What is the effect of studying logic or mathematics on general thinking skills? 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, any resources in the relation between mathematics and psychology more generally would be beneficial.

(I posted this on the MathSE, but was told this would be a better place for this question. If this needs retagging, let me know. I see that this question is similarly related, but I'm particularly interested in intro formal logic courses).
Here are some references that may be of use to you:

Contrasting the cognitive effects of graphical and sentential logic teaching: Reasoning, representation and individual differences (Stenning et al, 2007).

The shaping of deduction in Greek mathematics: A study in cognitive history (Netz, 1999). - a bit of a historical context, but I'd imagine that there are similar ideas

A cognitive theory of graphical and linguistic reasoning: Logic and implementation (Stenning and Oberlander, 1995).

A Cognitive Analysis of Problems of Comprehension in a Learning of Mathematics(Duval, 2006)

Perhaps related to your request - The Logic of Scientific Discovery (Popper, 2005).