Mathematics in the news this week

The week of 30 May 2016

2sciencemuseum0106a

Mathematics Education for the next Decade, September 10-15, 2017

The 13th International Conference of the Mathematics Education for the Future Project in Catania, Sicily September 2015, was attended by 130 people from 22 countries. The next conference will be held NEXT YEAR at Balatonfüred, Balaton lake, Hungary from September 10-15, 2017. The conference title, Mathematics Education for the next Decade, continues our search for innovation in mathematics, science, computing and statistics education. Our thirteen previous conferences since 1999 were renowned for their friendly and productive atmosphere, and attracted many /movers and shakers/ from around the world.

We now call for papers and workshop summaries for presentation at the conference and publication in the printed conference proceedings. For further details and updates please email alan >>at<< cdnalma.poznan.pl

The international conference on E-Assessment in Mathematical Sciences

The international conference on E-Assessment in Mathematical Sciences is a two-day academic conference organised by Newcastle University.

The conference aims to bring together researchers and practitioners with an interest in e-assessment for mathematics and the sciences. It will consist of a mix of presentations of new techniques, and pedagogic research, as well as workshops where you can get hands-on with leading e-assessment software.

The conference website is http://eams.ncl.ac.uk/.

The deadline for talk proposals is next Tuesday, the 31st of May (though that might be extended if we don’t get too many proposals in the next week), and the deadline for delegate registration is the 30th of June.

Thanks,
Christian Lawson-Perfect

Mathematics in the news this week

France DGSE: Spy service sets school code-breaking challenge

France’s external intelligence service, the DGSE, has sponsored a school competition to find the nation’s most talented young code-breakers.

It is the first time the DGSE has got involved in such a project in schools.

The first round drew in 18,000 pupils, and just 38 competed in the final on Wednesday, won by a Parisian team.

 

STEM Competitions Motivate Students :

“The main message is mathematics is not about numbers and figures,” [Mark] Saul said. “It’s about figuring things out. Whenever you’re figuring something out, you’re doing something mathematical.”

Rebecca Hanson Launches A Breakthrough in Maths Teaching for Primary Students :

Rebecca Hanson has opened her agency Authentic Maths to help Primary School Teachers in the UK offering solutions to the difficulties being experienced with the implementation of the Government’s changes to the primary mathematics curriculum.

UK follows Russia’s example to set up specialist sixth form maths colleges:

A key figure in the establishment of specialist maths institutions in the UK was Baroness (Alison) Wolf, a professor at King’s College London. She knew about Russian maths skills because of her work in universities, where maths departments often attract a fair few Russian academics.

Initially, the idea in the UK was for universities to set up a nationwide network of specialist maths schools. However, only King’s College London and Exeter have taken the plunge.

Tony Brown: Can England Staff its Schools?

Key issues in the supply of Qualified Teachers in the light of the Education White Paper 2016 – a Scrutiny Seminar 4-6pm Monday June 6th 2016.

The Education White Paper 2016 makes bold claims for the supply of teachers in English schools and the future training of qualified teaching staff. The key thrust of the paper is to shift the balance of teaching into schools, asserting that existing moves to schools’ level, notably School Direct, have proved successful. Involvement of universities (HEIs) is to be limited to a few ‘top’ universities, while standards would be set by headteachers in a few elite training schools.

But are the proposals in Chapter 2 acceptable? Given the widely reported claims of teacher shortages, have the current systems proved successful? And will the proposals improve or damage the supply of Qualified Teachers? How do they relate to the ongoing policy of academisation, with the intention of allowing all schools to employ unqualified teaching staff?

It is a fundamental contradiction that schools following the plans outlined must apply a lengthy, variable accreditation process for qualification – without Qualified Teacher Status being granted – but academies can employ unqualified staff in the classroom.

The Scrutiny Seminar will examine three key issues in the light of the overall thrust of the paper and the ongoing debate on teacher shortages in English Schools. These are

  • the implications for teacher training/education in English schools through accreditation at school level
  • the role of school based training notably School Direct
  • the effect on individual subject provision, with mathematics as a case study, with the definition of a mathematics teacher and the current drive through bursaries and adverts to attract staff suggesting specific and general issues with supply.

The speakers will be

  • Alison Ryan of the Association of Teachers and Lecturers on the implications for schools
  • Professor Tony Brown of Manchester Metropolitan University on the latest research on School Direct provision
  • Dr Sue Pope of the Association of Teachers of Mathematics on the case study of supply of Mathematics teachers

The meeting will be chaired jointly by Lord Watson of Invergowrie and Trevor Fisher of SOSS

To book a place at the seminar send your details to richardksidley >>at<< gmail.com. It will take place in the House of Lords. Attendance applications must be received by 5pm on 3rd June.

