You're reading the public-facing archive of the Category Theory Zulip server.
To join the server you need an invite. Anybody can get an invite by contacting Matteo Capucci at name dot surname at gmail dot com.
For all things related to this archive refer to the same person.
Eduardo Ochs (Jun 03 2020 at 22:19):Fabrizio Genovese said:
Now, if me, a total no one with barely a "real" CT experience can teach CT to random people without a mathematics background, I am 100% sure that everyone else can. And, most importantly, I am 100% sure that everyone else can learn.
I know some mathematicians that can only present things in the style "definition/theorem/proof" - and I like to believe that they are mostly unable to teach things to random people without a background in mathematics...
Some people develop intuition about mathematical objects by playing with concrete examples and by doing calculations and tests - and there are people who think that intution coming from particular cases is practically useless, and that you should work only by learning theorems and by trying to prove new theorems... also, some people think very visually, while others less so.
If you are able to teach CT to random people that probably means that you can deal well with different ways of thinking. :slight_smile:
Fabrizio Genovese (Jun 03 2020 at 22:20):Well, teaching is a skill, but as any skill it can be trained. I think many bad teacher simply didn't put too much effort in bettering their teaching, for whatever reason.
Fabrizio Genovese (Jun 03 2020 at 22:20):It's literally like dancing. Many people think it's an innate thing, but it's not. It can be learnt, you just need patience and motivation, like with everything in life. :D
Alexander Kurz (Jun 03 2020 at 22:24):Fabrizio Genovese said:
Well, teaching is a skill, but as any skill it can be trained. I think many bad teacher simply didn't put too much effort in bettering their teaching, for whatever reason.
I like your dancing metaphor ... it is easier to dance with one partner ... but most teachers have big classes
Fabrizio Genovese (Jun 03 2020 at 22:25):Alexander Kurz said:
Fabrizio Genovese said:
Well, teaching is a skill, but as any skill it can be trained. I think many bad teacher simply didn't put too much effort in bettering their teaching, for whatever reason.
I like your dancing metaphor ... it is easier to dance with one partner ... but most teachers have big classes
Precisely!
Fabrizio Genovese (Jun 03 2020 at 22:28):Maybe it's a stupid way to put it but people like dopamine. And feeling like you have unlocked a whole new way of thinking is adrenalinic. It's also super cool for a teacher, when you see your student happy because of this. :slight_smile:
John Baez (Jun 03 2020 at 22:32):Fabrizio Genovese said:
Well, teaching is a skill, but as any skill it can be trained. I think many bad teacher simply didn't put too much effort in bettering their teaching, for whatever reason.
John Baez (Jun 03 2020 at 22:33):I imagine that people who are bad at teaching are probably also bad at learning how to teach, e.g. knowing that they should learn to teach better.
John Baez (Jun 03 2020 at 22:33):The people who are good at teaching seem to be people who realize it's a constant process of learning how to teach.
Alexander Kurz (Jun 03 2020 at 22:45):Rongmin Lu said:
Alexander Kurz said:
Fabrizio Genovese said:
Well, teaching is a skill, but as any skill it can be trained. I think many bad teacher simply didn't put too much effort in bettering their teaching, for whatever reason.
I like your dancing metaphor ... it is easier to dance with one partner ... but most teachers have big classes
Many dancing teachers have big classes and make us switch partners all the time. Sorry, I'm not sure I understand the concern here.
I was thinking of a school setting where students go because they have to ... I assume in your dancing lessons students go there because they want to
John Baez (Jun 03 2020 at 22:47):Rongmin Lu said:
In academia, at least in the institutions I've been in, teaching is considered secondary to research.
John Baez (Jun 03 2020 at 22:47):In research universities, yes. Community colleges in the US are different.
John Baez (Jun 03 2020 at 22:51):But I guess none of them are gonna be teaching category theory anytime soon.
Henry Story (Jun 03 2020 at 22:51):For people like me who are really working from home this channel and all the videos online are great resources.
zulipchat is a bit like trying to drink from a firehose though :-)
Fabrizio Genovese (Jun 03 2020 at 22:52):Rongmin Lu said:
Fabrizio Genovese said:
I think many bad teacher simply didn't put too much effort in bettering their teaching, for whatever reason.
