When was the last time you repeated something over and over in order to keep it in your head?
I do this a couple of times a week on average - and for a very specific reason: when I dial into a conference I have to hold the pin code in my head while I switch from outlook to the number pad on the iPhone. It's very annoying. I do it because the information is - roughly speaking - garbage. A long number is the kind of thing that doesn't have any affective significance for us. You don't feel about 2734214 much differently than you feel about 2734212 (I hope). You might feel something about 18 (18 is my birthday).
This matters because (as I have proposed here and here) affective significance governs learning. If two blokes have a punch-up on your train to work you don't have to repeat 'two men had a fight on the train' under your breath until you get to work, so that you can tell people about it when you arrive. Stories we tend to remember - although since it is our reactions that get encoded, they change in the retelling*.
There's some good science and bad science around this. The working memory model* gives us a good idea how this mechanism works: we use a system called the 'acoustic loop' to temporarily hold information in memory by repeating it. But of course the point is that we do this precisely when we know it's the kind of thing that our long term memory naturally rejects. 'Neurons that fire together wire together'* - so there's a neurological reason for favoring repetition - but this misses the central point that if something isn't terribly significant, there's not much firing going on to start with.
The bad science is the multi-store model*, which was roughly the theory that in order to transfer things to long-term memory we need to repeat them (acoustically). This is so patently absurd it hardly seems necessary to point out why - so let me just say that we remember lots of things that we haven't repeated to ourselves and people without language can still learn. Despite this, there is evidence to support it (which just goes to show that evidential support alone is no guarantee of a theory's decency).
Ebbinghaus* did some of the more famous research into how we process garbage information. He found we forget it. Quickly. He also found that if we repeat the garbage at regular intervals (as distinct from under our breath) we are more likely to remember it. Which of course tells us little or nothing about learning in normal circumstances, but suggests an interesting - if brutal - technique for when we are trying to force-feed people stuff in which they see little worth, but which we might want them to recall - say, for a test.
Of course I'm being a little unfair: for motor skills repetition is essential. We should definitely practice behaviours that we want to become automatic. And there are times when, in modern life, we have to use repetition to bypass the idiosyncratic learning capabilities of a system designed to function around affective significance: for example my passwords are significant but my brain wasn't designed for random alphanumeric strings - equally, I will repeat words from a foreign language in an effort to learn it since I am not learning it as a native would, i.e. in contexts where it matters (of course if we could simulate those contexts - say using a VR headset - we could reintroduce some of that relevance).
Some people take this trick too far though and imagine 'spaced learning' is a good approach to education, i.e. as a way of getting students to remember stuff they aren't especially interested in, in order to pass tests. But as anyone who has actually taught students knows they tend to cram for tests once they are sufficiently anxious. Then forget it all soon after. Perhaps it would be better if they were actually interested. I can recommend Roger's Schank's book on this.
Overall though the point I wanted to make is that it is always best to design learning with affective context in mind. Rather than depending on repetition as a 'brute force' tactic, it is worth looking either at what is already meaningful to a learner (if you love baking, you'll remember a good recipe) or ways of making information meaningful (such as stories, scenarios, simulation). And yes, you're right - in an ideal (natural) world learning would be both meaningful and repeated, in that order.
I'll end with an example of the kind I used to use 20 years ago:
106 - 691 - 100 - 7
How many times do you have to repeat that PIN code to learn it?
How about
1066 - 911 - 007 ?
*Bartlett, F.C. (1932). Remembering: A Study in Experimental and Social Psychology. Cambridge: Cambridge University Press.
*Baddeley, A .D., & Hitch, G. (1974). Working memory. In G.H. Bower (Ed.), The psychology of learning and motivation: Advances in research and theory (Vol. 8, pp. 47–89). New York: Academic Press.
*Hebb, D.O. (1949). The Organization of Behavior: A Neuropsychological Theory. New York, NY: John Wiley & Sons.
*Atkinson, R. C., & Shiffrin, R. M. (1968). Chapter: Human memory: A proposed system and its control processes. In Spence, K. W., & Spence, J. T. The psychology of learning and motivation (Volume 2). New York: Academic Press. pp. 89–195.
*Ebbinghaus, H. (1885). Über das Gedchtnis. Untersuchungen zur experimentellen Psychologie. Leipzig: Duncker & Humblot; the English edition is Ebbinghaus, H. (1913). Memory. A Contribution to Experimental Psychology. New York: Teachers College, Columbia University (Reprinted Bristol: Thoemmes Press, 1999)

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