Mathematics in the Primary School

‘Innumerate school children cost the taxpayer up to £2.4bn a year’. In 2007, Sir Peter Williams the then chair of the Advisory Committee on Mathematics Education (ACME), was commissioned to consider and make his recommendations in response to the teaching of mathematics in early years settings and primary schools, with a view to assessing and improving upon the current practices of mathematics teaching in early years settings (EYS) and primary schools (Adonis 2007).

By examining the available evidence, drawing from the best practice nationally and internationally and by working closely with the teaching profession, the William’s final report was published in June 2008. By means of 10 recommendations the report identifies methods by which children in primary schools and early years settings can acquire a greater understanding of mathematics, and a greater appreciation of its importantance with relation to a successful progression through life during and after their school career is over. Through ‘a high-quality curriculum and excellent teaching’ (Williams, 2008, p61), children should have confidence and feel comfortable with the concept of Mathematics within their day to day lives.

In the following, I will explore the implications of the ten recommendations outlined in the William’s Report and will conclude with some reflection on the value of the report and the likely impact it will have on me as a trainee teacher.

Recommendation 1

Considers the entry requirements necessary for Initial Teacher Training (ITT).

GCSE Grade C mathematics continues to be the mandatory minimum requirement level. However the report argues that grade B in GCSE maths is desirable with the long-term ambition of the government initiative the Training and Development Agency for Schools(TDA), being for all Qualified Teacher Status (QTS) graduates to have reached Masters-level accreditation. However, this is currently deemed “inadvisable given the possible risk of falling enrolment of trainee teachers”

A higher priority is given to teaching experience through teaching placements to increase the student’s pedagogical knowledge, Williams (2008, p7) states that, “a combination of deep subject knowledge and pedagogical skill is required to promote effective learning”, a view supported by the research body Mathematical Knowledge in Teaching (2007/2008).

The evidence of good grounding in these two fundamental attributes shows; “taken together they constitute a necessary condition to progress learning for all children up to the end of Key Stage 2, which prepares them well for Key Stage 3” ((Williams, 2008, p10).

The only currently acceptable route to raising mathematical understanding is through “properly funded and rewarded continuing professional development” (ibid p 12)

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Recommendation 2

Local Authorities (LAs) are to continue to up-skill and increase the numbers of their Mathematic Consultants.

A continued extensive budget is to be set aside by the Government for local LAs to implement this following the recommendations made by the Primary National Strategy (PNS) (via the National Numeracy Strategy (NNS)), and in partnership with the National Centre for Excellence in the Teaching of Mathematics (NCETM). This funding to be used to develop and track ‘refresher’ Continued Professional Development (CPD) courses for all LA consultants, evidence being that since the introduction of the NNS, a transformation in the way mathematics is taught can be “strongly correlated with the increase in the attainment levels of primary school children” (ibid p 16).

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Recommendation 3

Every school should have at least one mathematics specialist present (or have access to one), whose initial objective is to raise standards and narrow attainment gaps.

By utilising the highly-trained (circa) 400 LA Mathematic Consultants to their fullest, a phased proposal is given to have a Mathematical Specialist present in every school which will re-enforce the importance of mathematics within schools and enhance and allow flexibility for CPD provisions available to all teaching and support staff. Small and rural schools benefitting from pooled resources wherever possible. Many of these specialists could be sourced from Newly Qualified Teachers (NQTs) trained to a higher mathematical level through their ITT providers, and all specialists to be monitored by their respective head teacher.

Q14, Q15, Q19, Q20, Q25a,b,c,d

Recommendation 4

The Department for Children, Schools and Families (DCSF) is to commission a set of materials which will help early years practitioners understand the effect of children’s development as shown through their mathematical mark-making.

The resulting report supports the introduction of ‘children’s mathematical graphics’ (Worthington, M/ Carruthers, E, 2003), at the Early Years Foundation Stage (EYFS). The EYFS adheres to the principles of the ‘central importance of creativity and critical thinking in early learning and development’ (Mark Making Matters, 2008, p2).

By giving practitioners the tools to support and challenge a child’s thought process through encouragement and understanding of the young child’s mark-making, along-side open ended discussion (‘sustained shared thinking’ (Williams, 2008, p34)), the children ‘will become confident and competent communicators, both orally and on paper, in all six areas of learning and development’. (Mark Making Matters, 2008, p2)

In relationship to mathematics, by encouraging a child to mark-make from a very early age, ‘when children realise that marks can be used symbolically to carry meaning […] they begin to make marks as tools to make their thinking visible’ (ibid p3). Through drawing the child may develop their concepts in relationship to problem solving, reasoning and numeracy. The importance of the Early Years Practitioners taking the time to ‘observe, listen and analyse children’s mark making’ in order to understand, praise and enrich the child’s achievements’ (ibid p3), is affirmed.

However, I must agree with the importance of a young child’s mathematical understanding being developed through imaginative play and ‘effective mathematical learning for children in this age group needs to be predominantly social in nature’ (Williams, 2008, p36).

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Recommendation 5

The forthcoming review of the EYSF in 2010 is to consider the inclusion of time and capacity which Williams feel were omitted when the statutory early learning goals set out in the Statutory Framework for EYFS: Learning and Development Requirements (DCSF 2006) were first developed.

