In our math reading, the point was made that kids are natural pattern-finders. I think it is this quality that helps them to make sense of their world, and come to play an interactive role in it. They recognize the pattern of a face very early on, and then the pattern of language, and eventually the patterns in written words. This sophisticated ability to find patterns is also what helps them gain mathematical understanding.
In my kindergarten classroom, I saw an interesting example of a young girl determining patterns. We were working on a calendar activity where she needed to fill in the numbers on the calendar. This little girl wrote the following sequence: 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,110, 111, 112, 113, 114, 115... and so on. At first I thought, "What is she doing?" But then as I tried to figure it out, I realized that for her, the pattern of writing the numbers greater than 10 was to write 1 and the sequential (1 - 9) number. This works for 11, 12, 13 and so forth in the teens. But in her mind the pattern continued, so that "20" became 1 and 10, or 110, and then "21" became 1 and 11, written as 111, and then "22" was 112, and so forth. I was really quite intrigued by her thinking, and wondered what her "30" would look like, but unfortunately she did not have time to finish. I did end up telling her what a creative way she had written 20 (and so on), but I also pointed to our number line, and showed her the conventional way of writing 20. I told her that maybe one day she could write a story about a secret number system, and she could use hers for that!
I think if I had not been aware of the fact that children's brains naturally look for patterns, I may have simply gone over and told her she was not following the directions. I may have filed away a mental note that she is a bit behind in math concepts! But since I looked carefully, and tried to figure out what she was thinking, I gained a window into her very creative thought process.
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