International Mathematical Olympiad 2013

Results: a wonderful performance of the UK Team. From the UKMT’s Press Release:

The UK finished ninth in this year’s International Mathematical Olympiad (IMO), the highest finish since 1996, and top EU nation. Andrew Carlotti won gold to add to his IMO medal collection of two gold and one bronze, making him the highest achieving UK competitor of all time. All other members of the UK team won medals at the world’s most prestigious mathematics competition.

The six students representing the UK were:

Andrew Carlotti (Sir Roger Manwood’s School, Kent), gold medal.
Gabriel Gendler (Queen Elizabeth’s School, Barnet), silver medal
Daniel Hu (City of London School), silver medal.
Sahl Khan (St Paul’s School, London), bronze medal
Warren Li (Fulford School, York), silver medal
Matei Mandache (Loughborough Grammar School), gold medal.

The team was accompanied by the Team Leader, Dr Geoff Smith (University of Bath) and the Deputy Team Leader, Dominic Yeo (Worcester College, Oxford).

The 54th IMO took place from 18 – 28 July in Santa Marta, Colombia. The UK came ninth out of 97 participating countries, beating all EU nations and second in Europe behind Russia.

The UK team entry is organised by the UK Mathematics Trust. Rachel Greenhalgh, Director of the Trust, said “This is a fabulous achievement for the UK team. They have competed against the best mathematicians from across the world, by tackling six problems in two extremely demanding four-and-a-half-hour examinations. The team have all been awarded medals and a fabulous performance by Andrew Carlotti means he now has the best medal record at the IMO of any UK student!”

A PDF file (400kB) containing lots of BMO problems from the past (1993–2013).

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Sign the petition: “Mathematics Education category to arXiv”

Pleas consider signing the petition  “arXiv.org: Add math.ED – Mathematics Education category to arXiv” on Change.org.

The virtues of the arXiv are well known. Yet, there is currently no dedicated category on the arXiv for mathematics education research. The math.HO – History and Overview category lists mathematics education as one of the possible topics, but it doesn’t appear to be commonly used for this purpose. In contrast, there is an active physics education category (physics.ed-ph). Unfortunately, at this time, there is not a culture among math ed folks to utilize pre-print servers like the arXiv. However, if there is going to be a cultural shift, there needs to be a dedicated repository for math ed papers. Authors need to know where to submit papers and readers need to know where to look. A category called History and Overview doesn’t cut it. A precedent has been set by the physics education crew and we should follow in their footsteps. It is also worth mentioning that Mathematics Education is listed as one of the American Mathematical Society’s subject classification codes (number 97). If you are in favor of the arXiv including math.ED – Mathematics Education as a category, please sign the petition.  If you would also utilize this category by uploading articles related to mathematic education, please leave a comment indicating that this is the case.

Here’s the link:

http://www.change.org/en-GB/petitions/arxiv-org-add-math-ed-mathematics-education-category-to-arxiv?share_id=RNyDHszadl&utm_campaign=signature_receipt&utm_medium=email&utm_source=share_petition

The Pythagoras Theorem: a demonstration (but not a proof)

From Prokhozhyj:

This animated gif has gone viral. I would like to be able to attribute it to the photogropher and the designer.

Raspberry Pi

I am pleased to report that I am writing this post via Raspberry Pi. It was dead simple to buy, set up, and start using.

At the school education level, Raspbian OS distribution comes with Scratch. Two more languages, Haskell and BCPL, highly promising for use in mathematics education at advanced level, appear to be easily available.   From Martin Richards:

BCPL, an interpretive implementation of the BCPL language and system, including many demonstration programs. Click on BCPL.html to obtain a copy of the current version. This version can be installed easily on most machines running Linux, Windows and MAC OSX. In particular, it is easy to install this version on the Raspberry Pi machine. See the Young Person’s Guide to BCPL Programming on the Raspberry Pi (bcpl4raspi.pdf) for details.

 

Early Spatial Reasoning Predicts Later Creativity and Innovation, Especially in STEM Fields

From  a press release of the Association for Psychological Science:

Exceptional spatial ability at age 13 predicts creative and scholarly achievements over 30 years later, according to results from a new longitudinal study published in Psychological Science, a journal of the Association for Psychological Science.