In academia, at least in the institutions I've been in, teaching is considered secondary to research. I know people who routinely negotiate to reduce their teaching workload so they can focus on their research. Tenure is ostensibly granted on the basis of research, teaching and service, but the balance is heavily tilted in favour of research. In fact, people have often viewed getting a teaching award as a kiss of death, career-wise.
This is true. But still... I did some TAing during my PhD in Oxford, mainly to get some money. I hated that. Still, hating it was no good reason to not to try to do it as best as I could. The way I saw it, they were paying me for a service, and it was my responsibility to give the best service I could. The fact that I did not like it was marginal
John Baez (Jun 03 2020 at 23:07):At UCR most students need to be TAs, and some of them get pretty good at teaching that way. @Jade Master, @Christian Williams and @Joe Moeller all earn their living that way.
Joe Moeller (Jun 03 2020 at 23:08):4 courses per quarter (usually the same or just two different ones), secondary lectures + grading + office hours.
Henry Story (Jun 03 2020 at 23:20):My previous remark was just to point out that perhaps this discussion on teaching needs to take into account the new technical opportunities that are offered by the Web and the Internet. (that is not to say that university teaching in Academia is not important -- of course it is -- but just that there may be a lot of potential out there of people who are or could be interested in CT, but are not near an institution that teaches it correctly, or sees the value of it)
John Baez (Jun 03 2020 at 23:34):Many of the grad students feel weighed down by heavy teaching requirements. But yes, they learn how to teach small classes, and some choose to teach larger classes in the summer.
Fabrizio Genovese (Jun 03 2020 at 23:51):Henry Story said:
My previous remark was just to point out that perhaps this discussion on teaching needs to take into account the new technical opportunities that are offered by the Web and the Internet. (that is not to say that university teaching in Academia is not important -- of course it is -- but just that there may be a lot of potential out there of people who are or could be interested in CT, but are not near an institution that teaches it correctly, or sees the value of it)
Well, if you see our next two courses will be held online :slight_smile:
Daniel Geisler (Jun 03 2020 at 23:52):With all respect to @John Baez, Analytic Combinatorics explanations of combinatorics is both beautiful and deeply practical.
Todd Trimble (Jun 04 2020 at 00:04):Feynman tells a story somewhere of how he explicitly rejected an offer of a research-only position, knowing well what happened to some of his colleagues at the Institute of Advanced Study. He admitted that sometimes teaching was the greatest pain in the ass, especially when you're hot on the tail of research. But he also found the real contact with students stimulating, and that it sometimes moved his thoughts in ways they wouldn't have otherwise.
Nathanael Arkor (Jun 04 2020 at 00:16):On the other hand, I think it's entirely understandable that some people do not wish to teach. Teaching is a different skill set to researching, and it appears to me that the reason they are conflated in academic roles so frequently is partially historical and partially practical. If you don't enjoy teaching and are not very good at it, but are an accomplished researcher, there seems no reason you should be forced to teach. Some people (e.g. Feynman) may have found teaching useful, but that's not to say everyone would benefit in the same way.
Nathanael Arkor (Jun 04 2020 at 00:17):As a student, one can tell who enjoys teaching, and they are generally the better teachers. Forcing those who do not enjoy teaching into it is of limited benefit to anyone.
Nathanael Arkor (Jun 04 2020 at 00:23):I'm particularly talking about a different context to learners/graduate students, which those research pieces focus on. I'm rather talking about more senior academics teaching, e.g. lecturing.
Nathanael Arkor (Jun 04 2020 at 00:23):I can see the benefit in encouraging graduate students to teach.
Joe Moeller (Jun 04 2020 at 00:26):Rongmin Lu said:
John Baez said:
they learn how to teach small classes, and some choose to teach larger classes in the summer.
That's great, because there's some evidence that teaching helps to improve their research skills and enhances their own learning.
Which is why, to me, it made no sense that people are trying to get out of teaching to focus on their research. I mean, I understand that this means that the research and/or teaching workload is too damn high for them to do both effectively, but this also indicates the presence of systemic problems.
I found out quite early that I learn a subject way better after I've taught it to someone else.
Nathanael Arkor (Jun 04 2020 at 00:47):I definitely agree that one should not be able to lecture without some degree of formal training. It's arguable whether that should happen at the graduate level or later; it'd probably be helpful to have training for smaller-scale teaching (e.g. talks/seminars/reading groups/teaching assistants) at the graduate level, and full teaching for any academics that go on to do lecturing. I think lecturing is a skill that many academics are expected to employ, but is separate from smaller-scale teaching, and not necessary for graduate students to learn.
