Shiv who is nine was working on completing factor houses with me. I pointed out that 1 is the only number with a one story house as 1x1 is the only factor - it is neither prime nor composite, unique. Then I showed him how the primes are two story houses. Take 2 as an example -- 1x2 and 2x1. Then we looked at some factor houses for other numbers.
We noticed that some houses had an odd number of stories. "Which numbers are those?" I asked. "Ahhh, they are, umm...perfect squares," he answered. I put my finger on the house for the number 24. "Wow! Look at this house. It's really tall compared to the other houses, isn't it?" I queried. Shiv started to write the facts in the stories, then he looked up and said, "It's not as big as zero's house."
His brother who is going into the eighth grade stopped working on his math and looked over at Shiv's paper. He then looked at me quizzically. I returned the look when it hit me, "Ah, yes, Shiv. Zero's house is infinitely tall. Anything multiplied by zero equals zero. God's house, we could say, because it's infinite. Good one, Shiv."
The older brother continued to look at me a little bewildered by his younger brother as I went on. "I have never heard anyone mention that before, Shiv. I am going to write about what you have told me. I can't wait to tell my math mentor. He will like how you are thinking about zero's house."
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Wow, what a cool story. I love the connection your student made between infinity and zero, and the one you made with his ideas. It is so neat when someone else understands you and can help you take it a step farther.
ReplyDeleteWhat a very insightful child! And aren't they all, when we take a moment to listen?