I'd claim (perhaps not even contrary to what you're saying) that memorization and competent analysis/understanding are really two sides of the same coin.

"Here is some long sentence that doesn't really say anything and which you've probably never read in your life before."

You could now probably recite that sentence with near perfect accuracy; at worse changing it in very slight ways that are still functionally identical. That's an absolutely remarkable degree of memorization - one pass for 22 words, 119 characters!? Of course the reason it's easy and natural is because you have an intuitive understanding of what you're memorizing and so one word kind of flows into the next to create the singular whole.

Amateur chess players often find chess masters able to recite their games from memory as evidence of some sort of super-human memory that must be what enabled them to become masters in the first place, but it's completely false. It's the exact same story - when a strong player plays or sees a game, the game tells a story to him not especially different than a very short story. And so people are not recalling random moves or positions from memory but instead the story that those moves and positions tell. A master reciting a game is no more impressive than a "normal" person reciting the plot of a famous short story, let alone one that they wrote!

So for instance I remember from high school memorizing the order of the presidents (yeah... great school...) but finding it relatively easy by instead remembering the logical stories there. For instance instead of just remembering JFK-LBJ-Nixon, etc you remember the story of JFK getting assassinated, LBJ coming to power (and JFK's wife's view of him), then Nixon coming to power and grinding the old axe he had with JFK and scrapping the space program, followed by his VP (Ford) becoming president after Watergate, then losing to good but incapable Carter which led to TV Star Reagan, etc, etc.

I couldn't tell you the order of the presidents at all, unless you give me one and then I can recount the story of how we got from him to where we are now. Because like most of all people I suck at memorization, but also am pretty decent at recalling interesting stories.

There is a lot of evidence that I think backs up your anecdata. For example Massachusetts has the highest performing public school system in the US (arguably, but by many measures) and their curriculum is based on the content heavy Core Curriculum (not to be confused with the watered down Common Core) created by E.D. Hirsch. Hirsch was a college professor and his argument is that knowledge is a significant portion of literacy, he witnessed this first hand trying to teach college freshman that simply didn't have the background knowledge to understand the college level books Hirsch was teaching, even though they had no problem reading the words. Hirsch's books "Cultural Literacy" and "The Schools We Need and Why We Don't Have Them" go into detail about this and he has some essays available online that are worth reading.

Anecdata plus one. My exact experience tutoring high school kids. Some could totally solve the problem, but the inability to remember the basic facts to start with meant getting the wrong answer, despite an impeccable logic trail.

The cost in time to derive basic facts that would have been instantly available had they been memorized also harmed the ability, especially on tests, to get to the end within the time available. 'Drill and kill' has its merits and, if done right, gives the kids a sense of accomplishment and progress.

If you start with the wrong facts, or missing facts, you don't end in the right place.

>The biggest differentiator between the students who scale up quickly and those who scale up a bit more slowly is their aptitude for memorization....

>But the students who struggle all struggle for the same reason: they cannot remember at the moment of writing their paper the basic facts that give context or even give meaning to the documents they are to analyze.

It sounds like what you're describing isn't about students' ability to memorize, but rather about students' ability to develop their own mental models. Luquet and Piaget demonstrated that the ability to synthesize information to develop mental models isn't particularly connected to the ability to memorize the same information.

I was having a conversation/debate with a friend this past weekend along similar lines:

I have an extreme amount of trouble memorizing basic facts, and so I can't recall a lot of historical dates. Things I didn't know which bothered her included the year America signed the declaration of independence and the year we entered World War I.

But, I knew how long World War I lasted, and that it coincided with the Spanish flu, and proceeded an economic boom period which ended in the Great Depression and then World War II. I'm quite good at remembering stories, and so I knew the context of these events—just not the specific year they happened.

Which I think is fine. Context is what matters.

My friend said that for her, knowing the date is what lets her recall the context. Because of what she memorized as a child, she's able to form a timeline of history in her head, and see when things happened and how they coincide. And I will admit that I sometimes have trouble forming a similar timeline, and it's a handicap. But I mostly manage; I have a limited number of hours in my life and I focus my energy where it makes the most sense.

I guess what I'm trying to say is that people are different. It may be that most students are like my friend and the children you tutor (which is something I should keep in mind, as I'm actually training to become an elementary school teacher). But it's not necessarily true for everyone. I resent the fact that when I was in high school, I had test questions which asked "what year did Christopher Columbus arrive in America". I studied for hours trying to commit these facts to memory, and I still got the questions wrong. But if the test had asked "how did Christopher Columbus's arrival in America affect the European economy", I could have answered easily.

Perhaps that explains why Indian and Chinese secondary education can perform so well for their top students: even if they emphasize memorization rather than critical thinking, at the end of the day they can still pick up the latter without suffering from the former.

