Tag Archives: maths

The Spectre of Maths Anxiety

What an anger-inducing report for a Monday morning. It is a good report, but the subject made me angry. Reading a full historical account of why there is such a thing as maths anxiety at all, and why it persists into the 21st century, and why it is especially more prevalent among women, is so depressing. Besides, I’m certain that things are better (or at least less bad) in countries other than the UK, especially in ex-state socialist education systems. The gender imbalance exists, but is far less horrible – and this is linked, I believe, with the far less rigid “class” structure of the societies. Also in places like Italy and Portugal. How come nobody bothers to look and steal the good ideas. 
 
The full report (very readable):
The Fear Factor: Maths Anxiety in girls and women, 2015, by Samantha Callan, a report commissioned by Maths Action.
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Fields medalist Klaus Roth (1925-2015) has left a fortune to health charities

Klaus Roth, Britain’s first Fields Medalist, who died last year at the age of 90, has left over £1.3 mln to the charities Chest, Heart and Stroke Scotland and MacMillan Cancer Support in Inverness, Scotland. How wonderful to read not only about a life full of mathematics, but also that is has been rewarded financially. It is not so often that I read of a successful professional mathematician who has passed away in their old age, and with a substantial fortune.

Roth’s life story is fascinating. One of the many British scientists of German origin, Klaus Friedrich Roth was born in Breslau (today Poland) in 1925 and came to Britain as a 8-year old child in 1933 with his Jewish-German parents. He went to St.Paul’s school in London and then studied mathematics in Cambridge. He was good at maths, but his anxiety during exams was so bad that he graduated with a 3rd class degree and his tutor advised him to “some commercial job with a statistical bias”. So Roth taught maths at school (Gordonstoun, in Scotland) for a year and then was accepted onto a Masters course at UCL. He went on to become a lecturer at UCL after completing his Masters. Times were different. Today he might not have made it to a MMath course so easily, let alone receive a lectureship so soon after. He would have had to move countries many times before having a shot at getting a permanent job somewhere.

Klaus Roth went on to make important contributions to number theory (analytic theory of numbers and more precisely Diophantine approximation) and to live happily with his wife, Dr Melek Khairy, until her death in 2002.  Pity the article in the Scotsman mentions only the lovely story of how they met (classroom romance! she attended his lectures at UCL), and that they did not have children, but omits the fact Dr Khairy was a medical and experimental psychologist at Imperial College London. Plenty of happy marriages in their generation were composed of an academic husband and a homemaker wife, with or without offspring. But when someone, especially a woman, of that generation isn’t a homemaker, this is worth mentioning. In fact I assumed that until I googled her name for no particular reason, only to come across a bunch of paper she had published in the 1950s and 60s.

Another relevant biographical detail is that she died of cancer in 2002. After her death Roth moved to live in a nursing home in Inverness. This may be why he felt so committed to the cause of health and cancer support in particular.

In the book Art in the Life of Mathematicians (edited by Anna Kepes Szemerédi and viewable on google books) there is a chapter written by the editor which is entitled “Conversations with Klaus Roth” (pp. 249-253). Klaus and Melek were avid dancers and loved Latin music and Mahler.

Klaus Roth got the Fields Medal in 1958 for his contribution to the Thue-Siegel theorem. Roth’s theorem proves that any irrational algebraic number has an approximation exponent equal to two (https://en.wikipedia.org/wiki/Thue%E2%80%93Siegel%E2%80%93Roth_theorem).

More about the story: http://www.scotsman.com/news/mathematician-leaves-1m-to-help-sick-patients-in-inverness-1-4111648

 

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Young US women in STEM

Depressing slide from Margaret Eisenhart and Carrie Allen’s paper at the AAA2015 (American Anthropological Association meeting) in Denver.

