One of the major problems is that most of the high school teachers are themselves not very familiar with math, and are more educated in the very different probl

One of the major problems is that most of the high school teachers are themselves not very familiar with math, and are more educated in the very different problem of corralling children. To be fair to your friend, 90 years ago they probably could've had a productive career in applied math as an expert computer. There was a point when calc tricks could get you a PhD, but those days are gone.