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.

33rd MATHEMATICS TEACHERS AND ADVISERS CONFERENCE/WORKSHOP

33rd MATHEMATICS TEACHERS AND ADVISERS CONFERENCE/WORKSHOP
Friday 27th June 2014 13.00-17.00 – No registration fee

The 33rd Mathematics Teachers and Advisers Conference/Workshop provides an interface between the School of Mathematics at the University of Leeds and teachers in schools and sixth forms.

Teachers and university staff alike are given a rare opportunity to exchange valuable experiences and re-invigorate their perspectives on the ever-changing world of mathematics education.

Please book the date of 27th of June 2014 in your diary and attend the event.

If you have not done already so, in order to register, simply JUST SEND an EMAIL to:

D. Lesnic >>at<< leeds.ac.uk

and give your name, name of the school and email.

Programme:

Julian Gilbey (University of Cambridge) “Cambridge Mathematics
Education Project”

Currently in the development phase, the project will provide innovative online resources to help support and inspire teachers and students of A-level  mathematics. The aim is to help to make sixth-form  mathematics a rich, coherent and stimulating experience for students and teachers. Join to get a preview of the web site, and to work together on some of the new A-level resources.

David Kaplan (Royal Statistical Society Centre for Statistical Education at Plymouth University) “SAS Curriculum Pathways”

Plymouth University has endorsed SAS Curriculum Pathways as a free-to-use online teaching and learning resource in order to promote the uptake of STEM subjects in further and higher education. The resource has been developed in the US over a number of years and has been successful for three main reasons:

(i) Commitment to Teachers. SAS Curriculum Pathways works in the classroom in large part because teachers have shaped every phase of the planning and production process.

(ii) Focus on Content. Teachers, developers, designers, and other specialists clarify content in the core disciplines. Content difficult to convey with conventional methods is tageted topics where doing and seeing provide information and encourage insights in ways that textbooks cannot.

(iii) Approach to Technology. SAS Curriculum Pathways makes learning more profound and efficient, not simply more engaging. Audio, visual, and interactive components all reinforce the learning objectives identified by teachers. It stands apart from other online resources becuase of its interactive nature students obtain immediate feedback. The resource promotes subject specific terminology and leads students through sometimes difficult methods in a structured way. http://www.sascurriculumpathways.com/portal

Sue Pope (Chair of the General Council of the Association of Teachers
of Mathematics) -“Post-16 Mathematics Opportunities and Challenges”

Despite increasing numbers of students studying level 3 Mathematics, England is remarkable in its low participation rates. The government is committed to increasing participation, yet will we have a curriculum and associated qualifications to do this? Will linear A levels, core maths, critical maths (MEI Gowers’-inspired) and other qualifications in development fit the bill? Have policy makers learnt from Curriculum 2000, or the Mathematics Pathways project? How do we ensure students have the mathematical skills to thrive whatever their future? And what are those skills?

Brain finds true beauty in maths

From BBC: Brain finds true beauty in maths. A quote:

Brain scans show a complex string of numbers and letters in mathematical formulae can evoke the same sense of beauty as artistic masterpieces and music from the greatest composers.

Mathematicians were shown “ugly” and “beautiful” equations while in a brain scanner at University College London.

The same emotional brain centres used to appreciate art were being activated by “beautiful” maths.

The researchers suggest there may be a neurobiological basis to beauty.

The study in the journal Frontiers in Human Neuroscience says,in partucular, that

The formula most consistently rated as beautiful (average rating of 0.8667), both before and during the scans, was Leonhard Euler’s identity

\(1+e^{i\pi}=0\)

which links 5 fundamental mathematical constants with three basic arithmetic operations, each occurring once; the one most consistently rated as ugly (average rating of −0.7333) was Srinivasa Ramanujan’s infinite series for 1/π,

\(\frac{1}{π}=\frac{2\sqrt{2}}{9801}\sum_{k=0}^\infty  \frac{(4k)!(1103+26390k)}{(k!)^4\cdot 396^{4k}}\)

which expresses the reciprocal of π as an infinite sum.

