Forced Awareness: Take Two
Well, our afternoon math session went well, but maybe not in the way I expected. Forced Awareness was achieved but we did not complete the series of questions.
I decided to go back to the very first set of questions in the series of questions provided in Dave Hewitt’s article. I stuck with the apple modification because it really made things go more smoothly. The kids understand apples. The kids really got into the rhythm of answering the questions, and this time I wrote down the arbitrary on our large white board.
1 apple divided into 1/nth = n
They loved this, and we started to just plug in random numbers to see if it was true. They knew it was true by the line of questioning, but I guess seeing it in the form above made them uncertain. I didn’t mind this exploration. It reminds me of how one takes apart a gadget, puts it back together, takes apart again and so on just to make sure they really understood how all the pieces went together.
We went through the next series of questions but this time to help them see the pattern I created a chart. My kids are very visual, and this I believed was a necessary and important addition to the line of questioning.
As we went through this series of question, they chanted away the answers, and soon I felt comfortable with providing the arbitrary of the next generalization. Again, I provided it in the context of the apple.
Number of apples divided by 1/2 = Number of apples times 2
Then I decided to tell them how we can use letters to represent the unknown number of apples, and then plug whatever amount of apples we want to get the answer.
x divided by 1/2 = x times 2
They quite enjoyed again plugging in different numbers. It felt different to them then me asking a series a questions. It wasn’t until they played with it that they decided that it was exactly what they had discovered. Sometimes children will go along with what you say just so that it would be the end of it. It’s why I value both deconstructing and constructing ideas.
We moved on to the next series of questions, and it was pretty much the same. I provided a chart for the answers they provided me, and they chanted away.
They began to describe what was happening, so I gave them the arbitrary again first in the form of apples.
Number of apples divided by number of equal pieces the apple was cut= number of apples times number of equal pieces of one apple
They always agree with this form of it, but when I make a move to the form below, I see that look of uncertainty.
x divided by 1/nth = x times n
I let them again play with it so they can confirm that it does represent their understanding. At this point, they were tiring out and losing interest.
I tried to proceed to the next series of questions. I should have stopped though before these questions. It became apparent that we might need to play the fraction race game quite a bit more before we are ready to transcend to the next series of questions. The wording of the question just confused them. As JoJo said, “The words are twisting around in my mind.”
I decided at this point it was time to be done with this exercise for a while, and I think we will have some fun this week playing a few different versions that I created of the fraction race game that I learned at the Gattegno conference.
The fraction race game is a very valuable exercise for students, and it should be played often. You can read about it more HERE in my very first post. I have a freebie in my TPT store that explains the game and provides a fun setting for repeated play. I also have different versions of this game in my Fraction Exploration for Cuisenaire Rods product.
We have really enjoyed this game, and for the youngest child, I wouldn’t play it as a game. I would just let them explore the length provided with a variety of different rods. The child will use it for a number building exercise in the beginning and then the exercise will turn into discoveries of fractions, factors, multiplication and division. The activity is quite versatile and that is because of the Cuisenaire rods really. I just made it more playful.
Now that I have practiced forced awareness using someone else’s line of questioning, I have been contemplating on how to use this for the discovery of the Fibonacci sequence. Look for a post soon on it and I will include a Fibonacci Freebie!
Have an idea on how to use Forced Awareness? Comment below. I would love to hear.