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I then asked which would be more sucessful in a math class, a liberal or conservative approach? Do you have an answer?

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Your characterization does not conform to reality. Look, I'm one of the most liberal people I know... so I know where you are coming from. But, it does no good to make ridiculous analogies like that.

I could just as easy say:

A conservative says: 2+2=4 was true yesterday, so it's true today. A liberal wants to take a vote, and make sure everybody is OK with 2+2 being equal to 4. Which would do better in a math class?