The language of Mathematics (part one)



Steven White is the Nursery Manager at Tiptoes Nursery and an education consultant in Outdoor education, with 13 years of experience in childcare and early years education. In this blog, he shares his insight with us into how children's natural curiosity can be nurtured to support the development of maths skills and confidence in maths. Look out for part 2 coming soon for further discussion on the Language of Mathematics, and ideas on how practitioners can encourage children to engage with the maths all around them.  

The language of mathematics

Boy aged 4 exploring the riverIn a world where Mathematics surrounds us daily and talks with us regularly, why have we become deaf to this language? I am often asked “How do you do Maths outdoors?” in response I say “Possibilities are endless, and one must ask themselves, what opportunities for Mathematics (Maths) does this experience make?”  

Boy, aged 2, explores dry sandThe best resource for Mathematics is within the creative mind of the practitioner: through coaching and nurturing, a connection to this language can be created to engage our Children in the Maths that surrounds us and is within us.

“…when an independent approach to mathematics is encouraged and nurtured, and children are licensed to consider a range of possibilities, they discover and absorb more about mathematical concepts and attain more than their perceived best.”

(Carruthers and Worthington., 2003)

My eldest son (aged 2) was enjoying his time on the golden sands by St. Andrew’s beach, engaging with his environment (loose parts) he began to manipulate the sand as he attempted to build a sand castle. He attempted this approach several times and stopped when he theorised “sands are blowy and won’t stay for a castle”. Sometime later, that same day, he began exploring wet sand and picked it up, squishing it, changing its form. He started processing his thinking as he explored the sands properties, and based around his previous experience of the dry sand earlier he commented “it’s sticky to build a castle”. With the help from his Granddad together they built a sand castle fort. 

Boy, aged 2, explores wet sandThis is a perfect example of allowing free flow to occur, and how it is more beneficial to allow problem solving creativity to happen, rather than simply completing a task where the outcome is the sole motivation for success. Huge learning opportunities presented themselves throughout this experience, and this is where we begin to go beyond the guidance of a curriculum, allowing expansion through the endless possibilities that interests can nurture. Mathematics should be responsive to children’s interests, in keeping with something that is meaningful to them.

Den building presents many possibilities for mathematics through problem solving Den building presents many possibilities for mathematics through problem solving (Children aged 3-5 - see photo)

“Problem solving is an important way of learning, because it motivates children to connect previous knowledge with new situations and to develop flexibility and creativity in the process. Therefore, it is important that children see themselves as successful problem solvers who relish a challenge and can persist when things get tricky.”

(Dr Sue Gifford)
Den building, children aged 3 - 5

What does problem solving look like for Children? A problem in the simplest term, is anything you don’t know how to solve. If a Child is told how to solve the problem, then no learning is taking place. How often have we done this in our own practice, or, noticed it in the practice that takes place around us? Some experiences may be easier to solve for one child but not another.

A young girl explores chicken feedAlternative solutions

A sum: There are 30 bags of feed in the Chicken feed store

8 bags have been eaten, 6 have become damaged in the rain

How many bags of feed are left in the store?

The answer is 16!

The point of this exercise is to think about how we came to the answer. This becomes of more interest (to myself at least) than the giving of the final answer.Children aged 0-2 years Some of us may have had to make a quick mental conclusion, whilst others may have used their fingers and toes, sticks or stones, pencil and paper, whilst for others the calculator on our mobile phones may have been the favoured choice of the day.

One day we were (3-5-year-old Children) down by the local river, and we came across a collection of stones, the stones had been stacked one on top of the other. Observations had been made from the practitioners, that the Children in our group came to count the stack of stones using 5 different concepts of counting.


  1. Stones stacked by a riverOne to one principal: match counting words to each stone tagged

  2. Stable order principal: counting words are in order no matter where the Child started from in the stack of stones

  3. Cardinal principal: the final stone counted represented the number of stones in the stack

  4. Abstraction principal: a few sticks had been added and they were included in the count of all that was stacked, not just the stones

  5. Order irrelevance principal: the order in which the stones were counted did not affect the Cardinal number


A young girl takes part in cake makingThis experience of alternative solutions is a rather complex one to record. So how can we replicate it in our settings, when access to a river is almost impossible? This experience actually occurs every day in our settings, and it’s the time where we set out our tables for lunch time. Two Children in our 3-5 room, asked to help set out two tables for the group to sit between. One Child counted the seats set at the table and then counted and placed out a plate at each seat. The other Child stacked more plates than there were seats and said “there’s more plates than seats so everyone can help themselves and they will have a plate for lunch”. Both accomplished the desired outcome through alternative solutions.

Carr et al (1994) highlights 3 concepts that we should consider when planning for problem solving and creating good problems:

  1. Familiar contexts
  2. Meaningful Purposes/Outcomes
  3. Mathematical complexityA young girl cuts her birthday cake

Young girl blowing out candles on her birthday cakeAn example of these concepts in action would be: a Birthday occurs in our 3-5 room, the Child requests to make a Birthday cake and engages in this. The cycle of making the cake to eating the cake, provides several opportunities for Mathematics to occur. There is a familiar context for the Child, the outcome matters to them, controlling the making of the cake the final outcome is achieved, done so through a Mathematical experience where they are confident.  Subtracting, dividing, fractions, time, measurement, weight etc. are all being experienced through a context that matters to the Child, whilst subtly providing Mathematical complexity throughout.




Look out for part two of Steven's blog, coming soon. 

Further Information

If you're interested in finding out more about engaging children with maths through play, you might like the Alliance publication, Discovering Maths through Play.

Find out more about Steven's setting Tiptoes Nursery here

Visit the Tiptoes Nursery Facebook page here

Read more from Steven on his blog here