We have all felt it. Imagine walking through a thick fog and you can even barely see your feet. Suddenly, the fog clears and you can see for miles in many different directions.
Today, after a short discussion on simplifying expressions, a student that frequently needs assistance in class had asked for my help with a problem. I started with the basic:
Me: What did you do?
Student: (explained exactly what he had done)
His solution was exactly what I was looking for, but not at all what I had expected.
Me: Okay, so what is your question?
Student: Well, I am stuck. I don’t know what to do next.
Me: There is nothing you can do.
Student: (with a puzzled look on his face) so that is all I need to do?
Student: Really?! I get it now!! It makes sense after you showed us that a simplified equation is equal to the given equation!
He proceeded to perfectly complete every problem on the activity.
Bingo. Seeing it all come together for that student was a special feeling. I could see the excitement and pride in his eyes. He had felt accomplished, but not as much as I. Especially after a day when I felt like I was talking to 25 mannequins sitting in desks, witnessing this was very refreshing. It also reminded me that I do know what I am doing after all.