I have dyslexia (specifically a weakness in memory) and agree with everything you say. When not armed with a decent computer I can use as a crutch for my memory I'm noticeably weaker at critical thinking given the time spent recollecting fundamentals.

> Good memorization skills are a huge leverage and it is something that can be learned and practiced.

Any recommendations in how to get better at memorization?

If we're slinging anecdata around I may as well offer mine up as a long-underperforming student that also somehow took night classes at college for software when I was 11 years old.

The teachers may force the kids to memorize, but that doesn't mean it does them any good in the long run. I met tons of kids that memorized mathematics from 8 to 13 years of age in Canada. I struggled badly with fractions when I was 8 years old. The fact that there wasn't one canonical representation broke my little brain. Before in mathematics you could always "keep going until you were done" and the number looked like 1.75 and that was it. Now you could stop at 14/8 or 1 6/8 or 1 3/4 or 7/4 or even 1.75 again! And sometimes they made me round it all the way up to 175/100 instead! Madness!

But unlike the kids in my class that seemingly did better than me in grade 4 while I was wasting my time trying to make this slippery math reliable I naturally ended up memorizing little gems like 7/2 being 3 and 1/2 because I kept at doing the actual work over and over again until my brain remembered it for its own sake. I'm not fighting my brain and trying to squash stuff that I don't care about into it, I'm letting it make the tradeoff as to what to memorize and what to keep as I keep doing the work over and over again.

By grade 6 (age 11, same time I started college) I was starting to wonder why we hadn't learned anything in a couple years in math. When you understand the building blocks or "first principles" so well, what looks to be a new lesson (the area of triangles!) barely registers because it's such a basic application of what you've already learned before. By grade 8 (age 13) I was actually complaining that we'd barely made any progress in 5 years of education. I believe my exact words were "we've basically learned nothing other than maybe the Pythagorean theorem" and I still mostly believe that.

When it comes to things like science, computer science, visual (ie, non-statistical) mathematics, and probably economics, physics, optics, and some areas of statistical mathematics we could probably move 3x as fast if we would just really hammer home the first principles until we were absolutely sure they were sticking.

We don't let babies fill containers with soup because they haven't demonstrated that they understand what a hole is and does. I feel like too often we force children to remember that 3*7 is 21 without really making sure they understand multiplication. The key to getting a child to really learn something isn't by jumping to intentional memorization. Not with mathematics, anyway. The key is to get them to reason about it and to practice over and over again. Not to memorize, but to understand and though knowledge and understanding are different things, understanding always comes with some knowledge though the reverse is not necessarily the case.

On the other hand, a good memorization skill must not necessarily mean you come to the right conclusions. Your sources, peers, genetics and a mind that is by nature chaotic, do it's part.

For example, having good memory may lead you to become more arrogant. If other people praise you for your skill, you become so confident in your conclusions that you stop questioning them and rather see confirmation in an echo chamber of sources.

This arrogance is the source of much evil, I think. You see it a lot in politicians and management.

Recently I realized that when you had paper documents—books, manuals, libraries, filing systems, whatever—the only way to make them accessible at all was to have organizing principles. Some of these were brilliant.

Most people gave all that up because "search."

But aside from search being flawed (good luck finding an old Google Doc), when information was actually organized, you might be able to remember where it was. Without structure, you can't remember where it is because it isn't really anywhere.

I'd say that being able to make use of a good reference manual is still the process of learning the basic outline of the material, learning what it is that you know and what it is that is contained in the manual (and what isn't in the manual!), and even learning your way around the manual itself in order to find stuff quickly.

I'd say this skill is very different than never learning any geography because you "could" look it up on Google Maps some day if you wanted to.

I had a similar view as a kid, driven mostly by the fact that I wasn't very good at memorisation. I found that I could get by in maths without it, eg. deriving the quadratic formula by completing the square rather than memorising it. I didn't value memory much as a tool in maths.

After having studied maths and physics at university and worked as a programmer in a mathematical field for 20 years (and studied much more maths in my spare time), I now see my poor recall as the limiting factor in my abilities in maths. The main reason I don't think I could ever have been a professional mathematician is that I would have reached (and have reached in my own learning as an amateur) a ceiling.

I have maths books that are beloved to me, that I have read multiple times (actively, working with pen and paper as one should) and which I will enjoy again in future. But the concepts in those books do not remain in my mind. I don't reach a point where the structure of basic linear algebra, say, is baked in.

I am good at the problem solving, but maths is an edifice, one people have been building onto for millenia. I explore that edifice, and keep returning to my favourite bits of it, but the portion of that structure that is resident in my mind is, and I think always will be, small. It's a window, and as more comes into it, more slides out. Everybody must have such a window, but I know others have much larger windows than me. And that's fine - I'm a programmer, not a mathematician. But I think it's something I would have benefitted from understanding earlier in my life. Perhaps I would have set about "learning to learn" differently. Rote memorisation and active curation of memories already formed could have benefitted me greatly.

