I’m teaching mathematical proof writing to a few of math teachers (in the US) this summer. In the beginning of class, I send a survey asking them why they are here. Most of them are here for getting master degree in teaching to further secure their teaching position. I sense a bit of reluctance, since on the nose mathematical proof writing does not relate too much to teaching mid/high schoolers.
I wish I know how to motivate, but I don’t. I was trained formally, and was not aware of some concrete applications of higher math until I taught an applied algebra course last year. It’s definitely great to see how group theory is actually used in a nontrivial way to real life problem (coding theory, crypto.. etc).
While my knowledge base was extended a bit from that, it seems to only motivate those who are interested in CS. How about other students? I sincerely believe that there are ways to motivate the not-yet traumatized! Please share your experience on (could-be) successful ways to motivate mid/high schoolers. Thank you very much in advance.