Nathanael Arkor (Jun 04 2020 at 00:57):I think presenting a talk and giving a lecture are significantly different, due to the technical ability of the audience (and the gap in knowledge between the presenter and the audience) as well as the opportunity in a lecture to teach for an extended period of time.
Nathanael Arkor (Jun 04 2020 at 00:57):There's certainly an overlap, but the two involve distinct sets of skills as far as I can see.
John Baez (Jun 04 2020 at 16:36):Daniel Geisler said:
With all respect to John Baez, Analytic Combinatorics explanations of combinatorics is both beautiful and deeply practical.
John Baez (Jun 04 2020 at 16:37):Yeah, I love that book. I think math can be both beautiful and deeply practical. That's why I'm a mathematical physicist.
John Baez (Jun 04 2020 at 16:46):Todd Trimble said:
Feynman tells a story somewhere of how he explicitly rejected an offer of a research-only position, knowing well what happened to some of his colleagues at the Institute of Advanced Study. He admitted that sometimes teaching was the greatest pain in the ass, especially when you're hot on the tail of research. But he also found the real contact with students stimulating, and that it sometimes moved his thoughts in ways they wouldn't have otherwise.
John Baez (Jun 04 2020 at 16:47):He also said that if you're working in a place where your only job is to think great thoughts it can be stultifying.
John Baez (Jun 04 2020 at 16:48):He also said he got a great idea by watching students play frisbee and wondering why the frisbee wobbled at the rate it did.
John Baez (Jun 04 2020 at 16:49):Maybe I'm getting my stories mixed up, but this is the "wobbling" story:
John Baez (Jun 04 2020 at 16:49):"I was in the cafeteria and some guy, fooling around, throws a plate in the air. As the plate went up in the air I saw it wobble, and I noticed the red medallion of Cornell on the plate going around. It was pretty obvious to me that the medallion went around faster than the wobbling. I had nothing to do, so I start figuring out the motion of the rotating plate. I discovered that when the angle is very slight, the medallion rotates twice as fast as the wobble rate—two to one. It came out of a complicated equation! I went on to work out equations for wobbles. Then I thought about how the electron orbits start to move in relativity. Then there's the Dirac equation in electrodynamics. And then quantum electrodynamics. And before I knew it… the whole business that I got the Nobel prize for came from that piddling around with the wobbling plate."
John Baez (Jun 04 2020 at 16:50):So yeah, here he was at Cornell - which is where he went after he fled the Institute for Advanced Studies.
John Baez (Jun 04 2020 at 16:52):Rongmin Lu said:
It's almost a certainty that nobody had formally taught John how to teach...
John Baez (Jun 04 2020 at 16:53):Yeah, nobody taught me how to teach, and I was never a TA in grad school. I was just expected to walk into a classroom one day at Yale and start teaching. I was pretty bad.
Ralph Sarkis (Jun 04 2020 at 18:07):What made you improve? Only practice or other stuff?
Ralph Sarkis (Jun 04 2020 at 18:07):I am trying to teach as much as I can, but I don't like that I don't get enough feedback. It's also hard to ask students for more because I know I don't give enough to my profs either (not because I don't want to but because I don't think about how they teach, only about what they teach).
John Baez (Jun 04 2020 at 18:48):I kept trying to teach better. I got a big kick in the ass when I taught for two years at Wellesley, where the students expect the teachers to really care about them. One of my teaching evaluations said "Fire him".
John Baez (Jun 04 2020 at 18:49):Then when I went back to U. C. Riverside it struck me how easy to please the students are here, compared to Wellesley.
John Baez (Jun 04 2020 at 18:50):And so it seemed possible to become not only tolerable but quite good.
John Baez (Jun 04 2020 at 18:51):I have a bunch of advice about teaching here:
John Baez (Jun 04 2020 at 18:52):It's short, and I think every point listed is extremely important. Most poor teachers violate several or all of these rules.
sarahzrf (Jun 04 2020 at 20:24):chiming in to add to the pile of people saying that teaching helps them learn
sarahzrf (Jun 04 2020 at 20:25):pretty sure half the things i know clicked for me when i was forced to piece them together coherently because i was trying to explain them to someone