an un-systemized artefact to her colleague, but it wasn’t worth mentioning as conversation was flowing. A received the paper over the table and without commenting about the pages being out of order started to put them into order while talking about the topic under consideration. A and B both realised the desire to have an ordered paper and had a laugh about recognising their shared systemizing trait.

Gender issues: female systemizing

She was a woman who gave her life to housework, to the kind of daily routines of polishing, dusting, vacuuming and tidying that were once common, and these days are only undertaken by patients with obsessive compulsive disorders. … The invisible sides, the obverse, the underneath and the insides of everything were clean. The oven and its racks were scrubbed after every use. Order and cleanliness were the outward expression of an inward ideal of love. …