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

Dominic Cummings: Some thoughts on education and political priorities

Dominic Cummings, the former special adviser to the Secretary of State for Education Michael Gove, published a 237 page document, Some thoughts on education and political priorities. It is a very interesting paper, and it is much concerned with mathematics education and deserves attention from the mathematical community — even if some readers might find some points raised controversial.

The paper is written by a thoughtful and well-informed person who is passionate about mathematics and mathematics education. However, the paper’s most striking feature is that it bears the hallmarks of “the voice of one crying in the wilderness” (John 1:23). The pages overflow with untested (although frequently brilliant) ideas, that have apparently blossomed outside any structurally sound referential framework. These 237 pages effectively document the absence of a proper public discourse on mathematics education policy.

And it is something we should not blame Dominic Cummings for; it is we in mathematics education community who are largely responsible for the silence that replaces policy discussions relating to mathematics education in this country.

The De Morgan Forum and The De Morgan Gazette have been set up with the aim to provide a space for voicing opinions — and maybe raising controversies — about issues in education policy which affect mathematics. Despite 500,000 hits over the last two years and some excellent papers and curriculum documents published in The De Morgan Gazette, we are still far from reaching this objective. We wish to invite the readers to face the challenge and use Dominic Cummings’ paper as an opportunity for a well-informed discussion of mathematics education.

QS World University Rankings by Subject 2013 – Mathematics

Mathematics in British Universities with their world rank according to QS World University Rankings by Subject 2013

1 University of Cambridge
5 University of Oxford
12= Imperial College London (shared with Caltech and U. Toronto)
23 The University of Warwick
38 University of Bristol
46= The University of Manchester (shared with Nanyang and Auckland)
51-100 King’s College London
51-100 The University of Nottingham
51-100 University College London
51-100 University of Edinburgh
51-100 University of Leeds
101-150 University of Glasgow
101-150 University of Southampton
151-200 London School of Economics
151-200 Queen Mary University of London
151-200 University of Bath
151-200 University of Birmingham

Is ATM against “formal written methods”?

From a letter published by the Association of Teachers of Mathematics (ATM) in The Guardian, 29 July 2013:

The Association of Teachers of Mathematics is dismayed at the programmes of study for mathematics just published [...] The curriculum as presented will result in more attention spent on developing technical competence in outdated written methods for arithmetic at the expense of developing secure foundations for progression through mathematical concepts and skills. [...] Appendix 1, entitled formal written methods for multiplication and division, but including addition and subtraction as well as multiplication and division, is a complete travesty and needs to be removed.

See the original letter at The Guardian

Schools ask pupils to sit GCSE maths exams twice

From The Independent:

Thousands of teenagers are being put in for multiple GCSE maths exams in the hope they will get crucial C grade passes in at least one of them.

The practice is exposed by the exams regulator Ofqual today as it reveals that 15 per cent of candidates sitting GCSEs  – around 90,000 candidates – were last year submitted for maths exams with more than one board. Ofqual officials believe there will be a repeat this year because the pressures that drove schools to do it  – including boosting performances in league tables – are still there.

Read the full article.