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Independent Review of Mathematics Teaching in Early Years Settings and Primary Schools (2008)

RESOURCES REPORT - Williams.pdf (589.68 KiB)

Sir Peter Williams June 2008
Department of Children, Schools and Families

This final report sets out the Williams review’s findings, regarding educational best practice to enable young learners in primary schools and early years settings to acquire an understanding and appreciation of mathematics and of its importance to their lives.

The main recommedation is that every school should have a mathematics specialist. It also focuses on the need for improved training for teachers and the vital role of parents.

This comprehensive report responds to the remit set out in July 2007 by the Secretary of State for a review of mathematics teaching in early years and primary school settings.

To see the full report click here

The report confirms that the UK is still one of the few advanced nations where it is socially acceptable – fashionable, even – to profess an inability to cope with the subject. The review therefore looks at the role of parents and families and their influence on the young learner.

However it is a central conclusion of this review that:

  • the teacher, even more than the parent, determines learning outcomes in mathematics, the more so given that the way in which mathematics is taught has undergone considerable change since most parents’ own schooling.

The review has made the following principal recommendation:

  • that there should be at least one Mathematics Specialist in each primary school, while recognising the need to make sensible allowances for small and rural schools.

The review, having looked at the present mathematics programme of study for Key Stages 1 and 2, makes no recommendation for radical change. Indeed, it judges that the curriculum, by and large, is well balanced, and recommends that it should continue in its current form.

But two issues are singled out:

  • the need for an increased focus on the ‘use and application’ of mathematics

  • classroom discussion of mathematics. It is often suggested that ‘mathematics itself is a language’ but it must not be overlooked that only by constructive dialogue in the medium of the English language in the classroom can logic and reasoning be fully developed – the factors at the very heart of embedded learning in mathematics.

The review looks at the Early Years Foundation Stage (EYFS) The learning processes of very young children require tailored pedagogies and a highly sensitive approach. The review also lays great store by play-based learning of a mathematical nature, and makes specific recommendations regarding early mark-making as a precursor to abstract mathematical symbolism.

Under the section on Initial Teacher Training (ITT) and Continuing Professional Development (CPD) the report made several recommendations:

  • recommendation 1: When GCSE mathematics I and II are firmly established, the Government should review whether attainment of a minimum of grade C GCSE in both subjects should become a requirement for entry into ITT. For students who have taken or will take GCSEs before then, a grade C in single award mathematics should remain the requirement.

  • recommendation 2: Local authorities should upskill their field force of mathematics consultants. The National Strategies, in partnership with the National Centre for Excellence in the Teaching of Mathematics, should develop ‘refresher’ CPD for all local authority mathematics consultants.
  • recommendation 3: There should be at least one Mathematics Specialist in each primary school, in post within 10 years, with deep mathematical subject and pedagogical knowledge, making appropriate arrangements for small and rural schools.
  • the main thrust of this review, therefore, is that a combination of deep subject knowledge and pedagogical skill is required to promote effective learning.


Estimates are made of the costs associated with these proposals, whilst also looking at the long- term benefits to society of successful mathematical learning in primary and early years. The Every Child A Chance Trust estimates that for every pound spent on early intervention for the lowest attaining pupils, at least £12 will be saved long-term on the costs to the public purse.

It sets out preliminary ideas on the financial implications of the recommendations for ITT and CPD. It also sets out proposals for appropriate incentive structures for those teachers who successfully complete the multi-year CPD programme and become Mathematics Specialists.

The total cost of this programme over 11 years of £187 million averages less than £20 million per annum, and should be seen as an investment in the nation’s future, not as a cost.

Early Years:

  • recommendation 4: That the DCSF commissions a set of materials on mathematical mark making and children’s mathematical development which can be used to support early years practitioners’ CPD.

  • recommendation 5: That the forthcoming review of the EYFS in 2010 considers the inclusion of time and capacity within the early learning goals.

  • recommendation 6: That the DCSF continues to increase the proportion of graduate practitioners in early years settings, recognising the respective contributions of the Qualified Teacher (QTS) and the Graduate Early Years Practitioner (graduate EYP). The review supports the goals which are currently in place.

Under-attainment and Intervention

At the invitation of the Secretary of State, and working closely with the Every Child a Chance Trust, the review sought to identify the essential requirements in a successful intervention in maths. Specific recommendations (see review) are made on this, following an extensive review of many programmes currently deployed in schools or under development.

The evidence suggests that the opportunities afforded by the Foundation Stage Profile (FSP) are frequently not being exploited at the moment. If this assessment information is used well, it is conceivable that fewer children will need intensive support programmes in later years.

Recommendation 7: Before any intervention programme is implemented, it is important that the child is committed to it and that the parents or carers are involved and understand the nature of the programme.

