Jeremy Côté

Where's the Surprise?

Do anything enough and you will get used to it.

This is an unfortunate truth in the realm of mathematics and science education. As teachers and tutors, we know our subjects well. We know the punchlines and the proofs. We know the end result of any lesson. Through years of working within a subject, there is little surprise about how things fit together. Everything is planned out, which means there is a lack of novelty with respect to the subject.

This is inevitable. Ideas won’t be new and shiny forever. Instead, they become like old acquaintances, familiar players in your classroom. Because the ideas are less “fresh” in our minds, we can start to become disillusioned with the results. Of course the Pythagorean theorem holds, how could it not? It’s obvious that the shortest path between two points in a plane is line! These are just two examples, but they illustrate the fact that the novelty wears off.

Triviality implies lack of novelty?

When there’s a lack of novelty, slipping into a routine is easy. I’ve seen it with many teachers. They can teach their subject just fine, but the enthusiasm is gone. Classes go by monotonically, and students can feel the lack of energy.

We need to do better. We need to bring the element of surprise back into the classroom.

When is the last time you were surprised by something you learned? Simply the fact that a thought jumped out at you as you are reading this shows how great a surprise can be while learning. It creates an experience that sticks in the mind of the student, and they can remember it for a long time. I think we can agree that this is preferable to taking down notes day after day.

We need to instill more elements of surprise in our teaching of mathematics and science. A byproduct of surprise is delight, which will make students both enjoy and remember your classes more than others.

“Wait,” you might say. “That sounds great, but there’s nothing surprising about the topics I teach. They’re all basic!”

If that’s your response, you aren’t working hard enough.

I didn’t say that crafting surprise was easy. I’m arguing that it’s necessary. As teachers, we have the creative control over how material is going to be presented (to a certain extent). This means we are in the possession of the idea, the punchline, and the formal result. It’s up to us to mix these ingredients together in the right proportions to create lessons that are surprising. Yes, we can just give the results to the students one after another, show them example problems where they calculate a number, and finish the topic with a quiz. Or, we can work harder to create learning experiences that deliver these same results and equations through surprise.

Remember, you know everything beforehand. You’re not the audience for this surprise. It’s the students who don’t know the punchline, who are blank slates. You wouldn’t tell a joke by giving away the ending, would you? But this is exactly what we do in a lot of our mathematics and science classes. We forget to build up to the moment of surprise! We waste countless opportunities to surprise and delight students with results that they would never have guessed. Class gets reduced to taking notes of a bunch of results, and there’s no context to them.

This is more than a complaint about our educational system. It’s an observation about learning in general. Surprise cements the memory of a lesson into the students’ minds. It isn’t surprising to go to class, take notes, and listen as the teacher goes through a little bit of theory and works out problems. But it is surprising if you work through a bunch of unrelated concepts and then find that they all share this beautiful link in between them. Of course, you knew this as the teacher, but the students don’t know. This makes the reveal so much more powerful than if you told students right at the beginning.

As the teacher, the students have a natural inclination to take anything you say as the word of law. If you write an equation on the board, the students will all bend over and write it down, even if they have no clue what it means. This is a terrible way to go about teaching. Yes, it transmits the information in an efficient manner, but it doesn’t mean the students will understand it. On the other hand, if students are working for a long time on smaller cases of a larger problem, there’s a good chance that the introduction of the magical relation that captures exactly what they are trying to do will be more surprising.

I’m not saying that you should just withhold the information from students. Forcing them to slog through problems isn’t always a good thing. But, you have all the ingredients concerning the topic, so use them well! You get to choose how they are presented, and this is what makes all the difference.

Think the theorem you are teaching today is too boring or bland? You have to be more creative with the presentation! Every lemma, conjecture, result, and theorem has some surprising connection or insight associated to it. To the students, topics aren’t so obvious when first learning them. Use this to craft your lessons, to weave surprise into the classroom atmosphere. It could be as simple as asking students what they think will happen during a science experiment, or perhaps taking a few minutes to set up some counter-intuitive scenario. At minimum, you need to avoid teaching your class in the same manner every single day.

By changing up the way things are done in your class, students will have to be nimble and ready for surprises. There is no way I can undersell the important of this, so I will say it again: education in mathematics and science needs more surprise. Efficiency is great, but we have to remember that students are served better if we give them learning experiences that stick with them, versus paying lip service to the fact that the material was covered.

I know, this isn’t an easy wish. You already have plenty of topics you need to cover, and so little time during the year. What I ask of you is to try it, at least for a few classes. It’s not practical to transform every class into one that’s filled with surprise, but I recommend that students should get to have a surprise every time a new concept is introduced. I know that there’s at least one thing that you can say about the topic that will be surprising to students. If we want our students to be more engaged and enjoy our classes, it’s our responsibility to deliver these surprises.