>I'm of the opinion that this leads to a good rule of thumb: never memorize anything

Did you ever learn another language? It's impossible without memorizing a massive amount of things, especially when the writing system is different than the one one is familiar with. In fact the most famous researcher in vocabulary learning (Paul Nation) states in one of his book that rote learning is one of the most efficient use of time.

I'm of the reverse opinion that memorizing things is a "secret trick" particularly effective, that is put aside by a lot of people because it takes effort.

> I've never regarded memorization highly

You were probably taught that memorization means "memorization, plus you will be examined and punished and rewarded accordingly, in many cases against any natural inclination to memorize the object of conditioning".

I doesn't, but you're right to not regard this highly.

> never memorize anything - if you use the thing often enough

You'll memorize it, yes.

> Whenever we had to learn the times tables or the squares at school, I would just work them out in my head instead of memorizing them.

I took a slightly different approach: memorize what is important.

For some reason, they wanted us to memorize the times table up to 12 when I was a kid. I quickly recognized that it was only important to memorize it up to 9, and even then there were patterns. Why is 9 more important than 12? Because it is incredibly inefficient to figure out a product each time you need it, but the rules for multi-digit multiplication were generals whereas the rules for single-digit multiplication only worked for single digit (and were necessary for multi-digit multiplication anyway). The trick is to figure out when the efficiency outweighs inefficiency.

I never learned times tables in schools. Just struggled on through until they stopped asking me to memorize them.

Then way later in my 20s, when it was handy to know how to remember some multiples quickly, I realized that obviously there's a lot of patterns in there, and of course the magic of looking for an easier problem to do mentally to solve a more complex one.

No amount of effort at memorization ever succeeded in even trying to give me those tools, and they're so general - you can apply them to everything.

My entire 90s educational experience is a memory of teachers saying "you need to know your times tables" and no one actually trying to teach even basic reasoning about how numbers worked (which I suspect is why programming lept out at me - it's all number manipulation but it's all about the algorithms and patterns and finally things started to make sense).

If you don't memorize anything, what is your name, and where do you live?

My brain works the same. When it comes geography, I tend to learn and remember a lot about the countries I visit. But empty learning just doesn't work for me.

i highly recommend reading "make it stick". i thought the same way as you until i read the book

Excellent comment. This is exactly how I explain it to the students I tutor.

I tend to use the term "contextual recall" rather than the term "memorization", since the former emphasizes that it's okay to rely on a combination of memorization and pithy resources.

Hand anatomy is the best example I can think of. A good diagram can help you recall enough information to answer complex questions that would otherwise require an incredible amount of memorization. You still need to memorize some things in order to answer questions -- mostly the kinematic aspects and various properties of the things being represented (tendons, bones, muscle, etc.) -- but far less than you would need otherwise.

The one pager of theorems and proof construction techniques sometimes allowed in mathematics courses is another example.

This is why generative models are exciting as the next "tool for thought" for me, up there with calculators and search engines. Contextual recall is a powerful tool, especially when combined with memorization, and is a limiter for lots of folks (including me).

I think people are confusing "memorization" with "practice". "Practice" is really important and "memorization" is both the prerequiste and result of "practice".

I often tell people "Calculus is just algebra. However, it's fast, repeated algebra. If you aren't excellent at algebra, calculus is going to be terrible for you. On the flip side, calculus forces you to use your algebra so much that you get much better at it."

This comment makes the point in far fewer words and more effectively than TFA.

Yes! I learned a number of languages from O'Reilly books and it is a qualitatively different experience than learning through a bunch of disconnected StackOverflow questions.

Both modes of learning have their place and a combination of a comprehensive overview plus detailed treatments of specific corners gives so much more understanding than either alone.

This is honestly so important. Almost every issue or confusion I have had while studying is because I didn't remember or never learned a fact from "the basics". Over time I like to think I've corrected most of them, but only by finding and saving high-quality references that help me learn them again quickly - although ironically the process of conciously doing that usually means I no longer need the reference!

I avoided memorizing mathematics for a long time, but eventually created some spaced-repetition flash cards about math. I find the math I have memorized gives me something to reason about. While I'm in the shower, for example, I can think about stuff I've memorized and gain deeper insight. The memorized facts are hooks upon which I can hang new knowledge.

Sounds like a great prof. Mastering the basics cannot be overstated, if you ask me. Everything else can build upon those basics, worst case it can just be looked up when needed.

what were the facts?

So, active recall?

Active recall (asking yourself questions about the text) is better than passive recall (rereading the text).