By: Steven Klee, Seattle University
After my day-to-day interactions with students, one of my favorite things about teaching is talking with other teachers. There is no shortage of amazing teachers who are working hard to make their classes better and improve student learning. Likewise, there are plenty of opportunities to find inspiration in our colleagues’ work, ranging from attending talks at conferences to simply getting coffee with coworkers to talk about how our classes are going.
A few years ago, I realized that the proportion of inspiring ideas that turned into measurable change in my classroom was essentially zero. As I thought more about this, I realized that I was the biggest hurdle to this change. There was a little voice in the back of my head with a constant and emphatic message: No. I can’t do that, and here are fifteen reasons why.
I know I’m not the only one who hears this voice. Of course, the reason we have these thoughts is that they are often true. No two people experience teaching in the same way. We have different personalities, different styles, and allow for organized chaos in different ways. As a community, it is easy for us to despair in the challenges we face in our teaching.
Joan Baez said, “Action is the antidote to despair.” At the end of the day we are all mathematicians and we have been trained in solving problems. To be apathetic in the face of the challenges put before us is antithetical to our training as problem solvers. And teaching, particularly teaching well, should be viewed as a problem that desperately needs to be solved. Like many real-world problems, the problem (“What does it mean to teach well?”) is not clearly defined. The data is messy. There is not one single correct answer.
In the rest of this post, I would like to discuss some methods for moving beyond the little voice that says “no” and changing your teaching without reinventing the proverbial wheel. And, as with many real-world problems, I will not answer the question at hand (“What does it mean to teach well?”) and instead I will address a different question – How do I teach better?
Seek inspiration, not recipes
In 2012 I saw David Pengelley give a wonderful talk in which he outlined a rather intricate system of assigning and grading calculus problems of varying difficulties over several sections of the textbook, all of which were meant to be done by the students before class and accompanied by an email to the professor reporting on the section of the textbook they had just read. This happened for every class meeting. The mental yoga of keeping track of so much material at once made my head spin, and I did not (and still do not) have the confidence to implement something on such a grand scale. (A summary of David’s method can be found here: https://www.ams.org/publications/journals/notices/201708/rnoti-p903.pdf)
But the ideas in the talk were inspiring. I left the talk telling myself, “I should create opportunities for my students work on math more regularly.” I started giving mini-assignments in all of my classes on a daily basis. The mini-assignments consist of about five relatively simple problems related to the material covered in a given class, which are due at the beginning of the next class.
I can mark the papers and record grades in about 15 minutes per assignment (I do this by hand – if you use WebWork it takes no time at all). It helps make sure the students are engaging with the class material throughout the week instead of just the night before a bigger homework set is due. It also lets me focus my grading efforts on problems with more substance that better measure what the students are learning. This works well for my teaching philosophy and helps make the students stay on top of the course material.
Our teaching experiences are shaped by a large number of variables, including student preparation, class size, resources, research expectations, and other demands on our time. Because of this, the things that my colleagues who work at ivy league schools are able to do in the classroom often are not feasible for me, just as the things that have worked well for me in a class of 20 students might not scale well to a class of 300 students. However, rather than finding all the ways that a technique cannot be applied to your classes, look for ways to transform that solution into something that will work for you.
When I dissect the “no, because…” statements that persistently come to my mind, I find two main themes. The first main issue is one of practicality – what works for person X may not work for person Y – and we have already discussed this. A second main theme, whether we like to admit it or not, can be boiled down to an issue of discomfort or fear.
Change is hard. For most of us, our educational lives consisted largely of lectures to be observed and internalized. This is comfortable because it is what we know best. It is a known quantity in which we hold significant control. Letting go of some of that control is scary. What if it doesn’t work? What if the students don’t like it? What if I don’t do a good job? These are all legitimate concerns, and we can work through those concerns once we are honest with ourselves about their root causes.
Change does not happen overnight. Maybe you are interested in having a more active classroom or having a flipped classroom where students do more work outside of class, but you don’t want to give up complete control to the potential chaos that might come from this. Maybe you don’t have the time or resources to completely re-invent your differential equations course because you’re on sixteen committees and teach three classes per semester. I get it.
You don’t need to do it all at once, and you don’t need to do it all by yourself. Ask colleagues to lend you worksheets or materials. Find activities that help you move towards this goal and try them out a couple times over the course of a term. After a few years of doing this, you will have developed more resources and gained more confidence in this approach, homing in on techniques that work for your personality and style while also better serving your students.
Reflect and revise
New teaching methods aren’t going to be perfect the first time. You’ll probably mis-judge the difficulty of some tasks. Students might get frustrated. You might get frustrated. But it also won’t be a disaster. Students will still learn. So will you. It will be better next time.
Be prepared for the eventuality that a lesson won’t go as planned. It is hard to know how long an activity will take, but you can bet that it will usually take longer than you think. Don’t be afraid to change an activity in the middle of class if it is taking longer than you expected or the students aren’t getting it. You can always change your course schedule to adapt to this change. Besides, if you try five new lessons in a semester and two of them don’t go as well as you had hoped, that still accounts for a relatively small proportion of the overall class.
At the end of a course where you’re trying new things, reflect honestly about the successes and struggles you faced. Were there common themes in the struggles you faced? How can you fix them next time? Make a list of three things you’d do differently next time. Don’t be too hard on yourself.
There’s a rule in improv comedy called the “yes, and…” principle. If you’re in the middle of an improv comedy skit, you can only react to the material you are given from your collaborators. You may have been ready to tell a very good joke about Care Bears, but now someone has decided that there’s a grizzly bear running around the stage and you need to act on that instead. You can’t stop the skit and ask for a retake, so instead you have to accept the reality of the grizzly bear and add your own brand of humor to it.
The same principle applies to teaching. We can all become better teachers by finding inspiration in others. This takes work, and it can be scary to take a risk and try something new in the classroom. In many cases, we fail to apply the lessons our peers have learned because we feel their experiences do not directly translate to our own. Next time you go to a talk about teaching, I challenge you to move beyond the naysaying gremlins in your head. View the reasons to say no as equations that bound the parameter space of your problem. Say yes to new ideas and apply them in your classroom in a way that works for you. Over time, these small changes can add up to more effective teaching.