By the way, that is a common misconception that you implied.
That there is a shortage of math teachers mainly because the
requirements to become one are prohibitive. Actually, if all
the math teachers with credentials would teach math there
would not be a shortage.
A significant reason for the shortage is the high numbers of
credentialled math teachers who quit teaching math. Teaching
math is a revolving door or if you think of the supply of
math teachers being a partially filled bucket, then picture
that bucket having a hole in the bottom.
What made that hole? Miserable working conditions are the
cause of the hole in the bottom of the math teacher supply
And it isn't exclusively bad math teachers who quit.
Statistically speaking, the highest qualified math teachers
(highest IQs, highest SAT scores, highest college GPAs,
attended the best colleges, etc.) leave in higher
proportions than the least qualified ones. Being a "good"
math teacher will not protect you from the horrid working