this post was submitted on 22 Jul 2025
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I mean... Fuck AI and all, but hard way = better is definitely not some universal principal we should be applying to education.
The most famous example is all of the people who grew up when calculators were large and expensive pieces of equipment, who were told "you need to memorize your multiplication tables because you won't always have a calculator with you", which sounds absolutely ridiculous to anyone today.
I think it's important for humanity to ask itself: which cognitive processes should we dedicate our fleshy organic brains to, and which cognitive processes are better off outsourced to external technologies? "AI" as a modern buzzword seems to be trying to positively brand these products that are trying (and usually failing) to take on processes that are best left within the brain.
Did you really not memorize your multiplication tables? Can you do mental math? For me, knowing multiplication tables is a matter of convenience; it takes a few seconds to pull out a calculator and type in the numbers when I'm perfectly able to do it instantly. Even two by one digit multiplication is faster than pulling out a calculator.
It's important to distinguish between what you memorized as part of a rote process as a child as part of your formal education process versus what you have remember as part of your lifetime of experiences. And if your own personal first exposure to multiplication tables was being made to memorize them, you are probably going to think that's the only way to do it.
For example, most adults would probably the ones they use the most often memorized without any formal education. People use halves, quarters, doubles, and quadruples all the time, so the brain creates shortcuts for those.
Personally my older sister taught me the principles of multiplication and division a couple of years before I encountered them in elementary school. So I had already started to think of it as like... A nested adding function. And also using the algebraic properties (communicative, distributive, associative... I'm probably forgetting some of their names) helped me to understand the numbers and their relationships. So memorizing that 10x means you move the decimal place, but then extrapolating that so that n x 5 = n x 10/2 , which is often easier. Or that n x 9 = (n x 10) - n. So memorizing not the results, but the process.
So when I got to 2nd grade and they started teaching multiplication tables my experience was different from my peers. They would hand out sheets of multiplication problems for the class to do quietly, and at first I was about average: faster than the kids who weren't trying, but slower than the ones who had begun to memorize the table. But I was less prone to the errors that other kids would make: mixing up 6's and 9's or 1's and 7's because they look similar, for example. And I quickly got faster than them, especially when we expanded beyond aingle-digit tables. It also helped me in the process of learning division: when we on from just leaving remainders as an R# to actually writing out decimals or using fractions. My peers would get tripped up trying to divide a number that did not fit nearly into the tables they had memorized. Then they introduced exponents, which a lot of people struggled with but for me was the next logical step to take (although my sister probably showed them to me earlier too).
And even today I totally break out the calculator app or even spreadsheet app on my phone. Not for help with the algebra, but to make a record and make sure that I'm including everything I need to. If I were in the grocery store trying to predict what my end cost will be at checkout, it's much more likely I would get it wrong from missing an item, missing a promotion, or not knowing enough about sales tax eligibility than from any algebraic mistake.
You make a good point. I'm interested to know how old you are, because the 'correct' way to teach math has been debated for 70ish years New math was introduced in the 50's, and emphasized the understanding of how base-10 works. This is commonly mistaken for common core math,which put even more emphasis on understanding the procedures used for math rather than the right answer. When I grew up, addition was mainly based in new math, whereas multiplication was introduced as successive addition, but was mostly focused on memorizing tables.
I'm in my 30's. Just barely missed Common Core but I remember hearing parents with younger children complaining about it. I don't remember the math I was taught having any specific branding with it, though it may have been a late variant of New Math.
What I was taught in schools definitely still had a lot of memorization involved. I consider myself lucky that my sister taught me earlier, because I saw a lot of my bright peers struggle with the way it was taught in schools. I never had to study math outside of school for my entire academic career. She helped me to understand computers (she also taught me binary, octal, and hexadecimal systems. Hexadecimal is very useful for a kid with a GameShark and Pokemon).
I don't mean to be picking fights with you but this is a topic I care about - I really think it's a mistake to say "I was exposed to this material much earlier and therefore picked it up faster and more robustly" and then claim that's an argument against rote memorization. Especially considering how few kids are keeping up in math. Your experience was very fortunate and largely uncommon.
The rules and shortcuts you're describing are absolutely part of the work I'm doing with my daughter, but they go hand-in-hand with the "spaced repetition" (ish) approach we're focusing on, of just iterating a lot. One without the other is much weaker - mnemonics are extremely valuable aids, but none of it sticks without repetition. I'd say that all tasks involving remembering lots of minutiae (contrasted with remembering processes) greatly benefit from mnemonics, but fully require rote memorization practice in order to have the dexterity needed for quick recall that doesn't get in the way. So things like chemistry, anatomy, case law.
