When it comes to mathematical development, the ability to recognise and use numbers takes pole position. But there are many other aspects of mathematical thinking that need to be recognised and planned for, says Kate Lee
"I'm hopeless with numbers, but I am a perfectly competent mathematician."
This might seem a strange assertion, until you consider how mathematical thinking in its myriad forms permeates everyday life.
Take this morning, for instance: I worked out how best to stack the dishwasher to get the maximum number of items in; I decided that the letter I was holding was light enough for an ordinary stamp; and I estimated that I had enough milk by looking at the level in the carton. Later on, I found an empty parking space, reversed in just far enough, and guessed that I had enough change for the meter by giving my purse a quick shake. I did not write down (or even use) a single number, but I used mathematical thinking and - importantly - experience to solve a whole range of problems.
Every day, we use our knowledge of time, distance, weight, shape and space to make decisions. Problem-solving, an understanding of sequence and cause and effect, and the ability to estimate and approximate are vital when it comes to using maths in every day contexts. The tendency to see guessing as slapdash, rather than a sensible strategy, can have an adverse effect on a child's perception of his or her competency. Yet self-confidence is vital to successful learning, and particularly so with maths, since any sense of inadequacy may be carried into adulthood, compounded by the insidious, unwritten lore that it is somehow OK, even endearing, for certain members of society (particularly women) to be "hopeless at maths".
When it comes to mathematical development, young children need the freedom to "get it wrong", secure in the knowledge that they won't be criticised.
As early years practitioners, we can contribute to children's confidence by presenting lots of opportunities for making comparisons, guessing, measuring and using our whole bodies to explore concepts such as "over" and "under", both indoors and out. We can also make sure that the notes kept on each child reflect all the mathematical development that is going on, by observing and recording each child's body language and the expressions he or she uses.
For instance, records for three-year-old "Harry" might read: "Harry uses mathematical language accurately to describe position (behind, in front, over there) and size (big, bigger, medium-sized, small). He uses body language to express his thinking, for example by stretching out his arms to convey 'really big' when describing the plane he recently went on."
It doesn't say: "Harry can count up to five", but it does convey a good appreciation of the way his mathematical thinking is developing - reassuring for parents and Ofsted inspectors alike.
Use the days of the week as a platform for thinking creatively about maths or, for slightly older foundation-stage children, why not create a circle challenge that involves parents and the wider community?
Parents may not be aware that music supports learning by stimulating both sides of the brain, and that it's especially useful in relation to maths.
Start the week with music with a strong rhythm, beat or refrain - anything from hymns to the Beach Boys.
Arrange a walk around the area and encourage the children to map where they have been - first we went past the church, then we got to the river, next we saw the paper shop and on the way back we went past the bus station.
Most educationalists agree that learning works particularly well when it is rooted in real life. A "maths walk" offers opportunities to think about sequencing, order, position and, significantly, the language we use to describe them, so that other people know what we mean. You might draw a map of your own area and see if children want to trace their route using pens, paint or fingers. This also helps children see where their nursery or school belongs in the wider locality.
Ask children to bring in something (or someone) to measure, from the smallest Polly Pocket to the tallest grandad. Make a big wallchart. Use rulers, tape measures and height charts. Introduce vocabulary such as taller, tallest, small, tiny. Children often make up their own words for describing size (tinsy, eeny-weeny) - a good response will encourage them to view maths positively and see that maths and creativity can and do go hand in hand.
How and why do we use clocks and watches? How do we describe what time it is? What do we mean by "early" and "late"? When does morning start? What is an alarm clock for? You can have lots of fun exploring these concepts, perhaps encouraging children to bring in different sorts of timepiece. You could play waking-up games, and look at the things people in a range of cultures do at particular times of day. Look out for stories, songs and sayings which pivot on timekeeping (the early bird catches the worm, "Hickory Dickory Dock", Cinderella).
Use the last day of the week to encourage the children to explore the physical aspects of their environment. What can you find today? A corner, a slope, something high up, the lowest step? Play hide-and-seek; ask the children to make themselves into patterns (start with a simple boy, girl, boy, girl sequence and see where they take it). Play jumping games. Who can jump highest, farthest, the most quietly?
The Mindware range includes some unusual and interesting resources.
Natural maple blocks enable children to build pyramids, the leaning tower of Pisa, even the Coliseum (from pound;32.99). Pattern Play comprises 40 coloured, wooden pieces in a tray for designing endless patterns, building spatial skills and an appreciation of colour, shape and form (Pounds 16.99).
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You could also try recycling projects in your area for lengths of old pipe and other things on a bigger scale than children may be used to. Your local garage may be happy to give you old tyres to start a circle challenge - who can find the biggest, smallest or tiniest ring-shaped thing? Among the items may be a CD, a little white mint, an old pram wheel, but preferably not Grandma's antique diamond ring.