Perhaps you are correct. I don't remember the order in which I learned various concepts but I probably learned about degrees before pi and certainly before trig.
Since radians involve irrational numbers I can understand it being more difficult to learn than degrees. However degrees are a completely arbitrary unit that are used for historical reasons.
Getting stuck thinking in degrees hindered my ability to understand trigonometry, and I don't think I'm alone. It is my belief that teaching trig using radians would be less confusing than teaching trig using degrees first, then radians (as was my experience). With degrees there is no direct correlation between 90 degrees and the values of the trig functions which leads to people simply memorizing values. The same is true (to a lesser extent) when using 2 pi.
True, but you are now setting up a false dilemma. The point is not that arbitrary units are hard, nor that any 2 are relatively harder. It is that a consistent unit that is not arbitrary is easier than the arbitrary ones, and usually involves quite a few useful "symetries" (by which I don't mean real symetries, but conceptual linkages).
As for why people think degrees is easier: it is simply because common usage of degrees makes the concept familiar to learners. I totally agree that teaching trig in terms of radians first would be much better.
Comments
Perhaps you are correct. I don't remember the order in which I learned various concepts but I probably learned about degrees before pi and certainly before trig.
Since radians involve irrational numbers I can understand it being more difficult to learn than degrees. However degrees are a completely arbitrary unit that are used for historical reasons.
Getting stuck thinking in degrees hindered my ability to understand trigonometry, and I don't think I'm alone. It is my belief that teaching trig using radians would be less confusing than teaching trig using degrees first, then radians (as was my experience). With degrees there is no direct correlation between 90 degrees and the values of the trig functions which leads to people simply memorizing values. The same is true (to a lesser extent) when using 2 pi.
True, but you are now setting up a false dilemma. The point is not that arbitrary units are hard, nor that any 2 are relatively harder. It is that a consistent unit that is not arbitrary is easier than the arbitrary ones, and usually involves quite a few useful "symetries" (by which I don't mean real symetries, but conceptual linkages).
As for why people think degrees is easier: it is simply because common usage of degrees makes the concept familiar to learners. I totally agree that teaching trig in terms of radians first would be much better.