5,6,7,8 - supporting maths development
Many of us are frightened of maths. Our memories of it from our own childhood can be traumatic and it fills us with dread. Over the years, many practitioners that I have worked with have shied away from maths activities with children and any interaction that could involve maths, usually concerned with asking questions about numbers, shapes or colours! The EYFS outcome for numeracy is one of the top areas where children are not achieving. This is a worrying trend.
“Being bad at maths” is a very common saying and attitude. It doesn't seem to be an attitude that concerns us, it is almost socially acceptable and this perhaps, leads all of us into perpetuating a lack of confidence and competence regarding mathematics with our youngest children. We therefore, need to be positive about maths around children and to model the attitude that maths is important and it is possible for all of us to develop good mathematical skills. We need to equip our children with a “can do” attitude regarding maths.
Learning about maths begins from birth as children explore the world around them. As they develop, they are supported in their learning by the people around them. The environment is a rich resource for engaging with mathematics, especially when it provides opportunities to listen to and use mathematical language and to engage in mathematics with everyday experiences. Through the assistance of others, children’s attention and activity are directed in ways that enable them to reason and to grow in their abilities to communicate mathematically. As they do so, they develop an affinity with mathematical tools and they take pleasure and interest in thinking mathematically.
For children, however, maths is not something separate from any other area of learning - their learning is holistic in nature. Using mathematical language can be developed most appropriately when children have the opportunities to practice in contexts which are not specifically mathematical.
A lack of child-initiated play severely limits possibilities for children to explore and communicate their own interests and mathematical ideas. It also restricts opportunities for children to engage in the sort of dialogue that can scaffold their understanding about their graphical marks and symbols, limiting their mathematical thinking and communication. Genuine child initiated play is spontaneous and belongs to the child or children, it is not imposed by adults with a maths agenda!! Maths needs to have personal meaning for children and to be deeply rooted in their play. They learn mathematical skills through their daily experiences and the more meaningful to them it is, the better. It should not be about checklists and never ending questions.
Ensuring that your environment inside and out, is full of mathematical opportunities and has exciting things for children to explore, sort, compare, count, calculate and describe, enables children to be creative, critical thinkers, problem solvers and to have a go, developing that ‘can do’ attitude mentioned earlier. Allowing children to make mistakes is crucial for mathematical development, if they do not make mistakes, they will not be learning and making errors can show practitioners what the children are thinking and then give them the required support.
One of the key methods children use to learn is trial and error; therefore, using a hands-on approach, and allowing them to experiment, is a good way for children to develop their mathematical thinking skills. Knowing when to intervene or not when children are heading for mistakes is crucial as voicing what they are thinking can help children to identify the inconsistencies in their understanding of something.
Early years pioneers Jerome Bruner (1966) and Jean Piaget (1952) advocate physical exploration that helps children to develop understanding of basic concepts. They believe children internalise the knowledge they gain through hands-on experience and this later leads to more complex abstract thought. This theory is supported by the hugely influential Researching Effective Pedagogy in the Early Years (REPEY) and Effective Provision of Pre-school Education (EPPE) research projects, which advocate planning practical experiences for children to ‘actively construct conceptual knowledge’ (Siraj-Blatchford et al., 2002) through a balance of taught and ‘freely chosen yet potentially instructive child- initiated activities’ (Siraj-Blatchford et al., 2004).
Vygotsky discussed the role that social interaction has on children's learning maintaining that children extend and consolidate their learning through dialogue with more knowledgeable others - adults or peers. The REPEY and EPPE research also supports this view as they identified the need for good, high quality verbal interactions that extend and develop children's thinking.
Children learn maths in a variety of ways:
This is the ability to count accurately, forwards initially and then, later in school, children will learn to count backwards. A more complex skill related to number sense is the ability to see relationships between numbers for example, adding and subtracting.
Stories, books, songs and nursery rhymes are a fantastic way to consolidate children's number sense. Having to think about numbers in the correct order takes a lot of effort and practice - it is much easier for children to do this through songs and rhymes and, perhaps more importantly, it is fun and maths needs to be fun! During these sessions give them time to talk, play and practice using numbers. Using your fingers or having objects that the children can see and touch will help too.
