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Memorize first, context second, or memorize with context


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Given that younger kids can easily and fairly happily memorize things without being capable of understanding the context. I'm thinking of Latin and math, particularly, but it applies to other subjects, too. And for the purposes of this post, I'm assuming that *both* memorization and conceptual understanding are necessary and desirable for complete mastery of a subject - the question at hand is whether memorization can/should come *before* conceptual understanding, or whether memorization and conceptual understanding ought/must go hand-in-hand.

 

So, my understanding of classical ed (both neo-classical and traditional classical) is that it is largely in favor of getting necessary memory work started in the younger years, and it's ok that they don't understand it right away - get the foundation laid now, and teach them how to use those facts when they are capable of it in later years/stages. Of course, if they *are* capable of it in younger/grammar years, then go ahead and provide the context - but I'm talking about where a given child, at least, just isn't capable of understanding the context/concepts yet, but *is* capable of memorizing the facts that will be necessary in order to use those concepts. Thus the emphasis on math facts and Latin paradigms without worrying overmuch if they can't understand the necessary math or grammar concepts yet - basically, that memorizing without context won't hurt them so long as you *do* bring in the context eventually. And in fact, delaying the memorization *until* they can understand the underlying concepts is actually counterproductive and slows down the overall mastery of the subject.

 

But evidence shows that, in many cases, students just never moved beyond memorization without understanding in math and Latin. Lots of ink has been spilled trying to sort out the problem (part of which is undoubtedly because many of those students were never *taught* anything beyond memorization in the first place :glare:) - and one common answer is that students should *never* memorize without being able to understand the concepts - that once they get in the habit of thinking that all there is to a given subject/skill is rote memorization and all problems are/can be solved by straight regurgitation of memorized facts, it is very hard, and in some cases impossible, to now teach them to *think*, to break the habit of mindlessly regurgitating facts and instead *use* all those memorized facts to learn and apply the underlying concepts. Therefore, you should be training the proper habits of the mind from the start, teaching students to *think* from the start, and thus never have them memorize anything outside of the context in which it will be used.

 

And now, I'm sure, you see shades of the conceptual math debates, and the Latin debates over teaching the language as a logic puzzle versus as a language ;). I've been pretty strongly on the conceptual math side, as well as the Latin-as-a-language side, as a result of my own learning experiences and the end goals espoused by those positions (too many classical types don't seem to realize there is more to math than memorization and the standard school applications, and don't consider reading Latin as Latin to be worthwhile).

 

But as I'm starting to teach my dd4, I'm running headlong into reality ;), which is that she just doesn't get some math concepts, won't even let me show her them (they are apparently things that should not be :tongue_smilie:). And I'm waffling about whether I should stop any formal math until she is more ready, or keep on with the bits she likes, which undoubtedly are going to get into memorizing without understanding, or go whole hog on memorizing, and do lots of chants and such (which she'd like, I'm sure).

 

Also, I've been reading up on Latin teaching - Bennett's "Teaching Latin and Greek in the Secondary School", which is rec'd by Cheryl Lowe, and Distler's "Teach the Latin, I Pray You", which is rec'd by teach-Latin-as-a-language advocates - it's been interesting seeing the similarities and differences b/w the two approaches. I'm mostly in favor of Distler's approach, which is a rigorous, in-favor-of-memorization-and-drill approach (but always and only in context!) to teaching how to read Latin as Latin. But unless one's kids are language/grammar types, you would hit a wall really quickly if you started in the grammar years - a lot of the grammar topics are the sort that seem to require logic-stage thinking (and the book was about teaching high schoolers). So what is better? To stick with context, and thus memorize mostly vocab and a few forms, but you can use them all? Or to just not worry about context, memorize all the forms along with vocab, even though you can't use them yet, relying on memorized prayers/songs/etc to provide enough context to be getting on with until they are ready for real grammar/syntax study?

