Originally Posted by

**Soroban**

My experience was almost magical.

I did okay in college, got my A's and B's in my major (Math).

Then I started teaching.

For example, I was to teach the Law of Sines the next day.

I reviewed the derivation in the current textbook, taking careful notes.

About halfway through, I said, "OMG, this is so simple!"

The steps were so logical, I didn't need notes.

This happened with 99% of the topics I taught.

Everything fell into place . . . piece of cake!

Question: Why wasn't all this equally clear when I *first* learned it?

I took notes, memorized formulas, did practice problems,

. . and still worried when I took an exam.

And now I wonder how I could get only a "B" on such simple stuff.

I assume it has a lot to do with Maturity.

By the time I began teaching, I had had graduate-level courses:

. . Projective Geometry, Topology, etc.

Perhaps my newly acquired "height" gave a better perspective

. . on the "lower" topics?

That's my guess.

The same happened with Calculus.

Once I had to teach a topic, it was forever simple.

(I can still derive the Product Formula

from the definition of the derivative.)

I assume that many of you have had the same experience

while tutoring. .Once you explain a concept to someone

the whole idea seems to crystalize in the brain, and you

have an *ah-ha!* moment. .And your reaction is "I see!" ...

or better yet, *"Of course!"* .And it's yours forever.