The study, conducted by psychology researcher David Lubinski and colleagues at Vanderbilt University, provides evidence that early spatial ability — the skill required to mentally manipulate 2D and 3D objects — predicts the development of new knowledge, and especially innovation in science, technology, engineering, and mathematics (STEM) domains, above and beyond more traditional measures of mathematical and verbal ability.
“We live in the age of human capital,” says Lubinski. “Creativity is the currency of the modern era, especially in STEM disciplines. Having a better understanding of the human attributes that facilitate innovation has clear practical implications for education, training, business, and talent development.”
And yet, despite longstanding speculation that spatial ability may play an important role in supporting creative thinking and innovation, there are very few systems in place to track skill in spatial reasoning:
“Current procedures for identifying intellectually precocious youth currently miss about half of the top 1% in spatial ability,” Lubinski explains.
Using data from a study that began in the late 1970s, Lubinski and colleagues followed up with 563 students who had scored exceptionally well — in the top 0.5% — on the SATs at age 13. The researchers also examined data on the participants’ spatial ability at age 13, as measured by the Differential Aptitude Test.
Confirming previous research, the data revealed that participants’ mathematical and verbal reasoning scores on the SAT at age 13 predicted their scholarly publications and patents 30 years later.
But spatial ability at 13 yielded additional predictive power, suggesting that early spatial ability contributes in a unique way to later creative and scholarly outcomes, especially in STEM domains.
Importantly, these results confirm longstanding speculation in the psychological sciences that spatial ability offers something important to the understanding of creativity that traditional measures of cognitive abilities used in educational and occupational selection don’t capture.
Lubinski believes cultivating these skills is imperative for ensuring scientific innovation.
“These students have exceptional and under-challenged potential, especially for engineering and technology,” Lubinski explains. “We could do a much better job of identifying these students and affording them better opportunities for developing their talents.”
Co-authors on this research include Harrison Kell, Camilla Benbow, and James Steiger of Vanderbilt University.

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Press release available at: http://www.psychologicalscience.org/index.php/news/releases/early-spatial-reasoning-predicts-later-creativity-and-innovation-especially-in-stem-fields.html

For more information about this study, please contact: David Lubinski at david.lubinski@vanderbilt.edu.
The APS journal Psychological Science is the highest ranked empirical journal in psychology. For a copy of the article “Creativity and Technical Innovation: Spatial Ability’s Unique Role” and access to other Psychological Science research findings, please contact Anna Mikulak at 202-293-9300 or amikulak@psychologicalscience.org.

“Measurement”, by Paul Lockhart

From Harvard University Press:

For seven years, Paul Lockhart’s A Mathematician’s Lament enjoyed a samizdat-style popularity in the mathematics underground, before demand prompted its 2009 publication to even wider applause and debate. An impassioned critique of K–12 mathematics education, it outlined how we shortchange students by introducing them to math the wrong way. Here Lockhart offers the positive side of the math education story by showing us how math should be done.Measurement offers a permanent solution to math phobia by introducing us to mathematics as an artful way of thinking and living.

In conversational prose that conveys his passion for the subject, Lockhart makes mathematics accessible without oversimplifying. He makes no more attempt to hide the challenge of mathematics than he does to shield us from its beautiful intensity. Favoring plain English and pictures over jargon and formulas, he succeeds in making complex ideas about the mathematics of shape and motion intuitive and graspable. His elegant discussion of mathematical reasoning and themes in classical geometry offers proof of his conviction that mathematics illuminates art as much as science.

Lockhart leads us into a universe where beautiful designs and patterns float through our minds and do surprising, miraculous things. As we turn our thoughts to symmetry, circles, cylinders, and cones, we begin to see that almost anyone can “do the math” in a way that brings emotional and aesthetic rewards. Measurement is an invitation to summon curiosity, courage, and creativity in order to experience firsthand the playful excitement of mathematical work.

• Read excerpts from Measurement at the blog Brain Pickings

 

 

National Curriculum

From Department for Education:

The Secretary of State for Education, the Rt Hon Michael Gove MP, has today launched a statutory consultation on the draft legislative Order for the new national curriculum.

As you will know, the government has been reviewing the national curriculum in England since January 2011. In February of this year we published proposals […] Our formal public consultation, which closed in April, received over 17,000 submissions from a wide range of respondents. The summary report of those responses, along with the government response (which includes an update on the implementation of the new national curriculum), can be seen at https://www.education.gov.uk/consultations/index.cfm?action=conResults&consultationId=1881&external=no&menu=3.

[…] we have made a number of revisions to the national curriculum framework document and the draft programmes of study. You can view the new framework document and programmes of study, along with the consultation document on the Order for the new national curriculum and details of how to respond, at www.education.gov.uk/nationalcurriculum. The consultation will close on 8 August.

A local copy of the document file: The national curriculum in England: Framework document.

National Curriculum to be published today

From BBC:

The re-written national curriculum, to be published on Monday, will set out the framework for what children in England’s state schools should be taught between the ages of five and 14. […] However academies – which are now a majority of secondary schools – will not be required to follow the curriculum. […]

The changes will include fractions for five year olds […]

Education Secretary Michael Gove said the new-look curriculum would provide the “foundation for learning the vital advanced skills that universities and businesses desperately need – skills such as essay writing, problem-solving, mathematical modelling, and computer programming“.

In maths, there will be an expectation of a higher level of arithmetic at an earlier age. There will be a requirement for pupils to learn their 12 times table by the age of nine, rather than the current 10 times table by the age of 11.