  

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Girls, math, and bullshit

After 9 years in the UK, I’ve reconciled myself to the realisation that I will always remain a foreigner. When I’m stressed, like when speaking to my bank on the phone today, my spoken expression and listening comprehension skills in English go out of the window. If someone woke me up at night, I’d speak to them in Bulgarian (my native language), but if I were really fast asleep, it would be Russian (my mother’s tongue which I learnt first).  But what is especially hard for a social scientist is that I am unable to overcome some taken-for-granted ideas that I had before coming here, and get used to their opposites which should be obvious to me. This evening I’m reminded of one: women and maths. This stuff is doing my head in. Each time I read about it, I get a headache. You know that peculiar blackout feeling when you hear something that is either blatantly, in-your-face, unjust or untrue, or something whose premises are so flawed that it’s not even wrong. I get that each time I encounter the obvious, common knowledge that women and math don’t mix. I just found an article about Shirley Conran’s new project aiming to make maths attractive to girls by convincing them that it will help them manage their personal finances. The article had the awesome title “Math is a feminist issue”, and it linked to what must be a very interesting and useful new report on women and the fear of mathematics. I’m sure it’s a very useful report. I must read it for my research. But I am stuck with the pdf like a horse in front of a river. I can’t read it because just reading the chapter titles makes me wince:

“1 Why maths and maths ability for women matter 13

2 Why confidence about maths ability matters 19

3 How do we know that women fear maths? 25

4 Why is maths perceived to be innately male? 29

5 Being female 37

6 Women’s education in history and the place of maths within it 47

7 Attacking the Maths Myth that drives the Fear Factor”

Clearly, I must have grown up with a different Myth. I grew up with the conviction, supported by empirical observations, that girls are better at all subjects. I don’t know why. And because I never had a reason to question this belief at the time I was at school or university, now I’m finding it really hard to accept that things are so obviously not the case. I don’t even know if my belief was justified about Bulgaria in general, or about Bulgarian “elite” primary and secondary schools. I may not be. Maybe I grew up in a bubble (a bubble in which all but one of my maths teachers were women, like almost all my other teachers; and in which schoolkids who were good at maths were equally likely to be girls or boys, and those who weren’t were more likely to be boys).

But I like having grown up in a bubble. I like the fact that the obviousness of “girls don’t like math, girls are no good at math” pisses me off. The really painful thing is that with each new item of information on the “women and maths” subject, doubt and desperation trickle in. I fear the thought that, if I had heard of this at a younger age, this belief might have turned into a self-fulfilling prophecy, and would have made me worse at maths – and worse at believing in my own capabilities, talents and worth. I hate the thought that there are young people out there growing up right now who entertain the freaking insane belief that interest and talent in various parts of human culture may have anything to do with their genitals.

Even less rationally, reading stuff which generalises a whole gender into one box according to a negative criterion, such as lack of ability or fear, makes me uncontrollably angry. When you, as a woman, read something like this, you just can’t win. If you happen to be bad at maths or hate it, well, there, there, little darling, we said it first, women suck at math. If you happen to be good at maths or like it, then you are not a woman, you’re an honorary man. &%£$@£$&?{}$£% Rage is not a good companion to research. Imagine, my research isn’t even about gender, actually, it’s about all mathematicians regardless of their gender. Imagine how angry I’d be if I were actually studying gender.

Incidentally, most of the female professional mathematicians I have talked to say that they were never aware of a negative gender stereotype in relation to maths when they were little. When they did realise it (often upon arriving to university), it was not a pleasant realisation.Some say that they were aware, but consciously rebelled or ignored it.

Perhaps we ought to not just combat the stereotype, but also shield from it those young kids who are lucky to don’t know about it yet…at least until they are old enough to be brave and rebellious rather than conformist?

P.S. Upon rereading, this sounds like an unusually personal and non-rational research-related blogpost. Unprofessional pubic expressions of unpolished thoughts, tut-tut. But it will have not been in vain, if it helps me at least read that report which, I’m sure, has lots of interesting and depressing data…

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My pet hate: I wish people stopped opposing “math” to “creativity”!

What a bad article to read before going to bed at 1am. Now I won’t sleep, grr. No, the article itself isn’t bad, it is even making a valid point: “Creativity just as important as math and science”. What made me angry, you ask? 

