Quite some time ago while in a colege class on Genetics on exam day I was sitting in the front row while the professor and his assistant were looking over the incoming exams. I overheard his grumblings about the lack of math training students were getting these days and how it was effecting there work.

In particular he said " .. and all they teach kids these days is manipulation."

I was not and still not exactly sure what he meant. Though I can see the manipulation of equations is sometimes tedious and mundane and a matter of routine .. I have also seen some rather slick and amazing manipulations of equations.

I can rememner my class being deadlocked in a rather stubborn Calculus derivative and not knowing what to do to get things moving. The teacher added +1-1 to part of the equation .. adding zero and pow the whole equation started to unfold. I thought that was slick.

In the movie the "Karate Kid" the wise teacher stressed "balance" as the key to practicing Karate and even life. If balance is off best go home as everything will be off !!

So .. if you were the wise mathematician starting on day one with a new student .. What would your grand lesson be ? What is the essence the very foundation of becoming a mathematician ?

Cheers ...