[davidmurdoch]

I guess I'm just trying to suggest that teachers sometimes might think they know why things are being taught, and make claims like "you wont always have a calculator" as the reason for learning mathematics.

One conclusion might be that it'd be better for some students if teachers understood the why, as they might change their approach on some subjects. An example: knowing that certain equations and patterns EXIST, and which kinds of problems they apply to, is generally much more important that knowing the actual equations by heart themselves.