Helen Hann considers how we can support children in the learning of maths from early years, by nurturing their emerging mathematical concepts and understanding
Esther usually does not comment or offer a response to mathematical questions in class. It doesn’t seem to matter if she is in a one-to-one situation or a pair or a small group, she just does not seem to feel comfortable mathematically.
Today her teacher was filling in the absence form of the class register, as she always did in front of the children. It was a familiar routine. The children knew that their teacher ‘counted the blobs’ on the register and sometimes asked them for help in working out how many children were away, how many here and other such variations upon simple addition and subtraction. Completely unprompted and in a loud clear voice, with a huge grin on her face, Esther called out: ‘That’s the “away” register and you’re writing down how many children are away. The other one is the “here” register.
That’s where you write down how many children are here. “Here” and “away”, “Here” and “away” [gesturing her hands up and down as if balancing them]. So everyone is on there somewhere … and that’s how you know what everyone is doing!’ She then laughed and giggled for several minutes.
According to the Cambridge Advanced Learners Dictionary, mathematics is ‘the study of numbers, shapes and space using reason and usually a special system of symbols and rules for organising them.’
There is a vast amount of research into how young children develop mathematical concepts. It is generally agreed that babies are born with an innate mathematical ability that they employ from a very young age as they attempt to make sense of their world. As early years leaders, we should promote this area of learning in a way that works in tandem with the child’s natural quest to understand the systems and principles, patterns and symbols of a mathematical world. It should reflect the way we manage ‘emergent writing’; the way we encourage it, develop it and give children tools at just the right moment, to help them on their journey to literacy, without squashing or cramping their initial motivation and passion for communicating a message with marks. Unpicking the example in the box above could help us establish some principles for developing emergent mathematicians.
Recognition and routine: Esther’s teacher clearly recognised that part of becoming a mathematician is using systems and logic to gain an understanding of a situation. Building these types of mini-routines into daily life at school and developing a team-wide grasp of why and how this constitutes real mathematics is crucial. Esther’s teacher had made the attendance system that she used very transparent to the children and mathematical discussion is common place in her classroom. It seems to be important that it is not just the number aspect but also the problem-solving aspect that is valued. Hence Esther had plenty of opportunities to observe, process and develop her own take on how it worked, and developed an awareness of mathematical meaning that was clear and accurate.
It should also be noted that developing the support of the senior leadership team when reviewing approaches to mathematical teaching and learning is of utmost importance. Likewise developing a clear understanding with parents/carers of what genuine mathematical understanding for a young child may not look like is integral to moving forward as a team.
A balanced approach: As early years leaders, we know the importance of intertwining academically rigorous challenge within a balanced range of inviting and motivating child-initiated, adult-led or child-initiated/adult-extended learning activities. Close observation and Assessment for Learning systems help us to have a very good reading of the ‘learning temperature’ of each child in each area of learning, including their level of wellbeing.
Knowing just when to introduce new skills, for example, recording of numbers, needs to be judged very carefully. Encouraging children to explain and record their mathematical ideas pictorially and symbolically is developmentally a very important step (see the example of Jonathan and Megan below). However, the timing of when and how to move children’s mathematical graphics1 towards traditional numbers must be pitched just right or we run the risk of moving numeracy forwards in one respect but hindering the problem-solving aspect of many children’s mathematical graphics.
In KS2 SATs, there continues to be a nationwide issue regarding children’s ability to solve problems systematically and logically, as well as difficulty in identifying general rules. Yet Esther at the age of four could do this, and so could Megan and Jonathan (see below). Could some of this be that somewhere in the mathematical past of the KS2 children, they have been moved either too quickly or slowly or not quite appropriately onto formal mathematical recording and that this has hindered or possibly not enhanced their mathematical potential?
This highlights how crucial it is for us to really understand what true mathematical understanding looks like and does not look like and our role in promoting it. As practitioners we are a good way along this journey but may need to sometimes check our route.
Jonathan and Megan were asked to help the ‘waitress’ (their teacher) lay the table and to help her to work out how many of each item of cutlery and crockery was needed for everyone to have a place setting. After being initially unsure, the children soon hit upon putting a whiteboard by each space, laying a place setting on it and drawing around each item. After doing this three times, they agreed with each other to count how many items were on each place setting and asked their teacher (‘the waitress’) to write down ‘number five, so we don’t forget’. They then told their teacher to write down everyone’s name and write a ‘5’ next to it. They then decided that just the first letter would do. Seeing this written down, the children then realised that if it was five items for everyone that they had to add ‘5’ ‘lots of times’. Megan then counted over each item on one place setting nine times; while Jonathan moved his finger from one initial to the next. Using this method in two stages they were able to work out that they needed 45 items in total and nine of each type. Their teacher’s scribing of their ideas helped to move their mathematical thinking forward dramatically.
- 1 – The term children’s mathematical graphics originated in the work of the Children’s Mathematics Network. The Network carries out leading research in early written mathematics.
- Carruthers, E. and Worthington, M. (2006) Children’s Mathematics: Making Marks, Making Meaning, London: Sage Publications (2nd Ed.).
Dr Anna Franklin, Surrey Baby Lab, Department of Psychology, University of Surrey, UK