All aspects of creative development can contribute to the development of mathematical understanding, and the links between the two areas of learning are all the greater now that 'Mathematical development' has been renamed 'Problem-solving, reasoning and numeracy' (PSRN) under the EYFS.
As 'Creativity and Critical Thinking' (EYFS Principles in Practice 4.3) makes clear, creativity is not just about expressing ideas through the arts. Creativity is about making connections (between home, nursery and the wider world, between a child's own experience and those of other children, between all areas of learning and development). It is about linking ideas and about problem-solving.
As children communicate their ideas through the expressive media, new connections are made, and as ideas are explored, they develop interests. Their enthusiasms provide the motivation to become not merely problem-solvers, but problem-finders.
Problem-finding involves passionately wanting to know something. It provides children with a much greater drive than simply being presented with a problem to solve. Remember that a problem isn't a problem until or unless someone wants to solve it!
Reasoning is just one of the ways in which human beings solve problems. Another important strategy is to identify patterns - something integral to maths. Many of our problem-solving strategies arise out of a trial-and-error approach. We guess what will work based on what has worked elsewhere, try it out and then try something else if it doesn't do the trick.
When planning for learning within areas that are usually thought of as 'creative', practitioners should consider:
- the links between creativity and mathematical development
- the shift of emphasis brought about by the change of name to 'problem-solving, reasoning and numeracy'
- both the resources and the support that will help develop a child's mathematical understanding in areas usually thought of as 'creative'.
'Creative' areas can, of course, still be enjoyed for their own sake - playing with blocks doesn't always have to be about problem-solving. However, these areas make mathematical learning fun rather than dull, rich and varied rather than predictable. They give space and opportunity for reflection in a variety of ways - promoting both mathematical learning and a strong disposition to learn.
WHAT SHOULD ADULTS PROVIDE?
Construction
Wooden unit blocks are intrinsically mathematical. For best effect you need a large number, and although they are expensive they will last a lifetime. If you can afford more, include some other construction sets such as Lego and Mobilo. Large quantities enable children to construct more challenging and complex models, giving more learning potential.
The workshop area also offers lots of opportunities for constructing models from recycled materials, paper, cloth and so on. Don't forget that cardboard boxes, tyres, lengths of drainpipe and other big junk materials can also support large-scale construction - challenging and requiring collaboration. Large-scale materials promote measurement because children can't so readily judge just by looking.
Dance and music-making
A rich and varied music area with a range of instruments, recorded music, and books and pictures about music and musicians is an integral part of good continuous provision. Ideally, the area should be large enough to allow for a small group to dance together and to observe themselves in a mirror, seeing and feeling the shapes they are making and the space they are filling.
Outdoor provision for music allows children to explore space, time and loudness in ways that are less possible indoors. Lengths of plastic drainpipe played with a flip-flop are fun, highlighting the musical and mathematical idea that length and sound are linked.
Instruments or sound-makers in the music area may be chosen to highlight mathematical concepts. Maybe all the instruments are cylindrical. Perhaps each instrument can be presented in two or three different sizes - drums, shakers, xylophones.
Imaginative play
To support imaginative role play, ensure a rich range of resources inside and out so children can create their own play spaces. Creating a den from crates or a table with a cloth over the top has huge mathematical potential.
For small-world play a range of figures, animals and vehicles should be available. The key to making this a rich mathematical experience is in having plenty of materials. Counting and categorising only become necessary with lots of things - why bother if you only have one or two of each?
Add materials that chime with children's current interests and have strong mathematical content. Following a journey, blocks for roads (and a big space to play in) will enable children to explore space and position. A farm visit might support problem-solving and exploration of shape, space and measures if squares of pretend grass and a number of fence pieces are added to extend the play.
A combination of large-scale and small-world play opportunities reinforce learning in both contexts, such as a garage role-play area and play with cars and roadways in the block area, giving opportunities for mathematical comparisons.
