Tony Gardiner: “The Man Who Knew Infinity”

The film The Man Who Knew Infinity  goes on UK general release from 8th April.

It is a compressed, and beautifully dramatised version of the theme treated more fully in Robert Kanigel’s double biography of the same name – which treats Ramanujan alongside a partial portrait of G.H.Hardy.
Mathematicians can be remarkably unforgiving about attempts to present mathematics to a general audience.  And Ramanujan’s story could so easily be cheapened – with awkward aspects being trivialised, in order to pander to current prejudices.  The Good News is that, not only has this been avoided, but the film manages to incorporate much of the detail and spirit of what we know, while using its dramatic freedom to confront important issues that are often either treated too tritely, or passed over in silence.  The project may have taken 10 years in the making, but the result has been worth it.
As someone who does not usually watch movies, I simply encourage everyone to see it
(perhaps several times), to encourage others to see it, and to use it to discuss the issues which it raises.
A film is not meant to be a reflection of reality.  This film would seem to be a fairly faithful representation of what we know in those areas where fidelity matters. In other respects it  exercises flexibility.  In contrast to Ramanujan, Dev Patel is slim and beautifully formed; yet he manages to capture an essential seriousness and devotion which is entirely plausible.  His wife is portrayed as older and I suspect much more beautiful than the real Janaki; yet her portrayal of profound simplicity is moving in a way that seems entirely appropriate (whether or not it is documented).
In his review for the February issue of the Notices of the AMS
George Andrews suggested that the film will help students appreciate the importance of “proofs”.  In fact, the struggle between proof and intuition, between Hardy and Ramanujan, is not so cleanly resolved, and there is a danger that the film may leave many strengthened in their belief in mathematical invention as “magical intuition”.  So the film should be used to actively encourage a deeper discussion of the relative importance of proof, and what is too often simply labelled “intuition” (as if it were not susceptible to, any further explanation).
Here is a chance to grapple with the often neglected interplay between
   (a) technical, or formal, training in universal methods – whereby my individual “mental
universe” is disciplined to fit with yours (or with some imaginary “Platonic ideal”),
and
   (b) our individual, idiosyncratic way of thinking about these shared objects and processes – whereby my thoughts avoid being mechanical replicas of everyone else’s, and so provide scope for originality.
Without the second, we are little better than machines.  And without the first, we are almost bound to go astray.
Almost all students need a significant dose of (a) before their (b)-type thoughts can become fruitful.  But some individuals’ (b)-type thoughts flourish – mostly unerringly – with relatively little (a)-type formalism. One thinks of Euler, or Schubert, or 19th century Italian algebraic geometers, or Feynman, or Thurston, or … .  The problem is then how to check the resulting claimed insights, to embed them within mathematics as a whole, and to make the methods available to the rest of us.  By neglecting such delicate matters we leave a vacuum that is too easily filled by half-truths.
Tony Gardiner

Response to Simon Jenkins

I have read his paper with mixed feelings:

Charge the maths lobby with the uselessness of its subject and the answer is a mix of chauvinism and vacuity. Maths must be taught if we are to beat the Chinese (at maths) (Only those arguments that can be linked to immediate pragmatism are regarded as worth voicing!). Or it falls back on primitivism, that maths “trains the mind”. So does learning the Qur’an and reciting Latin verbs. (So what? I would adore an education system that offers the opportunity of learning such things, provided that it is not compulsory. When I was 15 years old I was annoyed by the idea that I – as a child of the 20th century- had to miss the opportunity of learning Latin, so I took private Latin lessons. I was lucky enough that I was in the German highschool such that the wife of one of our teachers could teach me Latin. Later I did the same for Ancient Greek, too.)

Meanwhile, the curriculum systematically denies pupils what might be of real use to them and society. There is no “need” for more mathematicians. The nation needs, and therefore pays most for, more executives, accountants, salesmen, designers and creative thinkers. (Who has the priviledge to decide what the society needs? After all, those who have this priviledge are able to create these needs in the first place. So, it is a tautology.)

