I thought I was weird for always breaking apart multiplication problems in my head like that.

Good to know I'm not alone.

Same with addition, 1324 + 1872 is just 2000 + 324 + 872 which is just 3100 + 24 + 74 which is 3196.

Math is about creativity, somewhat ironically. ;)

And fives are just (x*10)/2

I consider memorizing multiplication table as caching, and find it incredibly useful when doing mental computations.

There is a distinction to be made when discussing 'rote learning'. It's always better to understand than to memorize, but there is a case to be made for memorizing some (more mundane) information as an optimization.

I learned my multiplication table in Chinese (mother tongue), which was way easier when every line has the exact number of syllables (4), almost like a poem. I believe I was taught at school in grade 1 or 2 back then, but I (and most other people) had it memorized at an earlier age. It's easy enough to "teach" my 3-year-old just by reciting it in front of him.

Memorizing multiplication table in English is a lot less intuitive, which I attribute to many people's disdain (or pure hatred, depending on whom you ask) of it.

I'm all for teaching a man to fish, but if he's starving at this moment, save him now by giving him the fish fish first before teaching. A dead man doesn't do much learning.

As for my son, he hasn't learned the multiplication table yet, but he's always interested to have us repeat it to him. (Ah, the curious minds of 3-year-olds.) In a few years, once he has learned the concept of multiplication, it'll be easier for him to apply it for the rest of his life if he has the table memorized. Before that time comes, the table is nothing but nursery rhyme to him. And that's fine with me.