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.

Challenges for UK mathematical scientists in HE

This invitation for a dialogue is written by Professor Ken Brown, Vice-president of the LMS and  is published on the  LMS Members Blog.

Some current developments in UK Higher Education Institutions raise serious concerns for mathematicians. The issues involve complex changes in the relationships between career development, the impact agenda, and external funding. While many of these changes affect academics in other fields, I will concentrate here on their particular effects on those working in the mathematical sciences. These effects are, broadly speaking, of two sorts: changes in our working conditions as individual mathematical scientists, and changes in the overall structure of academic mathematical science in the UK. Here are some examples of the sort of thing I have in mind: the first 6 predominantly concern individuals, at least initially, while the remainder are more structural.

  1. award of sabbatical leave only to those winning Research Council (RC) grants;
  2. allocation of PhD students only to those winning RC grants;
  3. supervision of research student(s) a necessary condition for promotion;
  4. substantial external research income a necessary condition for promotion;
  5. move to “tenured” status dependent on winning external income and/or PhD supervision;
  6. non-submission of an individual’s outputs to the REF, despite availability of a full set of internationally-published outputs;
  7. departmental decisions on number of outputs submitted to the REF influenced by the number of sufficiently strong Impact Statements;
  8. decisions on research fields to support or appointments to make dependent on likelihood of future Impact Statements being generated;
  9. loss of service teaching leading to reduced student FTE numbers and reductions in staffing.

The purpose here is not to provide a detailed analysis of each of the above issues—rather, I want to open a dialogue, letting others develop topics which they feel are of particular concern, whether from the above list or not. Instead, I’ll simply comment briefly below on a couple of the points.

Of course, not everyone will think that each of these developments is by definition “a bad thing”. Regarding point 8, for instance, areas of research focus and consequently of appointments must change over time if our subject is to remain vital. The increased focus on Impact in the UK is part of a world-wide trend which we as mathematical scientists cannot and should not try to oppose—rather we must continue with and redouble our efforts to make funders’ definitions of and ways of measuring impact more in tune with the full range of our activities. We must also continue to emphasise the huge long-term impact of the mathematical sciences, as catalogued for example in the Deloitte report; and we should develop a portfolio of examples of the profound influence of the mathematical sciences on all aspects of our lives—one excellent example is the USA’s National Research Council report “The Mathematical Sciences in 2025”. (This is available as a free download at

On point 4, we all know that RC grant income in the mathematical sciences is very low compared to many other STEM subjects. This is in part because the main costs of much of most of the research in the mathematical sciences has been for people and for time, costs which, though very significant, have in the past been adequately covered for many of us in the UK by the dual support system of funding.  Perhaps also it is the case that what we do has historically been undervalued, thanks to long lag times for impact, but also—let’s be honest—thanks to our sometimes relaxed attitude in the past to the need to make the case for more funding. The LMS, both on its own and in conjunction with the Council for the Mathematical Sciences, has been working hard to make these cases and to assemble relevant data, for grant income and more broadly: for example, the Deloitte report, produced with CMS backing last year, has generated a lot of publicity, and the LMS is producing data documents on UK HEI staffing in the mathematical sciences (November 2013, and on UK research funding in the mathematical sciences (to be published July 2014).  A CMS report on the “people pipeline” in the mathematical sciences will come out later this year.

I should also briefly explain what I have in mind with the point 5. At least two Russell Group universities have recently introduced contracts for newly-appointed lecturers, which lead the appointee through a career path set up to complete probation in 2-3 years, with an expectation of promotion to Senior Lecturer or Reader (possibly called something different),  within 5-7 years of initial appointment. All to the good, you might think—except that milestones expected to be passed en route to promotion include winning substantial RC grant income, and supervising a PhD student to completion. The consequences of failing to achieve these targets in the specified time frame are left unclear.

So, why am I writing this article? The first and very important reason is to gather information. At the moment our community has no way of knowing how widespread are these and similar changes. Those of us directly affected can feel isolated, powerless and undervalued. I’m therefore inviting two sorts of response. First, I will very much welcome information about particular cases along the lines of those listed above. It will be equally valuable to learn of examples of good practice with regard to these issues. Naturally, I’ll treat all such communications in the utmost confidence, but will hope to share what global data I can gather, in due course. More generally, it will be good to hear other views on the issues raised here: perhaps, for example, some of these changes should be welcomed? Most importantly, we need to consider what we as a community should be doing in the face of these developments. What should the LMS be doing?

Comments can be placed at the blog, sent to for inclusion in the Newsletter, or, in the case of more confidential material, sent to me

Ken Brown

Vice President, LMS

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).

Nick Gibb: “Join our battle against progressive educationalists”

in The Guardian:

As an ex-schools minister I see value in the unions. But they are wrong not to join our battle against progressive educationalists. [...] This might seem like an odd thing for a Conservative MP and former schools minister to say, but teaching unions are not the problem with our schools. [...]

[...] who is to blame for our education system slipping down the international rankings? The answer is the academics in the education faculties of universities. This is where opposition to the use of phonics in the teaching of young children to read lies, despite vast evidence from this country and other English-speaking countries that systematic synthetic phonics is the most effective and successful method.

Within these education departments lie the proponents of so-called progressive education, which advocates that education should be child-led rather than teacher-led; many advocate a play-based classroom until children are seven years old. It is an approach that espouses learning by discovery rather than having teachers directly teaching children. For decades many education academics downplayed the importance of spelling, punctuation and grammar. Textbooks are regarded by many in the education departments as appalling teaching tools, and in the 1970s they virtually disappeared from primary schools. Progressive educationalists oppose testing and believe that a knowledge-rich education is pointless in the Google age.

It is challenging the hegemony of the education departments of the universities that must be the focus of any serious education reformer and anyone who believes, as Gove does, that the attainment gap between those from poorer and wealthier backgrounds needs to be closed. There are many in the teaching profession who share this view. There are many on the left who hanker for the type of education provided in the independent sector – largely untainted by the progressive ideology of the education faculties – but who want their children educated by the state. They, too, should be railing against these educationalists.


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.


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?