Abstract—In a 9-year longitudinal investigation, 4 subjects learned and relearned 300 English-foreign language word pairs. Either 13 or 26 relearning sessions were administered at intervals of 14, 28, or 56 days. Retention was tested for 1, 2, 3, or 5 years after training terminated. The longer intersession intervals slowed down acquisition slightly, but this disadvantage during training was offset by substantially higher retention. Thirteen retraining sessions spaced at 56 days yielded retention comparable to 26 sessions spaced at 14 days. The retention benefit due to additional sessions was independent of the benefit due to spacing, and both variables facilitated retention of words regardless of difficulty level and of the consistency of retrieval during training. The benefits of spaced retrieval practice to long-term maintenance of access to academic knowledge areas are discussed.
source:
Maintenance of Foreign Language Vocabulary and the Spacing Effect
Harry P. Bahrick, Lorraine E. Bahrick, Audrey Bahrick, Phyllis E. Bahrick
Psychological Science, Vol 4, Issue 5, pp 316-321, September 1993
Assuming I'm reading this right (haven't looked at the article yet), you can swap repetition for spacing.
You can spend less time studying if you space that studying out over a substantial period of time -- and vice versa.
Maybe.
overlearning overrated?
how long does learning last?
shuffling math problems is good
Saxon rules
Ken's interval
same time, next year
remembering foreign language vocabulary
I'm not sure that learning foreign language vocabulary is similar to learning math. Of course, at least for languages with some relationship to one's native language it's not entirely random.
ReplyDeleteI remember that in the eighth grade we had to memorize all 100 NC counties and their county seats in alphabetical order by counties. This was almost completely random so I made up various ad hoc associations.
Anyway, math has an internal logic which is why you can do problems you've never seen before. Once you understand the logic, it should be much harder to forget than a collection of random facts.
I agree that it's valuable to have quick recall on the number facts. But even more important is knowing how to count and hardly anyone forgets which is three and which is eight.
In other words, I'm wondering if kids sometimes disguise their lack of understanding via memorization. This is a poor strategy for succeeding in math.
I'm not sure that learning foreign language vocabulary is similar to learning math.
ReplyDeletegosh, I wouldn't think so....(didn't mean to imply that there is)
I've just read a fascinating study on "cumulative practice," though, that points out that many (most?) subjects can be ordered sequentially and hierarchically.
When "Concerned" is around, she can tell us about learning & remembering foreign language vocabulary.
In fact, I think she may already have written a post about it.
Speaking as a math student, though, there is a HUGE amount of material one needs to be able to recall & recall quickly.
ReplyDeleteI guess I'm saying that recall is the necessary but not sufficient condition for being able to use math and to carry on learning math.
I wish, too, that we had a slightly more developed vocabulary for speaking of "memorization."
Simple memorization, in the flash card sense of the term, doesn't seem to be used by effective math programs. "Drill" in math always means doing calculations, simple problems, or perhaps mental math.
I like your idea of fluency. Sort of like a good piano player still doing the Hanon exercises.
ReplyDeleteTo me building fluency in math would include things like just copying numbers accurately in neat handwriting. Possibly doing a page of number facts.
On the other hand, I'm not aware of knowing a HUGE amount of material in math, especially when we are talking about pre-calculus.
I'm wondering whether perhaps we are spending too much time on special cases. For example, when you start learning about fractions, you begin with simple fractions, such as 1/3, that you can visualize as a slice of pizza. But this isn't very helpful for, say, 5/13. At some point all fraction problems should seem the same so once you forget about pizzas, that would actually reduce the amount of information.
I'm not sure that learning foreign language vocabulary is similar to learning math.
ReplyDeleteLearning foreign language vocabularly would not be similar to learning math because vocabulary is only one component of learning another language. It would be equivalent to learning what numbers and perhaps mathematical symbols mean without ever putting them together.
I do believe though, that there are parallels between learning a foreign language (understand, read, write, speak) and learning mathematics. When I say learning a language I mean not only vocabulary, but gender, tense, conjugation, sentence structure, grammar, and exceptions. Just as in math you begin with basic components and learn to manipulate them correctly and efficiently to form ideas that have meaning. In my mind, at least, learning a foreign language and learning mathematics are quite similar keeping in mind that foreign language learning is much more elaborate than merely learning vocabulary.
Once you understand the logic, it should be much harder to forget than a collection of random facts.
ReplyDeleteHere, again, I only see similarities. Communicating in any language requires putting the memorized vocabulary together coherently so that is has meaning. The "logic" employed in this case would be the rules of grammar that apply a pattern or formula to the random vocabulary.
I'm wondering if kids sometimes disguise their lack of understanding via memorization. This is a poor strategy for succeeding in math.
Again, this would be similar to a foreign (or any) language. You can memorize words to kingdom come but if you can't string them together logically you're not going to make a whole lot of sense. Even translating from one language verbatim from a dictionary frequently results in incomprehensible jibberish. Have you ever tried the computerized translation? It's the reason flesh and blood interpreter/translators still have work.
I agree that there as some parallels between learning the "language" of mathematics and learning a particular natural language, especially a foreign or second language.
ReplyDeleteHowever, there is one KEY difference that needs to be stressed over and over.
Natural languages are not required to be logical. They are in large part artifacts of human intelligence, history, and so forth.
Mathematics, on the other hand, is an internally consistent, coherent system. If you forget something in mathematics, you can often reconstruct it by knowing that it has to be consistent with the rest of mathematics.
By contrast, if you forget how to spell a word or decline a verb or whatever, you may be able to make a good guess by analogy with something else you know, but there is no guarantee that you are correct.
Yes you need to string words together logically to make sense but as any reader or writer knows, there are many different ways to say the same thing. And it is to a large extent a matter of opinion whether one of these ways is somehow better than the others.
Again, mathematics is not like this. Opinion doesn't come into it.
I feel very strongly that students cannot understand mathematics without becoming aware of its unique character.
Again, mathematics is not like this. Opinion doesn't come into it.
ReplyDeleteAgreed.
This is the beauty of mathematics.
To me building fluency in math would include things like just copying numbers accurately in neat handwriting. Possibly doing a page of number facts.
ReplyDeletesynchronicity
Just this morning I read the introduction to my "cursive handwriting" text.
We're going to have to add cursiev writing (and numeral printing) to the list of afterschool subjects.
I'm not aware of knowing a HUGE amount of material in math, especially when we are talking about pre-calculus.
ReplyDeleteIt sure feels huge to me.
I misspoke earlier.
ReplyDeleteI think we do have terminology for the kind of "memorization" involved in math versus vocabulary.
Vocabulary is "declarative knowledge"; a fair amount of math is "procedural knowledge."
I'm talking about being able to do calculations rapidly & accurately. Liping Ma calls that procedural knowledge, which stikes me as correct (though obviously there is a large "declarative" component...)