Truly learning math makes wise thinkers

[pangaia]

1. As stated, this is true when studying anything.

When I was a freshman music student back in the 1960's at a rather prestigious music school, I was fortunate to have quite a few brilliant, creative, one-of-a-kind teachers.

My freshman music history teacher did not have us memorize this piece by this composer. No, he gave what he called 'drop the needle tests.' He would literally drop the needle on the record and we had to give the period, decade and which composer wrote the piece....AND WHY.

In a course on Mozart and Hayden, the focus was on learning the differences between the two composers, which, at that young age, was not easy for us. Part of the final exam was to sing an aria from a Mozart opera in front of the class, whether or not we were singers! I am not and never have been a singer.

I sang "Konstanze, Konstanze, dich wiederzusehen … O wie ängstlich" from Die Entführung aus dem Serail. I could sing it to this day, although you would NOT want to hear it.

I am in the debt of these and other fine teachers for encouraging me to think, ponder and question, and not just spit out memorized garbage.