An internet friend of mine recently asked for some advice about starting to teach. After giving it a lot of thought, these are my suggestions. Please let me know if you'd like anything added.
This is the highest rule of teaching (and life). Be really kind and forgiving. If you’re too kind, nothing bad will come of it. If you’re not kind enough, everyone suffers.
What does it mean to be kind to your students? Treat them as people with complex lives. They’ve probably got their own jobs, and their own love lives, and their own hang-ups. So, whenever possible, cut them some slack and lift them up. Compliment them when they do something cool. This can be really small: if a student wears really cool sneakers, let them know. If a student comes up with a genuinely interesting question, let them know. If you can choose an easy and instructive example, choose it over a hard and complicated one.
Remember that there is a very strong power dynamic at play in teaching. You’ve got the ability to bury these students, fail them, or make them miserable. Don’t. Just be kind.
This advice also sounds like it is common sense. However, in teaching, it is very tempting to bend the truth. If you’re teaching a course in Advanced Nose Picking1, it is tempting to pretend like nose picking is very important. Yet, in reality, nose picking is just a small part of life. Remember that they’re taking your course to pursue their life and career goals, not to become nose picking experts.
It is hard to be honest when faced with the perennial question: “Will this be on the test?” It is tempting to (always) say: “Oh yes! Listen up or you will fail.” And the reality is that there is always more material than you can possibly assess, so sometimes that answer should be: “No — This is not on the test, but it is worth knowing for reasons X, Y, and Z.” Most people will tune you out the moment that you say something will not be assessed, but that’s their loss.
And lastly, it is helpful to let your students know that you’re new at this teaching thing. If you run in to a tricky point that you can’t explain, or the learning management system blows up, or you get totally mixed up and tell people something nonsensical, just say: “Hey — I’m pretty new at this teaching thing. Could y’all be patient with me? I’ll try to get this sorted out for our next class.” If you are kind to your students, then they’ll be kind to you.
I love this quote from Paul Halmos:
“The best way to learn is to do; the worst way to teach is to talk.”
All the evidence seems to indicate that active teaching, where students are engaged in activities throughout class, produces much better results than passive teaching, where students are primarily listening and making notes. The landmark meta-study of this effect is: Freeman et al. (2014). One study that says that we must establish a new standard of care in calculus classes Kramer et al. (2023) and argues that if “traditional lecturing” were a drug on trial with “active learning” then it would be professionally negligent to prescribe “traditional lecturing”.
On reflection, it isn’t especially surprising that “doing” is more effective than “listening”. If you reflect on how you’ve learned any complex skill, then you’ll find that it involved a lot of trial and error, re-adjustment, and doing.
What does this practically mean for classroom teaching? Throughout your class, interleave small activities. In an hour, you might pose three to four active tasks, mixed in with explanation and guidance. To get started in this teaching style, start small. Give your students a task relevant to the material, set a timer (to create a sense of pressure), and ask them to try the thing. The classic task is think-pair-share: students are given a task, asked to think about it, discuss it in pairs, and then the pairs share their thoughts with the class. It takes some time to develop a knack for finding good activities2.
This one is very practical. Give people time to form questions. If you say: “Any questions?” then count mentally (or on your fingers) to ten or twenty before moving on. It takes time for people to think about what they don’t understand and put it in to words. (Think about how frustrating it is when doctors or bankers rush you through the “Any questions?"-question. Don’t be that person!)
This is another easy to implement aspect of active learning. When you assign a task, and give it a time limit, then you’re left facing the question: What should I do while the students work on the task? You could sit at the front of the room and twiddle your thumbs, or you could engage the students. Walk around the room a bit, and chat people up. Ask them how the task going. Compliment them on their fashion choices. Just be present with them. You’ll probably get a lot of questions from shy people, and you’ll get to meet your students.
A friend of mine, Tyler Holden, taught me this early on and I’ve found it extraordinarily helpful: bring a water bottle with you and sip from it often. There are two reasons to do this. First, it is good to stay hydrated. Second, it is important to pause your teaching. Walking over to your water bottle, opening it, taking a sip, and closing it, gives a nice cover for pausing for ten or twenty seconds while people catch up with the last slide or the example.
