I had to take a course in logic as an undergraduate and saw little point in it at the time. The reason we were given for having to take the course was so that we would be able to read papers that used logical symbols, but the symbols we were taught were not the ones most commonly used in readings we were assigned. And you don't need to take an entire course in order to know that this symbol should be read as 'or' and that as 'if ... then' (although translating from formal symbolism into ordinary language is not as straightforward as one might think). No one ever claimed, as far as I can recall, that studying logic would make us any more logical than we already were, any better at reasoning. Perhaps it does have that effect, but I've seen no evidence that it does, and this would surely be widely advertised by logicians if it existed (or have I just committed some fallacy right there?). I believe that argument mapping has good effects, but I haven't looked into it much. That's because I don't teach critical thinking, although if I did I expect I would start here and make my students do some mapping. Basically the (apparent) problem with teaching logic is that one course in anything is not likely to make a lasting difference to students, and if you're going to have students reason logically then you might as well have them do so about some particular subject, and then what you have is not a course in logic but a philosophy course on whatever area of philosophy you have chosen to focus on in the course. Perhaps it wouldn't even be a philosophy course, although if the primary focus is logical reasoning then I don't know what else it could be. In short, maybe logic should be taught across the philosophy curriculum rather than in a dedicated course. As David Papineau says:
I’ve long been unsure about the point of normal introductory logic courses. It is doubtful they do anything to improve argumentative skills, and they tend not to leave time for any philosophically significant metalogic. Of course, they are a necessary prerequisite for those who are going to go on in logic. But for the many who aren’t, it is not obvious what the philosophical payoff is.The problem with inculcating an informed skeptical tendency is that what's in question seems to be a virtue rather than some quantity of knowledge, and developing a virtue is going to take much more than one course. It's easy enough to educate students about the bias of Fox News, but (or because) they already know this. The ones who watch it will continue to do so, and will insist (rightly) that other news sources have their own biases. People generally know how to be skeptical when they want to be. It's developing that will in the right way that's the tricky part. I don't want my students to be skeptical about global climate change--they should trust scientists more than that. I don't want them to believe that 9/11 was an inside job by the US government--they should trust the government more than that. But should they believe everything that scientists tell them? Should they always trust the government? No. It might help if they knew more about how science is done, about how many scientists believe in man-made climate change, and if they knew something about the science of climate change itself. But how much of that could be covered in one general course on critical thinking? And what would prevent any students whose minds were changed as a result from starting to believe in some other irrational theory (or some other excuse to do nothing about climate change)? It seems to me that, once again, the habits of mind we're looking for need to be encouraged and developed across the curriculum.
Which means students need to be challenged to justify their beliefs more consistently. They need to be graded on their reasoning more and on knowing the right answer less. Which means less multiple choice and memorization, more papers, oral exams, etc. Which probably means smaller classes, more encouragement to teachers to challenge students even if students don't like it, and less pressure on teachers to do anything other than teaching (so that they have time to grade all those papers, for instance). It also means thinking less that a course or two can fix a major deficiency in anyone's education.
Having said all that, every time I visit the Critical Thinking on the Web site I start to want to teach a critical thinking course despite it all.