Paint by Numbers

Watch this video on teaching arithmetic.

The best thing a teacher can do when a student is struggling with a problem is show them another way to think about it. Once the "aha!" moment has been hit and the student gets it one way, you've opened the doors to understanding it from other angles. But you're not going to get anywhere unless you make some kind of connection first.

My concern about only teaching the standard algorithm is that it's... well... an algorithm. And an algorithm is just another calculator, except it's hopefully in your brain and not in the box where you sealed away your physical calculator after you realized that you'd never ever use it again (calc.exe doesn't count).

Math is all about reasoning, and if you're just turning another crank on the number machine then you're not building up to anything. I like that some of the other methods revolve around taking simple things that you know and working towards your answer using what you've got. That in a nutshell is the only way I stumbled through math in college. When all else fails, take stock of what you do know and see what it gets you. If you're dependant on an algorithm that you don't really understand, you can too easily find yourself in unknown territory and feeling completely helpless (which is how 90% of students in math class feel).

That said, proficiency with basic skills (like arithmetic) is too darn critical to be lost in a sea of touchy feely. Teaching other methods for arithmetic: good. Not teaching the algorithmic standard for arithmetic at all: bad!