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. 4750). 
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 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 roleplay 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 markmaking (Ref. 20.). (See
below for ‘Emergent
mathematics’ ).This misses a valuable opportunity to
encourage early experimentation. The role of markmaking in
children’s cognitive development is set out in the
taxonomy below. Early years
practitioners should encourage mathematical markmaking and
openended 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 markmaking 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 lettersymbols 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 