Let me try to separate two different issues here, teaching science and teaching rational thought. The latter should indeed be taught better and to most people. The standard "critical thinking" curriculum is probably inadequate and largely out of date with the current leading edge, which is hardly surprising.
And here's why I try not to separate those two issues: (1) Teaching science and teaching rational thought are largely interdependent. You can't do one wholly without the other. (2) 'Rational thought' and 'critical thinking' don't generally get their own curricula in schools. So we need to sneak them into science classrooms, math classrooms, philosophy classrooms, history classrooms -- wherever we can. Reminding ourselves of the real-world intersectionality, fuzziness, and interdependence of these fields helps us feel better about this pragmatic decision by intellectually justifying it; but what matters most is the pragmatics. Our field divisions are tools.
This is largely a typical mind fallacy. Plenty of people can find no joy in arithmetics, just like plenty of people find no joy in poetry, no matter how hard you make them.
The worry of typical-mind errors looms large on any generalized account, including a pessimistic one. To help combat that, I'll make my background explicit. I largely had no interest in mathematical reasoning in primary and secondary schools; hence when I acquired that interest as a result of more engaging, imaginative, and 'adventurey' approaches to teaching and thinking, I concluded that there were probably lots of other students for whom mathematics could have been taught in a much more useful, personally involving way.
Perhaps those 'lots of others' are still a minority; no data exists specifically on how many people would acquire a love of arithmetic from a Perfectly Optimized Arithmetic course. But I'm inclined to think that underestimating people's potential to become better lay-scientists, lay-mathematicians, and lay-philosophers at this stage has greater potential costs than overestimating it.
Part of the sequence: Rationality and Philosophy
Bertrand Russell
I've complained before that philosophy is a diseased discipline which spends far too much of its time debating definitions, ignoring relevant scientific results, and endlessly re-interpreting old dead guys who didn't know the slightest bit of 20th century science. Is that still the case?
You bet. There's some good philosophy out there, but much of it is bad enough to make CMU philosopher Clark Glymour suggest that on tight university budgets, philosophy departments could be defunded unless their work is useful to (cited by) scientists and engineers — just as his own work on causal Bayes nets is now widely used in artificial intelligence and other fields.
How did philosophy get this way? Russell's hypothesis is not too shabby. Check the syllabi of the undergraduate "intro to philosophy" classes at the world's top 5 U.S. philosophy departments — NYU, Rutgers, Princeton, Michigan Ann Arbor, and Harvard — and you'll find that they spend a lot of time with (1) old dead guys who were wrong about almost everything because they knew nothing of modern logic, probability theory, or science, and with (2) 20th century philosophers who were way too enamored with cogsci-ignorant armchair philosophy. (I say more about the reasons for philosophy's degenerate state here.)
As the CEO of a philosophy/math/compsci research institute, I think many philosophical problems are important. But the field of philosophy doesn't seem to be very good at answering them. What can we do?
Why, come up with better philosophical methods, of course!
Scientific methods have improved over time, and so can philosophical methods. Here is the first of my recommendations...
More Pearl and Kahneman, less Plato and Kant
Philosophical training should begin with the latest and greatest formal methods ("Pearl" for the probabilistic graphical models made famous in Pearl 1988), and the latest and greatest science ("Kahneman" for the science of human reasoning reviewed in Kahneman 2011). Beginning with Plato and Kant (and company), as most universities do today, both (1) filters for inexact thinkers, as Russell suggested, and (2) teaches people to have too much respect for failed philosophical methods that are out of touch with 20th century breakthroughs in math and science.
So, I recommend we teach young philosophy students:
(In other words: train philosophy students like they do at CMU, but even "more so.")
So, my own "intro to philosophy" mega-course might be guided by the following core readings:
(There are many prerequisites to these, of course. I think philosophy should be a Highly Advanced subject of study that requires lots of prior training in maths and the sciences, like string theory but hopefully more productive.)
Once students are equipped with some of the latest math and science, then let them tackle The Big Questions. I bet they'd get farther than those raised on Plato and Kant instead.
You might also let them read 20th century analytic philosophy at that point — hopefully their training will have inoculated them from picking up bad thinking habits.
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