In the US: this article presents an analysis how a person's chosen college major corresponds to their IQ. [qz.com] The interesting thing is that the relationship has remained essentially stable over the past 70 years. At the top of the list are math, science and engineering. At the absolute bottom of the list: education.
These data show that US students who choose to major in education, essentially the bulk of people who become teachers, have for at least the last seven decades been selected from students at the lower end of the academic aptitude pool. A 2010 McKinsey report [mckinseyonsociety.com] (pdf) by Byron Auguste, Paul Kihn, and Matt Miller noted that top performing school systems, such as those in Singapore, Finland, and South Korea, “recruit 100% of their teacher corps from the top third of the academic cohort.”
The article points out that it isn't quite this simple: Top schools place high requirements on all of their students; poor schools generally attract lower quality students in all of their programs. Still, the national averages are clear: overall, the least intelligent students go on to teach. This is an odd priority.
Educational organizations, of course, have a different view. This article claims that teacher quality declined from the 1960s through the 1990s, but has since recovered [hechingerreport.org], with teachers being barely below average (48th percentile) among college graduates.
On a related note, there is a strong international correlation between teacher pay and student outcomes [neatoday.org]. The (rather obvious) theory is that higher pay attracts better candidates to the teaching profession.
No conclusions - just thought this might spark an interesting discussion...