Film and discussion: “Colours of Math”

18 November 2014, , at Pushkin House.  From an advertisement:

The independent documentary “Colours of Math” (2012) by Ekaterina Eremenko – a German-based, American-trained, Russian-born documentary producer and mathematician – has been an unlikely runaway success.  It has been translated into 12 languages, and screened around the world.

With six mathematicians from different countries and six senses that lead them in their journey of discovery, the movie gives an insight into the mystery of abstract mathematical ideas and creative thinking.

The screening (60 min) is followed by a round table discussion. What is happening in contemporary mathematics? Are there particular national schools of thought and traditions of education? Prominent mathematicians will share their views on these questions.

Speakers:

Professor Sergey Foss, Heriot Watt University

Professor Leonid Parnovski, University College London

Professor Eugene Shargorodsky, Kings College London

Dr June Barrow-Green, Open University

The Imitation Game Cryptography Competition

From Charles Walkden, University of Manchester:

Dear all,

The Imitation Game Cryptography Competition:  www.maths.manchester.ac.uk/cryptography_competition_the_imitation_game

`The Imitation Game‘ is a biopic of Alan Turing starring Benedict Cumberbatch in the lead role (also starring Keira Knightley, Charles Dance,…) and will be released in cinemas on Nov 14th.

The film’s distributors asked us to get involved in the publicity and promotion for the film by running a one-off on-line `Imitation Game Cryptography Competition‘, www.maths.manchester.ac.uk/cryptography_competition_the_imitation_game.

It’s free to enter and is open to everybody.  There are some great prizes for you to win: film posters signed by the cast, DVD bundles, soundtracks, etc,  The competition runs until 14th Nov.
Please can you spread the word to anyone and everyone (and feel free to take part yourself!).
PS:  The School’s annual `Alan Turing Cryptography Competition’ will run again from Jan 2015, with registration opening on 1st Dec.  Unlike the Imitation Game competition, this is only open to school children in Year 11 or below – but again please spread the word!
Andrew, Charles, Kees, Sebastian, Helen

Ofsted: Low-level classroom disruption hits learning

From BBC http://www.bbc.co.uk/news/education-29342539 :

Low-level, persistent disruptive behaviour in England’s schools is affecting pupils’ learning and damaging their life chances, inspectors warn.

The report says too many school leaders, especially in secondary schools, underestimate the prevalence and negative impact of low-level disruptive behaviour and some fail to identify or tackle it at an early stage.

 

Source: Poll conducted by YouGov for Ofsted, http://www.ofsted.gov.uk/news/failure-of-leadership-tackling-poor-behaviour-costing-pupils-hour-of-learning-day

This is one of many low-level school issues that affect undergraduate mathematics teaching.  In a mathematics lecture, weaker students are more prone to “loosing the thread” than in most other courses. Also, students for whom English is not the first language,  in particular,  most from overseas are more sensitive to the signal-to-noise ratio than natives,  and, at a certain level of background noise,  their understanding of the lecture becomes seriously degraded. In my opinion,  this is one of many neglected issues of undergraduate mathematics education. I in my lectures always insist on complete silence in the audience (and usually start my first lecture with  a brief explanation of the concept of signal-to-noise ratio).

Mother’s thyroid level ‘may predict child’s poor maths’

From BBC:

Children born to mothers who have low levels of thyroid hormones during pregnancy tend to do worse in maths in early primary school, a study says.

Dutch researchers tracked 1,196 healthy children from birth to age five, having recorded their mothers’ thyroxine levels at 12 weeks of pregnancy.

They then looked at the children’s test scores for language and arithmetic.

Those born to mothers with low levels of thyroxine were twice as likely to have below average arithmetic scores.

However, the scientists – led by Dr Martijn Finken at the VU University Medical Centre in Amsterdam – said the five-year-olds’ language results were no different.

The maths results were the same even after taking into consideration the child’s family background.

Read the whole article.