At the very least, today’s pupils should go into the world with a knowledge of their history and geography, their environment, the working of their bodies, the upbringing of children, law, money, the economy and civil rights.

This is in addition to self-confidence, emotional intelligence and the culture of the English imagination. (As if these attributes can be acquired in a way that is isolated from learning mathematics!) All are crowded out by a political obsession with maths.

The reason is depressingly clear. Maths is merely an easy subject to measure, nationally and internationally. It thus facilitates the bureaucratic craving for targetry and control. (With this part I agree. In fact, this is closedly connected with my above comment on “determining the needs”. Quantitative measurements and statistics are important to give the decisions an objective aura and disguise their unavoidably ideological nature. For this purpose, one has to make sure to raise statistics-literate generations, which is not what mathematics education means to me.)

Altogether the article has brought to my mind the verses from “Murder in the Cathedral” (T.S. Eliott):

The last temptation is the greatest treason:

To do the right deed for the wrong reason.

Simon Jenkins: Our fixation with maths doesn’t add up

in The Guardian, Thursday 10 March 2016. A random paragraph:

There is nothing, except religion, as conservative as a school curriculum. It is drenched in archaic prejudice and vested interest. When the medieval church banned geography as an offence against the Bible, what had been the queen of the sciences never recovered. Instead Latin dominated the “grammar” curriculum into the 20th century, to the expense of all science. Today maths is the new Latin.

Read the full article. Refutation anyone?

 

A. Borovik: Sublime Symmetry: Mathematics and Art

A new paper in The De Morgan Gazette:

Form the Introduction:

This paper is a text of a talk at the opening of the Exhibition Sublime Symmetry: The Mathematics behind De Morgan’s Ceramic Designs  in the delighful Towneley Hall  Burnley, on 5 March 2016. The Exhibition is the first one in Sublime Symmetry Tour  organised by The De Morgan Foundation.

I use this opportunity to bring Sublime Symmetry Tour to the attention of the British mathematics community, and list Tour venues:

06 March to 05 June 2016 at Towneley Hall, Burnley
11 June to 04 September 2016 at Cannon Hall, Barnsley
10 September to 04 December 2016 at Torre Abbey, Torbay
10 December 2016 to 04 March 2017 at the New Walk Gallery, Leicester
12 March to 03 September 2017 at the William Morris Gallery, Walthamstow

William De Morgan, Peacock Dish. The De Morgan Foundation

William De Morgan, Peacock Dish. The De Morgan Foundation.

Stoke offers to pay tuition fees in maths drive

From BBC: A few quotes:

Stoke-on-Trent is trying to radically improve maths standards in its schools, including by helping to pay off the tuition fees of maths teachers who come to work in the city.

The maths project is aimed at improving the chances for young people growing up in a city where many traditional industries have declined. […]

The £1m maths project, a form of educational urban regeneration, is aimed at attracting bright young maths graduates to a city struggling with industrial decline and academic underachievement. […]

The Stoke project is offering cash to attract new recruits – £2,000 per year for three years towards paying off tuition fees and a further relocation payment of £2,000.

Read the full story

 

A School Built Entirely Around the Love of Math

in Mind/Shift. A few quotes:

Prodigies in piano or dance can study at schools like Juilliard to develop their musical or performing arts talent. By contrast, nothing like Juilliard exists for children who show great promise at math. But an ambitious experiment will soon change that: In fall 2015, a small, independent school that’s exclusively tailored for math whizzes will open in downtown San Francisco.

The new school takes its inspiration from math circles, an Eastern European and Russian tradition that spread to the U.S. starting in the 1990s. These weekly extracurricular clubs bring youngsters together with a mathematician who guides them in exploring numerical ideas and concepts in depth. It’s often a highly interactive conversation, with the kids avidly chiming in with questions and thoughts.

