Response to discussion about memorization and learning
drafting my response, eventual response here: https://forum.openbagel.com/t/some-anki-stats/62/8
First, this discussion is good and made realize there are a few different ideas going on here. I’ve also realized that Anki and spaced repetition tools are better described as tools for “not forgetting” than they are as tools for memorization. I would describe memorization as a type of “learning”, in a broad sense of the term. I’ll address your points before putting down the updated version of my own thinking.
There are some groupings in the periodic table, and using them would definitely help you learn the connections and make it easier to remember. However, even if some elements are have “logically derivable” names (I’m not sure any do, honestly), some definitely do not, since they were named after the person who discovered the element, a country, or random other name. So you can get part of the way with connections, for example Berkelium is 97 and Californium is 98, easy to remember together. But as far as I know, if you forget Curium is 96, there isn’t any way to get to that from other information.
Now, this brings up an interesting thought. More “memorizable” something is in this sense, also makes the knowledge feel “brittle”. And that type of knowledge also feels less “important”, in that perhaps it’s required for fluency (easily and smoothly communicating in a language or a given subject), but losing that knowledge is not a blow to some deeper level understanding of a subject area. Blanking on a definition or abbreviation is really only a time cost, not a knowledge cost.
Periodic Table. Caveat: I remember very little of the logical backing for the periodic table (part of why I wondered how pure memorization would work). There are groupings in the periodic table, but I don’t think it’s possible to deduce any possible forgotten element name or (especially) abbreviation if you don’t recall it yourself. Still, it’s a fair point, if there was a way to remember the table without memorization that would be all of (i-iii). Your point about multiplication tables is this in a nutshell, I think. From this point already though, you can kind of feel that the more “memorization required” some given content is, the less “intellectually valuable” it is. This alludes to your second question, addressed below.
Geography. There’s no doubt: knowing history or other contextual information makes it much easier to remember. If you’re starting from scratch with no prior knowledge, and all you need to do is know every capital of every country, I can’t imagine you could do it in less time than 5 minutes over a lifetime per country with anything other than spaced repetition. Maybe SketchyMicro could, if they really built an amazing memory palace of all the countries, maybe you wouldn’t need spaced repetition to recall that information for the rest of your life. Also, even if spaced repetition solves the brittle nature of remembering cognitively isolated information technically, relying on an external tool to maintain your memory is a different type of brittle, and an interesting discussion in itself.
- In a sense, this asks the question of what exactly is the difference between learning through reasoning vs memorization. I’m guessing the operative difference here is that the memorizer learns that x = y, whereas the reasoner also understands why x = y, and thus has some greater context and connection to the world outside of x = y. In that sense, I don’t think it’s elitism, you should pick reasoner over memorizer pretty much every time, simply because it’s more knowledge. Now, maybe the memorizer knows a lot more variations of x = y than the reasoner, who spent time learning the why. But in most subject areas, going deeper into foundational understanding is going to be more important than gaining memorized breadth. Obvious in arithmetic, maybe slightly less so in history, but still pretty clear that understanding the reasons for the civil war are more important than remembering the dates of all the battles, for example.
- I don’t think there is any field that is valuable by itself that is also sufficiently covered with rote memorization alone (at least in the way we’re discussing memorization, I’ll present a different way in a subsequent post). Vocabulary may be the closest thing to this probably, but it’s not really a whole subject space (and even that has etymology, which makes them not like randomly different bits). I also can’t really think of anything we teach as truly just rote memorization.
- Your follow up I think is the answer to this, Nielsen does a pretty good job of it. There’s a spectrum of value: At the minimum it saves time, at the maximum, it makes a subject area a first language, and allows you to think in that space more easily (super-chunking?). Even more basically, the value of memorization is dependent on what you memorize, and how long you remember it for. So if you don’t memorize valuable information (chunks that either save you time, or help you move up and down levels of abstraction easily) and don’t use spaced repetition, then probably not much value in memorization.
Some topics are not high volume and you can just memorize them (German states). Some things are higher volume and chunking them into groups would have been better than going through everything slowly and randomly like I did (e.g. the periodic table, despite these cards being pretty well designed in that they offer visual and written mnemonic hooks, as you can see from the images above. And they actually are designed to be learned in groups but I accidentally didn’t do it that way and randomized it).
I don’t know of any whole subjects that are “worth learning” that are like this. Usually the memorization, even if critical, is a part of a higher level whole (e.g. memorizing law for a lawyer, multiplication tables to do arithmetic). At which point, this pretty much switches back to being use case (1).
This is why for use case (2) with any non-trivial content, the design of the cards is important, and there needs to be desire for the learner to put in some effort to connect it mnemonically. I started a couple music interval recognition decks but stopped them because I quickly felt it was too hard to learn through only basic exposure and spaced repetition, and that combined with feeling like learning them was hardly any benefit in my life made going through those cards grueling.
And to be clear, I have not really heard of anybody advocating for (2) for anything more than things like vocabulary and other classic “memorization is sufficient” types of learning. Pretty much everyone that uses Anki says that creating your own cards is the way to make the tool much more useful, and admit that a lot of the work is in understanding a concept enough to create well-defined, atomic cards. It was more my own deviation thinking it was an interesting idea that, with essentially zero prior interest or contextual knowledge, I could spend cumulative <5 minutes to learn that Magdeburg is the capital of Sachsen-Anhalt, or whatever, and retain that “for the rest of my life” (conditions apply, lol).