Other highly rated equations included the Pythagorean identity, the identity between exponential and trigonometric functions derivable from Euler’s formula for complex analysis, and the Cauchy-Riemann equations. Formulae commonly rated as neutral included Euler’s formula for polyhedral triangulation, the Gauss Bonnet theorem and a formulation of the Spectral theorem. Low rated equations included Riemann’s functional equation, the smallest number expressible as the sum of two cubes in two different ways, and an example of an exact sequence where the image of one morphism equals the kernel of the next .

- See more at: http://journal.frontiersin.org/Journal/10.3389/fnhum.2014.00068/full#sthash.7b7Pdf5a.dpuf

 

EMPG 2014: Call for papers

You are cordially invited to attend the 2014 European Mathematical Psychology Group Meeting (EMPG 2014), held at the University of Tübingen, Germany, from Wednesday, July 30, 2014 until Friday, August 01, 2014.

Presentations

Proposals for paper and poster presentations as well as proposals for symposia related to all aspects of mathematical psychology are welcome. Relevant topics include:

  • perception and psychophysics
  • models of cognition and learning
  • knowledge structures
  • measurement and scaling
  • psychometrics
  • computational methods
  • statistical methods
  • mathematical models

Important dates

  • Abstract submission opens:  soon
  • Abstract submission closes:  April 30, 2014
  • Notification of acceptance:  May 15, 2014
  • Early registration deadline:  June 06, 2014
  • Start of conference: July 30, 2014
  • End of conference: August 01, 2014

Invited Symposia

Symposium in honor of Jean-Claude Falmagne celebrating his 80th birthday (organized by Michel Regenwetter and Jean-Paul Doignon).

Invited speakers

Andrew Heathcote, University of Newcastle, Australia
Ehtibar Dzhafarov, Purdue University, USA

For further information please consult the website of the EMPG 2014 (www.uni-tuebingen.de/psychologie/empg2014).

Play this book: “Moebius Noodles”

Moebius Noodles. Adventurous Math for the Playground Crowd

Text: Yelena McManaman and Maria Droujkova
Illustrations and design: Ever Salazar
Copyedits: Carol Cross

This brilliant book is published under Creative Commons Attribution-NonCommercial-ShareAlike license, and this allows me to reproduce the entire Introduction:

Why Play This Book

Children dream big. They crave exciting and beautiful adventures to pretend-play. Just ask them who they want to be when they grow up. The answers will run a gamut from astronauts to zoologists and from ballerinas to Jedi masters. So how come children don’t dream of becoming mathematicians?
Kids don’t dream of becoming mathematicians because they already are mathematicians. Children have more imagination than it takes to do differential calculus. They are frequently all too literate like logicians and precise like set theorists. They are persistent, fascinated with strange outcomes, and are out to explore the “what-if” scenarios. These are the qualities of good mathematicians!

As for mathematics itself, it’s one of the most adventurous endeavors a young child can experience. Mathematics is exotic, even bizarre. It is surprising and unpredictable. And it can be more exciting, scary, and dangerous than sailing on high seas!

But most of the time math is not presented this way. Instead, children are required to develop their mathematical skills rather than being encouraged to work on something more nebulous, like the mathematical state of mind. Along the way the struggle and danger are de-emphasized, not celebrated – with good intentions, such as safety and security. In order to achieve this, children are introduced to the tame, accessible scraps of math, starting with counting, shapes, and simple patterns. In the process, everything else mathematical gets left behind “for when the kids are ready.” For the vast majority of kids, that readiness never comes. Their math stays simplified, impoverished, and limited. That’s because you can’t get there from here. If you don’t start walking the path of those exotic and dangerous math adventures, you never arrive.

It is as tragic as if parents were to read nothing but the alphabet to children, until they are “ready” for something more complex. Or if kids had to learn “The Itsy-Bitsy Spider” by heart before being allowed to listen to any more involved music. Or if they were not allowed on any slide until, well, learning to slide down in completely safe manner. This would be sad and frustrating, wouldn’t it? Yet that’s exactly what happens with early math. Instead of math adventures – observations, meaningful play, and discovery of complex systems – children get primitive, simplistic math. This is boring not only to children, but to adults as well. And boredom leads to frustration. The excitement of an adventure is replaced by the gnawing anxiety of busy work.

