Copyright - permissions
Our work represents
over 20 years of original, in-depth research and the
content of this website and all our publications are
covered by copyright. We respectfully request
that anyone using the terms ‘mathematical mark
making’ or 'children's mathematical graphics',
or wanting to use or in any way copy or reproduce
any examples of children's mathematical graphics,
graphicacy or photographs, or use or
reference our work
- in any
- on any taught
course, seminar or presentation or;
- on any website
our research, publications and this website, and
includes both our names.
With the exception of
personal use, all other reproduction is prohibited
without permission from the authors, E. Carruthers
and M. Worthington & their publishers, or from the
web editor, M. Worthington.
We originated the term children's mathematical
graphics (see for example,
Worthington & Carruthers, 2003a,
2005, 2006) to describe
the range of children's own mathematical marks and
representations (graphicacy), identified from the
hundreds of examples we collected and analysed from our
teaching in the birth - 8 year age-range and from examples
collected for our research, from children in their homes,
nursery and schools. We continue to
and to present our
research and to provide professional development support. We
are also founders of this international Children’s
Mathematics Network with members throughout the UK and
around the world
Carruthers, E. and
Worthington, M. (2003a) ‘‘Making sense of mathematical
graphics: the development of understanding abstract
symbolism’. Paper presented at the European Early
Childhood Education Research Association (EECERA)
Conference, September 2003 at the University of Strathclyde.
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).
Worthington, M. & Carruthers,
E. (2003b), Children’s Mathematics, Making Marks, Making
Meaning. London: Paul Chapman Publishing.
Carruthers, E. & Worthington,
M. (2006) 'Children's
Mathematics, Making Marks, Making Meaning'. London:
Sage Publications, (2nd Ed.).
to this research
We were the first to analyse and chart
children’s mathematical graphics which we show through
Our work is regarded as
seminal in the field and is
independently acknowledged. Our publications are used
throughout universities as key texts, and our research is
used on courses for mathematics education and on courses on
symbolic representation relating to literacy and numeracy.
It is cited in the
Review (2008: p. 4 & p. 34-37) and in the
RECME research (NCETM,
2008) and included in several government publications,
including a forthcoming document Children Thinking
Mathematically, Problem Solving Reasoning and Numeracy in
the EYFS (DCSF, 2009).
the 'Williams Maths Review' / 'Children Thinking Mathematically'
'Mark Making Matters' (DCSF, 2008)