By far the best way to learn arithmetic facts is to ‘naturally’ use them in service of solving more interesting or relevant problems. The same amount of time spent doing nontrivial word problems, pattern-discovery projects, playing a game or solving a puzzle involving embedded arithmetic, or just talking about numbers in a group, is vastly more useful both to arithmetic ability per se and to mathematical fluency in general than narrow practice drills, which are not only a huge motivation killer for most people, but also just suck at aiding retention.

I’d say that’s the definition of “remember” rather than “memorize.”

To most people I’d wager “memorize” has a strong connotation for the synthetic version only, with an emphasis on a stripping-out of context.

I recognize that stripping away context can be valuable—-drilling a tennis serve over and over outside the real-time context of a game is extremely helpful.

Flashcards are rarely valuable in the same way. For semantically oriented tasks, an impoverished context is usually not very helpful. Receptive skills like letter and character recognition might be an exception. But even then you’ve got to make the leap to reading at some point.

> no one adds or multiplies enough in daily life for natural memory formation

To the contrary, there’s a fascinating study of children in South America who had very fluent mental math skills for making change because they sold fruit on the side of the road. They couldn’t solve the exact same problem in story problem format in a classroom, though. Synthetic contexts usually don’t transfer well to real life.

Actually, my understanding is that contexts in general are hard to transfer.

> Memorize means "to retain in and quickly recall from memory". Weather that is by synthetic or natural process is irrelevant. From the point of understanding how memory and recall work, yes burning your hand is an act of memorization.

I think in common usage the word "memorize" very strongly implies that it's the lossless storage and retrieval of some highly specified sequence of information. No amount of studying American Civil War history would be referred to as "memorizing the Gettysburg Address" unless you could recite the speech word for word.

> On the other hand no one adds or multiples enough in daily life for natural memory formation. Humans consider the skill vital enough that we have developed methods to memorize them.

Isn't that kind of the point for the other side?

Nobody memorizes the answer to 212+457. There are no flash cards for every possible addition up to infinity.

In my experience, the more people think that math is something to memorize, the worse they are at math.

Kumon students will be able to get 669 faster than the average non-Kumon student simply due to a large amount of practice though. Students don't memorizate of all the possible combinations, but imo that practice helps tune the mind to be sharp in that particular direction. very useful in some jobs.

it is to be noted that math isn't numeracy though. I have dyscalclia which hurt me with numbers but at the college level there are fewer numbers and more conceptual thinking. ended up with a math minor, though that's due to the CS degree requiring so many classes.