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.

• Investigating the effects of pain on numerical reasoning and decision-making, with Dr Nina Attridge.
• Use your numbers, with Dr Iro Xenidou-Dervou.
• Evaluating the validity of comparative judgement for assessing conceptual understanding in mathematics, with Dr Ian Jones.

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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

     http://www.ams.org/journals/notices/201602/rnoti-p178.pdf

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

Tony Gardiner Receives the 2016 Award for Excellence in Mathematics Education

Citation for the 2016 Award for Excellence in Mathematics Education to

Dr. Anthony David Gardiner

It is with great pleasure that the Award Committee hereby announces that the 2016 Award is given to Dr. Anthony D. Gardiner, currently retired from University of Birmingham, United Kingdom, in recognition of his more than forty years of sustained and multiple major contributions to enhancing the problem-solving skills of generations of mathematics students in the United Kingdom (UK) and beyond.

Gardiner’s major achievements include:

• orchestrating teams of volunteers from many constituencies, including teachers, mathematics educators and university mathematicians, to create a portfolio of mathematics contests, leading eventually to the creation of the UK Mathematics Trust, which creates problem-solving challenges taken by well over half a million students per year;
• creating structures that dramatically increased and broadened participation in mathematics competitions and other activities supporting UK participation in the International Mathematics Olympiad;
• leading the UK IMO team (1990 – 95);
• creating problem solving journals for school students (including grading thousands of solutions personally), leading eventually to the Problem Solving Journal for Secondary Students (edited by Dr. Gardiner since 2003, with a circulation over 5,000);
• authoring 15 books on mathematical thinking and mathematical problem solving, including Understanding Infinity, Discovering Mathematics: the art of investigation, Mathematical Puzzling (all reprinted by Dover Publications), the four volume series Extension Mathematics (Oxford), and the recent Teaching mathematics at secondary level (Open Book Publishers).

In addition, Gardiner’s expertise on the problem-solving abilities of English schoolchildren, and his insights into omissions in UK mathematics education has led to his being consulted by multiple UK Ministers of State for Education, and have influenced significant changes in the UK mathematics curriculum. Gardiner has also served in multiple high level leadership positions in mathematics education both in the UK and internationally, including Council of the London Mathematical Society, and member of the Education Committee (1990s), Presidency of the (UK) Mathematical Association in 1997-98, chair of the Education Committee of the European Mathematical Society (2000-04), and Senior Vice President of the World Federation of National Mathematics Competitions (2004-08). He has addressed major teacher conferences in more than 10 countries, and he was an Invited Lecturer at the 10th International Congress of Mathematics Education in 2004. He has organized many meetings and programs to support mathematics education, teacher professional development, and to promote problem solving. He has contributed numerous articles to newspapers and magazines to communicate the goals of successful mathematics education to a broader public. Both the extent and impact of Gardiner’s efforts are remarkable. He provides an inspiring example of how a mathematician can have a positive impact on mathematics education; he is a most worthy recipient of the Texas A&M Award for Excellence in Mathematics Education.

Gardiner received his doctorate in 1973 from the University of Warwick, UK. He taught at the University of East Africa from 1968-69, University of Birmingham from 1974 to 2012. During that time he worked at the Free University of Berlin on a fellowship, and held numerous visiting positions including at the University of Bielefeld in Germany, University of Waterloo, the University of Melbourne and the University of Western Australia.

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This  award  is  established  at the Texas  A&M  University to  recognize  works  of  lasting significance  and  impact  in advancing  mathematics  education  as  an  interdisciplinary field  that  links mathematics,  educational  studies  and  practices.  In  particular,  the award  recognizes major  contributions  to  new  knowledge  and  scholarship  as  well  as exemplary contributions  in  promoting  interdisciplinary  collaboration  in  mathematics
education.
This  is  an  annual  award  that  consists  of  a  commemorative  plaque  and  a  cash  prize ($3000).  A  recipient  will  be  selected  yearly  and  will  be  invited  to  give  a  keynote  talk, with  all  travel  expenses  covered,  at  a  workshop  dedicated  to  advancing  mathematics education.  Moreover,  subject  to  the  availability  of  the  recipient,  a  housing  allowance and  a  $5000  stipend  will  also  be  provided  to  the  recipient  to  spend  two  weeks  in residence  at  Texas  A&M  University  interacting  with  students  and  faculty  in  seminars and  informal  mentoring  sessions.