It's true that multiplication can be kept strictly a "learn the process" task, but your other points kind of just say that the repetition that comes in a person's life later on finishes that work / replaces the dedicated memorization phase. And frankly the process you went through sounds like it involved a standard amount of repetition, you just had a head start so it didn't feel as new or as uncomfortable.
I say only learning the processes is extremely inefficient and will make learning any more advanced math much, much harder. Lacking that strong basis of recall, kids have to think to do the multiplication that is merely an intermediate step and not at all part of the material being learned, moving forward. This reduces (greatly) their ability to engage with the actual subject matter because they are already working to complete the intermediate steps. I've seen it happen firsthand - I think you mean well, but I think your POV on multiplication is way wrong and actually harmful here.
E: I'm conflating mnemonics with arithmetic shortcuts here, I hope you'll forgive that. They're related - remembering one arithmetic shortcut gives you access to many answers, and usually mnemonics serve a similar "get lots of stuff for one significant remembered thing" kind of role.
Honestly I think you're trying to justify your own approach with your child rather than looking at what should happen.
This has been a trend in US education for decades, maybe a century. The days of the old 1-room schoolhouse with a nun who slapped your knuckles for not memorizing your times tables are long past. Another commenter here pointed out to me that, for math in particular, you can see this trend in the New Math and later Common Core.
My same sister who taught me as a child later got a teaching degree, and one of the key parts of that I remember talking with her about was how the overall trend in the industry was to move away from memorization. Especially because they ran into the common issue where students lose good chunks of what they memorized over summer breaks.
Memorization can be effective, but it can also be a crutch. Those same multiplication tables you memorize as a child you then need to find a way to forget if you ever need to work outside of base-10. The cost of the ease and speed of memorizationks flexibility. Sometimes that's a good trade-off to make, but sometimes it's not.
Beyond that, memorization is just plain bad. Human memory is bad- anyone in criminal justice can arrest to that. As an accountant I can as well. You may think you still have your multiplication tables memorized. Maybe you still do, maybe you don't. Maybe you will on a couple decades, maybe not. Depends on who you are and what you do to maintain that database.
I'm also surprised to see you describe learning the process as "inefficient". To me it seems far more efficient to learn the code or function to do something abstractly and how to apply it than to memorize whole tables of inputs and outputs. I also don't know follow how you think learning processes is harmful to advanced mathmatics either. There are very, very few advanced mathematical problems where memorization could be useful beyond what is taught in high schools. Like... Maybe Turing's Halting Problem in earlier iterations? Kids (or adults) don't have to think to multiply if they just remember the table- that's part of the problem. So I think you're the one with the harmful and outdated point of view here.
Well, memorization does have one good advantage. It's easier to teach. Just hand the student the table and tell them to learn it. Very easy to test and evaluate on.
I'm advocating for a mixed approach that serves more kids, and arguing that you had such a mixed approach yourself but don't seem to acknowledge it.
Memorization (done properly, that is - I invoked "spaced repetition", an evidence-based learning technique from the field of education, you're the one talking about corporal punishment from nuns) is effective in precisely this and related domains having tons of minutiae.
It's not that learning the process is inefficient, that's not what I meant - learning only the process and not focusing on rote memorization as well leaves you with only the process to rely on when learning further math (your experience sounds like you got both, regarding multiplication).
Relying on only rules/processes to complete intermediate steps that are not the subject under instruction is what is inefficient. Using rules to reach simple multiplication facts when trying to learn algebra or even just long division is brutal for kids with any attention difficulty whatsoever. By the time they've solved the multiplication answer they wanted, they've lost the thread on the new concept. Rote memorization reduces the effort needed to use multiplication when learning everything else. It doesn't feel that you're reading very carefully here, but it could be me who failed to make myself plain.
I myself am a process guy and high on pattern-seeking. I write software for a living and live in abstractions layered on abstractions - even the physics is invisible lol, nothing (but fans and I guess HDD heads where still used) ever moves. It all feels like pretend!
My point is that understanding processes and relationships in the space of numbers can arise FROM being forced to learn many small truths over and over. A student can identify patterns (the shortcuts) from just learning the facts. Similarly you can get to the facts if you understand the process - like most math there's a lovely symmetry there that you seem unwilling to agree with me about. They both inform and train the brain differently and you seem to have benefitted from that yourself.
We need both, and rote memorization is especially useful in a small number of domains, irreplaceable. Anyone who has gone through an Anatomy & Physiology class successfully will agree too, and I can give more examples. There's no "process" or rules involved.
Anyway, I think we're mostly talking past each other and probably mostly agree.
Never learned them. Can do basic math in my head except hard division, and can't really do it on paper either. Sucks but has t hurt me one bit in the real world. If it's applied math im fine with it.