What is the effect of studying logic or mathematics on general thinking skills?
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).