Being forced to do rote exercises sometimes makes you creative. Solve a thousand trivial multiplication problems and you will spontaneously discover lots of shortcuts, patterns, intuitions that can warn you when you make a mistake and so on.
A common issue I notice when people discuss the terrible state of math education in the US is that teachers demand that you solve a problem a specific way, such as multiplying two-digit numbers by drawing base-ten blocks and applying the distributive property.
People who are good at doing multiplication in their head think the method makes perfect sense and don't know what all the fuss is about. But I believe that those people learned how to apply the distributive property "by themselves". That is, by adults forcing them to multiply two-digit numbers over and over until they developed an intuition of the distributive property by necessity.
When people who didn't go through countless drills are taught the base-ten method directly, they have a harder time understanding it. So ironically it is the students who "mindlessly" drill trivial computations over and over that are more prepared to have a "true" understanding of the distributive property, while the ones whose teachers believe drilling is for chumps and try to just explicitly show them the true distributive right away, they end up memorizing the words of the distributive property without understanding it.
A common issue I notice when people discuss the terrible state of math education in the US is that teachers demand that you solve a problem a specific way, such as multiplying two-digit numbers by drawing base-ten blocks and applying the distributive property.
People who are good at doing multiplication in their head think the method makes perfect sense and don't know what all the fuss is about. But I believe that those people learned how to apply the distributive property "by themselves". That is, by adults forcing them to multiply two-digit numbers over and over until they developed an intuition of the distributive property by necessity.
When people who didn't go through countless drills are taught the base-ten method directly, they have a harder time understanding it. So ironically it is the students who "mindlessly" drill trivial computations over and over that are more prepared to have a "true" understanding of the distributive property, while the ones whose teachers believe drilling is for chumps and try to just explicitly show them the true distributive right away, they end up memorizing the words of the distributive property without understanding it.