It's always the combination of conceptual learning and memorization when it comes to learn math. It's like performing a complex computation job once, and then caching the result for fast retrieval. Memorization is for efficiency: it clears the way for our brains to focus on higher-level thinking. The great Euler "memorized not only the first 100 prime numbers but also all of their squares, their cubes, and their fourth, fifth, and sixth powers. While others are digging through tables or pulling out pencils and paper, Euler could simply recite from memory...". Besides, math is all about making invisible visible, about discovery patterns, or about connecting dots. That means we need to have dots to connect, and need to have patterns to work with. If we don't remember them, what the hell can we use for?
On the other hand, there's no need for rote memory. Just practice by solving interesting problems. There are plenty of opportunities to use math every day. There is also a very effective way of learning: work on slightly harder than usual problems. When learning calculus, I started to work on Demidovich's Problems in Mathematical Analysis, and I thought it was hard. Then, I stumbled upon solution book for college math competitions. Man, that was a huge help. After working through the problems, a lot of concepts became clear to me, and Demidovich's problems became reasonably easy too. It turned out the hard problems were hard because they required me to make non-obvious connections, which nudged me to really understand, from different angles, the concepts that I learned in the classroom.
By the way, when did arithmetic become so hard? It seems kids nowadays are being spoiled by their parents...
On the other hand, there's no need for rote memory. Just practice by solving interesting problems. There are plenty of opportunities to use math every day. There is also a very effective way of learning: work on slightly harder than usual problems. When learning calculus, I started to work on Demidovich's Problems in Mathematical Analysis, and I thought it was hard. Then, I stumbled upon solution book for college math competitions. Man, that was a huge help. After working through the problems, a lot of concepts became clear to me, and Demidovich's problems became reasonably easy too. It turned out the hard problems were hard because they required me to make non-obvious connections, which nudged me to really understand, from different angles, the concepts that I learned in the classroom.
By the way, when did arithmetic become so hard? It seems kids nowadays are being spoiled by their parents...