Doing math without memorizing some basic arithmetic facts is like reading without knowing what the hundred most common words in the English language mean, and having to look them up every time you encounter one. Sure I guess you can do that, but… you definitely shouldn’t.

This contradicts my own experience.

As a kid, and probably still now, I was very reluctant to memorise things, for some reason I never understood but that may be connected with distrust of authority. I still remember how long and hard I fought my parents and grandparents who tried to make sure I would eventually memorise multiplication tables. Instead, I had to develop many tricks to be able to retrieve the proper results without memorisation, effectively discovering patterns to retrieve quickly all the tables from very few memorised numbers. Years later, I remember having done a similar thing in history classes, refusing to learn any dates, so instead finding tricks to tell which events must have occurred before or after another, thus again getting more engaged with the material as a result.

Sure, some material do require pure memorisation, like language learning (that I still hate with a passion), but overall I believe memorisation gets the bad rep it deserves.

I find this attitude to be really frustrating. Based on my experiences teaching math a student is not going to learn how to do the impressive things that you might call thinking if they don't have a solid foundation in how to do the basics. Imagine saying that learning the alphabet or spelling rules is just rote memorization and therefore not worth doing. If a person needs to spend all of their brain power thinking through elementary operations then they will have very little left over for the things that we might call thinking. I have seen too many kids who struggle with Algebra not because they can't understand the concepts but because they cannot do basic things like multiply 3x4 without needing to add 3 to 3 to 3 to 3.