In response to Dax's posting concerning spiraling, I wanted to point out that at least part of the learning process is subconscious (I have never had an educational psych class, so forgive me if I use the wrong term or state the obvious). There is an article by Asimov called "The Eureka Effect" in which he describes how he solves his most complex problems. When he came to a difficult part of a story and wasn't able to figure out how to proceed, he would go to an action/adventure movie, which, as he put it, occupied all of his attention but none of his intellect (a pretty good description of most entertainment nowadays). At the end of the movie, he was invariably able to write himself out of the hole. He attributed this to his subconscious mind working out the details that he was too frustrated with to think clearly about.
Perhaps to people that have experimentally-tested theories of learning this sounds like a dilettante's rambling--it may in fact be that. But the more I have considered these ideas, the more I see (in myself and others) the power of the subcoscious mind to work on problems that we are not consciously making an effort to solve. As (perhaps anecdotal) evidence, consider how often people have made important discoveries in dreams, or just in their sleep, etc. Many times the answers to physics problems have come to me unbidden at dinner (when I had finally stopped thinking about them and just went home to eat).
This _could_ be an advantage in a spiralling curriculum, with one important caveat. I don't think your subconscious will work on things that you don't care about or find important in some sense. For this to be a help at all, kids would have to be curious about the concepts enough to want to understand them--which of course, is pretty much the key to any type of learning.
(all quote from here) From email@example.com Thu Jun 8 08:28 CDT 1995 >From: firstname.lastname@example.org (Dax Mitchell) >Date: Thu, 8 Jun 95 08:44:44 EDT >To: email@example.com >Subject: Re: Spiraling at the Elementary Level
>I've really enjoyed the postings on spiraling. I'm wondering if >anyone who has experience using this technique has opinions about >the following issue; namely, when a topic is revisited after a period >of a week (or perhaps several weeks?) at a more sophisticated level, >do the students have to _relearn_ what they studied on the previous >visit? Since on the previous visit, they studied the topic briefly >and then moved on, perhaps the basic ideas within the topic have not >soaked in. I don't mean to ask this as a skeptic, because the spiraling >idea has a lot of appeal for me personally. Nevertheless, in my own >mathematical learning, I know that if I see a new idea sketched in, say, >a seminar and then don't see that idea for a few weeks (or sometimes, >unfortunately, days), my feeble mind usually takes a while to retrace >the steps--I usually have to do some "reviewing" in my own mind to get >brought up to speed. And it seems that many times when I'm "reviewing" >the speaker has moved on to bigger and better things, leaving me in the >dust.