> do those "tricks" represent the way math is usually taught in America? Anecdotally, yes -- and damn proud of it! A lot of the backlash against Common Core Ma

> do those "tricks" represent the way math is usually taught in America? Anecdotally, yes -- and damn proud of it! A lot of the backlash against Common Core Mathematics is from people who want Mathematics education to stay that way. The reason is that a huge amount of mathematics educators in American secondary schools aren't properly trained in even elementary Mathematics. At the lower grades (ages < 15 or 16) it's mostly because you can go through all of high school and university in America without understanding anything about Mathematics. For example, most people at the university I attended never took a Calculus course. Everyone was required to take a Mathematics course, but there are math courses that are essentially repeats of what you would expect a non-exceptional sixth grader to understand -- matching linear functions to their graphs and the like. These courses even get recommended by teaching colleges because even Calculus I was perceived as "hard" or "advanced" "math". And Calculus I itself was entirely superficial and mostly trick-based (because calculus isn't proof based except at a tiny handful of elite universities). Result: most Mathematics educators a typical student encounters before the age of 15 have never written a proof (with practical consequences; e.g., they don't know what induction is). Even worse, these educators would probably have a hard time defining a function in terms that a working mathematician would find meaningful (educators now have their own cutesy but non-rigorous definitions for things like "number" and "function"). At the upper ages (~15 until university), I'm convinced it's because teachers are not properly compensated and so teaching doesn't appeal to the best students. Many high school teachers that teach math at least complete an undergraduate degree in Mathematics, although even that is not actually required in many states. However, based upon my anecdotal experience tutoring and interacting with peers while in university, Education students are typically in the bottom half of Mathematics students and often rely on (and prefer :-( ) "trick"-based "mathematics", even in proof-based courses (memorizing formats of theorems and corresponding proofs, then figuring out what symbols/numbers to plug in. But with zero understanding of the underlying argument).