When lecturing, saying the word “obvious” is a signal for the students to begin panicking and self-doubting. I wonder if some instructors do this intentionally.
Saying that something is ‘obvious’ can provide useful information to the listener of the form “If you think about this for a few minutes you’ll see why this is true; this stands in contrast with some of the things that I’m talking about today.” Or even “though you may not understand why this is true, for experts who are deeply immersed in this theory this part appears to be straightforward.”
I personal wish that textbooks more often highlighted the essential points over those theorems that follow from a standard method that the reader is probably familiar with.
But here I really have in mind graduate / research level math where there’s widespread understanding that a high percentage of the time people are unable to follow someone who believes his or her work to be intelligible and so who have a prior against such remarks being intended as a slight. It seems like a bad communication strategy for communicating with people who are not in such a niche.
When lecturing, saying the word “obvious” is a signal for the students to begin panicking and self-doubting. I wonder if some instructors do this intentionally.
Saying that something is ‘obvious’ can provide useful information to the listener of the form “If you think about this for a few minutes you’ll see why this is true; this stands in contrast with some of the things that I’m talking about today.” Or even “though you may not understand why this is true, for experts who are deeply immersed in this theory this part appears to be straightforward.”
I personal wish that textbooks more often highlighted the essential points over those theorems that follow from a standard method that the reader is probably familiar with.
But here I really have in mind graduate / research level math where there’s widespread understanding that a high percentage of the time people are unable to follow someone who believes his or her work to be intelligible and so who have a prior against such remarks being intended as a slight. It seems like a bad communication strategy for communicating with people who are not in such a niche.