When I was young, I never managed to remember all of the multiplication facts (up to 12) despite doing flash cards and such. I don’t know why it was never addressed, but I managed to get by in school. In my adult life I have tried several times to remember them, but none of my approaches have been really fruitful. It seems that remembering them feels too arbitrary; I just see a bunch of numbers that don’t mean much to me. I like to do things in a dignified and logical way, so assigning unrelated imagery to numbers also feels arbitrary for me. Any ideas? Perhaps I am too stubborn about my approach, but I like things to have a justification.
I posted here (up to 9 x 9). Maybe this will help.
For learning any sorts of dry data (times tables, memory encoding systems, etc.) I recommend two things:
Find notable patterns within the data
For example, in the 9-times table, every pair adds up to 9 (e.g. 3x9 = 27 and 2 + 7 = 9). In the 5-times table, every odd answer ends in 5. Icosencephalic has a lot of great ideas in the post they linked, and I’m sure you can find others too.
Use a flashcard software / spaced repetition
You want to review the items little and often until they are easy. You can make your own flashcards on paper or a spreadsheet, but there are great apps that can help you here - such as Mnemosyne, Anki and Flashcard Deluxe.
I’ve written more about here about spaced repetition for mental calculation, but the principle is fairly straightforward.
With a combination of these two approaches I expect you can learn them fairly quickly. Then progress to another type of calculation training that uses the times tables, such as cross-multiplication.