Below are a bunch of little things I typically mention at some point when I’m teaching my class on how to teach. But my new approach is to minimize lecturing, and certainly not to waste students’ time by standing in front of a group of them, telling them things they could’ve read at their own pace.
Anyway, here I am preparing my course on statistical computing and graphics and thinking of points to mention during the week on classroom teaching. My old approach would be to organize these points in outline format and then “cover” them in class. Instead, though, I’ll stick them here and then I can assign this to students to read ahead of time, freeing up class time for actual discussion.
Working in pairs:
This is the biggie, and there are lots of reasons to do it. When students are working in pairs, they seem less likely to drift off, also with two students there is more of a chance that one of them is interested in the topic. Students learn from teaching each other, and they can work together toward solutions. It doesn’t always work for students to do homeworks pairs or groups—I have a horrible suspicion that they’ll often just split up the task, with one student doing problem #1, another doing problem #2, and so forth—but having them work in pairs during class seems like a no-lose proposition.
Students don’t pay attention all the time nor do they have perfect memories; hence, use the blackboard as a storage device. For example, if you are doing a classroom activity (such as the candy weighing), outline the instructions on the board at the same time as you explain them to the class. For another example, when you’re putting lots of stuff on the board, organize it a bit: start at the top-left and continue across and down, and organize the board into columns with clear labels. In both cases, the idea is that if a student is lost, he or she can look up at the board and have a chance to see what’s up.
Another trick is to load up the board with relevant material before the beginning of class period, so that it’s all ready for you when you need it.
It’s becoming standard to use beamer (powerpoint) slide presentations in classroom teaching as well as with research lectures. I think this is generally a good idea, and I have just a few suggestions:
- Minimize the number of words on the slides. If you know what you’re talking about, you can pretty much just jump from graph to graph.
- The trouble with this strategy is that, without seeing the words on the screen, it can be hard to remember what to say. This suggests that what we really need is a script (or, realistically, a set of notes) to go along with the slide show. Logistically this is a bit of a mess—it’s hard enough to keep a set of slides updated without having to keep the script aligned at the same time—and as a result I’ve tended to err on the side of keeping too many words on my slides (see here, for example). But maybe it’s time for me to bite the bullet and move to a slides-and-script format.
Another intriguing possibility is to go with the script and ditch the slides entirely. Indeed, you don’t even need a script; all you need are some notes or just an idea of what you want to be talking about. I discovered this gradually over the past few years when giving talks (see here for some examples). I got into the habit of giving a little introduction and riffing a bit before getting to the first slide. I started making these ad libs longer and longer, until at one point I gave a talk that started with 20 minutes of me talking off the cuff. It seemed to work well, and the next step was to give an entire talk with no slides at all. The audience was surprised at first but it went just fine. Most of the time I come prepared with a beamer file full of more slides than I’ll ever be able to use, but it’s reassuring to know that I don’t really need any of them.
Finally, assuming you do use slides in your classes, there’s the question of whether to make the slides available to the students. I’m always getting requests for the slides but I really don’t like it when students print them out. I fear that students are using the slides as a substitute for the textbook, also that if the slides are available, students will think they don’t need to pay attention during class because they can always read the slides later.
It’s funny: Students are eager to sign up for a course to get that extra insight they’ll obtain from attending classes, beyond whatever they’d get by simply reading the textbook and going through the homework problems on their own. But once they’re in class, they have a tendency to drift off, and I need to pull all sorts of stunts to keep them focused.
The board and the projector, together:
Just cos your classroom has a projector, that don’t mean you should throw away your blackboard (or whiteboard, if you want to go that stinky route). Some examples:
- I think it works better to write out an equation or mathematical derivation in real time rather than to point at different segments of an already-displayed formula.
- It can help to mix things up a little. After a few minutes of staring at slides it can be refreshing to see some blackboard action.
- You can do some fun stuff by projecting onto the blackboard. For example, project x and y axes and some data onto the board, then have a pair of students come up and draw the regression line with chalk. Different students can draw their lines, then you click onto the next slide which projects the actual line.
Paper handouts can be a great way to increase the effective “working memory” for the class. Just remember not to overload a handout. Putting something on paper is not the same thing as having it be read. You should figure out ahead of time what you’re going to be using in class and then refer to it as it arises.
I like to give out roughly two-thirds as many handouts as there are people in the audience. This gives the handouts a certain scarcity value, also it enforces students discussing in pairs since they’re sharing the handouts already. I found that when I’d give a handout to every person in the room, many people would just stick the handout in their notebook. The advantage of not possessing something is that you’re more motivated to consume it right away.
Live computer demonstrations:
These can go well. It perhaps goes without saying that you should try the demo at home first and work out the bugs, then prepare all the code as a script which you can execute on-screen, one paragraph of code at a time. Give out the script as a handout and then the students can follow along and make notes. And you should decide ahead of time how fast you want to go. It can be fine to do a demo fast to show how things work in real life, or it can be fine to go slowly and explain each line of code. But before you start you should have an idea of which of these you want to do.
When doing computing, I like to have four windows open at once: the R text editor, the R console, an R graphics window (actually nowadays I’ll usually do this as a refreshable pdf or png window rather than bothering with the within-R graphics window), and a text editor for whatever article or document I’m writing.