The argument is always “science and math are essential, especially in today’s job market”. I agree, they are essential on the job market. Just as literacy, the ability to retell, interpret, improvise, communicate, the knowledge of history, cultures and languages. Many things are important “on today’s job market”. But I do wish people asked themselves more often what is essential for the development of a person, for the wellbeing of society, and for the enjoyment of life. Perhaps then – to come back to our “not enough people do math” problem which is only a symptom of  a bigger problem in the way we treat learning – more people would enjoy playing with maths. But Peter Lockhart said it better. I am going to shamelessly quote the first 1.5 pages from his amazing essay just to make sure that more people read it. Please, read it, whether you have always liked, hated, or been undecided about mathematics. I will check in my stats how many people click on the link.

Amusician wakes from a terrible nightmare. In his dream he finds himself in a society where music education has been made mandatory. “We are helping our students become more competitive in an increasingly sound-filled world.” Educators, school systems, and the state are put in charge of this vital project. Studies are commissioned, committees are formed, and decisions are made— all without the advice or participation of a single working musician or composer.

Since musicians are known to set down their ideas in the form of sheet music, these curious black dots and lines must constitute the “language of music.” It is imperative that students become fluent in this language if they are to attain any degree of musical competence; indeed, it would be ludicrous to expect a child to sing a song or play an instrument without having a thorough grounding in music notation and theory. Playing and listening to music, let alone composing an original piece, are considered very advanced topics and are generally put off until college, and more often graduate school.

As for the primary and secondary schools, their mission is to train students to use this language— to jiggle symbols around according to a fixed set of rules: “Music class is where wetake out our staff paper, our teacher puts some notes on the board, and we copy them ortranspose them into a different key. We have to make sure to get the clefs and key signatures right, and our teacher is very picky about making sure we fill in our quarter-notes completely. One time we had a chromatic scale problem and I did it right, but the teacher gave me no credit because I had the stems pointing the wrong way.”

In their wisdom, educators soon realize that even very young children can be given this kind of musical instruction. In fact it is considered quite shameful if one’s third-grader hasn’t completely memorized his circle of fifths. “I’ll have to get my son a music tutor. He simply won’t apply himself to his music homework. He says it’s boring. He just sits there staring out the window, humming tunes to himself and making up silly songs.”

In the higher grades the pressure is really on. After all, the students must be prepared for the standardized tests and college admissions exams. Students must take courses in Scales and Modes, Meter, Harmony, and Counterpoint. “It’s a lot for them to learn, but later in college when they finally get to hear all this stuff, they’ll really appreciate all the work they did in high school.” Of course, not many students actually go on to concentrate in music, so only a few will ever get to hear the sounds that the black dots represent. Nevertheless, it is important that every member of society be able to recognize a modulation or a fugal passage, regardless of the fact that they will never hear one. “To tell you the truth, most students just aren’t very good at music. They are bored in class, their skills are terrible, and their homework is barely legible. Most of them couldn’t care less about how important music is in today’s world; they just want to take the minimum number of music courses and be done with it. I guess there are just music people and non-music people. I had this one kid, though, man was she sensational! Her sheets were impeccable— every note in the right place, perfect calligraphy, sharps, flats, just beautiful. She’s going to make one hell of a musician someday.” 

Waking up in a cold sweat, the musician realizes, gratefully, that it was all just a crazy dream. “Of course!” he reassures himself, “No society would ever reduce such a beautiful and meaningful art form to something so mindless and trivial; no culture could be so cruel to its children as to deprive them of such a natural, satisfying means of human expression. How absurd!”

Meanwhile, on the other side of town, a painter has just awakened from a similar nightmare…

I was surprised to find myself in a regular school classroom— no easels, no tubes of paint.”Oh we don’t actually apply paint until high school,” I was told by the students. “In seventh grade we mostly study colors and applicators.” They showed me a worksheet. On one side were swatches of color with blank spaces next to them. They were told to write in the names. “I like painting,” one of them remarked, “they tell me what to do and I do it. It’s easy!”

After class I spoke with the teacher. “So your students don’t actually do any painting?” I asked. “Well, next year they take Pre-Paint-by-Numbers. That prepares them for the main Paint-by-Numbers sequence in high school. So they’ll get to use what they’ve learned here and apply it to real-life painting situations— dipping the brush into paint, wiping it off, stuff like that.
Of course we track our students by ability. The really excellent painters— the ones who know their colors and brushes backwards and forwards— they get to the actual painting a little sooner; and some of them even take the Advanced Placement classes for college credit. But mostly we’re just trying to give these kids a good foundation in what painting is all about, so when they get out there in the real world and paint their kitchen they don’t make a total mess of it.”

