I hope you have enjoyed a good break over Christmas and managed to re-charge your batteries. The break allowed me some time to reflect on the furore caused by the publication of the PISA results in early December and to think about what use we can make of them.

The Programme for International Student Assessment (PISA) survey takes place every three years and compares the performances of 15-year olds from different countries in mathematics, science and reading skills. PISA 2012* had a particular focus on mathematics, so the mathematics performance was assessed in greater depth than the other two areas. The results from the PISA 2012 survey were published in early December. They show England’s position in mathematics as mid-table, just as in 2009 and 2006 (see the National Foundation for Educational Research (NfER) website for analysis of England's performance and a link to the full report).

The PISA results generated great interest in the media and from politicians because it is recognised that mathematics underpins science, technology, engineering and finance in particular, as well as many other areas, so a population well-educated in mathematics is considered to be of great economic importance. As someone who believes mathematics is a vitally important discipline in its own right, I consider the economic benefits as a desirable side-effect, rather than as the main purpose of mathematics education. However, I am pleased that its economic importance means maths education is so highly valued. The price of being highly valued is that maths education is newsworthy, and the performance of English pupils in mathematics in PISA 2012, relative to those from some other countries, has meant much of the media coverage has been highly critical. Is the criticism fair, and how should we respond?

As mathematics educators, what can we learn from the PISA 2012 results? There is some good news. It’s encouraging that the report showed our pupils have a positive attitude towards mathematics when compared to the OECD average, with a lower level of maths anxiety. This should provide a good foundation for improving mathematical knowledge and understanding. Perhaps it’s evidence that, as a nation, we are developing a more positive attitude to mathematics. This view is supported by the large increases in participation in AS/A level Mathematics and Further Mathematics over recent years, which have far outstripped the growth in other major A level subjects [since 2005 A level Maths numbers in England have increased by 69% to 81 171 and A level Further Maths numbers by 135% to 13 232].

However, the headline news from the PISA 2012 results was that many other nations seem to be doing much better than us in mathematics education. It’s possible to criticise the methodology - that some nations ‘teach to the test’ to do well in PISA, that the samples may not be properly representative, that cultural differences mean such comparisons are invalid - but whether or not these are important factors, there are useful things to learn from the PISA survey. I think two issues highlighted by NfER in their analysis of the England’s performance in mathematics in PISA 2012 are of particular importance. These are:

1. There is a relatively large spread of achievement when compared to the OECD average.
2. Headteachers reported the biggest staffing issue was a shortage of qualified mathematics teachers.

Effective teacher professional development can make a major contribution to addressing both of these issues.

All pupils should have access to a good mathematics education. It should not be dependent on which school they go to, or which class they are taught in. Top quality teaching and learning in mathematics is available to many of our pupils, but there is huge inconsistency, both between schools and within schools. This was highlighted in Ofsted’s 2012 report Mathematics: made to measure, which recommends that schools should: tackle in-school inconsistency of teaching, making more good or outstanding, so that every pupil receives a good mathematics education.

The chart on page 23 of that report shows that even in schools with some outstanding mathematics lessons, there were also lessons that were inadequate, and there was also a wide range of performance between different schools.

We need to strive to make all of the mathematics teaching in our schools as good as the best. A key principle of the NCETM’s work is the use of collaborative practice, supporting teachers to share good practice both within schools and between schools: teachers working together with the common goal of improving mathematics teaching and learning for pupils. The NCETM’s Primary Host Schools Project** showed how this can work, and the new Mathematics Education Strategic Hubs (MESH) initiative is intended to support collaborative practice and effective mathematics CPD across the whole of England. This has the potential to help to address both the inconsistency in the quality of our mathematics teaching and the shortage of qualified mathematics teachers.

If we can work collaboratively to address the inconsistencies in the quality of mathematics teaching in our schools, levelling-up standards both within and between schools, we will significantly improve our mathematics education. This will benefit our young people as individuals, giving them the skills and confidence they need to use and enjoy mathematics. It will also contribute to the success of the nation as a whole.

* The BBC’s More or Less radio programme about PISA is worth listening to [in fact, I recommend maths teachers (and science and social science teachers) should make a point of listening to More or Less – it provides many interesting and topical examples on the use (and misuse) of data].

** Sheffield Hallam University's Evaluation of the NCETM Primary Mathematics Host Schools Project, and the NCETM conducted its own survey of the project’s participants, and has produced its own report too.