The annals of science are a series of discoveries of general laws which organised previous special cases. Take any of the monumental discoveries or theories—Copernicus’ model of the universe, Einstein’s theory of general relativity, Lavoisier’s law of the conservation of mass, Darwin’s theory of evolution via natural selection. In each of their respective disciplines, it's possible to detect a marked difference in the state of the field before and after these laws were discovered or these theories were posited. Before, the disciplines were a swirling mess of isolated occurrences, all of which shared some weird consistencies. After, every isolated occurrence morphed into a brick which had its proper place in the structure of the field. These discoveries or theories turned seeming chaos to seeming order.
Another consequence was that, from the point of these discoveries onwards, the teaching of their respective disciplines begun to take a top-down approach; teach the general law first and then explore its application in special cases. For example, students are often introduced to chemistry using the following process:
It makes sense, right? But the top-down approach only really works in highly legible domains, in fields in which it’s possible to organise knowledge and calmly step from basic to intermediate to advanced material. In fields which are less legible, you can invert the top-down method of meta-learning and go bottom up.
For example, Harvard Business School uses a bottom-up approach in its teaching. It uses the case method, which places students in a quasi-real scenario and forces them to make decisions according to current knowledge. This method puts students in situations which compel them to turn abstract knowledge into specific decisions: it gets them to pretend to be managers, department heads, CEOs, negotiators etc., and make choices with constraints and consequences. And after the exercise, the decisions are analysed and discussed to increase the yield of the participating students.
A simpler-to-remember example of the bottoms-up approach is taught by Josh Waitzkin, author of the The Art of Learning. He calls it “learning the macro from the micro.” Josh teaches chess noobs by emptying the board. As Tim Ferriss describes in Tools of Titans:
“The board was empty, except for three pieces in an endgame scenario: king and pawn against king. Through the micro, positions of reduced complexity, he [Waitzkin] was able to focus me on the macro: principles like the power of empty space, opposition, and setting an opponent up for zugzwang (a position where any move he makes will destroy his position). By limiting me to a few simple pieces, he hoped I would learn something limitless: high-level concepts I could apply anytime against anyone.”
The practical aphorism for the bottom-up approach is this: teach general laws using special cases. It’s similar to the top-down model described earlier—the emphasis is still on the few fundamental concepts/basic ideas/general laws, but the direction of approach is reversed.