This is kind of similar to (1), but the main difference is that you removed all the burden of learning from the spaced repetition process. This allows you to kind of backtrack and say to yourself, “what is an example of something that, if I forgot how to do, I would be regressing my knowledge”. This seems to enable some more free form types of spaced repetition prompts, like every repetition is a new problem of a specific kind that I should be able to solve, and I have to solve it to make sure that I haven’t forgotten how to do it. This is a bit outside of the normal research done regarding spaced repetition, since forgetting how to solve a problem isn’t usually remedied simply by seeing the solution (though it could be!). Nonetheless, even this kind of “spaced practice” probably has a similar type of forgetting curve and could be optimized with the similar algorithms.
Memorization is sometimes mistaken with the absence of richer learning, but I think they can coexist (and fix that “brittle” feeling). I would say that learning most things involves at some point or another remembering information “like the back of your hand”, i.e. you do not remember how or why you learned this fact, but it became ingrained in your memory. Remembering that piece of information alone is often useless without the greater context (e.g. how to take the derivative of an exponential function without knowing what a derivative is), but still seems to be a part of the learning that is happening. The worry here is that memorization would “remove” the connection from the more “connected” learning happening, but I’m not sure it needs to.
- the benefits of the dull student are an example of how memorization can be useful. not memorizing 1212 and thus not knowing how to do 1213, but memorizing the steps for multiplication. Learning that 1213 is the same kind of problem as 1212 is the kind of thing that I don’t see as being within the scope of memorization, and is the core problem of learning.
For example, I wouldn’t say a teacher should change their lesson plan to incorporate more memory based techniques in the person to person activities. Rather they could modify some homework to be oriented around spaced repetition (with the option having some of that homework be simply recall, and not application)
Sawyer’s dull and clever students come to mind. The clever student may learn by “reasoning”, thinking using language and logic, etc etc, not sure what else describes the process of learning through reasoning alone. Meanwhile, the dull student could do one of two things. Memorize the multiplication tables and have no idea what 12*13 is, or see the steps taken for multiplication and memorize those. The latter
As far as I can tell, memorization is taking a set of information, and learning each piece of information one at a time. Memory palaces and spaced repetition are tools for “not forgetting” pieces of information, and they both can be essentially independent from the information itself. This is why they are generalizable strategies for “not forgetting”. I imagine they work best when put together, but I think the fundamentally interesting part of spaced repetition is that it’s not a mnemonic device itself, but instead an “effortless” retention system with pretty clear time costs.
Most people who use Anki or discuss spaced repetition would say that it’s best as a tool to be used after learning either as preparation for future learning, or, most often, as maintenance in order to not forget. And that’s the key, spaced repetition is not actually a memorization tool as much as it’s a tool for not forgetting.
When you’ve learned a subject, it is also easier to answer the question: What is something that, if I forgot it, would indicate a regression in my understanding? In theory (even if Anki doesn’t support it), every answer to that question could be a spaced repetition “card”. For example, maybe every repetition is a new problem of a specific kind that I should be able to solve, and I have to solve it to make sure that I haven’t forgotten how to do it. This is a bit outside of the scope of traditional spaced repetition research, since sometimes seeing the solution to a problem you forgot how to solve doesn’t make you recall how to solve it yourself. Nonetheless, I think this falls under the umbrella of things that have a forgetting curve ( https://en.wikipedia.org/wiki/Forgetting_curve), and thus could be optimized using spaced repetition algorithms.
What’s funny is, we don’t usually consider a thing to be “learned” if we haven’t retained it, so in a way we have to reduce the bar something has to reach to be considered learned to then find value in using spaced repetition. The classic example might be reading a book or article, feeling like you’ve gained some new understanding, but only retaining some of the core ideas, or only being able to recall the core ideas from certain mental entry points that happened to stick around in your brain longer than others. I think the real win of spaced repetition is being able to “choose what you remember” from things you learn, and not relying on your brain and whatever subset of that learning it chooses to retain without assistance.
In fact, I have been thinking about how spaced repetition could be used in a classroom setting. @kevji I would be curious if you thought there was some content that could be surfaced to students using spaced repetition that would help bolster their learning. Or maybe just a spaced repetition deck to take away after class to help them forget less of it over time! My gut is that this understanding of cognition and memory is under-utilized in education, but of course I am also over-emphasizing it here because it’s the topic of discussion.
All learning is connecting elements from X using elements from Y, and internalizing those connections. To the degree that this is true, then I think all learning is dealing with bits of information that can be made atomic. This is because we can move up and down degrees of abstraction as needed (using conceptual chunking), and turn all our understanding and knowledge into connections between objects. Objects and actions are probably not general enough, so I’ll give some examples (possibly not correct).
To the degree learning can be represented by atomic pieces of information like this, I don’t see how learning with reasoning and memorization are fundamentally different. To me, it seems like memorization might just be implying that the order of learning doesn’t matter. But once we concede that order matters, then I kind of want to call reasoning “memorization with style”.
It still feels like there’s a difference between grokking ( https://en.wikipedia.org/wiki/Grok) something and memorizing it. If we break our intuition down to its atomic bits, there probably is a translation between our intuition and something memorizable. But does memorizing something connect the right neural pathways in our minds to eventually grok that something? I don’t see immediately a reason why not, assuming all our learning can be reduced to something like I describe above.