Are We Aware of Babies’ Scientific and Mathematical Thinking? By Elizabeth Carruthers

Dr Elizabeth Carruthers is a researcher and author. Her main research interests are leadership, teacher practitioner research and she has published extensively on early mathematics. Her work on Children’s Mathematical Graphics along with her co-author, Dr. Maulfry Worthington, was recognised by the Department of Education, Williams Review of Early Years and Primary Mathematics. Elizabeth was a teacher in primary and early years education for over 30 years and was privileged to work as a head teacher of a Nursery School and Children’s Centre for 12 years. She is an advocate for children’s rights and practitioner/teacher research. She is proud to announce the recent birth of her first grandchild who is delightful and she is enjoying every minute she can with him.

Are We Aware of Babies’ Scientific and Mathematical Thinking? By Elizabeth Carruthers

When I was at school, science and mathematics were subjects that most people disliked. I also found aspects of these subjects disinteresting. It was not until I became a teacher and began closely observing young children engaging with scientific and mathematical concepts that I realised how powerful they were in stimulating thinking.  In this blog, I put forward that babies’ early experiences in science and mathematics are part of a strong foundation for their cognitive development. I argue that early years’ practitioners have a vital role in understanding the mathematical/ scientific worlds of very young children to enhance learning opportunities.

Many early year practitioners and teachers in baby and toddler rooms already provide wonderful heuristic play, including treasure baskets. They also know about children’s schematic development (Athey, 1990) and many of children’s schemas are mathematical (Carruthers and Worthington, 2006) and scientific (Nutbrown, 2011). Knowing about children’s schemas and heuristic play are part of the firm foundations to build on the teaching practice of science and mathematics.

Babies have the right to make decisions for themselves, take risks and be challenged

Bristol Early Years’ Best Practice Hub

There is a wealth of literature on supporting very young children’s emotional and care needs and ‘looking after’ babies. However, research with babies has revealed that babies know more and learn more than previously noted (Kuhl, 2011). In understanding more about babies ever growing acumen to subjects, like science and mathematics, L’ecuyer (2014) expresses that early years practitioners need to consider, as well as emotional attachment, an ‘intellectual’ bonding with babies and toddlers. Stimulating the cognitive side of babies’ brains helps them thrive, it feeds their intellectual curiosity.

One of the rights of babies that the Bristol Early Years’ Best Practice Hub espouses is ‘Babies have the right to make decisions for themselves, take risks and be challenged’. 

Supporting children’s experiences in mathematics and science is a crucial way that early years teachers and practitioners can cognitively challenge babies’ thinking.

What science and mathematics do babies explore?

Young babies, as soon as they are born, behave like scientists and mathematicians as they examine their new surroundings. At two weeks old, a baby‘s gaze detects space and light, and when they move, they feel the space around them. As they develop, they explore objects at first, through their mouth, and they begin to find out about the properties of objects, for example, shape, corners, roundness, and smoothness.

For babies, mathematics and science experiences are often interconnected as they explore their real worlds. Babies’ laboratories are their homes, nurseries and communities where they busily investigate everyday experiences. As they grow and begin to move, their world expands, and they have more choices in what they engage with. The EEF evidence store states that ‘research shows toddlers engage spontaneously with maths during nearly half the time available for free play’.

Photo by Helena Lopes

Children are naturally curious about how things work which leads to them hypothesising about their experiences. For example, I observed a 9-month-old baby in his highchair, eating his dinner and also learning about spoons and how you hold them. He judged the distance between his mouth and the plate as he attempted to scoop up his food and put it in his mouth (spatial awareness). He put the spoon to his mouth and held it in his mouth without his hands. It appeared he found this interesting, watching the spoon handle project from his mouth as he looked at the length of the spoon from an unusual angle. By accident, he found out that if he put his hand on the spoon handle and quickly let go, it reverberated. He was surprised and delighted by this discovery. He may have wondered, if I do this again, will the same thing happen (hypothesising)? He repeated his actions, and the spoon reverberated again.

It is interesting to note that babies are attracted to real objects more than shop or online bought toys. They like pushing the buttons of the remote controls of the television and opening and closing cupboards. Car keys fascinate them as they enjoy the sound, touch and weight. I was talking to a mum with baby twins recently, and she said, “It is the things that are not toys that are the most interesting.” Perhaps this is so for two reasons:

1.There are more properties to real, everyday objects, such as different textures, sounds and heaviness. This makes them much more interesting than shop-bought toys, which are often plastic and, therefore, usually only have a smooth surface.

2. Every day and ‘real’ things are part of babies’ cultural world where their family and those close to them use these objects, and they are curious to know more about them.

Going outside

Photo by Daiga Ellaby

Outside can offer a myriad of real experiences for science and mathematics for babies and toddlers. For example, walking on different surfaces like cobbles, grass and stones, experiencing the shape of these on their feet. Being outside with children can generate unexpected happenings, like an aeroplane passing overhead and this can lead to how things move in different ways. It also brings into focus the sky and clouds, another source of wonder.

The weather offers opportunities to see how natural occurrences can change  situations. For example, feeling the wind and noticing how it blows the leaves around and how their hat can blow off their heads and umbrellas blow inside out. Toddlers notice the puddles after it has rained and love the experience of walking through them. Comments about where the puddles have disappeared can add to children’s emerging ideas about condensation.

