As I read the definition of a good mathematician (so often confused with someone who can follow directions), it reminded me of this anecdote about my daughter. I wondered if others have similar stories.
Twenty years ago, my then-4-year-old wanted to be a ballerina. I enrolled her in a beginner ballet/tap class. The second week in, her instructor came to me and said, “She’s such a natural! She picks things up so quickly! You should take her to a more serious dance class.” This puzzled me because my daughter had never seemed particularly athletic or graceful, but what did I know about dance? I decided to watch carefully to see if I could see what her teacher saw.
The next week the dance teacher asked the 3- and 4-year olds to do a simple tap sequence: tap-tap-tap-tap-tap-tap-tap-step (change feet). She would count for them, “One, two, three, four, five, six, seven, eight.” The step should come on “eight”. My daughter’s talent wasn’t for dance; it was that she knew that eight came after seven, so she stepped on eight, instead after the teacher said eight. I saw many more examples of my daughter’s counting knowledge helping her to get the steps more quickly than the other students. She did not go on to become an amazing ballerina, but she is an incredible mathematical thinker!