I was not planning on writing a post today, but I was so excited during my two minutes of math with Katie that I felt the urge to document and share the experience right away.
Recently I introduced Katie to the concept of multiplication (something I will write more about in a later post) and today we were computing 5 times 7. I was laying out the chips in rows of five, and Katie was counting after each row. In the past, whenever we had some number of objects already on the table and we added a few more, Katie would always count all of the objects from the beginning. But today, after each successive 5, Katie continued counting from where we left off. And this was not a consequence of me laying them out very quickly; after each row I would point out to her that now we have 5 times 2, 5 times 3, etc.
I am fairly certain that Katie did not realize that she had a revelation and was doing something differently from the way she did it in the past. I would not even be too surprised if next time she went back to counting from the beginning again. Nonetheless, it feels like a definite step forward :-). As usual, I would love to hear about other people’s experiences with this!