Toddlers especially like collecting ‘stuff’ on walks such as leaves in autumn and petals from flowers which are all scientific wonders. Often young children will find a stick or a stone which will become a favourite to keep. Early mathematics focuses on quantities (DfE, 2023) and as children gather natural materials they are also engaged in thought about quantities. The receptive adult, for example, might start to count with them or point out to a child, “now you have two leaves”.

Expressive arts and design

All areas of the EYFS (DfE, 2023) have significant learning opportunities for

science and mathematics. For example, Art and design is an area where there are great possibilities for children to nurture their scientific and mathematical inquisitiveness. Through exploring materials, like paint, paper, different textures, flour, gloop and string etc., children are on an intellectual journey, especially when they mix materials and notice change. Matthews’ seminal work (2003) stresses that children, when they begin to draw, make a systematic investigation, which is mathematical and scientific. When children mark- make they discover line and form through drawing enclosures, dots, arcs, core and radial and zig-zags. 

Knowing the child’s world

Johanssen (2004) affirms that knowing the child’s life world is vital and this involves trying to understand the child’s whole being by observing, listening and responding. Children cannot be separated from the life they live and the everyday situations in which they are involved. Similarly, mathematics and science are not separate subjects from the young child’s world. They are connected to each other and integrated into children’s lives. Adults, therefore, need to view the science and mathematics of children as different from the traditional school learning of these subjects. We will learn babies and toddlers’ mathematics through them, by observing, authentic listening and sensitively responding. Instead of saying “we are going to do mathematics and science with the children” it is beneficial to observe them as they play and follow their intentions and the learning encounters that may happen and identify the mathematics and science within them.

Mathematics and Science subject knowledge

Bruns et. al. raises the issue that early years’ teachers lack of subject knowledge of mathematics (and science) may affect their ability to facilitate mathematical/scientific learning in early childhood settings. This is confirmed by the EEF evidence store which stresses that early years’ practitioners and teachers ‘must have knowledge of maths itself’ to provide effective mathematics pedagogy. For example, do we see the explorations of babies and toddlers as mathematical and scientific?  When babies pick up a carboard tube and look through it. Do we observe it just as a babies’ curiosity or can we see the connections to science (testing materials that you can see through) or mathematics (experiencing the properties of a hollow cylinder). Can we plan science and mathematical experiences from these kinds of encounters with babies? Perhaps we could provide a variety of cylinders and more objects to look through, like glasses and coloured paper, to extend the children’s line of thought. If you are an early years’ practitioner working in a baby room or/and toddler space and you feel you do not know about the possibilities of science and mathematics that babies may be engaging in, collaborate with colleagues and discuss your reflections. As Beeley (2012) reminds us, you cannot know everything, and you probably know more than you think you know. There are very few books that concentrate solely on science and mathematics for babies and toddlers; however, you may find Brunton and Thornton‘s (2009) book useful as it refers to babies and young children. Beeley’s (2012) book also has some specific references to babies and toddlers.


Babies and toddlers have a natural urge to explore the scientific and mathematical phenomena of their world. Adults working with very young children, therefore, play a very important role in ‘intellectually bonding’ with them. This means early years professionals authentically listening to children and setting up experiences, based on their knowledge of young children’s latest enquiries. It also means bringing new scientific and mathematical experiences to the children. Finally, going outside with children adds an important dimension to their scientific/mathematical worlds. A walk to the park can be an adventure which uncovers many scientific and mathematical treasures.


EEF Maths on Evidence Store:

  • 3. Teaching children problem-solving skills for maths: teaching and modelling problem-solving skills including effective ways to apply purposeful thinking;
  • 4. Teaching and modelling how to make comparisons and connections: encouraging sorting collections into groups and promoting recognition of attributes that can also support with identifying and building patterns and sequences; and
  • 5. Facilitating mathematical language: intentionally using specific, informal, and formal mathematical vocabulary in context to develop children’s understanding of concepts (receptive) and explain their ideas (expressive).

Athey (1991) Extending thought in Young Children. London. Sage.

Beeley (2012) Science in the Early Years. London. Bloomsbury Publishing.

Bruns J. Eichen L. Gasteiger H.  (2017) Mathematics-related Competence of Early Childhood Teachers Visiting a Continuous Professional Development Course: An Intervention Study, in Mathematics Teacher Education Vol. 19.3, 76-93

Brunton P. and Thornton L. (2009) Science in the Early Years: Building Firm Foundations Birth to Five. London.Sage. 

Carruthers E. & Worthington M., 2006 Children’s Mathematics: Making Marks, Making Meaning. London. Sage.

DfE (2023) Early Years Framework–2

EEF Evidence Store (2023)

Bristol Early Years

Johansson, E. (2004) Learning Encounters in Pre-school: Interaction between

Atmosphere, View of Children and of Learning. International Journal of Early Childhood, 36(2): 9-26.

Khul, P. (2011) Who’s talking? Science,333:529-530

L’Ecuyer, C. (2014) The Wonder Approach Robinson publication

Matthews, J. (2003). Drawing and painting: Children and visual representations. Paul Chapman.

 Nutbrown, C. (2011). Threads of Thinking: Schemas and Young children’s learning. Threads of Thinking, 1-216. London. Sage.

Join Our Mailing List

Please sign-up to our SPH mailing list so that we can keep you informed of developments and opportunities.

🔔NEW: Kerry Murphy's Curiosity Circle Webinars
📢 New Blog Post: The Magic of Emerging Literacy in the Early Years by Ali Carrington