Malleable materials
Dough, clay, cornflour and sand are always popular experiences for young children of all ages. Because they change shape and area very readily, they have good mathematical potential, but by adding bun tins, candles, shells or pebbles, different kinds of mathematical learning around pattern, number and calculation can develop. Enhanced provision might focus on number and calculation by providing trays and containers with different numbers of holes set out in different patterns.
Mark-making
Resources for the writing and drawing area which highlight mathematical ideas include:
- rulers, tape measures, calculators
- calendars, clocks, numberlines, cut-out numbers
- tickets, cheque books, receipt books, raffle tickets
- birthday cards, diaries, recipe books.
Large-scale painting with rollers and household brushes may be contrasted with tiny paintings on tiny paper. Mark-making in the snow with squeezy bottles of paint or on hot sunny days with water on hard surfaces allows for mathematical conversations around time and distance. Encouraging children to devise scoring systems for games such as skittles promotes mathematical mark-making.
Songs and rhymes
Counting songs and rhymes with finger actions are very helpful, since:
- music (and musical elements such as the rhythms found in rhymes) aids memory
- the part of the brain responsible for fingers is next to the part of the brain responsible for number - so action songs make numbers more memorable
- adding props such as plastic ducks to the maths area aids visual and physical memory and helps children to go over and over their favourites.
Children's particular interests can also be developed by making up songs about counting or other mathematical ideas to known tunes. Tom Thumb's Musical Maths by Helen MacGregor (A&C Black) offers loads of suggestions for songs set to known tunes.
Stories
Narrative helps us to make sense of things and to remember, providing a sequence or structure to a string of events. Perhaps most important of all for children's long-term development is that in promoting imagination, stories promote the abstract thinking they need to become mathematical thinkers.
Ensure that the book area has a range of books involving problem-solving and other mathematical ideas, such as Mr Archimedes' Bath or Who Sank the Boat? by Pamela Allen (Picture Puffin), and Ten Seeds by Ruth Brown (Andersen Press).
Books and props focusing on children's concerns can contribute to mathematical thinking. For example, new babies in the family can give relevance to stories that deal with difficult PSRN topics like time, growth and life cycles. Try Once There Were Giants by Martin Waddell and Penny Dale (Walker Books), Rosie's Hat by Julia Donaldson and Anna Currey (Macmillan Children's Books) and Ruby Flew Too by Jonathan Emmett and Rebecca Harry (Macmillan Children's Books).
WHAT WILL CHILDREN LEARN?
Construction
Problem-solving strategies are developed as children find problems with their constructions
Pattern and sequence are common features of children's models
Shape, space and measures are integral aspects of modelling, when noticing how things fit together; whether one box is deeper or taller than another; cutting a longer piece of tape
Number is involved when counting how many blocks, boxes, or tyres are needed to complete a model
Calculation includes sharing blocks; estimating how many more blocks will be needed to make a model of a particular size or height
Dance and music making
Problem-solving strategies are developed as children try to work out sequences of sounds or movements
Pattern and sequence are integral to dance and music. If maths is the science of pattern, music and dance are certainly the art of pattern
Shape, space and measures All aspects are involved as children develop and perform dances and improvised music, which both involve time and space
Number It has been said that music and dance involve 'internalised counting'. As they dance or make sounds, children may experience or feel time and rhythm, often counting out loud in the early stages of learning something new
Calculation An often unspoken element of creating dances or music as children explore, for example, how to keep the beat but change the rhythm
Imaginative play
Problem-solving Strategies are an important part of setting up any imaginative game
Pattern and sequence are key characteristics of the stories that underpin children's imaginative games
Shape, space and measures feature in most imaginative games - time, money, larger and smaller quantities, positional language
Number is one of the ways in which children explore and make sense of the world. We can underline this by numbering wheeled vehicles, or providing a certain number of props such as capes and helmets and labelling where they should be stored
Calculation is promoted by providing materials and asking questions such as whether more cups will be needed or whether there are too many horses
Malleable materials
Problem-solving Strategies can be developed in the play as children attempt to make a model stand up; see how many shapes they can cut out of a flat piece of dough or clay; roll a long thin sausage that will stretch from here to there without breaking.
