I'm excited to share one of my daughter's math discoveries via video, for the first time ever! I just caught up to this technology last week and am thrilled that I can put my new phone to immediate use.
Yesterday she called me over to the keyboard to share something she had discovered. We have always left all kinds of musical instruments around the house for her explore as she will. She has not yet had any formal music lessons (except for three or four penny whistle lessons from her dad) but her current piano style can be loosely categorized as jazz improv and/or piano bar; she really listens to the rhythms and melodies she creates and, even without 'technique', she is making real music to my ears.
Anyhow, on this particular occasion, she had been noodling around and suddenly yelled to me from the piano, "Mama! I discovered how I can use the piano to count up by threes!" As you watch you might notice how her hand movement shows her understanding of groupings. I've been especially tuned into children's gestures since I read this study on how children show what they know mathematically through their gestures. Here's what she did:
After she showed me what she had discovered about threes, she realized she could do the same thing with fives. In this video I love her excitement about finding other, unexpected patterns in the black keys:
None of this is really earth shattering, but any time a child moves her understanding of a math concept into a new mode or realm, it is cause for celebration. I think it shows that real learning is happening.