Multiplication tables do not afford insight. Problem solving does. Solve lots or problems, and the multiplication tables will stick. Memorize multiplication tables, and you will forget them the day after the exam.
I disagree.
I memorized the “times” tables and somewhere down the line I figured out what they meant and how they worked...all on my own....prolly when we started to do actual arithmetic problems.
At least that’s the way I remember it, but the 70+ years since may have provided a lot of clouds. ☺