Read the whole story.

The Politics of Math Education

NYT Opinion Page, 3 December 2915, by

A quote:

The new math was widely praised at first as a model bipartisan reform effort. It was developed in the 1950s as part of the “Cold War of the classrooms,” and the resulting textbooks were most widely disseminated in the 1960s, with liberals and academic elites promoting it as a central component of education for the modern world. The United States Chamber of Commerce and political conservatives also praised federal support of curriculum reforms like the new math, in part because these reforms were led by mathematicians, not so-called progressive educators.

By the 1970s, however, conservative critics claimed the reforms had replaced rigorous mathematics with useless abstractions, a curriculum of “frills,” in the words of Congressman John M. Ashbrook, Republican of Ohio. States quickly beat a retreat from new math in the mid-1970s and though the material never totally disappeared from the curriculum, by the end of the decade the label “new math” had become toxic to many publishers and districts.

Though critics of the new math often used reports of declining test scores to justify their stance, studies routinely showed mixed test score trends. What had really changed were attitudes toward elite knowledge, as well as levels of trust in federal initiatives that reached into traditionally local domains. That is, the politics had changed.

Whereas many conservatives in 1958 felt that the sensible thing to do was to put elite academic mathematicians in charge of the school curriculum, by 1978 the conservative thing to do was to restore the math curriculum to local control and emphasize tradition — to go “back to basics.” This was a claim both about who controlled intellectual training and about what forms of mental discipline should be promoted. The idea that the complex problems students would face required training in the flexible, creative mathematics of elite practitioners was replaced by claims that modern students needed grounding in memorization, militaristic discipline and rapid recall of arithmetic facts.

The fate of the new math suggests that much of today’s debate about the Common Core’s mathematics reforms may be misplaced. Both proponents and critics of the Common Core’s promise to promote “adaptive reasoning” alongside “procedural fluency” are engaged in this long tradition of disagreements about the math curriculum. These controversies are unlikely to be resolved, because there’s not one right approach to how we should train students to think.

We need to get away from the idea that math education is only a matter of selecting the right textbook and finding good teachers (though of course those remain very important). The new math’s reception was fundamentally shaped by Americans’ trust in federal initiatives and elite experts, their demands for local control and their beliefs about the skills citizens needed to face the problems of the modern world. Today these same political concerns will ultimately determine the future of the Common Core.

As long as learning math counts as learning to think, the fortunes of any math curriculum will almost certainly be closely tied to claims about what constitutes rigorous thought — and who gets to decide. [Emphasis is by AB]

Christopher J. Phillips teaches history at Carnegie Mellon University and is the author of “The New Math: A Political History.”

Teacher shortages in England, spending watchdog confirms

This is a follow-up to the story about teacher shortages. , BBC:

Teacher shortages in England are growing and the government has missed recruitment targets for four years, the official spending watchdog [the National Audit Office]  has said.

Quotes about mathematics:

Teacher training places filled against targets, by subject

Filling_olaces_in_training_10Feb16[Source: National College for Teaching and Leadership 2015/16]

[…]

Head teachers’ unions said the report echoed their own research.

“The acute difficulties recruiting in maths, English, science and languages are now extending to most other areas of the curriculum,” said Malcolm Trobe, interim general secretary of the Association of School and College Leaders.

Proportion of trainee teachers with 2:1 degree or above
Average for all trainee entrants was 75%
2-1_and_higher
[Source: National College for Teaching and Leadership]
Political infighting:

National Association of Head Teachers general secretary Russell Hobby warned of “a significant difference between official statistics and the perceptions of those in schools.

We’d welcome the opportunity to sit down formally with the DfE… but as yet, they’re not willing to acknowledge the scale of the problem.

Labour’s shadow education secretary Lucy Powell called the report “a further wake-up call for the Tory government who have been in denial and neglectful about teacher shortages“.

