Both in school and at home, play is an essential part of life not only for children but also for adults. As an adult we might not feel that we play often but I know I spend many an hour in an evening playing, as my husband calls them, silly games on my phone. I argue that they are not silly as they are all puzzle based and therefore are working my brain. It is the thinking side of play, and how talk encourages thinking, that I want to explore in this blog.
What do we mean by play and why is it important?
A quick internet search will give you many definitions of ‘play’ depending on the context the word is used but we are thinking about play as a form of amusement or entertainment. The first definition in my Google search was:
- Engage in activity for enjoyment and recreation rather than a serious or practical purpose.
Of course this is a perfectly correct definition of play but I think a lot of children’s play is serious and does have both a practical purpose and massive learning potential. Dockett et al., 2020 explores multiple definitions of play and concludes the essential characteristics of play include:
- the exercise of choice
- non-literal approaches
- multiple possible outcomes
- acknowledgement of the competence of the players
- a disposition or habit of mind
This all sounds very complicated but if these characteristics of play are linked to characteristics of mathematical thinking – creativity, curiosity, problem posing and problem solving, play and mathematical thinking are closely linked and play does have a seriously practical and important purpose. Research tells us the importance of early play and other informal activities such as: comparing depth of puddles, counting the stairs, helping with setting the table, as these provide children with new information, support skill development, extend contextual understanding and provide extensive numerical information (Ramani and Siegler, 2020). Moreover, what children know when they enter reception and Year 1 predicts their maths achievement for years to come. Incredible as it may seem, what they know in maths can also predict their reading achievement later (Clements and Sarama, 2014).
Whilst this research is both terrifying and reassuring, it shows us that children’s understanding and application of mathematics at a young age can be very telling about a child’s future attainment and therefore a good early maths education is essential. Thankfully, good mathematics education can come from a great range of activities and play, done throughout the day, both at home and at school and doesn’t need to be formal maths. In section 2 of the summary of recommendations from the recent guidance report from the EEF on Improving mathematics in the early years and KS1 (page 6, 2020), it clearly lists a variety of ways to integrate maths throughout the day. Arguably sitting and completing arithmetic questions doesn’t develop those thinking mathematically skills listed above. Having said this, knowing what to focus on and how to engage with children to support thinking mathematically is important.
In Charlie Harber’s blog about gaming in KS2 she clearly explains how to select games and provides top tips for getting games going both in the classroom and at home. I think that these tips also relate to play for our younger children too, both when playing games but also in wider play. Keeping an eye, or your thinking, on what maths learning could be happening during play is helpful but the fluid and flexible nature of play might make this challenging.
What could the maths focus be in play?
- Subitising – seeing how many are there without counting
- Counting – knowing number names in order, linking a number name to thing, identifying how many things there are
- Comparing and classifying - having a feel for the relative sizes of numbers; ordering, estimating, sorting and giving reasoning for the groups within a sort
- Regrouping - understanding how each number can be made up in different ways and identifying number within numbers
This would be my list of key concepts to have in mind when playing. Some play may specifically be encouraged to develop one or more of these areas but all of these concepts can be integrated into most play and activities. The skill (or the tricky bit) is spotting the opportunities and intervening effectively.
Many games encourage subitising so teaching the children to play them and encouraging them to play them over again will support subitising. Dominoes, snap, rolling multiple dice to show the same value, are all good games to support subitising and children being very familiar with the dot patterns found on dice etc. is key when developing calculations strategies when they are older.
However, the children might be setting up a tea party for their toys or placing their toy cars into parking spaces. During this imaginative play opportunities for subitising are also available. For example if four toys are sat ready for a tea party you could ask, ‘How many plates are we going to need?’ ‘Are their enough cakes for everyone to have one?’
Traditional board games, such as Snakes and ladders, Ludo etc. are great for counting encouraging the children to rehearse the order of the numbers and matching each number to an action but they also support number magnitude as Rachel Rayner explained in her blog. Other traditional games such as hop-scotch are also great for counting and can be done outside.
[This is one of the home maths activities we are sharing with schools currently for Reception. Resources are frequently posted on our social media channels - @Hertsmaths and our Facebook group Herts for Learning: ESSENTIALmaths.]
