I wanted to add a video about teaching math to this “short film” collection on this blog.
“Lukey B.”. the Physics Genius, presents “Calculus at a Fifth Grade Level”, which is potentially aimed at an audience for age 10.
He says that calculus is difficult for some students (like freshmen in college) because they don’t get the concepts, not the calculations. The basic concepts are limit, derivate (rate of change) and integral (area, volume, or “space time” measure). From a philosophical point of view, “measure” is the most important concept, the size of something (in set theory). My entire life, as it has been lived to date, has a “size” which will exist forever (as a final value) after I’m gone.
So Lukey goes through examples of setting up limits (defining “one divided by infinity”, which is a concept but not a number) with real objects that become more numerous, and that get tinier in some sense.
The video causes me to ponder whether I could or should have become a math teacher “in retirement” (licensed) in the mid 2000’s. There were many reasons why I did not, but I certainly could have presented lessons this way (and would have).
Nevertheless, compare this to the videos solving tricking math problems (evaluating unusual integrals, for example, that abound on YouTube).
Illustration of integral as a limit, Wikipedia embed, click for attribution