I'm working on a review of the anti-PBL / pro-PBL fracas of 2006 and I just had the wind knocked out of me by this line from Sweller & Cooper in 1985:
It was assumed that motivation, while reading a worked example, would be increased by the knowledge that a similar problem would need to be solved immediately afterwards. (p. 69)
This is their seminal study that establishes (finally!) the best practice for math instruction: I work out an example, then you work out an example from the same family as the first.
The straw man on which they premise their study (which, in turn, has been the premise of two decades of direct instruction advocacy) has to be seen to be believed. Even if I suspend disbelief for a moment, though, here's the question I can't find anywhere in the literature on worked examples:
What if you manage to create a perfect system of worked examples, a perfect lecture, a perfectly-wound informational system, and no one cares? What if the perfect lecture provokes students to truancy? What if a year of perfect explanation produces students who don't want anything to do with math later in life, whether or not they're proficient in the near term? (Boaler, 1998).
But the cost-benefit analysis of the perfect lecture is left to the teacher. Sweller, Cooper, and their modern-day acolytes totally punt the issue. "We know what works for an eight-question experiment," they say. "You figure out how to make it work every day for a year."
Sweller and Cooper don't fully discount the issue of motivation but their answer — "You'll be motivated to watch me work out this example because you'll be doing one in a moment." — is simply stunning. This is why teachers find it so easy to dismiss researchers.
2011 Mar 14: Sweller and Cooper's straw man. In this study, the experimental group is taking a test on a problem while looking at an example of the same kind of problem worked out at the top of the page. The control group just takes the test. Unsurprisingly, the experimental group performs better. Surprisingly, Sweller and Cooper take this as evidence against any amount of guidance less direct than their worked examples.