Gentle Puzzle Solving Strategies
Number puzzle solving strategies have often evaded me and to be honest, I am guilty of abusing the trial and error puzzle solving strategy. However, today, I am going to share with you an amazing strategy I have learned that has changed the way we approach number puzzles.
Gattegno focuses on the ability all students do have and that is the ability to see and discover truth, and this strategy is just that, noticing what is truly there.
This is similar to the notice and wonder strategy we use for art, which you can read about here.
Notice What’s Truly There
First, we begin with the puzzle but remove all expectation of solving the puzzle. That is the hardest part of the task.
We all suffer from this, I think. We like to throw things at the wall and see what sticks. In honest truth, the trial and error strategy is instinctive to us all. It is how we all generally learn, but there is a better way.
To start, notice anything and everything about the puzzle. In this puzzle, the kids noticed how many arrows, how many hearts, the colors of the arrows, the shapes of the arrows, how many of each kind of arrow, which hearts had values, where were the arrows pointing, did all the hearts have arrows pointing to them?
What did it mean if it didn’t have an arrow pointing to it? What did it mean if the heart had only arrows pointing to it? How many paths to the end number? And on and on. Nothing is unimportant. Take all observations down.
Puzzle Solving from Noticing
After such an exhaustive study of the puzzle, I finally relented to let them solve. They had all the information to solve. To my delight, the kids solved rather quickly with strong reasoning behind their choices.
I just loved hearing their reasoning. “The heart with no arrows pointing to it is the starting number because no arrows pointing to it means there isn’t a smaller number before it.” “The heart with only arrows pointing to it is the largest number because an arrow pointing away means a number is getting bigger.”
Can I be amazed at how big of a difference of just simply noticing makes? Before, they would have just plugged in numbers randomly without reason. Sure, they would have solved it but we have to realize that the answer is not what's most important. It is the reasoning behind the answer that matters.
With reasoning under their belt, they became capable to use the information. But did they have enough reasoning?
Wondering to Creating
Of course, true to my nature of ensuring a deeper understanding, I asked the kids to create their own puzzles. This went terrible.
As I pondered this disaster, I tried another similar puzzle to see if it helped. This did improve things, but I wasn’t satisfied. Their puzzles were very simple or didn’t make any sense. After much thought, I realized I missed a crucial step, Wonder.
Wonder is a bit like play. When we play, we are acting on our wonders. We wonder what happens if we climb this? What happens when we build it this way? What happens if we use this object this way? What happens when we narrate the story this way?
In math, we wonder what happens when we play with numbers in different ways. And so, we did. We played with the puzzle. What happens if we add the same amount to each heart? What happens if we keep the start number the same but change the value of the red arrows? What will happen to the value of the other hearts and the other arrows?
Compose Puzzles to affirm Understanding
And so, wonder turned into creation. It was magical. They created their own puzzles and now, we can’t get enough. I am making a whole packet of puzzles to study and observe, but I know how you hate to wait. So, I have a sample puzzle study you can download now for FREE.
Also, don’t forget to get on Sonya’s (Arithmophobia No More) email list to find out how to get invited to her free training. It is in her class that I have most of my epiphanies. She is brilliant at showing you how to be a great math teacher and the kids have fun in her class. Who doesn't love theory in action?