"mathematics is a game of back-and-forth between intuition and logic" I teach/guide Math at our school (we run a small school and currently have kids under age 10) and this is so so true.
This was a very tiring blog post for me. And I have a quip about posts that open with questions but close without obvious definite answer, no matter how simple it is.
I just wrote about this. In fact, you can even see this at play in the video of the kids talking https://blog.comini.in/p/what-happens-in-math-class