By using these two extra concepts along with those already required i.e., shape, space, measures along with the use of correct mathematical language, it would enable the child ‘to apply their mathematical knowledge in practical and active ways’ (Williams, 2008, p36), whilst also enhancing the child’s understanding of problem solving.

The responsibilities of effective pedagogy for this remit falling to local authorities, leaders, managers and head-teachers.

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Recommendation 6

The DCSF is to continue to increase the amount of graduate practitioners going into Early Years Settings (EYS).

The Children’s Workforce Development Council (CWDC) (2010), states ‘High quality early years provision can have a significant impact on children’s development, performance at school and their ‘future life chances’ (CWDC, 2010, Areas of Work- Early Years) and the early years workforce must be ‘well qualified’. (ibid)

With reference to the Effective Provision of Pre-School Education (EPPE, 2004), the Millennium Cohort Study (MCS, 2005) and the evaluation of the Neighbourhood Nursery Initiative (NNI, 2000), it recognises the importance of having a good proportion of trained teachers on the staff. The recommendation being for one graduate early years professional per setting by 2010 and with provision for two graduates per setting in disadvantaged areas.

A member of staff having Qualified Teacher Status (QTS) and a Graduate Early Years Practitioner who has a specialism in working with early years children could have the most benefit to most children’s development and learning.

Standards could also be raised with additional funding given to implementing CPD within the Early Years Workforce where mathematics is given essential priority. It should however be noted that EYFS provisions are currently very erratic throughout the UK.

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Recommendation 7

Engaging the full understanding and commitment of participating children and their parents/carers before the onset of intervention, paying special attention to the integration of intervention in the class room and in a home-school partnership through official home-learning activities.

Where research is undertaken, it is proven that the inclusion and understanding of parents/carers before the onset of intervention is paramount in guaranteeing programme success, and parents/carers could support their child’s learning progress through official home-learning activities. Equally, children who understand exactly the nature of the programme show genuine delight in their progress and ‘the importance of this factor should not be under estimated for a successful programme’ (Williams, 2008, p55).

In terms of the integration of intervention, the DCSF National Strategy Standards (PNS) (1998) cites;

‘Intervention is not just about additional out-of-class provision. It also includes reviewing what happens in class to make sure it is appropriately tailored to the needs of the children’.

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Recommendation 8

The Wave 3 Intervention programme from The Every Child Counts (2008) initiative; a partnership between government, businesses and the charity Every Child a Chance (2007) aims to enhance achievement for approximately 5%-10% of children nationally who are ‘failing to master the basics of numeracy’ (Adonis, 2007).

Adonis (2007) states; there is no ‘single cause of under-attainment’ and therefore ‘no single answer'(ibid) It is best to summarise the implications, logistics and recommendations of wave 3 intervention in Year 2 as follows:-

Intervention should be led by a qualified teacher on a 1: 1 teacher pupil ratio.

The benefits of working in pairs or small groups should also be explored.

The child’s class teacher should be given responsibility to decide whether intervention is necessary. Investigation into of the efficacy of using video tapes for assessment and training should be undertaken.

Diagnostic tools should be developed to aid teachers with assessment before intervention and monitor progress after leaving the programme, using for example, Assessing Pupils’ Progress (APP) and the Early Years Foundation Stage Profile (EYFSP).

Intervention should ideally last for one term and be completed by the end of Key Stage 1. Where it is deemed that a child is in need of intervention for both literacy and mathematics, it is imperative that mathematics be given equal standing to literacy.

A wide range of (potentially costly) multi-sensory resources should be made available, for example, Numicom and the interactive whiteboard, to enable the teacher and child to select the appropriate aid to their specific issue.

CCD programmes should be developed for the teacher as intervention specialist and for LA intervention specialists. Currently there is only a small cohort of intervention specialists available.

Combining the roles of intervention specialist and mathematics specialist should be considered through the pooling of resources wherever possible to limit cost implications.

Teaching Assistants could be further trained to lead less intensive wave 2 and 3 interventions.

A longitudinal study is to be carried out over the next 10-15 years to assess the success of the programme.

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Recommendation 9 and 10

Refer to the importance of continued building on the currently solid curriculum, with more prominence being given to ‘use and application’ (Williams, 2008, p60) of Mathematics across all subjects and to give renewed focus to oral and mental mathematics.

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Conclusion

In conclusion, the above discussion has demonstrated the key features of the Williams Report and has reflected on the implications of the report for EYP, strategies for intervention and the roles of the curriculum, training, accreditation, head-teachers and the family.

I have demonstrated how the Williams Report has both drawn on existing regulations, recommendations, policies and practice but crucially, identified the weaknesses in existing legislation.

For me the key strengths of the report lie in its emphasis on the role of teacher pedagogy and practice and the shared responsibility of the LAs with schools, in particular the head-teacher, and with the parent/carer.

A key recommendation is being pro-active and understanding that every child matters.

I feel the weaknesses of the report relate to its over-emphasis on high-levels of formal accreditation, which do not reflect an individual’s natural gift to teach and which may jeopardise future recruitment.

Of course, the question remains what the effect of recent government changes and the very real and imminent threat of public sector cuts will mean for the practical implementation of the William’s report recommendations.