About this series
This year, we are exploring outdoors with our ‘maths champion’ hats on. Maths is embedded in every aspect of our lives, and yet a lingering fear of Pi, or complicated equations and formulas, prevents many adults from recognising themselves as the everyday mathematicians they actually are. In the early years, we have the chance to nip this fear in the bud, offering children exciting and fun foundational maths activities but also, crucially, showing them that maths is everywhere and that they use maths all day, every day.
The more we recognise this, using maths language in our normal daily routines, reinforcing concepts and highlighting where we need maths knowledge to carry out ‘non-maths’ tasks (such as filling a watering can halfway up), the more confident and competent mathematicians children will become. We will also, as always, include ‘bodyful’ ideas for outdoor learning and play, making the most of children’s physicality.
What it means
Counting: saying number names in order (or in reverse).
Cardinality: understanding that numbers have meaning and refer to quantities in a set. For example, children playing with a pile (or ‘set’) of conkers might count them from one to eight, and know that eight is the number name for the total quantity of conkers they have in their ‘set’.
Early childhood maths researchers suggest that the principle of cardinality is necessary for children to understand if quantities are equal or not. It’s important for knowing that adding ‘one’ to a set moves the quantity in the set onto the next number in the sequence. Counting and cardinality are essential for basic number sense and allow children to develop more advanced mathematical thinking, including addition, subtraction, pattern recognition, estimation, subitising and problem solving.
A few principles will help develop the concept of cardinality:
- When counting a set, say the cardinal number first and then count back up to it: ‘There are eight conkers: one, two, three, four, five, six, seven, eight.’ This reinforces the special nature of the cardinal number, and shows how we reach it by counting in sequence.
- Repetition – not just counting, but also of the cardinal number concept: ‘I think we have 20 children in the class today… one, two, three… 20!’
- Use and recognise counting and other maths words in everyday talk: ‘Yesterday we found three snowdrops. I wonder how many new ones have come out today? Let’s count them all…. aha! We now have 11 snowdrops, so eight tiny ones have blossomed overnight.’
- Every now and then, make a mistake when counting up to a cardinal number, missing it out and going to the next in the sequence, to check who is listening and who knows the correct cardinal number.
Everyday counting outdoors
Tidying up routines: label outdoor storage containers, for example a trug of bouncy balls, with the cardinal number (how many balls should be in the trug) marked on as a numerical digit as well as using domino dots or an annotated number line, to offer alternative ways of expressing that number.- Keep a bucketful of chalk outdoors so children can create their own number labels, such as for individual bike and trike parking bays.
- Connect the date with number and counting: ask children if they know what the date is (your cardinal number), then go outdoors and seek that number of objects (the counting).
- Mark the bases of resources with numbers so that children can practise checking quantities.
- Create tracks and targets with numbers on; to encourage full body movements with target games, make sure they aren’t too close to windows or other obstacles.
- Paint numbers in sequence on objects outdoors that repeat or have patterns, for example, on fence panels.
- Play counting games such as hopscotch.
Outdoors and active
Research on teaching early maths suggests that an abundance of maths opportunities is key to establishing and extending children’s mathematical understanding with ‘low floor, high ceiling’ activities that build confidence in early learners and challenge the more able. We also know that movement is intrinsically connected to cognitive development, so abstract concepts such as maths really do benefit from being taught outdoors where there is space to move and explore. Provocations or adult-led tasks that demand children use their whole body help to consolidate learning, as does repetition.
Ten frame scavenging
Start: use ten fabric or chalked ten frames to collect and count an agreed number of one type of object, for example, six pebbles, eight leaves, one flower. Encourage children to search across the whole of the garden to find their maths treasure. Extend: organise the objects into different sets, such as pairs or threes, or by texture or shape, and then count the total in each arrangement. Prompts: how does grouping affect the total number; what happens if one more object is added or one taken away; how many more do we need to make ten?
Estimating and counting steps or jumps
Start: choose a short route between two features and ask children to count their steps as they walk from one to another; repeat by running. Are there more or fewer steps when you run? Does everyone use the same number of steps? What would account for any differences? Extend: predict how many very long steps or very tiny ones would be needed to cover the same distance. Repeat the experiment and check if the predictions were correct. For a more physical challenge, take ‘normal’ steps between the features, counting up in ones, then walk backwards, counting back towards zero.
Maths resources
At Dandelion Education, a fully outdoor setting, the woodland environment is used as a resource, setting and inspiration for maths (and STEM).
Co-founder Hayley Room says, ‘Children are exposed to numbers in a huge variety of ways – from marks on vertical and horizontal surfaces (tree trunks and table edges) to recipe books and traditional number fans. Resources are stacked and stored in ways that enable maths thinking, and one of the water jerry cans is marked with numbers to indicate the number of litres in it. We use the labelled jerry cans to support the understanding of non-standard measurements and capacity, 1-1 correspondence and number recognition; children may use a range of receptacles as they fill the cans to an agreed level while using a tally recording system as we complete our task.’
Children have access to natural environment resources such as binoculars and magnifying glasses and use them to search for bugs or birds; practitioners encourage children to describe what they see, including counting quantities and using maths language (‘at the top… under the log… lots… one more/another one…’). Hayley says, ‘In one-to-one encounters, we try to support children’s counting and subitising skills with loose-parts resources such as conkers, bottle tops and parts of a china tea set. We may fill our teapot with a pre-agreed number of conkers, counting 1-1 as we add them; one child may be using a tally system, one may be counting using their fingers, to reinforce the understanding of number. The tea pot is emptied onto a saucer or into a cup and this leads to a discussion that reinforces subitising.’
