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As a math professor, I had an epiphany about the word "easily" several years ago. In my course notes, I used that word to mean "I guarantee you don't need any a

As a math professor, I had an epiphany about the word "easily" several years ago. In my course notes, I used that word to mean "I guarantee you don't need any additional ideas here, just do the obvious thing." Nothing more was meant. But I realized that many students either didn't think the obvious thing was really that obvious, or maybe realized it but were reticent to follow that path because it invoved some tedious work and the prof said it was easy, so that couldn't be it. Many students were also intimidated by that word, as if I were saying to them "if you don't find this easy, you shouldn't be here". So I went on a deleting spree, removing most instances of "easy", "simple", and "just a matter of", and replacing them with a clearer explanation of what to do. My notes got better as a result. Less filler, less intimidation, more useful details.

javajosh 3y ago
Thank you! I think you correctly guessed what the students were thinking, because I have thought similar things. One angle here is that academics are (rightly) proud of their specialist knowledge, and often using words like "simply" and "easily" really are a flex whether they know it or not. The best way as student can take this is as inspiration, that one day it will be easy for you, too. I personally believe empathy deserves high praise and recognition, a key part of pedagogy. However, the lack of empathy does not, in turn, deserve derision. Not everyone is a great, or even particularly good, teacher.
ellisv 3y ago
Whenever my professor said "it's easy to show" and then moved on it felt very hand wavy. The steps weren't obvious to me and didn't become more obvious as the course went on because no one taught me how to think of the "obvious" thing.
- javajosh 3y ago
  The worst situation in my college experience was when a prof would go over some mundane part of a proof in excruciating detail, and then hand-wave the important part. I realized later in life it was because they prof didn't understand it, either.
  - Tade0 3y ago
    I had a similar situation after a "last chance" exam for one course. The lecturer was unavailable, so he assigned a substitute to grade the exam. There was a problem there similar to the casting problem (assuming each subsequent candidate has probability P to be better than the previous one, when should we make our pick), only the probabilities were different each time - this wasn't covered in the course material. I deconstructed it by calculating all the probabilities by hand, because I didn't know any other way. The substitute asked me to come by and explain how I solved it, because apparently I was the only one to do so.
hnarayanan 3y ago
And as a math student, I found myself using this as a strategy in reverse. Finding myself in a tenuous part of a proof, I would say things like “clearly one can see that,” and jump a few steps. I think I was doing this to put the person looking at my work in the back foot, and it might’ve worked a couple of times!
furyofantares 3y ago
I read something a while ago that resonated, and I tried it out and have had a lot of success with my kid. If the kid is hesitant to try something that you know will end up being easy, the natural thing is to tell them it's going to be easy. But if you tell someone something is easy, and their personal experience is already that it's hard, well, the conclusion isn't necessarily "oh I was wrong, now it's easy, thanks dad, I'll actually try now". It may instead be "oh wow I suck at the easy thing I guess". So now I do the opposite. She's struggling with something? I tell her it's hard. And I pair it with some indication that it won't be hard forever and is worth learning. So now if I see her struggling I don't say "This is easy, let me show you". I definitely don't say "This is easy, just give it a shot". I say "Oh yeah, this part's hard at first. But I know a trick."
JoeyBananas 3y ago
Saying "easily" can be beneficial because it signals to the students "See? This is really not that bad." Many students think their grade is worse than it actually is, they think they're worse at math than they actually are or they think the course is harder than it really is
steve_adams_86 3y ago
I suppose too that if something truly is easy or simple, it should be self-evident. What is the purpose of taking the time and energy to point out that something isn’t difficult? If it were true, a person would likely discover it themselves readily enough. I find this kind of writing (and thinking in general) fairly commonplace. It’s a good exercise to take a step back and wonder: why did I write that? What did I actually mean by it? Is it necessary to state X or Y, or am I using it implicitly for some communicative purpose that should be explicit? Stuff like this is why writing is actually quite hard, in my opinion.
vuciv1 3y ago
I just want to say thank you for doing this. Please tell your community to do this too. I really struggled hearing such things in college. It’s crazy to say, but I think not hearing what was “obvious” would have helped me excel more in my classes.

javajosh 3y ago

Thank you! I think you correctly guessed what the students were thinking, because I have thought similar things. One angle here is that academics are (rightly) proud of their specialist knowledge, and often using words like "simply" and "easily" really are a flex whether they know it or not. The best way as student can take this is as inspiration, that one day it will be easy for you, too. I personally believe empathy deserves high praise and recognition, a key part of pedagogy. However, the lack of empathy does not, in turn, deserve derision. Not everyone is a great, or even particularly good, teacher.

ellisv 3y ago

Whenever my professor said "it's easy to show" and then moved on it felt very hand wavy. The steps weren't obvious to me and didn't become more obvious as the course went on because no one taught me how to think of the "obvious" thing.

javajosh 3y ago
The worst situation in my college experience was when a prof would go over some mundane part of a proof in excruciating detail, and then hand-wave the important part. I realized later in life it was because they prof didn't understand it, either.
- Tade0 3y ago
  I had a similar situation after a "last chance" exam for one course. The lecturer was unavailable, so he assigned a substitute to grade the exam. There was a problem there similar to the casting problem (assuming each subsequent candidate has probability P to be better than the previous one, when should we make our pick), only the probabilities were different each time - this wasn't covered in the course material. I deconstructed it by calculating all the probabilities by hand, because I didn't know any other way. The substitute asked me to come by and explain how I solved it, because apparently I was the only one to do so.

hnarayanan 3y ago

And as a math student, I found myself using this as a strategy in reverse. Finding myself in a tenuous part of a proof, I would say things like “clearly one can see that,” and jump a few steps. I think I was doing this to put the person looking at my work in the back foot, and it might’ve worked a couple of times!

furyofantares 3y ago

I read something a while ago that resonated, and I tried it out and have had a lot of success with my kid. If the kid is hesitant to try something that you know will end up being easy, the natural thing is to tell them it's going to be easy. But if you tell someone something is easy, and their personal experience is already that it's hard, well, the conclusion isn't necessarily "oh I was wrong, now it's easy, thanks dad, I'll actually try now". It may instead be "oh wow I suck at the easy thing I guess". So now I do the opposite. She's struggling with something? I tell her it's hard. And I pair it with some indication that it won't be hard forever and is worth learning. So now if I see her struggling I don't say "This is easy, let me show you". I definitely don't say "This is easy, just give it a shot". I say "Oh yeah, this part's hard at first. But I know a trick."

JoeyBananas 3y ago

Saying "easily" can be beneficial because it signals to the students "See? This is really not that bad." Many students think their grade is worse than it actually is, they think they're worse at math than they actually are or they think the course is harder than it really is

steve_adams_86 3y ago

I suppose too that if something truly is easy or simple, it should be self-evident. What is the purpose of taking the time and energy to point out that something isn’t difficult? If it were true, a person would likely discover it themselves readily enough. I find this kind of writing (and thinking in general) fairly commonplace. It’s a good exercise to take a step back and wonder: why did I write that? What did I actually mean by it? Is it necessary to state X or Y, or am I using it implicitly for some communicative purpose that should be explicit? Stuff like this is why writing is actually quite hard, in my opinion.

vuciv1 3y ago

I just want to say thank you for doing this. Please tell your community to do this too. I really struggled hearing such things in college. It’s crazy to say, but I think not hearing what was “obvious” would have helped me excel more in my classes.