“Um, these high school classes you mentioned…”

“You mean Paint-by-Numbers? We’re seeing much higher enrollments lately. I think it’s mostly coming from parents wanting to make sure their kid gets into a good college. Nothing looks better than Advanced Paint-by-Numbers on a high school transcript.”

“Why do colleges care if you can fill in numbered regions with the corresponding color?”

“Oh, well, you know, it shows clear-headed logical thinking. And of course if a student is planning to major in one of the visual sciences, like fashion or interior decorating, then it’s really a good idea to get your painting requirements out of the way in high school.”

“I see. And when do students get to paint freely, on a blank canvas?”

“You sound like one of my professors! They were always going on about expressing yourself and your feelings and things like that—really way-out-there abstract stuff. I’ve got a degree in Painting myself, but I’ve never really worked much with blank canvasses. I just use the Paint-by-Numbers kits supplied by the school board.”

***

Sadly, our present system of mathematics education is precisely this kind of nightmare. In fact, if I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done— I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.

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Women: Stop shrinking, “Take up space!”

This video isn’t about mathematics. But when you think about it, it really is about mathematics. I believe that the chief reason behind why there are few women in mathematics (relative to the number of men) is the same reason that urged Vanessa Kisuule to write this awesome poem.

Here is a selection of serious and funny descriptions from some of my interviews (I’ve done 50 so far, mostly in Germany, and some in the UK, with more to come), referring either to an abstract, or a real successful mathematician. Try to imagine the people with these attributes which are necessary, though insufficient, for success in absolutely any competitive field:

“arrogant”,

“confident”,

“undrownable”

“robust”

“not be afraid to experiment and fail”

“must have fun with maths”

“resilient”

“barges forth”

“does not get discouraged”

“single-minded”

“you know the old saying, ‘fuck up early, fuck up often”

“focused on the thing s/he is doing and not so much on success itself”

“determined”

“believe in yourself, believe that you can”

“a bit bloody-minded”

“self-directed”

“not a shrinking violet when it comes to maths!”

“ready to make mistakes”

“get used to the idea that you will fuck up all the time”

“…seeing them helped me realise I’m not the only one getting stuck”

“focused on the work, not on how others see you”

“We mathematicians are a very tolerant bunch: we don’t care how you look or sound, as long as you have an interesting theorem to talk about!”

It is also the same reason for why many “mathematically-minded” men don’t make it into mathematics, or into other areas for which they might otherwise have a potential ability or even a full-blown talent.

That is not to say that this reason is simple or easy to overcome.  And it certainly can’t be overcome just by individual willpower – even if it may be useful in each individual case to realise that “yes, I am just as valuable as any other person and I deserve to take up all the space that I need”.

Taking up space, obviously, isn’t meant just in the physical sense. There are plenty of women who take up space and men who don’t. Just look next time you are on the Tube. (OK, some people think that men do it more often – I don’t have reliable quantitative data on that). But it’s a useful reminder that there is something fishy with any system in which many people belonging to any one group (in this case, women, though there are many other groups that face similar problems) face an inequality unrelated to the definition of their group. “Women” are simply “female people” – there is no intrinsic reason in being a woman that directly leads to the group of women not being represented equally in certain human activities, instead there are plenty of social, historical, institutional, political, personal, as well as plain stupid, reasons.

 

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What should we teach to liberal arts students who will take only one math course?

Interesting discussion about what and how much mathematics university students on liberal arts courses in the US should know on mathoverflow – here

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Apparently someone came to this blog by searching for “active learning in maths good or bad”… I wish I could tell them, without active learning there CAN BE no maths. Maths is all about DOING it yourself. But what do I know, I’m just a sociologist who thinks maths is fun.

Passive learning in maths!?

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What do zombies have to do with maths?

UK maths educators are going more and more overboard in their attempts to make maths popular with young people.  Consider this Halloween special by the Oxford Science blog:

Or maybe I’m just too old to understand what the hype with zombies is all about. More pure human maths for me, please.

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