One of my favorite aspects of math is how, in many cases, we developed new tools to account for the limitations and inefficiencies of the old ones. One of my favorite parts of math education is how we can highlight those inefficiencies with a well-posed problem and justify the use of new tools.
For instance, let’s say some students are awesome at calculating the slope between (-2, 5) and (1, 11) by counting unit squares by hand and then dividing. (ie. “Three over, six up. The slope is two.”) Unhelpful High School Teacher teaches them the slope formula, assigns them the same kind of problems, and punishes the students who don’t use the newer tool even though the older tool is easier. Helpful High School Teacher asks the students to find the slope between (-2, 5) and (999998, 2000005).