Basic teaching theory states that experts don't think like novices, and further, they are likely to not remember the misunderstandings and difficulties they encountered as novices, because the novice problems are what they now consider simple. This is a being studied a lot in the world of education.
I call it expert idiocy when the expert refuses to accept that his understanding is actually a pretty advanced state of thinking, and not immediately obvious to the beginner. It is this form of idiocy that leads to people feeling that "only freaks can get math" or "I'm not smart enough for physics" or "computer geniuses can only do basic tasks".
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.
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You are exhibiting what I call "expert idiocy".
Basic teaching theory states that experts don't think like novices, and further, they are likely to not remember the misunderstandings and difficulties they encountered as novices, because the novice problems are what they now consider simple. This is a being studied a lot in the world of education.
I call it expert idiocy when the expert refuses to accept that his understanding is actually a pretty advanced state of thinking, and not immediately obvious to the beginner. It is this form of idiocy that leads to people feeling that "only freaks can get math" or "I'm not smart enough for physics" or "computer geniuses can only do basic tasks".
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.