But it doesn’t work to display 4 windows on a projected screen: there’s just not enough resolution, and, even if resolution were not a problem, the people in the back of the room won’t be able to read it all. So I’m reluctantly forced to go back and forth between windows. That’s one reason it can help to have some of the material in handout form.
What I’d really like is multiple screens in the classroom so I can project different windows on to different screens and show all of them at once. But I never seem to be in rooms with that technology.
That’s “just in time teaching”; see here for details. I do this with all my classes now.
This is something where students work together in pairs on hard problems. It’s an idea from physics teaching that seems great to me but I’ve never succeeded in implementing true “peer instruction” in my classes. I have them work in pairs, yes, but the problems I give them don’t look quite like the “Concept Tests” that are used in the physics examples I’ve seen. The problem, perhaps, is that intro physics is just taught at a higher level than intro statistics. In my intro statistics classes, it’s hard enough to get the students to learn about the basics, without worrying about getting them into more advanced concepts. So when I have students work in pairs, it’s typically on more standard problems.
In addition to these pair or small-group activities, I like the idea of quick drills that I shoot out to the whole class and students do, individually, right away. I want them to be able to handle basic skills such as sqrt(p*(1-p)/n) or log(a*x^(2/3)) instantly.
Getting their attention:
You want your students to stay awake and interested, to enter the classroom full of anticipation and to leave each class period with a brainful of ideas to discuss. Like a good movie, your class should be a springboard for lots of talk.
But you don’t want to get attention for the wrong things. An extreme example is the Columbia physics professor who likes to talk about his marathon-fit body and at one point felt the need to strip to his underwear in front of his class. This got everyone talking—but not about physics. At a more humble level, I sometimes worry that I’ll do goofy things in class to get a laugh, but then the students remember the goofiness and not the points I was trying to convey. Most statistics instructors probably go too far in the other direction, with a deadpan demeanor that puts the students to sleep.
It’s ok to be “a bit of a character” to the extent that this motivates the students to pay attention to you. But, again, I generally recommend that you structure the course so that you talk less and the students talk more.
Walking around the classroom:
Or wheeling around, if that’s your persuasion. Whatever. My point here is that you want your students to spend a lot of the class time working on problems in pairs. While they’re doing this, you (and your teaching assistants, if this is a large so-called lecture class with hundreds of students) should
Teaching tips in general:
As I explained in my book with Deb Nolan, I’m not a naturally good teacher and I struggle to get students to participate in class. Over the decades I’ve collected lots of tricks because I need all the help I can get. If you’re a naturally good teacher or if your classes already work then maybe you do without these ideas.
It’s not clear how much time should be spent preparing the course ahead of time. I think it’s definitely a good idea to write the final exam and all the homeworks before the class begins (even though I don’t always do this!) because then it gives you a clearer sense of where you’re heading. Beyond that, it depends. I’m often a disorganized teacher and I think it helps me a lot to organize the entire class before the semester begins.
Other instructors are more naturally organized and can do just fine with a one-page syllabus that says which chapters are covered which weeks. These high-quality instructors can then just go into each class, quickly get a sense of where the students are stuck, and adapt the class accordingly. For them, too much preparation might well backfire.
My problem is that I’m not so good at individualized instruction; even in a small class, it’s hard for me to keep track of where each student is getting stuck, and what the students’ interests and strengths are. I’d like to do better on this, but for now I’ve given up on trying to adapt my courses for individuals. Instead I’ve thrown a lot of effort into detailed planning of my courses, with the hope that these teaching materials will be useful for other instructors.
Students won’t (in general) reach your level of understanding:
You don’t teach students facts or even techniques, you teach them the skills needed to solve problems (including the skills needed to find the solution on their own). And there’s no point in presenting things they’re not supposed to learn; for example, if a mathematical derivation is important, put it on the exam with positive probability. And if students aren’t gonna get it anyway (my stock example here is the sampling distribution of the sample mean), just don’t cover it. That’s much better, I think, than wasting everyone’s time and diluting everyone’s trust level with a fake-o in-class derivation.
The road to a B:
You want a plan by which a student can get by and attain partial mastery of the material. See discussion here.
What, if anything, did the students actually learn during the semester?
You still might want to evaluate what your students are actually learning, but we don’t usually do this. I don’t even do it, even though I talk about it. Creating a pre-test and post-test is work! And it requires some hard decisions. Whereas not testing at all is easy. And even when educators try to do such evaluations, they’re often sloppy, with threats to validity you could drive a truck through. At the very least, this is all worth thinking about.
Relevance of this advice to settings outside college classrooms:
Teaching of advanced material happens all over, not just in university coursework, and much of the above advice holds more generally. The details will change with the goals—if you’re giving a talk on your latest research, you won’t want the audience to be spending most of the hour working in pairs on small practice problems—but the general principles apply.
Anyway, it was pretty goofy that I used to teach a course on teaching and stand up and say all these things. It makes a lot more sense to write it here and reserve class time for more productive purposes.
One more thing
I can also add to this post between now and the beginning of class. So if you have any ideas, please share them in the comments.