## Overall comments and observations

All but six reports include recommendations. This section synthesises the recommendations and a later section, ‘Progress’, reports on the ways in which some of the recommendations have been acted upon.

In some cases recommendations are implicit, such as ‘research evidence strongly suggests that careers education and guidance should be provided earlier than Years 9 –11 to encourage the uptake of STEM subjects’ (NFER, 2013, p. 3). In others, they are more explicit, although they do not always make clear who should act on the recommendation. For example:

New courses for post-16 students will require careful design. Their statistics content must be up-to-date and relevant to the future lives of the target students, whether in higher education or employment. (Porkess, 2012, p. 4)

In many cases, however, the reports are explicit about who the recommendations are for. For example, Clark-Wilson et al (2011) preface each of their five recommendations by stating who should act on the recommendation: policy makers, policy makers and teachers, policy makers and school leaders. In another example, the ACME report on the mathematical needs of learners (ACME, 2011) has two sets of recommendations: one for policy makers and one ‘For the Department for Education when reviewing the National Curriculum’.

Overall, the recommendations fall into a set of categories related to the areas identified in the problems, or symptoms, and the causes of these, identified in mathematics education. The categories inevitably overlap because the areas they address are highly inter-related. For example, as explained in the section on causes, a common claim within the reports is that current assessment regimes and cultures of performativity mean that many teachers tend to ‘teach to the test’. This sort of high level of relatedness means that recommendations sometimes address two concerns within a single recommendation. Another reason categories overlap is that a recommendation in one area (e.g. curriculum; such as ‘Science and mathematics curricula need to be inspiring and engaging…’ (Royal Society, 2011, p. xii)) is intended to address a concern in another area (e.g. student attitudes) although this connection is often left unsaid.

Some recommendations, however, are overarching and can be seen as highly ambitious. For example, in ACME’s response to the draft programmes of study for mathematics (2013), it is stated that the mathematical experience of students should be engaging, inspiring and successful. The Vorderman report’s overarching aim relates to attainment:

We should aspire to reach the mathematical attainment levels of the most successful countries (Vorderman, Porkess, Budd, Dunne, & Rahman-hart, 2011, p. 7).

Whereas these overarching recommendations do not specify the educational phase to which they refer (but could be seen to refer mainly to schools mathematics, given the context of the reports), at least two reports make the strong case that primary school mathematics should be addressed as a priority (Burghes, 2012; Jerrim & Choi, 2013).

This section is organised in a similar way to previous sections, addressing first the mathematical activity of young people, second the curriculum, qualifications and assessment and third teachers, teaching and schools. The recommendations related to the review of the National Curriculum are also given, although the new National Curriculum has now been published. There is a final section which includes recommendations which fit into none of the above sections; use of data and future research.

# References

ACME. (2011). *Mathematical Needs of Learners*. London.

ACME. (2013). *ACME’s response to the consultation on the draft programmes of study for the National Curriculum*. London.

Burghes, D. (2012). *Primary Problems: A First Curriculum for Mathematics*. London.

Clark-Wilson, A., Oldknow, A., & Sutherland, R. (2011). *Digital technologies and mathematics education: A report from a working group of the Joint Mathematical Council of the United Kingdom*. London.

Jerrim, J., & Choi, A. (2013). *The mathematics skills of school children : How does England compare to the high performing East Asian jurisdictions?* London.

NFER. (2013). *NFER Thinks: Improving young people’s engagement with science, technology, engineering and mathematics (STEM)*. Slough.

Porkess, R. (2012). *The Future of Statistics*. London.

Royal Society. (2011). *Preparing for the transfer from school and college science and mathematics education to UK STEM higher education*. London.

Vorderman, C., Porkess, R., Budd, C., Dunne, R., & Rahman-hart, P. (2011). *A world-class mathematics education for all our young people*. London.

Are there any recommendations about the way mathematics should be developed and notated/written to improve the value to society and make it easier to learn and to teach?

Quite a lot of the difficulties come from the bizarre notation of mathematics, which is mostly historical accident. Calculus and trigonometry are good examples of areas which could do with a makeover.

There’s also the question of whether leading mathematicians are developing maths that is useful to society, teachable, and structured so that it can be learned and used without unnecessarily long preparatory learning.