Alexander Bogomolny at "CTK Insights" has a particularly interesting, or even provocative, recent post (entitled, "Regarding the Mess We Are In"), relating to math education, here:
"It is often asserted that, mathematics being a deductive science, the study of mathematics is bound to have a positive effect on students' thinking ability. The evidence that this is so is mostly anecdotal. The evidence that there are other and more effective ways to improve students' thinking (and along the way their math scores) is traditionally and consistently being ignored….I suspect most of us who love math, do indeed instinctively feel that the logical, precise thinking math entails would, if all citizens attained it, translate to a better society… but, as Bogomolny suggests, there may be nothing more than anecdote or intuition to support that notion. Still one can't help but believe that raising the national level of math literacy (or decreasing what John Allen Paulos calls "innumeracy" is an overall positive). And while it's true that mathematicians themselves may run the gamut of politics, religions, lifestyles, etc. I still can't help but think that, mathematicians (and even more generally, "scientists") likely fall more significantly into the "liberal" and "Democrat" categories than the general populace as a whole. And surely somewhere, there are some surveys out there, that may indicate such (or show it false)? Can anyone point me in the direction of such studies…?
"I may be mistaken, but it seems to me that the idea that study of mathematics leads to a betterment of the general thinking ability contains if not a plain logical flaw then at least an overlooked ambiguity. It's implicit in that belief that improved general thinking would bring about positive effects like avoidance of economic downturns, and in lives of individuals would lead to reaching better, more advantageous decisions. Would not that mean that (at least in the limit - so to speak - when all think masterfully), all would be expected to arrive at the same conclusions? If so, then the argument is patently based on a faulty assumption. As a matter of fact, mathematicians - those ultimate, professional thinkers - would not agree as a group (i.e. arrive logically at the same conclusion) on almost any trifle or a matter of importance.
"There are Republican and Democrat mathematicians. There are among them liberals and conservatives, good investors and bad investors, happily married and multiply divorced…."