It's an important concept for children to understand and appreciate about maths.
Especially when schools love to beat into them that maths is about getting a correct answer. It's not.
Maths is about playing. We play with numbers, shapes etc to find patterns or connections.
Mathematical thinking is also creative thinking.
To help us understand this a bit more and to tie in with our enquiries into multiplication strategies, we were presented with this question:
We had a minute or so to write down the best strategy we could think of and then we were invited to share with the class. Here were some of our thoughts:
After we shared and explained our mental strategies, we voted on which we felt is the easiest to do mentally.
We had a tie:
I made a mental note of who chose the following strategy because it is a possible indication of weak number sense. Children who are doing written calculations in their mind do so often because they haven't yet learnt how to see relationships between numbers:
To play with numbers, we then changed the question to the WORST mental strategy:
Play with the numbers was the simple instruction.
It's an interesting word to use- play.
It relaxes the mind to enjoy.
The discussions these 10 year olds were having with each other were rich in number understandings. Odd-even, decimals, square roots place values etc were being heard amongst the excited chatter.
They were all beaming with pride of how incredibly complex they were able to play with the numbers.
We publishing our strategy and gave it a name. We used these to teach each other how it worked.
Some really CREATIVE mathematical thinking took place:
We loved the name of this one:
Listening to the children beam with pride as they shared and explained their overéy complex mental strategy, I overheard one student saying:
"......then we thought about making it a decimal by dividing it into quarters. X said it would be too hard but I reminded him the best way to play is to go to the extreme. He agreed so we played hard and then divided the number......"
Can't get much better than that.
Maths is about playing - playing hard at times too it seems. :)