There are lots of in incidental opportunities for counting all the time: going up and down stairs, counting out snacks, seeing how many people are in the room to name a few. There are also lots of lovely books that involve counting, one of my favourites is Abigail by Catherine Rayner which highlights how challenging counting is. In a blog the HfL maths team put together for world book day this year we recommend lots of lovely books that link to counting, and other aspects of maths.
Comparing and classifying
Comparing is a concept that is done across all areas of mathematics number, shapes and measures and encourages lots of opportunity to develop language. Children compare and classify things all the time, so can be incorporated into many daily activities and play, and this concept is great for encouraging children to explain their thinking. The use of open ending questions that encourage children to explain why they have made decisions invite children to verbalise their thinking. Having a bank of question stems in your arsenal can help, so here are a few to get you started:
- How did you…
- Why did you…
- What do you notice…
- I really want to know more about…
- Why does this…
- So you think…
- Do you think we should…
When children response echoing their answer back adding appropriate mathematical language is important but ask the child to clarify what you said was correct. For example:
Adult: What do you notice about the cakes we have made?
Child: Little, big, bigger, bigger.
Adult: So is this the littlest one and then the cakes are bigger each time, with this one being the biggest?
Child: Yes this one is the biggest.
This subtle way of adding precision to the children’s use of language is a great way to support the use of correct mathematical language without the children feeling corrected.
Games such as Guess who or the post-it on your head game (where you have a picture or the name of an object on your forehead and you ask questions to identify who or what you are) are great for developing the children’s questioning for comparing and classifying. These games encourage them to start more general and refine their questions to help them identify who or what is the correct answer.
The ability to regroup and recognise parts and the whole is arguably one of the most important mathematical concepts as it is the foundation stone of calculation. This builds on from comparing and classifying because without these skills children won’t be able to recognise what can be separated from a whole to create a part. For example you might have a collection of shells. All the shells are the whole, all the twisty shells could be put together to make a part of the whole and the other shells will become the other part.
Once this is understood the concept of regrouping can be linked to numbers and how numbers are made or other numbers. Visual representations of amounts, like the dot patterns we talked about earlier in subitising, are a great starting point for spotting numbers within numbers. Think about the dot pattern for five, within this other numbers can be spotted. What other numbers can you see?
Rolling a dice and using small toys, counters or natural objects such as shells, children can copy the pattern rolled and then look for other amounts within the number rolled. For other ideas for simple games that support regrouping please sign up to our YouTube Channel that includes a video with games that support developing number sense, including regrouping, and many other games ideas.
So remember maths is happening all the time, in play, during daily routines, both in school and at home, and young children are naturally curious about mathematical problems and enjoy solving them. They don’t need to be made aware they are ‘doing’ maths but through careful interactions mathematical skills and thinking can be constantly developed, honed and improved. It is the language you use in your questions, ensuring that they are open and invite children to explain their thinking; how you react to those answers, modelling precise vocabulary and clarifying the thinking with the child, which will constantly develop mathematics. So go and play!
Further professional development opportunities
Using manipulatives in the foundations of arithmetic - main report and Using manipulatives in the foundations of arithmetic - examples for teachers are two articles that might be of interest to teachers looking for professional development about play and mathematics.
In addition I would highly recommend reading the guidance report on improving mathematics in the early years and KS1 produced by EEF.
Dockett, S., Perry, B., Bobis, J., de Vries, E., Highfield, K., Hunting, R., Lee, S., Thomas, L. and Warren, E., 2020. Playing With Mathematicas: Play In Early Childhood As A Context For Mathematical Learning. [online] Files.eric.ed.gov. Available at: www.files.eric.ed.gov/fulltext/ED521030.pdf [Accessed 7 May 2020].
Ramani, G. and Siegler, R., 2020. How Informal Learning Activities Can Promote Children's Numerical Knowledge. [online] Available at: www.researchgate.net/profile/Robert_Siegler/publication/263503931_How_Informal_Learning_Activities_Can_Promote_Children's_Numerical_Knowledge/links/53f227180cf272810e4ca12e.pdf [Accessed 7 May 2020].
Clements, D. and Sarama, J., 2014. Learning And Teaching Early Math. New York, NY: Routledge.
Educationendowmentfoundation.org.uk. 2020. Improving Mathematics In The Early Years And Key Stage 1: Guidance Report. [online] Available at: www.educationendowmentfoundation.org.uk/public/files/Publications/Maths/EEF_Maths_EY_KS1_Guidance_Report.pdf [Accessed 7 May 2020].