Memorize first, context second; or memorize with context

Especially since 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 ) - 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 ). 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.

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?