‘Negative picture’

A Department for Education spokeswoman said the report made clear

that despite rising pupil numbers and the challenge of a competitive jobs market, more people are entering the teaching profession than leaving it, there are more teachers overall and the number of teachers per pupil hasn’t suffered“.

Indeed the biggest threat to teacher recruitment is that the teaching unions and others, use every opportunity to talk down teaching as a profession, continually painting a negative picture of England’s schools.

 

Long hours, endless admin and angry parents – why schools just can’t get the teachers

From theguardian,  Monday 1 February 2016, by , @johnharris1969

Paragraphs referring to mathematics:

On top of all that are the effects of the pay policy which froze teachers salaries for three years from 2010, and recently capped rises for most teachers at 1% until 2020. As any maths teacher could tell you, that means pay cuts in real terms – and more disaffection, as wages in the private sector start ticking up. […]

 

He echoes concerns about subjects such as maths and the sciences feeling the pinch. “I think that’s a combination of the economy picking up, and the fact there’s just not that straightforward route into teaching,” he says. Howes runs a course for people who haven’t got degrees in physics – an A-level is the basic requirement – but want to become physics teachers. “The number of schools I’m working with who haven’t got properly trained physics teachers is massive,” he says. “You just keep coming across the fact that trainees are working with teachers who are not themselves trained in physics.” It takes me a while to process what this means, in some cases: people without physics degrees being helped to teach physics by people who don’t have physics degrees either. […]

 

Barber hands me a sheet of paper recording all the vacancies he has advertised over the last few years, and how many applications he got back. A job teaching art attracted 18 – because, he says, thanks to the changes pushed through by the government, “schools are now actively reducing numbers of art teachers”, and many are going spare. By contrast, the numbers of people applying for jobs teaching English, science and computing never got any higher than four – and appointing a new head of maths, he says, was “an absolute nightmare”.

 

Finding heads of departments, he says, is a particular problem, what with Ofsted ready to pounce, and results in key subjects so crucial for a school’s reputation: “If you’re the head of maths or the head of English, you are so accountable: if the maths department goes down, the whole school goes down.” For this job, the school got four applications, three of which were “no good”, leaving one that he says was outstanding. The applicant came from a large academy chain, which for some reason, had given her a poor reference.

 

“We couldn’t understand it – what we could see in front of us, and what the reference said were completely at odds with each other,” he says. He decided to employ her, and she accepted – but a few weeks before the end of term, he received a call saying she wouldn’t take the job after all. “The next thing I know, this chain was announcing its new head of maths in a brand-new academy,” he says. “Presumably, they offered her a better deal.” He suddenly looks pained. “I feel like the corner shop up against Tesco. These academy chains have huge resources, and lots of lots of schools. I won’t appoint anyone I don’t think is capable of doing the job. That would still be my official line. But the truth is, you do find yourself thinking: if I don’t appoint this person and I advertise again, that’s going to cost me another £3,500 when money is really tight.”

 

 

OECD: Students, Computers and Learning

This OECD Report is in news (see, for example, Too much technology ‘could lower school results’ at the BBC). What follows are some quotes from the Report related to mathematics.

The results also show no appreciable improvements in student achievement in reading, mathematics or science in the countries that had invested heavily in ICT for education. And perhaps the most disappointing finding of the report is that technology is of little help in bridging the skills divide between advantaged and disadvantaged students. Put simply, ensuring that every child attains a baseline level of proficiency in reading and mathematics seems to do more to create equal opportunities in a digital world than can be achieved by expanding or subsidising access to high-tech devices and services. (p. 3)

What the data tell us
• Resources invested in ICT for education are not linked to improved student achievement in reading, mathematics or science. […]

• Overall, the relationship between computer use at school and performance is graphically illustrated by a hill shape, which suggests that limited use of computers at school may be better than no use at all, but levels of computer use above the current OECD average are associated with significantly poorer results. (p. 146)

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