This one is controversial. The anti-“teach the test” people will tell you that you are not preparing your students for real life. They’ll claim that it is important for students to be able to respond to novel tasks, and apply their knowledge to new situations. This is totally reasonable. I’m not about to say: “Teach your students the exact material on which you will assess them and nothing else.”
The point that I want to make is about the perceived fairness of your assessments. It is all about the subjective impression that the students have of the material. You want the students to see that the instruction is relevant to the assessment. As a teacher, you can easily dupe and blindside your students. There are all sorts of reasons people do this: to control course averages, to assert dominance, or to teach people that life is hard. This is the point that I want to make clear: Students find it very disheartening when the assessment doesn’t line up well (in their view) with the instruction.
And so, try to align your assessment with your instruction. This has the added benefit of giving you an actionable plan for creating a course: Create the assessments such as tests or assignments, and then plan backwards from them to create your instructional content.
As an instructor, it is very easy to fool yourself in to thinking things are straightforward for your students. This effect is called the curse of knowledge.
To go back to the Advanced Nose Picking example from above: if all your instruction is centered on picking human noses, then you shouldn’t assess the students with a “real life” example of picking equestrian noses. For an expert on nose picking, the situation is obvious: Horses lack fingers. Therefore, horses must use the nearest available limb and so they lick their noses. Mucus is pretty much the same across the whole mammalian family, and it dissolves in saliva. The horses get by just fine by licking their noses to pick them.
Anyone taking Advanced Nose Picking would be able to figure out this obvious generalization of nose picking. Unfortunately, it is not so. There is a lot of implicit expertise being deployed here; you need to have a bit of horse sense.
The flip side of the curse of knowledge is that the students don’t know the material. This sounds so obvious that it is embarrassing to write it down, but it’s helpful to remind yourself from time to time: The students don’t know the material. If you find yourself talking with a student, red in the face, asking the same question over and over, remind yourself: “The student doesn’t know.”
The very first lesson that I ever taught was a complete train wreck. I had asked a colleague, a leader in mathematics education, if they could write a letter of recommendation for me. The colleague noted that they’d need to see me teach, and offered me a chance to teach two back-to-back sections of their class. I had never taught before; I had no idea what to do. After a week of flailing around, I read up on the topic, sketched some notes on an index card, and decided to work out examples on the fly. The examples blew up in my face, I gave lousy explanations, and everything was a total disaster.
It sounds like I’m catastrophizing the situation, but I’m not. This is the feedback that I got from the expert colleague in-between the two sections. The colleague was furious, and they even offered to take over and give the second lecture. I persisted and gave the second lecture. It too was a train wreck, but a smaller better-managed train wreck. It was more like a toy train set crashing than a full passenger train.
The students probably learned nothing from my haphazard lecture. I learned3 that it pays to take the time to prepare detailed lesson plans. My workflow for preparing lectures has evolved a lot over the years. Initially, I wrote everything out long hand in a notebook. Now, I typeset everything, use version control, and post material far in advance. Everything depends on what you’re teaching and how you plan to teach it. The best way forward is to experiment.
If you’re working towards an assessment: try to imagine what experiences your students will need to undergo in order to do well on that assessment. Usually, this takes the form of examples and tasks. Pick illustrative examples, write out all the examples in advance, see all the computations through to the end, and prepare some tasks for the students to do. Write it all up somewhere (on a blog would be great) and you’re good to go. Be patient with yourself, and start small though. It takes a long time, over many iterations, to find a workable way to store lesson plans. Usually, you can go about preparing week-to-week: using your spare time in Week $N$ to write the material for Week $N+1$.
In addition to detailed lesson plans, it is helpful to have a detailed syllabus. I think of the syllabus as the rules of the boardgame that is my course. If any weird or unexpected corner cases turn up, I can point to the syllabus and say: “Look, this is the policy. I committed to it in advance. I cannot change it now.”
