

Where in other subjects the knowledge you gain is related but not completely contingent on everything else you were taught, e.g. you don’t need to remember too many exact details about the Mayflower pilgrims to understand the American Civil War, math requires a solid throughline from the basic arithmetic, through algebra, geometry, and so on. You can’t really do anything with trigonometry if you didn’t understand algebra well. You can’t really do algebra if you didn’t understand arithmetic. You definitely can’t do calculus if you struggled with any of the previous areas.
So the problem is the continuity required, combined with the way most students learn simply not being thorough enough to completely internalize the intuition for each math concept they’re being exposed to. Ask a 9th grader about the differences between rational numbers and irrational numbers that they may have learned in 7th grade: you’ll probably get answers that are about right, but might start to get a little vague or confused. Thankfully I might be overstating the interconnectedness a bit, but I know I definitely had some hiccups in college related to how I had only learned some of the advanced concepts halfway in previous courses, which led to me just barely understanding the really abstract concepts I started to get into like Stokes’ Theorem and Greene’s Theorem at the end of Calc 3.
GOOD post