Cultivating Awareness: Seeing the Consequences
Today, I am going to talk more about how the Grapes of Math activity went for us, and I will also discuss two important awareness strategy.The first strategy is allowing the student to see the consequences for themselves. Dave Hewitt discusses this strategy on raising awareness in his article HERE.
First the activity must be designed to allow the teacher to see the awareness of the student. I discussed how the Grapes of Math activity provides such an opportunity last time, but a short review is that it is an activity that focuses the student on providing a process to solve the problem quickly. Focusing on creating a process forces the student away from mindlessly using algorithms.
Let’s examine the first activity in Grapes of Math, the school of fish. When I first sat down with the children, the children wanted to provide all sorts of rods to represent the fish. Pictured above is the blue rod laid over three fishes. This is what Hannah provided me at first. I could have told her no that won’t work, and that was my instinct at first. However, I held back and asked her why she choose that rod. She said, “Three times three, so it can represent three.” I saw what she was thinking.
FOLLOWING THE CONSEQUENCES
She thought each fish could be represented by 3. I confirmed that we could do that, but it is often hard for me to pursue this rabbit trail off the cuff, so I left it as Josiah offered to use the white rod to represent the fish. I was of course more comfortable with this as this is what I wanted. The joy of writing for you what I have done is it gives me time to think about how I would do things better the next time.
How I should have pursued this is by letting her represent each fish in threes. She would have probably come to a point where she decided white rods would be easier to count or we would have delve deep into counting by threes and maybe reducing it back to white rods. I shouldn’t be afraid of such opportunities, but often times our plans distract us from the opportunities to tap into a student’s awareness.
Even though I did not pursue this rabbit trail, the activity was very much a success as I was able to see the kids’ awareness through the many strategies they employed. When Josiah offered ones to represent each fish, we placed a white rod over each fish. They first choose to use a different rod to replace each row of fish. Then Hannah decided to manipulate the blocks into a shape. Josiah saw what she was doing and saw that it could make a square shape.
I asked them if they could see another way to represent the fish to count them more quickly, and Josiah offered another solution using white and green rods. We were getting much closer to the most ideal answer, and I hardly could contain myself. I proposed that we should find another answer. I encouraged them to start again with all white rods, and to this time see what shape the fish made. I reread the poem and emphasized the word, askew. It was time to employ the strategy of directing their attention.
We talked about askew and how it means to look sideways at things or to have a different perspective, so we began to look from all angles at the rods on the picture. Josiah finally saw the square, and Hannah saw it too. She began to push the rods together. I asked them if the fish could be represented with just one color rod besides all white rods, and both the children proposed the purple rod immediately with Josiah providing that four times four is sixteen and is a square. We checked our answer by overlaying the purple rods over the white.
We continued on through the book, and each activity offered a view point that the kids tried to employ on the next activity. The first one being looking for shapes. They had become aware that shapes can help them add quickly and this was a favorite strategy for them. Sometimes it worked, and sometimes it didn’t.
We enjoyed this activity very much. Very little teaching had to go on here on my part and it has given me much perspective about the opportunities I have created with my own worksheets. As my children play with my interactive notebook, my job is to ask why they saved the princess that way and to provide opportunities to stretch their thinking with challenges that match their awareness like “What if you only had red rods to save the princess? Could you save her?”
We must realize as Dave Hewitt pointed out in the beginning of his article that children do come to us already with a mathematical mind. We only need to become aware of their awareness and cultivate opportunities to grow and challenge their awareness.