If the research described in the link below is correct, then it seems the "smarter" we are, as measured by SAT scores, the more likely we are to take erroneous mental shortcuts, and not be aware of it.

"And here’s the upsetting punch line: intelligence seems to make things worse. The scientists gave the students four measures of 'cognitive sophistication.' As they report in the paper, all four of the measures showed positive correlations, 'indicating that more cognitively sophisticated participants showed larger bias blind spots.'”

http://www.newyorker.com/online/blogs/frontal-cortex/2012/06/daniel-kahneman-bias-studies.html

Maybe this is why insight into problems has always been considered an art, rather than a calculation. Maybe it is why innovation has been so hard to teach. Maybe it is why engineering education can't teach innovation. What do you think?

Spoiler Alert! Don't read the following until after you've read the article!

Not that I'm so smart, but after consulting my chihuahuas (who did not get very high SAT scores), I think the first problem in the article should be set up this way:
x+y=1.10
x=y+1
The second problem should be set up as
(2^n)/(2^1), where n is the number of days to fill the lake (48), which we divide by 2 to the first power to get the number of days until the lake is half filled (n-1).

http://www.lulu.com/spotlight/poconoarmchairreview

6/16/2012 10:10 AM EDT

I'm thinking the conditions under which this research was performed may have set up less critical expectations among the test subjects. That is, maybe they breezed through the questions uncritically, knowing it was not important to their future.

On the other hand, it's possible that people "train for the test," so that high scores on the SAT reflect practice in recognizing certain problem types. Maybe that skill fades quickly when it is no longer needed, with the result that the subjects default to mental shortcuts.

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