Converting radians to degrees

The question shown on the left is actually quite well answered (81% of students got it right at the first attempt) especially since it is in the formative-only practice assessment rather than the summative end-of-module assessment.

However it is interesting that the most common error to all variants of this question (in 4.4% of responses) is to calculate the value of the fraction (3π/4 in the variant shown) rather than converting to degrees.

I find this particularly interesting because this error feels conceptually similar to  that made when students give the values at which a line has zero value rather than where its gradient is zero (see ‘Function or derivative?‘) or when they give twice a number rather than squaring it. I’m not sure whether there really is some conceptually similar misunderstanding or whether the students who make these mistakes  just haven’t a clue!

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