I tutor middle school math. I find that many of the kids are not really fluent in their multiplication tables. I don’t bet they are required to memorize them (’too boring’)(’not conceptual enough’). But kids are concrete. Give them memorization, they will do it and master it and then they will have success.
(don’t get me started on math textbooks)...
Memorization of tables is not concrete, it's the ultimate abstract. Now if you use something like base10 blocks or other manipulative to illustrate what addition, multiplication, and even area and volume really mean or are, that's something concrete. Not something that will work with all kids, but it helps to some extent with all, and it does "work" with many or most.
Then once they understand what they are memorizing, the memorization goes faster, and they can use what they've memorized.