Programmes of study for Mathematics at Key Stage 4

Programmes of study for  Mathematics at Key Stage 4, which will be taught in schools from September 2015 alongside the new English and mathematics GCSEs, are published today. This appears to be the final pack of statutory documents:

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 after 16: the state of play, challenges and ways ahead

On Wednesday 02 July the Nuffield Foundation published report Mathematics after 16: the state of play, challenges and ways ahead. It argues that reforms to GCSEs and A levels risk undermining the government’s goal of universal participation in post-16 mathematics education, particularly if new ‘Core Maths’ qualifications are not backed by universities. The report brings together a wide range of evidence and warns that plans to make GCSE Maths more demanding, detach AS from A levels, and replace the modular structure in favour of terminal exams could actually discourage students from continuing to study the subject beyond the age of 16.

The report is available to download from the Nuffield Foundation website.

Consultation on Key Stage 4 mathematics

The government response to consultation for key stage 4 English and mathematics on December 2nd 2013 can be found here; pdf.

DfE are now consulting on the draft Order and Regulations that will give effect to the new programmes of study for English and mathematics at key stage 4 from September 2015 and to extend the disapplication of the key stage 4 science programme of study for a further school year (2015/16).


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<<

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


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.

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


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:


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.


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 (

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.