Children's mathematical graphics: Making mathematical connections with their world

The future of early childhood mathematics and its inclusion in young children’s lives has become an important educative discussion for children under the age of five. In recent years, research has begun to include the importance of the multiplicity of languages for young children’s learning and development. One of the languages children use in the early years is children’s mathematical graphics revealing the importance of accessing, processing and expressing knowledge through symbols and images, and not words alone. These graphics signify mathematical meanings. Previously though, children’s graphics have been viewed as scribbles and critiqued as a developmental precursor to more mature and realistic drawings. Yet they represent powerful beginnings in children’s abstract thought and symbolism that help to create mathematical meanings. These are crucial for their mathematical trajectories, particularly for the more standardised written mathematical notation for school-based learning. Like children’s play, it is the symbolism expressed in children’s mathematical graphics that hold the key for adult’s understandings of how children access, process, and express mathematical knowledge. These reveal children’s lived experiences and their connections to familial, socio-cultural events and their physical world which mediate children’s mathematical thinking and their graphics. Recognising and valuing children‘s mathematical graphics with their embedded symbols and signs is critical to see children’s emerging mathematical conceptual knowledge. This learning is essential for 21st century living and learning, and for later professions such as engineering, science, technology, and economics.
This research study examined children’s connections to the mathematical world expressed through their mathematical graphics, and explored their graphical construction of mathematical conceptual knowledge. My study applies a conceptual framework based on Vygotsky’s Cultural-historical theory, Malaguzzi’s One hundred languages of children theory, and Bruner’s Representation theory to examine mathematical conceptual knowledge embedded in children’s mathematical graphics. Drawing on a cultural historical methodology and a dialectic-interactive approach, this study observed a group of 4–5-year-old children from an early childhood setting to reveal how children’s mathematical graphics highlight their acquisition and expression of mathematical conceptual knowledge to signify mathematical meanings. This methodology sees young children in relation to their socio-cultural and physical environments and how children minds orient themselves to the mathematical aspects of their world.
The findings show that many of the mathematical concepts children express include, positioning and movement, seriation, symmetry, parallel lines, one-to-one correspondence, classification, differentiation, size. Comparison, and spatial awareness. The study also found that children’s emerging use of the symbolic nature of mathematical concepts is an important steppingstone for children’s future knowledge of abstract nature of symbols and signs, important for written mathematics in school-based learning and beyond. The findings also show that children’s mathematical graphics help children to access, process and express both everyday concepts and scientific (mathematical) concepts, both important in supporting children’s construction of mathematical knowledge. Children’s mathematical graphics with or without a verbal description, is the starting point for children’s emerging mathematical thinking. This study highlights the connection between children’s mathematical graphics, their personal worlds, and emerging mathematical meanings. It reveals how children’s mathematical graphics and children’s everyday experiences allow children to access, process, and express mathematical concepts. Furthermore, it foregrounds the importance of children’s invented mathematical graphics for their emerging symbolism and cognition, critical for learning the standardised mathematical written notation required at main-stream schooling.