Gardner (1993:76) states that children around the age of four are beginning to and wanting to count everything. He describes that children at this stage of development are “looking everywhere for evidence of numbers.” Daily routines like preparing snack lend themselves to the development of mathematical learning and skills. Fruit can be halved or quartered, enabling discussions about how many pieces of fruit there are and if there is enough for everyone.
Making mathematical ideas “real” by using words, pictures, symbols, and objects (like blocks). It is useful to remember that children's mathematical development does not progress in a straight line. It may appear that they have achieved and made a breakthrough in their thinking but they suddenly revert back to their earlier understandings - making these ideas real may well support their thinking. Real life experiences are required to extend and develop children's understanding of the world and such experiences are rich in mathematical potential.
Being able to compare quantities by looking at sets of objects and deciding which is larger or smaller is the very early stages of calculating. During this type of play, children can start to learn vocabulary associated with it, such as, more, less and same - as they add more objects they can practice the concept of multiplication. If objects are taken away they can experiment with subtraction. Snack time provides a great opportunity to sort different fruits etc onto plates comparing them using the senses such as look and smell and deciding whether the pieces are bigger or smaller than each other.
Later in school, children will call this “geometry”, but for toddlers it is introducing the ideas of shape, size, space, position, direction and movement.
Froebel understood the importance of teaching the idea of the interconnectedness of objects. He designed solid three dimensional shapes which are called “Froebel’s Gifts”. Froebel intended children to explore the idea of a relationship between the part and the whole. Children explore mathematical and scientific concepts (such as number and shape) through direct manipulation of physical objects. As children build and experiment with such objects they develop richer ways of thinking about mathematical concepts such as number, size, and shape. The Froebel block play research project, (Bruce and Gura - 1987- 90) has continued Froebel’s work and the purpose was to show the development of the child's understanding of competence in controlling the dimensional shapes.
Babies learn about space, shape and size through mouthing, handling and exploring objects. Older children are more likely to understand mathematical concepts like position and size if they're able to use their body movements and senses to feel what it's like to be in, on or under something.
Measuring involves finding the length, height, and weight of an object using units such as millimetres, centimetres or metres; of course for children, it is a much more practical concept and draws heavily on children's day to day activities. Measurement of time also falls under this skill area. Visual timetables are a really useful way to sequence the order of routines and time. Again, real life experiences consolidate learning and cooking lends itself beautifully to measuring. Scientific concepts can be explored and plenty of maths vocabulary can be worked on. It is a great sensory experience and can also develop small and fine motor skills. Cooking includes capacity and volume and estimation. Snack can also provide opportunities as children can measure capacity when pouring drinks and checking to see whether there are enough chairs or cups for everyone and if you need to take some away.
Patterns are things—numbers, shapes, images—that repeat in a logical way. Patterns help children learn to make predictions, to understand what comes next, to make logical connections, and to use reasoning skills. It is worth noting that patterns do not only occur in mathematics, but in many other areas such as, the natural world, music and art. These areas can be explored to consolidate children's understanding of patterns in a very practical and creative way.
Problem solving is the ability to think through a problem and to recognise there is more than one path to the answer. It means using past knowledge and logical thinking skills to find an answer. Being playful and creative are useful when problem solving - the thinking process involved in play is vital for the development of mathematical thinking to support problem solving. Children need to be encouraged to offer explanations to each other and accept everyone's contributions which is not easy and needs plenty of practice!
Maths is everywhere, in all aspects of our lives, it touches us every day. Yet for many of us, maths is something to fear and avoid. For young children, maths is an exciting part of their lives, it offers so many opportunities to explore, discover and to enjoy. We need to harness this attitude and encourage these skills so our children can feel confident and enthusiastic about all things maths. This can best be achieved through rich, child initiated play and an environment where maths is valued and supported.
Gardner, H (1993) The Unschooled Mind. London. Fontana.