 

Classical advocates say the former makes the grammar/syntax study more difficult than it needs to be, since you have the memory burden on top of learning how to use all those forms. Reading-Latin-as-Latin advocates say getting in the habit of using the forms out of context makes learning to apply them *in* context much harder than if you'd done it right from the start. (And there's the related issue of whether an early emphasis on translation and otherwise constantly turning the Latin into English at every turn - seemingly inevitable with a memorize-first approach - sabotages later efforts to comprehend Latin without *having* to go through English.) Conceptual math debates tend to go along the same lines - does memorizing without understanding the concepts first inhibit learning the concepts later? And if so, how do you deal with kids who just can't seem to get the concepts at all - is it really best to just drop math entirely until they *are* able to understand?

 

And, just to make things more interesting, classical advocates are all about the necessity of memorizing in context when it comes to teaching reading. Memorizing sight words outside of the context of being able to divide the word into phonemes/syllables and sound it out - phonics - is considered a bad, bad thing. It is better to wait until the child is ready to comprehend phonics than to go ahead and memorize whole words now, figuring you'll go over phonics later, when the child is ready. Why? Because teaching sight words sets up bad habits, habits that take longer to break than just doing phonics from the start. For some kids, *years* longer, it seems. So classical educators *do* acknowledge the issue of out-of-context learning causing bad habits. (And cognitive science has established that we use different parts of our brains when we read via memorized words versus phonically.)

 

But on the other side of the coin, the idea that the best way to teach expert thinking in a subject is to teach those thought processes from the very first - no setting up bad habits of thinking wrongly or not at all - is likewise rejected by cognitive science. Expert thinking requires a *lot* of domain knowledge, and trying to reason like an expert *without* that domain knowledge is futile at best, and establishes its own bad habits at worst. Their findings support the classical idea that it is best to learn facts, lots and lots of facts, before trying to think about them. And certainly reality tells me that my kids are ready to memorize a *lot* earlier than they are ready to logically think through things.

 

But a lot of things can be memorized *with* enough context to be getting by - like history and science stories/sentences and poems and songs - even if the kids don't understand them now, what they've memorized still contains quite a bit of context, that is available to them with no further effort than growing up. But math facts and Latin paradigms aren't quite the same - on their own, they give little-to-no hint of how they will eventually be used (bare lists of history facts or science facts have the same problem). Which isn't a problem if they can be memorized without causing damaging bad habits - but is a *big* problem if the memory-work-without-context *does* build bad habits.

 

(Part 2 in next post; some people might think that hitting the post character limit means you ought to start hacking and slashing ;) - but not me :D.)

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Wrt what sorts of memory work is more prone to causing bad habits of thought, the phonics/whole word thing seems to hinge around memorizing core facts - phonograms, say - versus memorizing facts that are actually composed of other facts - whole words. That the problem comes in when you memorize stuff that you really ought to have been logically figuring out. Like in math, maybe it's fine to rote memorize the basic number bonds up to 10 (the facts up to 18 and beyond can be logically determined from there, and are good practice in using math laws and learning mathy thinking), and skip counting through the multiples of 10/12/15/whatever (to get useful patterns into one's head without getting into the potential minefield of whether memorizing the mult/div facts without understanding mult/div causes problems). In Latin, I don't think rote memorizing the paradigms and being able to give specific forms - so long as you didn't get into the trap of using English all the time, and thus develop habits of turning Latin into English - would *hurt*, but I wonder if it is really the best use of time. By avoiding bad/false contexts, you are left with *no* context, hardly - other than looking at Latin sentences/passages and parsing by giving all possible options for the given endings, since you do *not* have the context required to actually figure out which one it probably is. The only point would be to rote memorize the endings, really - is it worth that?

 

And it seems that *some* level of context is required, because *way* too many people *do* end up thinking of math, or Latin, or history, or science - any school subject, really - as nothing more than a bunch of random crap to be memorized and regurgitated. They *never* get beyond that.

