The situation becomes more dire once you realize how essential mastery is for a proper education: if you fail to fully dominate fundamental concepts as a kid, things will seem inevitably harder to understand as you progress throughout the years and accumulate knowledge gaps. Cumulative subjects build on top of themselves, so if you don’t fully understand fractions, there’s no way you can learn geometry properly, and if you don’t understand Algebra, you can’t ever gain deep knowledge of Calculus. These correlations also branch off into different subjects as well — Physics assumes mastery in branches of Mathematics to be fully understood, and high-school Biology assumes basic understanding of Chemistry.

You can go as far to say that all knowledge is interconnected and cumulative in the grand scheme of things, which makes the consequences of said gaps even more unpredictable — they stealthily cascade difficulties into a number of subjects without making themselves known, leaving students disoriented, lacking confidence and with the false belief that they’re incapable of learning certain topics because of an innate ability to do so.

This is why so many people claim to be “bad at math” — it is not because they lack math genes, but because they rushed through the earlier stages of math without fully understanding them. It is no wonder certain subjects can become so incomprehensible through the years — lack of understanding leads to lack of intuition, and lack of intuition leads to subjects seeming non-nonsensically arbitrary. The only way to survive the semester becomes memorization or doing what your teacher wants you to do, not learning what it all means. This is why there’s a high likelihood you know that pi is 3.14 — but you don’t know what pi actually represents.