Learning is a fundamental process, and one believed to be life long. Subsequently, education allows for learning to be progressed through the acquisition of knowledge and development of reasoning and judgment. Providing children with the necessary attributes to both read and communicate fluently, as well as count and calculate confidently are of significant importance, hence, to review progression, the Government insist on the analysis of frameworks.
In July 2007, the Secretary of State asked Sir Peter Williams to review the teaching of Mathematics within Early Years and Primary schools. Through extensive research, Williams (2008) made ten final recommendations about how to improve the teaching of mathematics, addressing its distinctive requirements. Williams (2008) expressed that,
“The high standards achieved in mathematics in recent years
can be maintained and improved further only by addressing the
unique needs of this subject, a discipline which is not always
embraced with enthusiasm and confidence.” (ibid 2008 p.1)
The recommendations highlighted that the improvement for the quality of mathematical teaching should not solely rely upon teachers and practitioners. Parents and families are of significant importance, particularly where an intervention programme is required. In addition, Head Teachers and members of Senior Management play an active role in ensuring that every child receives the best mathematical education. The accomplishment of this is very much dependent upon children having an unassailable start to their educational journey; hence, Williams (2008) proposed three specific recommendations for early years. Recommendation six highlighted that there should be a continuing increase in the proportion of graduate practitioners in early years settings:
“The review agrees that the presence of someone with
Qualified Teacher Status, with early years specialism, working
with children wherever possible is vital.” (Williams 2008 p.38)
This recommendation could signify considerable changes for early years education, encouragingly echoing a key aim outlined within The Children’s Plan; Building brighter futures (2007), that there shall be a graduate early years professional in every full day care setting in England by 2015. Furthermore, practitioners would require a firm understanding of mathematical pedagogy, expressing distinctive features that would support high quality learning.
Children require an array of opportunities to learn in an environment that is stimulatingly rich and appropriate to their development, achieved through positive enthusiasm and direct teaching of mathematical skills and knowledge. There is significant value for the understanding of how the range of children’s educational experiences, during their first five years, can have profound implications on their mathematical learning. Consequently, Williams (2008) expressed there was a broad consensus on the importance for the need of uniformly good early years environments providing quality teaching. Central to that are the teachers and practitioners creating enabling environments and positive relationships, adopting effective pedagogy throughout all aspects of learning. Williams (2008) explored how children’s experiences with mathematics should be built upon play and spontaneous learning, fostering their natural interest in numeracy and problem solving. Achieving this requires the understanding of how the use of children’s own graphical explorations, though mark making, is highly significant and of great value to practitioners. Williams (2008) however discovered that support for mathematical mark making was very rare, needing specific focus, as allowing children to develop their ability to extend and organise their thinking was defined as highly important. Williams (2008) commissioned recommendation four to highlight the significance of early years practitioners having specific mathematical mark making materials to support their professional development. Previous research into children’s mathematical graphics lays further emphasis on the value of these materials as Worthington (2008) expressed:
“The emphasis with children’s mathematical graphics is very
much on children making sense of the written language of mathematics
and effective pedagogy to support their thinking.” (Ibid 2008)
Worthington (2008) highlighted the importance of understanding how mathematical mark making could have dramatic effects on children’s learning, as allowing children to adopt their own form of mark making to symbols, will in future years, encourage them to combine their representations with that of standard mathematical symbols.
As children progress through the primary curriculum, it is clear how there is a logical pattern to teaching and learning. Williams (2008) stressed the significance of children receiving excellent teaching and a high quality curriculum: each relying on the other for successful learning. Furthermore, within the mathematic curriculum, Williams (2008) believed there to be a well-structured programme that took into account how to develop most children’s learning. From this, Williams (2008) proposed, under recommendation nine, that the primary national curriculum for Mathematics should continue as currently prescribed, subject to any changes proposed by Sir Jim Rose. On the other hand, however, Williams (2008) identified how the transition from Early Years to Key Stage one can lead to discontinuity in learning through attempts to match early learning goals to the National Curriculum. A preceding review to Williams’ (2008) report expressed the importance of smooth transitions, conveying further certainty of its significance. The Children’s Plan: Building brighter futures (2007) expressed,
“Smoothing these transitions will benefit all children and allow
each child to progress at a speed that best suits their needs while
they are adjusting to their new environments.” (ibid 2007 p.63)
The effects of this transition on children’s mathematical learning may generate significant problems, leading to a loss in interest, omitting the opportunity to develop good attitudes towards the subject.
Ensuring that a positive approach towards mathematics is a predominant feature, Williams (2008) outlined his key recommendation; a mathematical specialist in ever school. Engaging with a deep mathematical knowledge, the specialist would be central to effective teaching and learning, aiding quality instruction and intervention. The specialist would encompass attributes and characteristics that could advance mathematical learning, developing enthusiasm across the school. Continuing Professional Development (CPD) would incorporate a specifically designed programme, facilitating critical reflection on how to implement learning practices, and how to interrelate all strands of the mathematical curriculum. Williams (2008) also expressed how such programmes of studies could build upon complimentary Government aspirations, leading to the introduction of teaching becoming a Masters – level profession. Through greater access to valuable recent research into mathematics, the specialist would offer head teachers an array of opportunities to circulate effective practices and models of learning. Consequently, the mathematical specialist would become an invaluable constituent to primary schools; however, Williams (2008) needed to address the necessary training and professional development concerns. Williams (2008) proposed that mathematical specialists would receive an additional five days for Continuing Professional Development; however, the logistics could raise considerable barriers, and therefore still require further analysis.
