20150908 YOURS IS NOT TO REASON WHY,

Just invert and multiply.

The name of Steven Leinwand's article was "It's Time To Abandon Computational Algorithms". He explained what exactly had to be abandoned in the following words.

...the formal, paper-and-pencil computational algorithms that constitute the core grade-school mathematical experiences of most American youngsters. It's about mindless procedures like "carrying threes into the tens column,'' "six times seven is 42, put down two and carry the four,'' and "eight from two, can't do, cross out the five, make it a four, and borrow 10.'' It's also about memorized rules like "yours is not to reason why, just invert and multiply'' that, for most students, meaninglessly enter one ear and leave the other.

To me, the most striking part was "yours is not to reason why". If that's how they taught, such practice should have been abandoned immediately. Or was it just an innocent piece of school folklore?

I launched a brief investigation (I believe, it was two years ago), and my findings were even more striking. Many people were asking why invert and multiply. Many people were answering, and the answers were quite unsatisfactory. Moreover, some people were asking where did the line came from - probably, because it was distorted - and I did not see any such question answered.