Originally Posted by tortuga
Originally Posted by 22B
A deeper understanding of mathematics allows one to mathematically reason much more quickly. This is true at all levels.
This is true. But its converse -- "Reasoning more quickly in mathematics allows for a deeper understanding" -- is false. These timed tests assume the latter because the former is true and more importantly because timed testing is an easily quantifiable, low-cost measure of 'progress' in an education system that currently rewards schools for performance on short-term metrics. So perhaps a basic failure in logic (assuming a converse to be true) is to blame, which is ironic since logic gets such short shrift in the math curriculum!
I would say that if someone tried to measure future advanced mathematical ability by testing speedy arithmetic in kids, then there would be unacceptably too much "noise" compared to the "signal" they are trying to measure. But nevertheless there is a signal there whereby some people have certain characteristics that enable them to have advanced mathematical ability in the future, and those same characteristics enable them to be speedy at arithmetic as kids.