Problem Solving
One day I was spending a bit of time with my youngest child; she was six years old at the time. We had made scones, and then snatched a few moments to read a book together while we waited for them to cool down. We were reading an old favourite, and were enjoying the story, when suddenly she asked “What is 1 and 8?”
“Nine”, I answered, and carried on reading. I noticed that she was counting on her fingers, but knowing this active young mind to be more than capable of doing more than one thing at a time, I continued reading. I did wonder what she was doing...
“Mom, you’re wrong!”, she triumphantly interrupted our book reading, “It’s eighteen...”
“Oh” said I. Now she had my attention. “Why did you want to know?”
“Well, we made nine scones, and I wanted to know how many there would be if we cut them all in half”
“Oh. Why do you want to cut them in half?”
“Because there aren’t enough for us all to get the same number of scones. But if we cut them in half, there are enough...” (There were six of us at home at the time.)
I was quiet, once again effectively silenced and in awe of the privilege of witnessing the learning process. My young daughter has had no formal tuition in arithmetic. When she has asked for number information, it has been given. She loves board games and card games. We build structures with Cuisenaire rods. And of course she sees the maths in her world when she sets the table, shares out a packet of biscuits, spends her pocket money. Maths is part of our world. Thus, she has experienced it.
What did she do that was so amazing in this case? Think of the complexity of the problem. Experience and practise has made these kinds of calculations seemingly simple to our adult minds. But they are not...
First, she had ascertained (and remembered) that there were nine scones on the tray. Then she had figured out, while listening to a favourite story, that 6 did not fit into 9 (with none left over). She identified the problem, and came up with a possible solution – cut them in half. She calculated in her head, and while still listening with at least part of her attention to the story, realised that this would work, although she was not sure what the name of that number was (18) without counting her way through the sequence from 1. (I also did not find out if she had figured out exactly how much each person would get, although she was confident that we would all get the same amount.) Finally, she knew that my answer (9) was incorrect.
Impressive, when you break up the process. And very reassuring to those who worry that maths cannot be learned without being formally taught...
“Nine”, I answered, and carried on reading. I noticed that she was counting on her fingers, but knowing this active young mind to be more than capable of doing more than one thing at a time, I continued reading. I did wonder what she was doing...
“Mom, you’re wrong!”, she triumphantly interrupted our book reading, “It’s eighteen...”
“Oh” said I. Now she had my attention. “Why did you want to know?”
“Well, we made nine scones, and I wanted to know how many there would be if we cut them all in half”
“Oh. Why do you want to cut them in half?”
“Because there aren’t enough for us all to get the same number of scones. But if we cut them in half, there are enough...” (There were six of us at home at the time.)
I was quiet, once again effectively silenced and in awe of the privilege of witnessing the learning process. My young daughter has had no formal tuition in arithmetic. When she has asked for number information, it has been given. She loves board games and card games. We build structures with Cuisenaire rods. And of course she sees the maths in her world when she sets the table, shares out a packet of biscuits, spends her pocket money. Maths is part of our world. Thus, she has experienced it.
What did she do that was so amazing in this case? Think of the complexity of the problem. Experience and practise has made these kinds of calculations seemingly simple to our adult minds. But they are not...
First, she had ascertained (and remembered) that there were nine scones on the tray. Then she had figured out, while listening to a favourite story, that 6 did not fit into 9 (with none left over). She identified the problem, and came up with a possible solution – cut them in half. She calculated in her head, and while still listening with at least part of her attention to the story, realised that this would work, although she was not sure what the name of that number was (18) without counting her way through the sequence from 1. (I also did not find out if she had figured out exactly how much each person would get, although she was confident that we would all get the same amount.) Finally, she knew that my answer (9) was incorrect.
Impressive, when you break up the process. And very reassuring to those who worry that maths cannot be learned without being formally taught...