Questions

I never tire of seeing glimpses into Casia's thought processes. Yesterday, she was reviewing mitotic cell division and came to me with a question. She wanted to know what happens to the parent cell, in a single celled organism, when it divides its DNA in half during replication and then, through the stages, splits into daughter cells. I thought she was confused about the process, so I started to review the various stages and she stopped me. She explained that she understands how the process works, she wants to know what happens to the original cell. Does it cease to exist? Is it dead? Are there now two of them? Just half of it? Wow! Well, that was an unexpected questions and it led to an interesting discussion, one more philosophical that biological in nature.

Then this morning, Casia was given a new problem in algebra that she hadn't seen. Previously, we had covered multiplying polynomials and she had that down. Today, a question popped up about factoring a quadratic equation (x² + 7x + 10 = 0). I was prepared to have to break it down for her and explain how to figure out what two two-term polynomials could be multiplied together to get the three term polynomial. Again, she stopped me in the middle and told me she's got it. Skeptical, I asked her to show me what she has to do. She said it's obvious; the first term is a square, so the first term of each of the factor polynomials will be the square root of that term, or x. And if in the first polynomial we call the second term 'a' and in the second polynomial we call the second term 'b', then a + b must equal the coefficient of the second term, or 7,  and 'a' x 'b' will equal the coefficient of the third, or 10. She proceeded to quickly do the math and find the answer.Yup, she got it and on her first introduction with no instruction. Sometimes she makes my job so easy. But it leads me to a more important question....

If my nine year-old can figure out algebra on her own and contemplate the demise of the parent cell in its quest to replicate itself, why can't she figure out that if she wears a skort and a short sleeve t-shirt when it is only 40 degrees out she will be cold?