There are two very different ways a student can "do" math, and most people never learn to tell them apart. The first is what I'll call "processing math". "Processing" math is fundamentally limited: it can only take you to a destination whose route you already know. You've seen this exact type of problem before, you recognize the pattern, you run the procedure, you arrive. That's it. That's the whole trip. The trouble is that real math problems don't work that way. A well-desi