Sponsored by the Symposium on Sustainable Schools (SOSS)

Why undegraduate students should not use online matrix calculators

Since 1 April 2011 I from time to time was trying to convince Wolfram Alpha to fix a bug in the way they computed eigenvectors, see my post of 28 April 2012. It survived until May 2016:

Screen shot of Wolfram Alpha, 01 May 2016

As you can see, Wolfram Alpha was thinking that the zero vector is eigenvector. On 5 May 2016 this bug was finally fixed:

Screen shot of Wolfram Alpha, 07 May 2016

But there is still one glitch which can send an undergraduate student on a wrong path. The use of round brackets as delimeters for both matrices and vectors suggests that the vector \((1,0)\) is treated as a \( 1 \times 2\) matrix, that is a row vector. This determines which way it can be multiplied by a \(2 \times 2 \) matrix: on the right, that way:
\[
(1,0) \left(\begin{array}{cc} 1 & 2 \\ 0 & 1\end{array}\right)
\]
and not that way
\[
\left(\begin{array}{cc} 1 & 2 \\ 0 & 1\end{array}\right)(1,0),
\]
the latter is simply not defined. Therefore the correct answer is not
\[
\mathbf{v}_1 = (1,0)
\]
but
\[ \mathbf{u} = (0,1) \quad\mbox{ or }\quad \mathbf{w} = (1,0)^T = \left(\begin{array}{c} 1 \\ 0\end{array}\right),
\]
depending on convention used for vectors: row vectors or column vectors. Indeed if
\[
A = \left(\begin{array}{cc} 1 & 2 \\ 0 & 1\end{array}\right),
\]
then
\[ \mathbf{v}_1A = (1,0)\left(\begin{array}{cc} 1 & 2 \\ 0 & 1\end{array}\right) = (1,2) \ne 1\cdot \mathbf{v}_1,
\]
while
\[
A\mathbf{w} = \left(\begin{array}{cc} 1 & 2 \\ 0 & 1\end{array}\right) \left(\begin{array}{c} 1 \\ 0\end{array}\right) = \left(\begin{array}{c} 1 \\ 0\end{array}\right) = 1\cdot \mathbf{w}
\]
and
\[
\mathbf{u} A = (0,1) \left(\begin{array}{cc} 1 & 2 \\ 0 & 1\end{array}\right) = (0,1) = 1\cdot \textbf{u}.
\]
The bug is likely to sit somewhere in the module which converts matrices and vectors from their internal representation within the computational engine into the format for graphics output. It should be very easy to fix. It is not an issue of computer programming, it is just lack of attention to basic principle of exposition of mathematics and didactics of mathematics education.

Alexandre Borovik: Decoupling of Assessment

BBC reported today that

Thousands of parents in England plan to keep their children off school for a day next week in protest at tough new national tests, campaigners say.

Parents from the Let Our Kids Be Kids campaign said children as young as six were labelling themselves failures.

In a letter to Education Secretary Nicky Morgan, they said primary pupils were being asked to learn concepts that may be beyond their capability.

The government said the tests should not cause pupils stress.

These new tests, known as Sats, have been drawn up to assess children’s grasp of the recently introduced primary school national curriculum, which is widely considered to be harder than the previous one.

The letter from the campaign, which says it represents parents of six- and seven-year-olds across the country, says children are crying about going to school.

There is a simple solution – decoupling of assessment of schools from assessment of individual children.

As far I remember my school years back in Soviet Russia of 1960s, schools there were assessed by regular (but not frequent) “ministerial tests”. A school received, without warning, a test paper in a sealed envelope which could be open only immediately before the test; pupils’ test scripts were collected, put into an enclosed envelope, sealed and sent back. Tests were marked in the local education authority (and on some occasions even a step up in the administrative hierarchy — in the regional education authority); marked test scripts, however, were not returned to schools, and schools received only summary feedback — but no information about performance of individual students.

This policy of anonymised summary tests created a psychological environment of trust between pupils and the teacher — children knew that it was not them who were assessed, but their teacher and their school, and they tried hard to help their teacher. Good teachers could build on this trust a supportive working environment in a classroom.  Schools and teachers who performed well in such anonymised testing could be trusted to assess pupils in a formative, non-intrusive, non-intimidating way — and without individual high stakes testing.

Of course, all that are my memories from another historic epoch and from the country that no longer exists. I could be mistaken in details, but I am quite confident about the essence. In this country and in recent years, I happened to take part in a few meetings in the Department for Education, where I raised this issue. Education experts present at these meetings liked the idea but it was not followed by any discussion since it was outside of meetings’ agenda — we had to focus on the  content of the new curriculum, not assessment. I would love to see a proper public discussion of feasibility of decoupling.

I teach mathematics at a university. I think I am not alone (I heard similar concerns from my colleagues from Universities from all over the country) in feeling that many our students come to university with a deformed attitude to assessment — for example, with subconscious desire to forget everything as soon as they have sat an exam. It could happen that some of them, in their school years, suffered from overexamination but were not receiving  sufficient formative feedback. At university, such students do not know how to use teachers’ feedback. They do not know how to ask questions. Could it happen that the roots of the problem could be traced back to junior school?

Disclaimer. The views expressed do not necessarily represent the position of my employer or any other person, organisation, or institution.

Alexandre Borovik

Three PhD studentships at Loughborough

The Mathematics Education Centre at Loughborough University has three fully-funded PhD studentships available to start in October 2016. Each project is full time for three years.

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