 

But *how much* context is the question . And how *specific*. Are lots of living books on the subject, read contemporaneously to the memorization, whether or not they apply to the specific things being memorized, sufficient? Or do they need to be specifically related to the things being memorized? Or is rote memorization - memorizing things without context - inherently going to cause bad thinking habits, for which no amount of secondary context - living books, real life applications, anything that is not *explicitly* how it will be used - can prevent?

 

I mean, whole language types are all about context - but the context they provide is secondary, the context of "why you want to read in the first place" - similar to the use of living books to flesh out memorizing - and in teaching how to read, it seems that, for many kids, that context just isn't good enough. They need the primary context that words are made out of phonemes, and are combined in these ways, and are sounded out like this. Do other subjects have that same issue? Or maybe just skill-based ones?

 

Thoughts? (I'm particularly interested in btdt advice, either with one's kids or with oneself, but all theories are welcome :).)

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no btdt, but I think the first question to answer is 'is it worth the time.' for my youngest I've decided no, and am using a CM approach for early years.

 

In SWR the phonograms are learned first, but not mastered until being used a few times.

 

There doesn't have to be a lot of application. My Byo is doing the 1st conjugation & declension. I could teach that whole concept simply by charting amo, amas, amat, etc, comparing it to English (2 words 'I love' in English are 1 in Latin; now we change the end...). So if the child wants to know why, they don't need it all.

 

In practice, we are doing CC's timeline and math by rote (maybe a quick explanation to the olders) but not the Grammar & Latin. I think that leaves me in the middle.

 

Hope this makes sense & sorry for typos - using my phone.

Amy

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A few random thoughts:

 

- one can learn something by using it rather than memorizing it by rote (e.g., practicing adding to learn to remember math facts, repeated translating to learn to remember Latin endings). Is that what you mean by context? It doesn't have to be one or the other. There is a middle road. For example, in GSWL, a new word is taught each lesson, and followed by several sentences using it and the words that were learned previously. Memorization by rote is not involved; learning takes place by repeated use.

 

- I think it's important to consider the sorts of kids who would struggle mightily to memorize by rote without context/meaning. Kids who do well at memorizing by rote usually do well in traditional elementary school. But a whole lot of kids are not good at memorizing by rote in spite of being otherwise bright. Having a context, a big picture, creates a sort of memory hook, or place in their brain to file the information. Meaningless information may go in one ear and out the other for such kids.

 

- I don't think it's fruitful to lump all areas of learning together in this sort of discussion. While there may be similarities between math, grammar, reading, and languages, there are significant differences.

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I haven't found this to be true

Given that younger kids can easily and fairly happily memorize things without being capable of understanding the context.

 

We did memorize some poems in K-3rd and tried some of the lists, but it never worked. Even if we were reading/studying/watching about the subject. But around 4th or 5th my boys memorization speed really took off. Even for the things I wanted memorized like periods of ancient egypt or chacteristics of living things or square roots or spanish vocabulary.

 

AND now that they are entering the logic stage, not only are they much better at memorizing, but they also will dig deeper if I start the list before they have studied it. We haven't actually gotten to plants yet, but they have started some plant memorization (because they've already done all the things I had planned for animals/anatomy). Not only do they have actual conversations with me about the things on the lists, they will pull books off the shelf so they can understand what the words mean.

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the question at hand is whether memorization can/should come *before* conceptual understanding, or whether memorization and conceptual understanding ought/must go hand-in-hand.

...

 

 

But evidence shows that, in many cases, students just never moved beyond memorization without understanding in math and Latin. Lots of ink has been spilled trying to sort out the problem (part of which is undoubtedly because many of those students were never *taught* anything beyond memorization in the first place :glare:) ....

 

But as I'm starting to teach my dd4, I'm running headlong into reality ;), which is that she just doesn't get some math concepts, won't even let me show her them (they are apparently things that should not be :tongue_smilie:). And I'm waffling about whether I should stop any formal math until she is more ready, or keep on with the bits she likes, which undoubtedly are going to get into memorizing without understanding, or go whole hog on memorizing, and do lots of chants and such (which she'd like, I'm sure).

 

 

 

Snipped bits so this is mainly what I'm responding to...

