American Revolutionary pamphleteer Thomas Paine said in Common Sense (1776), government is at best “a necessary evil.”
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Thirteen Baltimore City high schools don’t have a single student who has achieved grade-level proficiency in math.
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Some Math and Reason
Here is "the bat and ball problem:"
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Thirteen Baltimore City high schools don’t have a single student who has achieved grade-level proficiency in math.
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Some Math and Reason
Here is "the bat and ball problem:"
A bat and a ball cost $1.10 in total.
The bat costs $1.00 more than the ball.
How much does the ball cost? ____ cents.
In a paper in "Cognition," Meyer and Fredrick test multiple versions of the bat and ball and related problems to try to uncover where people’s intuitions go wrong. The most remarkable two versions of which are shown below:
The bat costs $1.00 more than the ball.
How much does the ball cost? ____ cents.
In a paper in "Cognition," Meyer and Fredrick test multiple versions of the bat and ball and related problems to try to uncover where people’s intuitions go wrong. The most remarkable two versions of which are shown below:
1. A bat and a ball cost $110 in total.
The bat costs $100 more than the ball.
How much does the ball cost?
Before responding, consider whether the answer could be $5.
$_____
2. A bat and a ball cost $110 in total.
The bat costs $100 more than the ball.
How much does the ball cost?
The answer is $5.
Please enter the number 5 in the blank below.
$_____
Remarkably, even when told to consider $5, most people continue to answer $10. Even more shockingly, most people get the answer right when they are explicitly told the answer and instructed to enter it, yet 23% still get the answer wrong!
The authors conclude:
"…this “hinted” procedure serves to partition respondents into three groups: the reflective (who reject the common intuitive error and solve the problem on the first try), the careless (who answer 10, but revise to 5 when told they are wrong), and the hopeless (who are unable or unwilling to compute the correct response, even after being told that 10 is incorrect)
…many respondents maintain the erroneous response in the face of facts that plainly falsify it, even after their attention has been directed to those facts….the remarkable durability of that error paints a more pessimistic picture of human reasoning than we were expecting."
The bat costs $100 more than the ball.
How much does the ball cost?
Before responding, consider whether the answer could be $5.
$_____
2. A bat and a ball cost $110 in total.
The bat costs $100 more than the ball.
How much does the ball cost?
The answer is $5.
Please enter the number 5 in the blank below.
$_____
Remarkably, even when told to consider $5, most people continue to answer $10. Even more shockingly, most people get the answer right when they are explicitly told the answer and instructed to enter it, yet 23% still get the answer wrong!
The authors conclude:
"…this “hinted” procedure serves to partition respondents into three groups: the reflective (who reject the common intuitive error and solve the problem on the first try), the careless (who answer 10, but revise to 5 when told they are wrong), and the hopeless (who are unable or unwilling to compute the correct response, even after being told that 10 is incorrect)
…many respondents maintain the erroneous response in the face of facts that plainly falsify it, even after their attention has been directed to those facts….the remarkable durability of that error paints a more pessimistic picture of human reasoning than we were expecting."
One element that is not addressed is, of course, participant insincere orneriness.
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