Assessment data in mathematics shows that, despite the great progress made since the introduction of the National Numeracy Strategy (NNS), there is still a group of pupils who fail to achieve level 3 in mathematics by the time they leave the primary sector at age 11. The data shows that since the introduction of the NNS, the percentage of pupils attaining no more than level 2 has been stable at around six per cent, with little fluctuation. This chapter is concerned with measures aimed at enabling these learners to attain a better mastery of mathematics in the future.

Before beginning to address what might be done about this problem, there is an acknowledgement of a growing body of opinion which cites evidence for a clinical condition, analogous to dyslexia, which may seriously impede young learners in mathematics. ‘Dyscalculia’, as this condition has been named is the subject of cognitive research using sophisticated clinical investigative tools such as magnetic resonance imaging (MRI).

In addition:

  • the report acknowledges that intervention can make a difference but there are many different forms of intervention being practiced.

  • it is a firm recommendation of this review that there should be a meaningful longitudinal study over the next 10 to 15 years, which measures the outcomes of the pupils who benefited from the Every Child Counts programme.It is a firm recommendation of this review that intervention in mathematics should be completed by the end of Key Stage 1.

  • both literacy and mathematics must be given equal priority over the course of Key Stage 1.

  • this review stresses the importance of providing intervention teachers who have insight, through their training, into what resources might help with key areas of difficulty.

In recommending a mathematics specialist the review acknowledges logistical issues but the following approach would seem a logical starting point for further, more detailed consideration, allowing for flexibility in local decision making:

  • in schools with fewer than 200 pupils the roles of Mathematics Specialist and intervention specialist should be combined.

  • in larger schools, with more than 200 pupils, there is a need for dedicated intervention specialists, shared, in all but the largest schools, between a small group of schools.

  • the local authority concerned must clearly take the lead in the complex coordination of intervention resources and teachers.

  • head teachers, once again, have a critical role in planning and management for the deployment of intervention specialists.

Curriculum and Pedagogy

Too little attention is paid to building good attitudes to mathematics.

Recommendation 9: The Primary National Curriculum in Mathematics should continue as currently prescribed, subject to any changes which may result from Sir Jim Rose’s forthcoming review of the Primary Curriculum; the latter should examine the concept of ‘use and application’ more generally across subjects to assess whether mathematical or other aspects of the curriculum need amendment.

Recommendation 10: This review recommends a renewed focus by practitioners on ‘oral and mental mathematics’.

Lessons from Ofsted and Primary National Strategy (PNS) findings:

  • is the need to strengthen teaching that challenges and enables children to use and apply mathematics (UAM) more often, and more effectively, than is presently the case in many schools.

  • osted evidence also shows that there is a lack of attention to these aspects of pedagogy in the Foundation Stage, despite the prominence of ‘using and applying mathematics’ in the EYFS areas of learning and experience

It is essential that the momentum in learning in mathematics is maintained through the transition from EYFS to Year 1.

  • play-based learning is extensive in the former, and during the course of this review practitioners have often stressed the abrupt nature of the transition from this to a more formal approach in KS1, at a time when many children may not be ready. A case can be advanced for slightly more emphasis in Reception and Year 1 on play-based learning, with a focus on extending the use of more structured activity to prepare children for this transition.

It is widely recognised that a teacher’s own enthusiasm for, and knowledge of, mathematics, as well as their beliefs about teaching and learning, will impact on their classroom practice, regardless of the external constraints on curriculum and lesson design.

The review believes that the Mathematics Specialist (described in Chapter 2) may have a role to play in the provision for gifted and talented pupils in their school.

The critical importance of engaging children in discussing mathematics is widely recognised.

Once again, the importance of ITT and CPD in these aspects of pedagogy and practice has to be noted, although this review would again wish to stress the need for focus on the learning and teaching-related content in ITT and CPD as the top priority, rather than its means of delivery.

Parents and carers

  • the overwhelming majority of parents want to do the very best for their children and the majority say they expect to need advice or help at some time or another.

  • regardless of class or income, the influence of the parent is the single most significant factor in a child’s life.

  • teachers need to recognise the wealth of mathematical knowledge children pick up outside of the classroom, and help children to make links between ‘in-school’ and ‘out-of-school’ mathematics

  • the panel believes that the lack of clarification and setting out of the methods of teaching is a missed opportunity for engaging parents and improving their children’s attainment. It is important that practitioners are encouraged to work with parents to bring them up to date with the methods currently used to teach mathematics, so that parents can support their children effectively.

  • there is an opportunity here for schools to work together with parents to dispel myths about the mystery of mathematics and give both children and parents a good grounding and positive attitude to this subject.

  • it is self-evident that parents are central to their child’s life, development and attainment. They cannot be ignored or sidelined but should be a critical element in any practitioner’s plans for the education of children. Both research and Government policy support this assertion. There are already many examples of successful projects that embrace these principles to good, and sometimes stunning, effect. The aim of the review should be to normalise and mainstream these approaches, not allowing any educational establishment to even consider leaving parents out of the equation.

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