In addition to any policies that your institution mandates must appear in your syllabus, it must contain:
After some experimentation, I started to write FAQ section into my syllabus. The point of the FAQ is to catch all the corner cases. The sections have grown as I’ve taught and re-taught various courses. One year, a student insisted that slipping papers under my door was an acceptable means of getting me to grade them. The next year, I added a clause to the syllabus clarifying that such work will not be accepted. Here is a complete FAQ section from a syllabus:
The summary of this section of the syllabus is: “Submit your work through Crowdmark, or it will not get graded.” The strictness of this rule is harsh, and distinctly un-kind. However, I think that it is only fair to communicate these things clearly and in advance. These are the rules of the game, and we must play by them.
One last point about writing a good syllabus: You can use it to plan backwards. Set the week-by-week syllabus for the course. Then, decide on what your assessments will be. And then go about preparing detailed lesson plans.
It helps to be at the right place before the right time. If you arrive early and get your tech setup, you are free to chat with students as they arrive. This saves you a tonne of e-mail, and builds rapport. At my institution, instruction begins at ten minutes after the hour. I try to consistently arrive on the hour, and then I have ten minutes to get setup and hang out.
If you can’t get in to the room early, because classes are scheduled back-to-back or you’ve got a long commute: don’t try to juggle socializing and setting up. First setup your teaching materials, then chat with people. Trying to do both at the same time just slows things down.
If you’re deep in to a lecture on marsupial nose picking, and running short on time, it is tempting to plow ahead blast through the remainder of your slide decks: “Wombats do this, and opossums do that, and quokkas are a special case. All macropods use their non-prehensile tails.” The words begin to rush out of you. You stop making time for questions. No one has any idea what quokka even is at this point.
When we rush, we’re slipping in to transmission: the philosophy of education that says knowledge is transmitted magically from instructor to student. It is a mistake to think that if the instructor says all the content (once and only once), then the students will learn all the content. The truth is: no one is learning anything in a rush. Most people’s pre-theoretical approach to teaching some form of transmissionism, and it’s the default mode of instruction that we slip in to when feeling rushed.
Teaching and learning are iterative, reflective, and interactive processes. You can’t rush them. If you find yourself short on time, grab a sip from your water bottle, make time for questions, and say that you’ll catch up with the rest of the material during the next class. In my opinion, it is better to dismiss a class early than it is to rush.
One non-obvious finding from the education literature is that students primarily retain material that is written down on the board or in the slides. This creates a strong asymmetry between teacher beliefs and student action: teachers believe the verbal aspect of a class is primary, and students act as though the written aspect of a class is primary. The effect is so strong, that students and teachers still act this way even once you make them aware of it Fukaway-Connelly et al. (2017).
How did learning about this effect impact my teaching? I started to write a lot more down, even some silly stuff. For example, before learning about this effect, I would often talk about how mind-boggling big infinity really is. I would jump around making hand gestures of largeness. As that material wasn’t written down, it didn’t make it in to students mental models of the material. Now, I write something silly on the board like:
Infinity is REALLY big:
$10,000,000,000 < \infty$.
Inifinity is bigger than EVERYTHING finite.
This advice is so important that I’ve included it twice. Be kind. That’s all. That’s my advice about teaching: be kind.
This is a pretty silly example course. It might get edited out later on. For now, I’m going to riff of this nose picking joke for the whole post. ↩︎
One meta-observation is that selecting active learning tasks is something best learned by doing! ↩︎
It is surprising that one needs to learn to prepare lesson plans. When I learned this lesson, I had attended thousands of hours of lectures and had naively assumed that they were improvised. There is a deep cognitive bias at play here: we don’t perceive the preparatory work of a performance. This is a common illusion in writing: a good piece of writing just flows and seems effortless. It feels as though the author merely started typing and the finished work emerged. Similarly, in music, one sometimes feels that the musicians are there just improvising, when in reality you are seeing the end result of endless rehearsals. (Thanks, Alex, for pointing out this deep cognitive bias.) ↩︎
Published: Apr 7, 2024
Last Modified: Apr 11, 2024
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