Personally, I think it can be said that the platform was removed and replaced by an elevator, so from the fifth floor to the third floor, his height has been (decreasing), and there is no increase in the middle (the elevator may stop a little in the middle, but it will never rise, and it is impossible for people who have not reached the lowest floor to restart halfway), so it is monotonous, that is, there is no callback (this is not true).
As for parity, I think it's a bit far-fetched. Odd function can consider a perfect four-leaf windmill. A perfect four-leaf windmill must be 90 degrees each, and the two opposite origins are symmetrical. Four-leaf fan can also be considered. What is the perfect s and so on. ? It's better to have a teaching aid, such as S. You set up a coordinate system with the midpoint of S as the origin, then rotate 180 degrees from it, then overlap, and so on, and then judge why they can overlap, so that you can draw f(-x)=-f(x). Even the function is easy to handle, just find some symmetrical figures and you will understand.
Talking too much, mathematics is actually boring. It is best to find a good teaching method. Personally, I think your idea is great. At least I didn't meet a teacher like you, or I might have improved my grades.