The past few months I've been transfixed by the concept that there are some things people just have to learn on their own. The classic example, of course, is "love." No matter how much you tell someone their freshman relationship is not going to last forever, they won't believe you until the breakup happens. There seem to be enough exceptions that EVERYONE thinks they are the exception.
As a teacher, it's interesting to see these life lessons play out in front of my eyes. Year to year I teach the same subjects to new groups of people. I often start out the year playing Carnac the Magnificent:
You will be challenged in calculus for the first time in your mathematical lives--for some of you, the first time ever. Some of you will rise to the challenge, some of you will want to give up. Many will try to transfer out of the class to keep your GPA high.
Those of you who stay in the class, you will learn more about the background of the math you already think you know and expand that understanding to new material. You'll have to rethink what you think you know about math and, in some cases, life.
At the end of 9 weeks you'll cry. This may be your first B or C. You will adjust your expectations. At the end of 18 weeks, you will cry again. Some of you will be happy just to pass, some of you will be surprised to hear that you have an A and are exempt from the semester exam.
You will not want to come in for help. You will try to skate by with your old methods of learning math. You will think you're a senior and be able to rise above all this stuff I'm saying and not work hard. You are thinking it right now.
Next year, you will come back and tell me how much my class has saved you in your college class.
So sayeth the Great Carnac.
But, regardless of the warning, it plays out the same.
It's interesting to see the light bulbs flash every year over the same topics. It's funny to hear the same "aha"s or "You know..."s every year.