Because I’m home with a broken foot, my daughter happened to overhear part of my latest tutoring session.  What she heard was my student abruptly asking, “Do you know how long ago dinosaurs became extinct?”  (This type of comment is very common during our sessions.)

Later, my daughter, who is 15, told me she was amazed I didn’t immediately shut down the dinosaur conversation.  I explained to her that listening to this student is an important part of teaching him.  Over several months we have built a relationship; we listen to each other.  As a result, I can challenge him to change how he solves problems, or to try something new.  It works.

It was only later I remembered another reason I listen (at least for a while) to these apparently random, off-topic utterances.  It’s because they frequently spring from a math-related source.  Take the dinosaur comment.  He wasn’t asking because he didn’t know how long ago dinosaurs became extinct.  Rather, he wanted to know if I knew because something about it was bugging him.  He wondered:  If 200 years ago scientists discovered that – 65 million years earlier – dinosaurs had become extinct, then why don’t we now say dinosaurs have been extinct for 65 million two hundred years?  (I chose to ignore the when-did-scientists-know-it question and instead focused on the concept of rounding.)

I used a whiteboard and wrote the numbers 65,000,000 and 65,000,100.  (Okay, I finessed the date a little and said, let’s just use 100 years.)  We talked about rounding and the fact that it would take a really long time before it would make sense to say anything other than dinosaurs became extinct 65 million years ago.  He seemed content and I was happy that I had answered what turned out to be a good question.

It was only a day or so later I realized I had missed an opportunity to make the concept more real.

What if, instead, I had said:  How long is 65 million seconds?  Next tutoring session we start with this one!