Getting to grips with maths: your child’s journey
There is a lot that we don’t know about the development of mathematical understanding. Much more research has been conducted into language development, for example. However, we do know that all children are born ‘ready for mathematics’ - even infants understand the fundamental mathematical concept of ‘more’! We also know that preschool mathematics, especially an understanding of numbers, predicts later achievement in school and enhances life choices. Once children fall behind in mathematics, they continue to do so throughout school. Yet just as with the development of writing, the focus in the early years should be on laying secure foundations, rather than racing to ‘get ahead’.
Researchers have shown that a person’s ability in maths is a combination of natural aptitude and the quality and quantity of opportunities to engage in early mathematical activities. We know that mathematical ability or difficulty is likely to be inherited – extreme giftedness does run in families. Yet interestingly, research suggests that genetic levels of ability in reading and maths are probably linked. If you are very good at one and not very good at the other, this is likely to be due to environmental factors and early experiences.
Early experiences of mathematics need to be regular, varied and enjoyable
Early experiences of mathematics count and they need to be regular, varied and presented as being as enjoyable as hearing a story, painting a picture or riding a bike. Unfortunately many children acquire maths anxiety from a very young age, either from the adults at home or at nursery. This is because it is culturally acceptable in the U.K. to be negative about maths, in a way that we don’t talk about other life skills. People may declare, almost proudly, that they ‘can’t do maths’, whilst it is very rare for someone to announce that they can not read. Neuroscience tells us that anxiety about maths interferes with processes in adults’ and children’s brains, and thus interferes with their learning. So a crucial element of laying strong mathematical foundations in the early years is spending time with adults who confidently weave mathematical experiences into the day and present them as exciting and enjoyable.
What effective preschool teachers of mathematics do
In the early years, mathematics involves introducing the concepts of numbers and counting, shape, space, measure and patterns in real life experiences and providing children with the language to talk about these concepts. The Early Childhood Mathematics Group says that “Opportunities for mathematical learning can happen anywhere and should be practical wherever possible”. In a nursery setting, singing nursery rhymes and playing games that involve numbers, as well as routines such as snack time, tidying and registration are authentic opportunities for mathematical learning. The mathematics in these contexts are meaningful to the child and provide them with a reason to problem-solve. Effective preschool teachers model mathematical behaviours throughout the day by thinking aloud and verbalising what they wonder, what they notice, the patterns that they see and the connections that they make. They also use mathematical vocabulary and support children to include standard symbols in their representations when appropriate and in meaningful contexts, such as keeping score in a game. Research shows that children’s ability to see patterns forms the basis of early mathematical thinking. Young children should be exposed to patterns in speech, nursery rhymes and songs, routines of the day, calendars and visual patterns both in the natural world and man-made materials. When children are taught to become aware of patterns, they will build up the skill of spotting patterns for themselves, see how patterns change and notice irregularities.
The foundation of all mathematics is counting
Even when children can not count reliably beyond the first few numbers, they can tell when adults make mistakes in counting aloud. Early counting is more like a song or poem, learned by rote, rather than a system for finding out ‘how many’. And although it may be impressive to hear a 2.5 year old count to 50, it is more important to acquire a greater depth of understanding of numbers from 1-10 so that preschoolers can:
Understand the value of numbers to 10
Understand number symbols
Understand the relative values of numbers (e.g. “3 is a greater number than 1”)
Subitise, which means recognising small numbers of things without counting them
Count out the number from a group
These are vital developmental stages, without which children will not be able to move much further into the world of calculation, shape, space and measurement.
In their early years, children should be encouraged to use their fingers for counting. Interestingly, the use of the index figure to count objects is a key feature in most cultures across the globe, suggesting that it is intuitive. We now believe that counting on fingers is a very important stage in learning about numbers, counting and early calculation.
Practice, practice, practice through play, play, play
To make progress in any aspect of mathematics, and particularly in understanding calculation, children initially need copious amounts of practice in manipulating real objects and substances. That’s why it is so important that an early years educational setting is a maths-rich environment. Instead of having a ‘mathematics corner’ or table, a nursery should provide a wealth of experiences of ‘more’, ‘less’, ‘add’, ‘subtract or take away’, ‘divide or share’ and ‘multiply’. Group activities, such as cooking, water play and den-building provide a good foundation for counting and calculation, if the adults take natural opportunities to talk about maths and use mathematical vocabulary during the activity. Large-scale outdoor resources such as water play, physical play, construction/blocks, loose parts, role-play and number tracks support important early mathematical learning. Having scales, timers, clocks, measuring tapes and calculators available for children to play with provides opportunities for foundational concept development long before children are expected to use this equipment accurately. In mathematics, just as in all other areas of development, learning through play is most effective.
We know from research into how children learn mathematics that adults must not move too quickly towards recording mathematical calculations in pictures or numbers. This is because children can easily lose their fragile grasp on the mathematical concepts and the activity can turn from a mathematical adventure into a writing task. Interestingly neuroscience tells us that ‘manipulatives’, drawing tools and much of the other equipment available for early years mathematics should be available until at least the end of primary school and probably into secondary years, until every individual’s brain is sufficiently well-developed to have established the permanent connections necessary for abstract mathematics.
Supporting your child’s journey at home
You can make a big difference simply by being a good mathematical role model, regardless of your confidence with mathematics. Let your child see you using maths in your daily life and think out loud if you are doing any simple calculations in front of them, such as comparing prices in a shop, looking at the weather forecast or finding the biggest saucepan.
You can also try to find ways to make it a fun part of your children’s lives and show them that maths is everywhere. For the youngest children, sing nursery rhymes and read books that involve numbers and find opportunities to count out loud to them. With preschoolers, ask your child to help you measure ingredients when cooking, divide up special treats with friends, draw their attention to written numbers in your environment, play games like ‘What’s the time Mr Wolf’ or identify opportunities for children to see subtraction and addition in real life. Make a game out of spotting patterns together and encourage your child to spot them too.
However, by age 3, the biggest difference you can make to your child’s experience of early mathematics is to ensure they enrolled in a nursery or preschool which has a maths-rich environment and curriculum.
“At Two Hands Preschool, we know children won’t learn well unless they enjoy learning. We are confident that our educational approach, which is grounded in the latest research in early years learning and has play and rich experiences at its heart, will set your child up to become a confident mathematician”
