The kindergarten children develop and use mathematical thinking, concepts, skills and language during their play and everyday activities in the same way that they develop their language skills- through imitation, experimentation and negotiation. Mathematical language and thinking emerge in an organic, fluid and social way as they explore, construct, interact with and make sense of their world.

Tuesday is bread roll baking day, and the children are involved with weighing, measuring, counting, making shapes, using fractions:
‘Mine is twice as big as yours.’ ‘I have cut mine in half.’ ‘Pass me the knife, I want to make a star on top.’ ‘They are too close together, there won’t be room when they are cooked.’ ‘I can see that it is a pint of water. It is the same as Daddy’s pint glass’.

During indoor free-play the children enjoy construction. Playing (alone and collaboratively) with wooden blocks involves working with ideas around shapes, space and patterns. Designing, building and operating a bookshop is even more complex:
‘How many are we?’ ‘How many racks can we have each?’ ‘How many all together?’ ‘How much do the books cost?’ ‘What shall we use for money?’ ‘The wooden blocks are worth a hundred, the smaller ones can be ten, conkers five and the shells one.’ ‘How many more conkers do we need?’ ‘How many do we need so we can have 4 each?’

Handwork helps to develop mathematical thinking as well as fine motor skills: ‘My finger-knitting is wider than yours, that is why it is shorter.’ ‘Mine is longer because I started before you.’ ‘Mine is as tall as the school.’ ‘We measured mine, it is as long as the hallway.’ ‘My sandpaper is rougher, look, the sand is bigger.’ ‘Yes, but mine has more sand.’ ‘Look, the numbers on the back tell you which has bigger sand.’

Snack time provides mathematical opportunities too: counting children, adding two teachers, placing the right amount of chairs and boards, discussing the snack: ‘I have more than you.’ ‘Mine is longer.’ ‘I have more left because I ate it slowly.’ ‘I have 36 raisins.’ ‘I have more.’ All the children start to count their raisins. They count together to 100. Conversation might turn to animals- Which are the fastest? What do tigers eat? How may sheep could seven tigers kill? ‘One tiger could kill one sheep, two could kill three, three could kill four, four could kill six, five could kill seven, six could kill nine, and seven could eat ten, because they couldn’t kill half a sheep’. Or Space- ‘How long would it take to get to the moon?’ ‘A bigger rocket would be slower than a smaller rocket, so it would take longer, it would take a year, a small rocket would take a week.’

During outside play there is more construction: the children use levers, judging weight, length, space. ‘If we put this plank here, it will make it high enough’, ‘Try this one, it is longer so it will reach’. They dig tunnels, deeper, to the middle of the earth. They run and skid- faster, further, longer. And ask questions- ‘How many short gnomes would have to stand on each other’s shoulders to reach the top of the gate post, if a gnome was as tall as my two fists on top of each other?’

During the course of the morning, like true mathematicians, the children work alone or collaborate, developing and testing their theories, developing language alongside concepts, naturally, without any interaction or intervention from the teacher. They use cardinal and ordinal numbers, positional language, explore direction, distance, speed, temperature, time, magnitude, shape, fractions and geometry. They actively look for, notice and construct relationships, organizing them into concepts that will later become regarded as mathematics.

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