I frequently hear comments from people to the effect that "Studies have shown that students who take (intro) logic courses don't show any signs of improvement in logical/rational/critical thinking." Yet, as an undergrad, I got the opposite impression: I felt that studying logic (and mathematics) in more depth sharpened those skills. My initial Google search on the issue didn't really turn up much.
So, I have some questions regarding the psychology of logic and mathematics.
Question: What studies have been done regarding the effects/benefits to cognitive thinking skills from taking intro logic courses? What about studying probability theory, or even mathematics more generally? How conclusive are they?
Any references would be extremely helpful. I now teach intro logic as a grad student, and if there's something that students consistently miss out on, I would like to know about it so that I can (hopefully) make improvements.
(Also, I apologize if this is the wrong place to ask this question. Please let me know!)