Brain works in sleep

Many mathematicians believe that that their brains continue to do mathematics during sleep. A paper

Kouider et al., Inducing Task-Relevant Responses to Speech in the Sleeping Brain, Current Biology (2014), http://dx.doi.org/10.1016/j.cub.2014.08.016

Proves that brain continues in sleep some mental activities of the day.

From the summary of the paper:

using semantic categorization and lexical decision tasks, we studied task-relevant responses triggered by spoken stimuli in the sleeping brain. Awake participants classified words as either animals or objects (experiment 1) or as either words or pseudowords (experiment 2) by pressing a button with their right or left hand, while transitioning toward sleep. The lateralized readiness potential (LRP), an electrophysiological index of response preparation, revealed that task-specific preparatory responses are preserved during sleep. These findings demonstrate that despite the absence of awareness and behavioral responsiveness, sleepers can still extract task relevant information from external stimuli and covertly prepare for appropriate motor responses.

The paper generated a huge response in mass media: BBC, New Scientist, NBC News. It is mentioned in this blog because the study of brain activity  is relevant to mathematics education. A naive question: do our students get enough sleep?

Why Do Americans Stink at Math?

An article by in the NYT; it is about America, but is very timely in the context of the National Curriculum reform in England. A quote:

It wasn’t the first time that Americans had dreamed up a better way to teach math and then failed to implement it. The same pattern played out in the 1960s, when schools gripped by a post-Sputnik inferiority complex unveiled an ambitious “new math,” only to find, a few years later, that nothing actually changed. In fact, efforts to introduce a better way of teaching math stretch back to the 1800s. The story is the same every time: a big, excited push, followed by mass confusion and then a return to conventional practices.

The trouble always starts when teachers are told to put innovative ideas into practice without much guidance on how to do it. In the hands of unprepared teachers, the reforms turn to nonsense, perplexing students more than helping them. [Emphasis is mine — AB.]

Read the whole article.

 

 

Can you pass the maths test for 11-year-olds?

A sample KS2 test based on the official publication from Standards and Testing Agency,
2016 key stage 2 mathematics test: sample questions, mark scheme and commentary,
was published in The Telegraph. One question attracts attention. In The Telegraph version, it is

A question as published in The Telegraph.

The answer given is £12,396.

And this is the original question from 2016 key stage 2 mathematics test: sample questions, mark scheme and commentary

The official version of the same question

In my opinion, both versions contain serious didactic errors. Would the readers agree with me?

And here are official marking guidelines:

Official marking guidelines

And the official commentary:

In year 6 pupils are expected to interpret and solve problems using pie charts. In this question pupils can use a number of strategies including using angle facts or using fractions to complete the proportional reasoning required.
Pupils are expected to use known facts and procedures to solve this more complex problem. There are a small number of numeric steps but there is a demand associated with interpretation of data (or using spatial knowledge). The response strategy requires pupils to organise their method.

Mathematics teaching in China: reflections from an Ofsted HMI

By Sean Harford HMI, National Director, Initial Teacher Education, Ofsted

Reposted from TES Connect.

In late February I was a member of a delegation representing HM Government that visited the three Chinese provinces of Shanghai, Beijing and Hubei with a specific focus on mathematics education.

I have waited until now to reflect on my visit to China because I wanted to go back into some English schools to test out the thinking I developed while there. The differences in maths outcomes for our young people between the two countries are stark and worrying for us, unless we act now to catch up – and I do not mean just in terms of PISA test scores. I am coming at this not only from an inspector’s point of view, but also from my background of being a physics teacher and so frequent user of maths, reliant on pupils being able to handle and manipulate numbers confidently. In this respect, Chinese children are streets ahead of ours, so the benefits of their high standards in mathematics go way beyond just this core subject.

 

As everyone knows, Her Majesty’s Inspectors are not concerned about the ‘how’ but ‘how effective’ with teaching. This approach requires a clear focus on the outcomes for the pupils and their response to the teaching, including crucially the evidence of learning and progress over time in their work books and folders. These were impressive in the classes we observed in China, and told a story of a consistency of approach and expectations that has led to the pupils being confident mathematicians, willing to have a go and able to tackle problems in different contexts.

