I disagree, the most productive moments in my math education were spent "discovering" patterns while trying to solve problems, having been given just enough too

I disagree, the most productive moments in my math education were spent "discovering" patterns while trying to solve problems, having been given just enough tools to attempt the problem. Credit to Szeszlér Dávid goes to those formative experiences. The next lesson, after we spent time "discovering" and likely failing, we would be given the last tool we needed to solve the problem. That discovery process cemented the lessons and understanding. I still believe that there is also value in rote memorization and practice, as you simply can't recognize patterns unless you have the fundamentals upon which those patterns are based, mastered. Only then can you start abstracting complexity away mentally, and then do effective "discovery" of new concepts. I didn't encounter this teaching method until college, but I don't see why it can't be applied at an earlier age. One of my earliest memories was when I "discovered" that 2 + 2 = 4. I distinctly remember the moment where the concept of addition and subtraction clicked for me, and it didn't happen in a classroom. I was playing by myself and counting my fingers out on the front lawn. http://www.cs.bme.hu/~szeszler/ http://www.cs.bme.hu/~szeszler/