February 26, 2015

This evening, when Robert was changing improper fractions into mixed fractions, he was suddenly startled by the fraction 49/9.  So instead of dividing in his head, he rewrote the problem in a long division format. He still didn’t come with the answer. He hesitated and then he wrote on the side of the paper: “9, 18, 27, 36, 45”  when he got to 45, he already knew the answer: 5 and 4/9

I don’t know why Robert was confused by this particular problem. He was changing many other improper fractions.  Many operations he performed in his head (  23/7, 5/4) and many he completed with the help of  long divisions (82/3, 47/2).  I don’t know either why he forgot how much 49 divided by 9 was. It just happened and there is no point in delving on the causes of his confusion.

The important thing is that Robert used an appropriate tool to help himself recover from a short confusion. He did that without any prompting coming from me.  Writing multiples of a divisor was a tool I introduced to Robert years ago when I was teaching him to divide with reminder. Over the years, I had an opportunity to suggest to Robert to do just that whenever he had difficulties with division.  Today, however, Robert used this tool of the mind (To use Vygotsky’s very appropriate terminology) all by himself.

He clearly appropriated this tool.