For example, given this problem…:

X = 2√ (7/14 x 28/7 x 3/9 x 24/8 x 18/9)

… none of the 12-year-old pupils reached for the calculator; they couldn’t because they have been banned from their classrooms. They calmly looked for the potential to cancel and reduce the fractions, and spotted that this expression is really just the square root of 4. Not a job for the calculator; not for them at least. This was clearly not about them learning ‘tricks’ either. This problem was one of just 4 or 5 set by the teacher in a 5 minute burst of practice, to help the pupils master the concepts covered by her in the latest part of the lesson before they moved on confidently together to the next stage of increasingly challenging maths. The key was not the teacher’s ‘performance’ in this lesson, but the demonstration of the depth of the pupils’ mathematical learning over time and the impressive armoury of knowledge and skills they had built up to deploy as and when needed. Evidence of solidly knowing their times tables was absolutely apparent across the pupils, as was the ability to use efficient methods of calculation without having to really think. Their mathematical toolkit was there to be used as surely as a mechanic’s spanners, or a surgeon’s scalpel

Read the rest at TES Connect.

A pardon for Alan Turing

Alan Turing has been granted a posthumous pardon, overturning his 1952 conviction for homosexual activity. Making the announcement, the British Justice Minister Chris Grayling commented “Turing deserves to be remembered and recognised for his fantastic contribution to the war effort and his legacy to science. A pardon from the Queen is a fitting tribute to an exceptional man.”

This has given rise to the most extensive national and international media
coverage of Alan Turing and his legacy ever.

Internationally the response has been predominantly positive – Peter van
Emde Boas caught the mood with his “Congratulations with this success; it
doesn’t make the UK any less strange however… “. The fact the pardon
was 61 years coming was universally commented on.

In the UK, many were unhappy with the word ‘pardon’ wanting something recognised that the fault was that of the state. Everyone was concerned about others who had had lives ruined by the same law – and, like Turing, had died before they or their families could benefit from the recent legislation, which enables those living to apply to have their convictions ‘disregarded’ and wiped from the records. Here is the Stonewall guide to the Protection of Freedoms Act 2012 (relevant to many of the “75,000 others” – in some places “50,000 others” – widely commented on):
http://www.stonewall.org.uk/at_home/hate_crime_domestic_violence_and_criminal_law/8064.asp

The Cambridge Student webpage nicely captured the mood “Alan Turing’s pardon is simply not enough”, and got the facts right:
http://www.tcs.cam.ac.uk/comment/0031341-alan-turing-s-pardon-is-simply-not-enough.html

Many first heard the Royal Pardon news via radio or TV on Christmas Eve – for instance on the BBC Today programme that morning, with JohnHumphrys interviewing Baroness Trumpington and Barry Cooper:

http://www.bbc.co.uk/news/technology-25503464

http://www.bbc.co.uk/programmes/p01nxh88

Baroness Trumpington was specially generous in her praise for Lord Sharkey, whose private members bill introduced in the House of Lords played such a large part in the eventual outcome. See also the BBC page “Royal pardon for codebreaker Alan Turing” with further videos: http://www.bbc.co.uk/news/technology-25495315

Other Christmas Eve interviews included Sue Black in one for The Telegraph “Alan Turing’s Royal pardon is long overdue”: http://www.telegraph.co.uk/history/world-war-two/10536644/Alan-Turings-Royal-pardon-is-long-overdue.html

And Barry Cooper’s interview for Sky TV News in the afternoon:

http://www1.maths.leeds.ac.uk/pure/logic/computability/BarryTalks/sky24_12_13.mov

You can also hear Barry interviewed on BBC Radio 3 Counties by Roberto Perrone (thanks to the BBC and Mark Cotton) at the Alan Turing Year AudioBoo webpage: https://audioboo.fm/AlanTuringYear