Primary school common core math is focused on teaching numeracy and conceptual understanding. Students who want a future in mathematics or related fields will take more formal rigorous math in secondary school, often via a "compaction" program that resembles older math programs that result in completion of Calculus by the 11th or 12th grade.
Once your kids get into higher grades, you may end up seeing them be taught the "tricks" that you may have come up with yourself as a math person in previous years. These solutions leverage the students ability to have a functional mental model of how the math works, even if they haven't done as much rote memorization. In a modern world with calculators everywhere, it's better to teach students to be able to identify incorrect calculations quickly over repetitive practice on large, complex sums and products. (Times tables up to 12x12 are still ubiquitous and emphasized, as having those down helps a lot when doing other math.)
Repetitive practice is important - it's about getting exposure to formal reasoning in a "toy" context. You can't get "conceptual understanding" in math without learning what formality and rigor is for.
Once your kids get into higher grades, you may end up seeing them be taught the "tricks" that you may have come up with yourself as a math person in previous years. These solutions leverage the students ability to have a functional mental model of how the math works, even if they haven't done as much rote memorization. In a modern world with calculators everywhere, it's better to teach students to be able to identify incorrect calculations quickly over repetitive practice on large, complex sums and products. (Times tables up to 12x12 are still ubiquitous and emphasized, as having those down helps a lot when doing other math.)