Hey #mtbos, here's the current argument in my department:
Should we require students to rationalize the denominator for full credit or not? What are your thoughts?
ex: For tan(30), is 1/sqrt(3) considered full credit or do students need to write it as sqrt(3)/3?
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Exactly. PEMDAS. Always put the function in standard form. It takes time to unspool these beliefs and get to the actual mathematics. It seems to be a part of the strength of active learning/IBL. Students get back some of the power that they lose to (unneeded?) simplifications.
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Alas, the essence of the problem is that the teacher corps, lacking real mathematical understanding, often cannot distinguish between conventions and axioms. Which is in turn a consequence of the irresponsible, self-serving indifference of mathematicians, who merely shrug at it.
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