Math for Good Thinking

Monday March 5, 2012

I was listening to this Freakonomics podcast and they had Ellen Peters on. She said:
"Numeracy in general, what it should do, is it should help you to better understand information, first of all, and that kind of comprehension is sort of a basic building block of decisions across a variety of domains. But numeracy should also do other things. It should also help you just simply process the information more systematically. It should, in general, help you to get to better decisions that are more in line with the facts."

and I agreed, and felt hopeful about the world, but it was all a setup for her research conclusion that even or especially people with higher education have preexisting beliefs that are not affected by good thinking:
"Greater scientific literacy and numeracy were associated with greater cultural polarization: respondents predisposed by their values to dismiss climate change evidence became more dismissive, and those predisposed by their values to credit such evidence more concerned, as science literacy and numeracy increased."

This is concerning! I would like to believe that my math-teachers colleagues are making students into better thinkers. I am inclined to hope that hard science majors are less inclined to be biased by "values" than, say, MBAs, but everybody has been through high school and ought to be better than this.

I also recently read "Thinking, Fast and Slow" by Kahneman, which is wonderful. He talks about how he helped develop a textbook on rational thinking that was never adopted by Israel after they finally finished it. I would like to see a textbook like that. I think that could be the kind of textbook American schools could use. Do you know of any resources in this vein?

And this idea of our-subject-should-make-people-better-thinkers is not unique to math, of course. It's everywhere, and here's a relevant selection from a science point of view:
"We need a more scientifically literate populace to address the global challenges that humanity now faces and that only science can explain and possibly mitigate, such as global warming, as well as to make wise decisions, informed by scientific understanding, about issues such as genetic modification."

That's from an article series that makes the point that unfortunately, too often the result of science classes is not a really useful better understanding of science. Good stuff.

I think that cross-discipline work between math and ELA could be really valuable too, and is the sort of thing that should probably be done more. I'm thinking of things like analyzing the logical structure of an argument, looking at symbolic structures of logical fallacies, etc. I'm sure there are more good ideas in this realm. Perhaps what I mean is really better-structured, deeper, more cognitively demanding ELA.

I'm also thinking about this in relation to the Common Core hullabaloo, which I think is generally wonderful - who wouldn't be for deeper better standards that encourage real understanding of concepts? But then I see stuff like this: which is supposed to be a *model* of Common Core-aligned work, and it kind of makes me retch. Am I wrong to retch? Is this an improvement on what's currently being done?

I hope the thread connecting all these things I've mentioned is evident to you! haha What are your thoughts? Are there really great math (etc.) curricula/texts being used now or being developed?

This post was originally hosted elsewhere.