I think this was completely lost on all my math teachers growing up. It wasn't until I started teaching myself programming and exploring the patterns of the uni

I think this was completely lost on all my math teachers growing up. It wasn't until I started teaching myself programming and exploring the patterns of the universe and reading philosophy and science and even too from being a musician and teacher did I start to FEEL and KNOW math and experience it's concepts directly. Not just memorize steps. I almost feel like math and philosophy should be combined in school into a hybrid course that is very experimental (verbal hypotheses, mathematic proofs) and should focus simply on investigating the world of ideas around you. Get them into a mode of thought where your creative and skeptical insights can get you into mental conundrum, and your mathematical skills can help you get out of it. How wonderful would it be to get students to "rediscover" fundamental insights about the world? THEN you crack the book open and teach them who discovered it first 2000 years ago.