We want to create rich, multi-sensory, deeply mathematical experiences for young children. The activities in this book will help you see that with a bit of know-how every parent and teacher can stage exciting, meaningful and beautiful early math experiences. It takes no fancy equipment or software beyond everyday household or outdoor items, and a bit of imagination – which can be borrowed from other parents in our online community. You will learn how to make rich mathematical properties of everyday objects accessible to young children. Everything around you becomes a learning tool, a prompt full of possibilities for math improvisation, a conversation starter. The everyday world of children turns into a mathematical playground.
Children marvel as snowflakes magically become fractals, inviting explorations of infinity, symmetry, and recursion. Cookies offer gameplay in combinatorics and calculus. Paint chips come in beautiful gradients, and floor tiles form tessellations. Bedtime routines turn into children’s first algorithms. Cooking, then mashing potatoes (and not the other way around!) humorously introduces commutative property. Noticing and exploring math becomes a lot more interesting, even addictive. Unlike simplistic math that quickly becomes boring, these deep experiences remain fresh, because they grow together with children’s and parents’ understanding of mathematics.

Can math be interesting? A lot of it already is! Can your children be strong at advanced math? They are natural geniuses at some aspects of it! Your mission, should you accept it: to join thrilling young math adventures! Ready? Then let’s play!

 

2014 Alan Turing Cryptography Competition

Registration is now open for the 2014 Alan Turing Cryptography Competition which starts on Monday, 27 January 2014.

Now in its third year, and organised by the School of Mathematics of the University of Manchester, this successful competition is open to secondary school children up to Year 11 (England and Wales), S4 (Scotland) and Year 12 (Northern Ireland). It is a great way for children to make use of their mathematical and problem-solving skills whilst having fun.  In addition, there is the opportunity to win some great prizes, which have been sponsored by the flight search company, Skyscanner. Skyscanner was set up by two former computer scientists from the University of Manchester, two people who directly benefitted from Turing‘s contributions to Manchester and computing.  People outside the age range can also take part, but they won’t be eligible for any prizes!

The competition follows the story of two young cipher sleuths, Mike and Ellie, as they get caught up in an adventure to discover the Lovell Legacy.  Every week or two weeks a new chapter of the story is released, each with a cryptographic puzzle to solve.  There are six chapters in total (plus an epilogue and just-for-fun code to conclude the story).  Points can be earned by cracking each code and submitting the answer.  The leaderboard enables the teams to keep track of how well they are doing.

New for this year is the Alan Turing Cryptography Day, to be held in the School of Mathematics  of the University of Manchester on Wednesday, 30th April 2014.  We anticipate plenty of code-breaking action, a live cryptography mini-challenge and a prize ceremony for the competition winners.  It’s not to be missed!

To register

Further information and registration details can be found at:

Rebecca Hanson: 2014 Primary Mathematics Curriculum is Not Fit for Purpose

Re-posted from Authentic Maths.

Rebecca Hanson:

Following the writing of my first report on the 2014 Primary National Curriculum in December I have been corresponding with the key people involved in its development.

As a results of their comments I have written a second report which calls for the immediate suspension of the implementation of the 2014 Primary National Curriculum for Mathematics. This new report dated 6 Jan 2014 can be downloaded here: Fundamental Problems with the 2014 Primary National Curriculum for Mathematics.

The press release which accompanies this report can be downloaded here:
Call for Suspension of New Primary Mathematics Curriculum.

6 JAN FAULT: If you experience problems downloading the report an alternative version (without hyperlinks) can be downloaded from the Times Educational Supplement site.

International Conference on Mathematics Textbook Research and Development 2014

International Conference on Mathematics Textbook Research and Development 2014

University of Southampton, UK, 29-31 July 2014

Conference themes:

  • Textbook research (concepts, issues, methods, directions, etc.)
  • Textbook analysis (characteristics, treatment of contents and/or pedagogy, etc.)
  • Textbook comparison or historical studies
  • Textbook use (by teachers, by students, and/or by other parties)
  • Textbook development (presentation, task design, publishing, policy matters, etc.)
  • Integration of ICT in textbooks (including e-textbook)
  • Other disciplines in maths textbooks & maths in textbooks of other disciplines
  • All other relevant issues about mathematics textbooks

Conference papers to be published in electronic proceedings
Opportunity to be considered for an edited book under negotiation with a major publisher.

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