I am an applied mathematician by degree but most of my math work has been as a teacher at a supplemental learning center focused on math and critical thinking. Most math teachers have a limit to their scope of mathematical expertise as teachers, i.e. 3rd grade teachers really only need to be masters of 3rd grade level math while being cognizant of what to expect coming out of 2nd grade and what 4th grade teachers expect to come into 4th grade. I taught all ages so I had to master pretty much everything up through high school level stuff.

That said, most of my stuff applies to learning grade school and high school level math. If someone wanted their kid to be bad ass at math, they could do a LOT worse than having me shadow and teach the kid. The track record doesn't lie. My students won awards in increasing quantities each year they competed.

I have a lot of mental math tricks. I look at etymology and morphology and use that to help students understand. I work narratives into my teaching. I lean heavily upon the Socratic Method.

I haven't taught in a while though. I've been working as an engineer. I still don't use a ton of high level math for that though.