Over the course of my studying and teaching, I've developed a number of reasonably strong opinions which could loosely be described as my teaching philosophy - I've tried to summarize some of these opinions on this page, in rough order of perceived importance.
Value over alternatives
Every student that takes my class makes a significant investment - probably a financial investment, and at the very least an investment in time. I aim to provide a return on that investment, and perhaps less trivially a greater return than they would get from other options. Thus, I know I've failed if a student feels they could have gotten just as much from reading a book or taking an online class.
How might I provide value over these alternatives? A few ways (1) if the topic is relatively new without any established textbooks, my choice of material and topics is often valuable in itself (2) teaching a way of thinking - watching someone thinking through a proof, or a new dataset, for example - can teach students how to think in a certain way; I still fondly remember Richard Samworth's in-class derivations (3) class discussions can facilitate learning in a way that can't easily be matched by independent or online learning (4) where appropriate, I try to provide opportunities to present in class and receive feedback from me and the rest of the class (5) where appropriate, I provide opportunities to work in teams - ideally with team members with very different skillsets (6) perhaps most importantly, providing structure - see the second point below.
For this same reason, I only ever make attendance compulsory as a way to "nudge" students to come to class in a world with many competing options. I have never refused to excuse a student's absence when they've asked, and hope never to need to - the onus is on me to make students feel my class is worth coming to, not on them to come to satisfy some arbitrary grading requirement. (One exception: when there is no other way to differentiate students in assigning grades, I have no option but to use attendance).
I am fortunate to get to teach a truly exceptional set of students, most of whom are very impressive in their own right, and I think of them as colleagues as well as students. In light of this, my initial impulse when I started teaching was to use a light touch on issues like classroom discipline, using laptops in class, case readings, assignment deadlines, etc...
I have since evolved to believe that this is a disservice to my students. Part of the value I offer is precisely that structure - both in the classroom and more broadly when it comes to work and assignments. Much like a personal trainer is empowered to push their client beyond their comfort zone, part of my job is to provide an environment in which my students can be pushed and learn as much as possible.
The delicate balance is to always remember that I have this authority by consent, not by fiat.
Slides are not textbooks
If you can look at my slides and know exactly what I'm going to say in class, then I've produced a textbook, not slides, and they're likely to distract from the point I'm trying to make. Ideally, slides are only there to support what I'm saying where needed.
Give a lot, get a lot
In teaching - and in life, really - there can sometimes be a race to the bottom when it comes to commitment. If I allow students to come to class a few minutes late, then maybe I can come a few minutes later. If I don't hold students to homework deadlines, then perhaps I can be slow posting the solutions. If I don't expect students to read the case, then I can get away with not thoroughly practicing every lecture.
I try to avoid this spiral like the plague - I try to give all of myself when I teach a class (time, commitment, energy), and this allows me to expect such as much from my students.
Exams should be easy and hard
In designing exams, one of my sole aims is to produce an exam with a high variance of scores. Exams that are too easy might lead to short-term happiness, but the scores end up clustered around 90%, and a silly mistake ends up making the difference between an A and a B. Exams that are too hard might be fun to write, but they are demoralizing and similarly lead to a bunch of very low scores. My aim is always to have a range from questions from the trivial to the very difficult.
Assessment and Learning are Conflicting Aims
A university class is about two things (not equally important) - teaching students, and assessing their performance.
At the University of Cambridge, where I was an undergraduate, these components were strictly separate. Assignments/homeworks/problem sets throughout the year were about learning, and did not count in our final grade, and exams at the end of the year, which determined our final grade. When I came to America, I was baffled to find out that homeworks here actually counted towards our final grade. This has two undesirable effects. First, there was a limit to how difficult homework problems could be - it's unfair to set an impossible problem when it will affect a student's grade. Second, students were incentivized to get the right answer even at the expense of learning (for example, by copying from past solutions, or sweeping misunderstandings under the rug). Neither these problems arose in Cambridge - when I didn't understand something, I'd specifically point it out to the grader in my homework to make sure they could help clarify these missunderstandings!
To try and get the best of both worlds, the homework policy in all my classes is that homeworks are graded on a pass/fail basis. Either students have clearly put some effort into the homework, and they get 100%, or they haven't and they get 0%. As well as grading the homeworks, I then provide detailed solutiosn to make sure that they can really learn from the problems.
Communication Friction is Sometimes Good
Much of the instant messaging revolution (I'm looking at you, Slack) is about reducing the friction inherent in communication. In some cases, this is great - when I'm working to a deadline with a team, being able to reach them quickly and efficiently is great.
I'd argue, however, that in the context of teaching, you sometimes want friction.
Since my first year teaching, I've never denied requests for time from students - if they want to see me, I'll make the time. I quickly found, however, that through no fault of their own, students would often show up without a clear idea of what they actually wanted to ask, leading to a lot of wasted time. My solution was to slightly increase the friction and work required to get acess to my time - I ask students to send me a half-page summary of exactly what they're going to want to talk about, and what they've done so far to try and answer the question. I still get as many requests, but the efficiency gains are striking - meetings are shorter, and we spend the entire time actually answering the questions at hand.