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    © Copyright M. Worthington & E. Carruthers 2012

The Williams Maths Review - please scroll down for details

Official recommendations on children’s mathematical graphics - (for teachers and practitioners in England):

DCSF, 2009. Children’s mathematical graphics focus of chapter 3, and threaded throughout (booklet written by Elizabeth Carruthers & Maulfry Worthington, (excepting p. 47-50).

The introduction to Children Thinking Mathematically states:

 ‘A local education authority advisor, involved in raising the profile of calculation through supporting reception class teachers in their understanding of children thinking mathematically through their own graphics, stated, “Maths is much higher profile now. Teachers and practitioners are talking about calculating significantly more; boys are representing mathematics and are extending themselves much more. This has had an impact on the way in which teachers and practitioners work: their expectations of the children are much higher.”

The Williams Maths Review

   The Williams review (DCSF, 2008a) also stressed that effective Early Years pedagogy should value and support children’s own mathematical graphics. Children’s own mathematical graphics help them understand the written language of mathematics and how it can be used’ (DCSF, 2009: 5). 

The Williams Maths Review, DCSF, 2008a. Children’s mathematical graphics featured in Chapter 3 and in Recommendation 4 of the final report.

Chapter 3: The Early Years

115. The EYFS guidance stresses the value of children’s own graphic explorations, and it is common to see children from an early age making their own marks in role-play to communicate or act out activities they observe in adults, such as writing letters or making lists. It is comparatively rare, however, to find adults supporting children in making mathematical marks as apart of a developing their abilities to extend and organise their mathematical thinking. While ‘emergent writing’ is a recognised term, that is not the case for ‘emergent mathematical mark-making (Ref. 20.). (See below for ‘Emergent mathematics’ ).This misses a valuable opportunity to encourage early experimentation. The role of mark-making in children’s cognitive development is set out in the taxonomy below. Early years practitioners should encourage mathematical mark-making and open-ended discussion in children’s mathematical development.

p. 37: Implementation of effective early years mathematical pedagogy

119. To secure effective pedagogy, local authorities, leaders, managers and head teachers should provide the following key elements of support in order for all settings to develop the conditions for learning:

  • A preliminary audit that supports the identification of strengths and areas for development within a setting
  • A review of the mathematical learning environment which enables staff to monitor and evaluate resourcing and organisation for problem solving, reasoning and numeracy
  • Examples of effective and good practice through modelling, demonstrating and coaching in order to enable settings to enhance the quality of their learning and development in problem solving, reasoning and numeracy
  • Models of open questions and discussions and a mathematical language list to support staff in their dialogues with children
  • A culture with a significant focus on mathematical mark-making in line with early writing through, for examples, role play and the use of popular mathematical signage in the environment
  • A learning environment that encourages children to choose to use their own mathematical graphics to support their mathematical thinking and processes

References in final report:

20. Carruthers, E. and Worthington, M. (2006) Children’s Mathematics: Making Marks, Making Meaning. London: Sage Publications. Second Edition.

21. Carruthers, E. & Worthington, M. (2005) ‘Making sense of mathematical graphics: the development of understanding abstract symbolism’ European Early Childhood Education Research Association Journal, (EECERA) Vo 13, No.1 (pp. 57 – 79).

Emergent Mathematics’?

  • Writing and written mathematics are not the same - the subject content, the children's thinking about writing’s symbolic language and the ways in which they are represent their ideas are inherently different. In ‘emergent writing’ children are focusing on the letter-symbols and their relationship with sounds and words, and on spelling, punctuation and handwriting. When writing, letters are gradually used to build words that together communicate meanings about content.
  • In mathematics children focus on quantities, numerals and other mathematical symbols. This helps children build their understanding of the abstract written language of mathematics including calculations, ways of representing data, measurement and space and shape though their choices of using a range of personal marks, symbols and representations. Children’s own mathematical graphics helps them think about and communicate their mathematical thinking.

Although children’s mathematical graphics have been compared to ‘emergent writing’ they are not the same. However, emergent writing and children’s mathematical graphics share one aspect in that in both of these symbolic languages children make and attach meanings to the graphical marks and symbols they use.

Origin

Practical mathematics

Challenges for children

Mark Making

Recording?

'Mark Making Matters' (DCSF, 2008)

Pedagogy

Publications

References

 

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