As I said in that other post, the main thing is to get kids to understand rather than just follow procedures. A derivation by itself may not be enough. I like to visualize things, so a visual explanation helps. It also helps to develop algebraic intuition. This means being able to look at an expression and knowing roughly what its graph look like. What happens when X is very big, very negative, zero, etc.
I home schooled my kids and used Singapore math books which are good. I also managed to be a math major without ever taking probability, so I learned this on my own with this book:
https://www.amazon.com/Elementary-Introduction-Theory-Probability-Mathematics/dp/0486601552/This Russian book is an excellent example of what good high school math could be.
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