"As to methods there may be a million and then some, but principles are few. The man who grasps principles can successfully select his own methods. The man who tries methods, ignoring principles, is sure to have trouble."
- Harrington Emerson
In school, we are usually taught "bottom-up processing". First we learn the components (alphabet, phonics, number system), then we learn how to connect them to build more complex units. There's nothing wrong with this - it's one half of the process of knowledge acquisition. But it's also putting the cart before the horse. Nearly everything that you have learned, or will learn, is the result of seeing the whole first, then breaking it down into smaller components until you can go no further. Once there, then you can combine elements into more complex systems, stacking them together until you have come full circle.
This first way of learning, that babies do intuitively, is still the best way. It's how you learned to walk. It's how you learned to talk. And nobody ever gave you a manual for either of those complicated tasks. It's how scientists discovered the elements, then the atom, then the sub-atomic particles. First principles thinking means taking something apart, testing our assumptions, understanding the governing variables, then tinkering - putting it back together, or creating something new by rearranging the components. Another word for this might be play.
I know how to deconstruct and rebuild complex subjects, because I've done it so many times before. As a child, I liked taking apart toys and machines to see how they work, then reconstructing most of them (sorry, Mom!) Disassembling things made it easier to see how to reassemble them, and also why they were assembled that way. If I only had a bin of components, with no context for their relationship to each other, the process would likely have only led to confusion and frustration, like trying to understand a building by looking at each individual brick. Keeping this in mind, I always teach the why, not just the how.
I also focus on prioritizing connections over content. Memorizing something without context is pretty useless. When you learn to cook by following recipes, you learn what to do, but not why to do it that way. It's hard to improvise under those conditions. Yet, this recipe approach is often the manner in which students are taught in school. We expect that once they've memorized the rules or steps, they will be able to apply them. By doing that, we teach students the final step of discovery, not the process that led to it. It's why they may perform well in one area of math, but struggle mightily in another. They see the trees, but not the forest. They know what the rules are, but they don't know why, so they don't know how or why or when they can break them. Teach them the principles of "cooking", however, and they can not only understand and modify others' "recipes", but create their own. That's true understanding, and that's power.