Who is listening to children’s mathematics?
by Elizabeth Carruthers and Maulfry Worthington
Oliver explained his sign for their pretend car park: “These are ticks. When there are three ticks you can go, when there are two you can’t go that way. I’ve made two ticks, that means you’re not allowed."
There needs to be a crucial focus in early mathematics teaching which concentrates on the wealth of mathematical knowledge children bring to nursery and school. However, in early childhood curricula the beginnings of ‘written’ mathematics are seldom addressed. Many early years settings still use worksheets, where the main task is often colouring in quantities to match to a number, and sheets of numerals to trace or copy. Whilst such activities may look like mathematics, an unintended consequence of working in this way leads to children's superficial understandings of the abstract written language of mathematics.
Children have their own ways of communicating their mathematical thinking: the problem is that children’s mathematics is not heard for three main reasons.
The standard mathematics curriculum takes over and there is no space afforded for teachers to listen and acknowledge the children’s ways of knowing mathematics.
Mathematics in early years settings and schools is often from an adult-centric perspective. Teachers seldom take notice and respond to children’s mathematical ideas. Teachers need to know the children well, not just as a group but individually. The importance of the key person’s role in tuning into children’s ‘funds of knowledge’ (Moll et al. 1992 )is crucial. Funds of knowledge are the understanding of mathematics that comes from children’s homes and community cultures, this would include their everyday knowledge of mathematics.
Educators often lack knowledge of children’s emerging mathematical ideas and the ways they form mathematical signs and symbols. There is not enough professional development and professional literature on this subject for teachers to access easily.
Teachers sometimes find it difficult to move to more democratic practices in mathematics, especially those who are rooted in strict mathematics teaching regimes. However, we have found that this is not the same in literacy and language teaching where early years’ educators, for the most part, always seem to be seeking ways to encourage children’s creativity and freedom to write their own ideas. Perhaps it is because mathematics, as a subject area, is viewed differently. Educators might see mathematics as a formal subject with only right or wrong answers.
A significant factor is the extent to which children have agency to communicate their mathematical thinking in their own ways, in contexts that are personally meaningful. In England this is not something that is acknowledged or understood by Ofsted, or any official curricula documents. Understanding of young children’s own early beginnings with the graphical signs and symbols of mathematics is sorely needed. Article 13 of the UN Rights of the child (1989) states:
“Every child shall have the right to freedom of expression; this right shall include freedom to seek, receive and impart information and ideas of all kinds, regardless of frontiers, either orally, in writing or in print, in the form of art, or through any other media of the child’s choice.”
In socially interactive and open contexts such as pretend play, children have agency in their learning through their play and explorations, and are free to build on and cultivate their own knowledge in partnership with their families, peers and teachers. They are active learners in all aspects of their learning and understanding, their skills of mathematical literacy developing over time.
Both oral and graphical languages are communicative, and are socially learned. As with spoken language, toddlers and young children watch and listen to adults and peers as they use graphical marks and signs, gradually building understanding of how they are used. Socially interactive situations allow children's growing knowledge and understanding of the culture of mathematics to develop through dialogue and graphicacy.
Sensitive adults and peers respect young children’s early graphical marks and signs as meaningful, valuing what they do, their communicative interactions supporting children's developing confidence in their use of graphicacy to communicate. Understanding and learning emerges, children developing over time to become proficient users of graphical, alphanumerical languages.
Early beginnings of the graphical language of mathematics often reveal complex thinking and are very easily missed. Our research reveals that democratic and open learning cultures empower children, allowing their self-initiated choices, interests and decisions, and fosters agency to communicate their mathematical thinking though their Mathematical Graphics.
Our findings imply that early childhood curricula and policies should acknowledge the importance of children’s own graphical signs and symbols, and the significance of spontaneous pretend play.
Our research proposes that a shift is needed in moving away from adult perspectives in mathematics, to authentically listening and noticing children’s own mathematics and their mathematical cultural knowledge.
About the authors
Elizabeth and Maulfry are the originators of Children’s Mathematical Graphics and have researched this important aspect for more than 30 years. Their seminal work ‘Children’s mathematics: Making marks, making meanings’ (2nd edition, Sage, 2006) continues to win much acclaim and was highlighted in the Williams Mathematics Review (DCSF, 2008), and they were commissioned by the government to write ‘Children’s mathematical thinking’ (DCSF, 2009). They have published extensively, and their work is internationally known.
Elizabeth Carruthers has taught in schools in England and the United States. She has worked in the advisory service as an early years and numeracy consultant. Elizabeth was the Executive Head of a Nursery School and National Teaching School. Her Phd is titled, The Pedagogy of Children’s Mathematica Graphics: Teacher Perspectives (2022). Recent publications include:
Carruthers, E. (2023). Early Years Teachers Perspectives on their Pedagogies of Play and Mathematics. Impact Journal. Issue 19
Carruthers, E. (2020). Mathematical teaching in nursery schools in England: Pretend play and democratic pedagogies. Review of Science, Mathematics and ICT Education 14(2), 25-41.
Maulfry Worthington taught children from 4 – 8 years of age for many years, and in addition to lecturing in higher education, was a numeracy consultant, and worked as an e-learning facilitator at the National College for School Leadership, managing early years online communities. Her PhD focused on the emergence and development of young Children’s Mathematical Graphics, explored through their spontaneous pretend play. Recent publications include:
Worthington, M. (2018). Funds of knowledge: Children’s cultural ways of knowing mathematics. In V. Kinnear, M-Y Lai & T. Muir (Eds.), Forging connections in early mathematics teaching and learning (pp. 239-258). Springer.
Worthington, M., & Van Oers, B. (2016). Pretend play and the cultural foundations of mathematics. European Early Childhood Education Research Journal 24(1). 51-66.
For full details of our work, see: The Children’s Mathematics Network: www.childrens-mathematics.net