Pattern and sequence are explored as children create two- and three-dimensional models and enhance them with feathers, stones, twigs and so on
Shape, space and measures are explored as children make clay or dough thinner, fatter, longer, higher
Number and calculation can become part of the conversation that is characteristic of children's deep engagement in malleable material, with remarks such as 'How many shells have you used?' or 'My cake has more candles than yours.'
Mark-making
Problem-solving Strategies can be developed as pictures support children's thinking
Pattern and sequence are often to be found in children's drawings
Shape, space and measures Children often explore these three elements together in their drawings. A single picture may, for example, be a car, with swirling lines indicating the speed and another set of lines indicating direction and distance
Number and calculation In drawing and painting, children are often to be found exploring quantity
Songs and rhymes
Problem-solving Strategies might include finding a new rhyme for a known song or rhyme
Pattern and sequence are key characteristics of both songs and rhymes
Shape, space and measures feature in the words of many songs and rhymes
Number is widely taught through songs and rhymes
Calculation Many counting songs can be used to support understanding of calculation - for example, how many of the Five Little Speckled Frogs are jumping into the pool
Stories
Problem-solving Strategies can be identified and developed through many stories
Pattern and sequence are key characteristics of stories
Shape, space and measures feature in most stories - time, money, larger and smaller quantities, positional language
Number appears in many stories, not simply as a sequence, as in counting books, but as integral elements of the story itself, such as seven princesses or the number of fruits
Calculation Like number, calculation often appears as incidental to the story, but it can be made more central by asking questions such as 'How many more ...?' or 'Will they have enough ...?'
Linda Pound is an early years consultant and author of Supporting Mathematical Development in the Early Years (Supporting Early Learning series, Open University Press)
What should adults do?
All areas that support creative development are rich in mathematical opportunities, including problem-solving (see 'What will children learn?'). But resources alone are not enough - the development is supported and extended through adult involvement.
LOOKING AND LISTENING
Supportive adults will observe the direction and focus of children's self-initiated activity, and so gain a window on children's mathematical thinking.
Creative media are rich areas for the development of problem-solving opportunities and also provide clues for what to provide next. Observations can help you to make decisions about providing more challenging den-making materials or when a song could be varied to include some calculating. These are not merely decisions based on mathematical understanding, but also on learning dispositions such as involvement, perseverance and interests.
JOINING IN
Music areas often gather dust - children are initially keen but when adults fail to join in, children give up on the area too. Block areas are also frequently avoided by practitioners. But indoors and out, early years settings are rich areas for mathematics, and an adult presence can do much to promote problem-solving strategies and understanding of shape, space and measures everywhere.
When adults join in with children's dance and music-making, they can draw attention to features such as pattern, sequence and number. Supportive adults can highlight mathematical features of children's early attempts at writing and drawing, imaginative play and engagement in books and stories.
TALKING AND THINKING
Communication is the key to developing thinking for children and adults. Being on hand to ask questions or make statements that challenge thinking and help children to persevere can make all the difference to children's understanding of PSRN and to adults' view of their progress. Malleable materials, for example, often provide an opportunity to engage in conversation. As they get busy with their hands, children naturally enjoy talking and reflecting on what they are doing. Encouraging children to represent or express mathematical ideas in a range of media also promotes their thinking.
Asking questions can be useful, but in general they should be open-ended and relevant to the child's interest. Barging in with questions such as 'How many?' or 'What shape is that?' may undermine their enthusiasm. Questions may be used to encourage children to think and talk about:
- how (or how else) problems might be solved
- what might happen next
- numbers and shapes that feature in stories and imaginative play
- patterns in the structure of the story, the songs they sing or the models they make.
MORE INFORMATION
- Bruce, T (2004) Cultivating Creativity (Hodder and Stoughton)
- Griffiths, N (2005) The Little Book of Maths Through Stories (Featherstone Education)
- Pound, L (2008) Thinking and Learning about Mathematics in the Early Years (Nursery World/Routledge)
- Skinner, C (2005) Maths Outside (BEAM)
- Worthington, M and Carruthers, E (2006) Children's Mathematics (Paul Chapman Publishing).