Effective learning through curriculum and pedagogy are central to both classroom practice and teacher’s knowledge and beliefs. Predominantly, pedagogy should be learner centred; embracing models of learning that encompass a collection of technique and effective assessment. Implementing this is very much dependent upon the teacher and through Williams’ (2008) recommendation, in future years includes the mathematical specialist. Assessment for Learning (AFL) is a tool used within schools to establish the progress of all children, aiming to improve individual attainment levels. Allowing children time to question, as well as answer and try out their own strategies, ensure that assessment becomes a collaborative procedure, offering teachers an array of opportunities to develop children’s learning. From reviewing evidence of mathematical achievement, Williams (2008) concluded that it appeared there was no single cause for under attainment, consequently leading to no single answer. One solution adopted by the Government is intervention programmes, aimed at children who are failing to achieve the basics. Intervention occurs across the curriculum, through, as the National Strategy describes, the ‘three waves’ model. Wave one outlines the necessity for quality, inclusive teaching, targeted at all pupil’s needs. Wave two furthers this with group intervention, designed to accelerate the learning for particular groups of children expected to draw level with their peers. The individualised programme of intervention occurs during wave three, when teaching becomes specifically targeted and personalised. According to Williams (2008), the importance of intervention to the subject of mathematics, is paramount.
“There is a growing body of international evidence showing that
a carefully considered response to these problems of under –
attainment in mathematics can restore young learners to a successful
pathway for future study in the subject.” (Williams 2008 p.45)
Throughout his review, Williams (2008) put forward a strong recommendation for early intervention and under recommendation eight, outlined that children with serious difficulties should receive daily intensive one to one teaching from a qualified teacher. Previous research into early intervention can lay further significance on Williams’ (2008) recommendation. Dowker (2004) set out general principles outlining that intervention should ideally take place during the early stages of a child’s education, aiming to reduce the risk of negative attitudes. Subsequently, Williams’ (2008) review sincerely welcomed the new initiative – Every Child Counts (2008), a coalition partnership, between the Government and the charity Every Child a Chance, aiming to engage in the search for solutions for mathematical under attainment. The Every Child Counts (2008) programme is aimed at the lowest attaining Year two children, imposed at this stage, as it is believed to have maximum impact at a timely and practical period of a child’s learning. In January 2009, Ofsted released the publication, An evaluation of National Strategy intervention programmes, incorporating a small-scale survey concluding on the impact of intervention. Ofsted explained that:
“Intervention is most successful when confident leaders and well
organised teachers select from the National Strategy programmes
and develop a curriculum that meets the needs of pupils and the
circumstances of the school.” (Ofsted 2009 p.18)
Building upon this, Williams (2008) outlined that intervention should be led by a qualified teacher, generally involving one child, and incorporate the appropriate use of multi sensory resources and diagnostic assessment. Achieving this lays further emphasis on the importance of having well-trained teachers, with support from mathematics specialists.
Leading an intervention programme would require significant support from head teachers and senior management, but additional to this the child must be committed, supported comprehensively by parents. Although this encouragement and assistance should occur for all children during their educational journey, it has been made evident how parents can further aid a child with mathematical difficulties. Williams (2008) identified that parents often miss the opportunity to help their child, as they are not aware of current mathematical teaching methods. Addressing this, teachers and practitioners should encourage parents, bringing them up to date on how they can support. Furthermore, Williams (2008) expressed the imperative need for teachers to recognise the wealth of mathematical knowledge a child learns outside of school, therefore, aim to encourage parents to use this ‘out of school’ knowledge to participate in mathematical activities together.
Williams’ (2008) review of mathematics could implicate significant changes within the structure of primary education and training of new and established teachers. Having an extensive knowledge of how effective interaction and instructive teaching can extend children’s thinking, with particular attention to their use of accurate mathematical language, lays further importance of having highly qualified and skilled teachers. Furthermore, Continuing Professional Development, with predominant reference to mathematics, is essential; with Head Teachers ensuring teachers have many opportunities to progress. With regard to intervention programmes, it is clear how essential training may need implementing, with specific focus on Initial Teacher Training and Continuing Professional Development programmes. As intervention is more widely adopted across primary education, it may become apparent for the review of Initial Teacher Training courses, ensuring that all trainees experience an intervention programme.
With regard to my personal teacher training, the Williams (2008) review made it evident how securing curriculum knowledge and effective pedagogy is paramount in aiding children to achieve their potential. Building upon the standards outlined by the Training and Development Agency (2009) it is apparent how knowing and understanding relevant national strategy frameworks can aid with the execution of inclusive teaching, overcoming barriers to learning and assessment. Furthermore, with the proposed national roll out of the Every Child Counts (2008) scheme in 2010 – 2011, the Williams (2008) report would become of significant value to my teacher training and future career, providing substantial information about the importance of effective mathematical teaching, encompassed with a positive and enthusiastic approach.