 

I teach math at the cc. Have for about 14 years now. Up through Calculus - but generally lower-level courses. I WANT (oh so badly) my students to understand WHY things work. I'll settle for them being able to do problems. Understanding why really helps with any memorization - it also keeps the math from being simply "rote learning".

 

If you look at Bloom's Taxonomy, memorization would be in the lowest level. It's also foundational. When my son was about 2 or 3 years old, I was teaching a course where students were supposed to know geometry formulas. I reminded them they needed to memorize the formulas. Many students don't (whether it's because they think I'm lying to them when I tell them what they need to do or if it's just because they think they can still pass... I don't know). I got my son to just be able to repeat after me... so he could tell me (at age 3) that the area of a circle was "pi r squared". Now he had ABSOLUTELY no idea what that meant.... but he knew the formula for area of a circle.

 

We still aren't to area in his math - but he has that formula memorized. He'll understand area in a while... but he does have some basic knowledge. And he WON'T be one of my students who's returning to school who doesn't know basic facts. Right now I've got him memorizing conversions between the US and metric system (2.54cm=1in. etc). He's not using unit conversions yet (although as he's had interest, I have shown him some), but when he gets there, he'll be able to focus on the concept since he already will have the memorization.

 

So yes, understanding is the goal. Memorization alone is useless (or mostly). BUT... while you're waiting for understanding (either by developmental readiness or just by not introducing topics yet), I see no harm being done by memorizing things that will be needed later.

 

I say, your daughter is 4. If she's interested in memorizing... go for it! (I tried to get my son to memorize the quadratic formula at 5... didn't work. But he would stop repeating me when I started reciting it, so it did have some benefits!)

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It seems to me that different kinds of memorization are good for different purposes, and that the age of the children is a factor, but not a rigidly binding factor.

 

Memorizing, say, at age 7 a song naming all the bones in the body is fun, legitimate, and useful even if no dissections will be performed in the immediate future. It can awaken an interest in science that will find more comprehensive expression later; it can awaken an interest in words that will have immediate and lasting benefit; it strengthens "memorizing muscles" for future service. There's not much "context" to this memorization, but still, it's hard to argue that the bone song would be of no value.

 

BUT, I can't accept the idea that there's a rigid "poll parrot" stage in which memorizing is practically the only thing children can do. I'm not saying that that is exactly what Dorothy Sayers said or precisely what Susan Wise Bauer says, but certainly you run into this idea today under the banner of classical education.

 

If there IS such a stage, in my experience it ends sooner than many might think. I've seen third graders start to sink their teeth into what might be considered "logic stage" Latin thinking and be much the happier for it.

 

On the whole I lean towards as much of what I'll call "application" as possible: learn facts, and do something with them. Either memorize, then shortly do; or introduce, manipulate, then memorize cold and manipulate some more, but apply as much as possible as often as possible as young as possible. It's motivating, it's fun, it's stretching, and it's where the subject is headed--and where the child is headed--anyway, so why not get started?

 

(Really, to be a bit heretical, I think we all have some evidence from our own experience that children actually get better at memorizing as they get older. I bet I'm not the only one who, say, memorized dozens of French vocabulary words in one night as a [procrastinating] teenager, which is not something I could have done in second grade when memorizing was supposedly easier . . . so it's not as if failing to learn some fact in grade 2 is going to rob our children of the opportunity to learn it later. So why not stretch their minds young by teaching them to start to use, already, what they are memorizing--and then, as they grow, have them keep memorizing, even more, and keep applying, even more?)

 

In all subjects, people who lean towards the poll-parrot idea of the early years can find programs that assume and support that view, and people who lean more towards application can find programs that support that leaning. What usually doesn't work is having one leaning and trying to use a program that supports the opposite leaning!

 

I've found that with Latin, choices about what is presented when can dramatically restrict or expand how much application is possible.

 

(What I mean by "application" isn't identical to what the OP meant by "context," but along with others I've headed into some overlapping territory.)

 

Thanks, OP, for the interesting question!

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