This is how science classes mostly went in high school. We would learn about a topic that had been discovered scientifically, for instance that if you add together two particular solutions of ions, some of the ions will precipitate out as a solid salt. Then we would do an experiment, wherein we would add the requisite solutions and get something entirely wrong in its color, smell, quantity, or presence. Then we would write a report with our hypothesis, the contradictory results, and a long discussion about all the mistakes that could be to blame for this unexpected result, and conclude that the real answer was probably still what we hypothesized (since we read that in a book).
Given that they had not taught the children anything about priors, this seems like a strange way to demonstrate science.
Meteuphoric 
Children don’t need to learn about science since most are incapable of contributing meaningfully to it. Focusing on ensuring they at least have a reasonable model of how the world works instead of on a model of how to properly model very complex things is a net benefit.
Also even learning good models of the world is secondary to the role of socializing them to accept hierarchy and authority.
It does however incur a slight cost of them not being sane on policy based on complex and ambiguous science. One might argue that more and more policies fall into this category and that the benefit calculation will soon (or has already) fallen to the side of rather teaching them how to model.
It escapes me however why this would be better that technocracy or even just plain old elitism.
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Excellent observation. Process control is very important, and it even plays a part in real scientific experiments, but it needs to be clearly distinguished from the part of the experiment where the correct result is not known in advance.
I can imagine the occasional chemistry assignment that gets around this by having mystery reagants whose identities you need to discover, and the occasional physics assignment where you have anonymous materials and need to figure out some of their properties. But it seems hard to me to extend this to an entire course worth of labs; any more ideas?
Slight modification: in many (majority?) cases, the children learn to address the ‘wrong’ outcome by just fudging the data so that it appears as if they got the expected, ‘right’ one after all. Plotting a straight least-squares-fit line, then scattering dots around it ‘randomly’. Etc. In a way, this is the most rational way to deal with it – less effort, for one thing.
Science!
Funny, I presented exactly this phenomenon as a unifying hypothesis for what is wrong with science at a dinner a couple months ago. I’m glad to see its independent generation, which is pretty significant Bayesian evidence.
People have a very rough intuitive idea of priors that may be coming into play here.
Personally, I’ve seen a fair number of high school lab reports that discuss sources of error that would make the results even more likely to go away from what the textbooks say should occur and yet they still decide that the error must have moved things away from the textbook answer. So it may be that we’re not doing anything here other than teaching kids to rationalize things away and call that science.
What should school be for most high school students?
As society, what’s our best use of that compulsory time?
Perhaps more narrowly tailored protean industrial training, with planned obsolescence built in for when they need to be retrained in a decade or so?
“People have a very rough intuitive idea of priors that may be coming into play here.” I agree – you could interpret this as a very useful lesson in the practical application of science: if you perform a shoddy experiment and get results which seem to contradict a lot of what we know about the universe, it’s almost certainly your experiment which is wrong. This is good to know when confronted with, for example, the latest “experiment” on the effects of homeopathy or intercessory prayer. (Not that I would be caught dead defending the way science is taught in schools.)
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