Describe your approach to facilitating student learning in smart classrooms. What factors contributed to your choosing that approach?

I was teaching numerical analysis here my first semester. In mathematics a lot of the teaching is information transfer. You’re really looking at algorithms and you’re trying to really describe the algorithms to the students and make sure that they get it.

What I realized is that I was reading the reference material: I was writing down notes, trying to distill the chapter down to a lecture, then I came into the classroom, I wrote down my notes on the board, and I tried to discuss the notes and tried to make sure that students understand—and they write down the notes in their notes.

So the material gets copied three times, at least. The students end up asking questions like “Is that an ‘i’ or a ‘j’?” or “Is that a ‘k’ or an ‘l’?”, because you’re writing down these mathematical formulas and loops and all those things. And, there is bound to be a mistake when something is copied three times. So you’re not really getting the intelligent questions, you’re not getting the discussion around “Well, what does it mean?” You’re just getting some of the detail questions of “What’s going on here?”

Also, it’s easy to make mistakes when you write on the board. And then you go back and realize “Oh, the thing I wrote over here ten minutes ago wasn’t quite right.” So then you remind the students, “The thing that was over here to the left, that I now have erased, should’ve looked like this...” That doesn’t sit that well.

So I figured, how can I make this better? I realized that I was teaching in the Smart Classroom, and I’ve always been interested in integrating technology in my teaching—I’ve been setting up websites for my classes long before it was fashionable to do that. I started writing down the notes in sort of a rudimentary format, I used to have something to discuss around on PowerPoint, and the students really seemed to like it, so I kept doing that.

It removes two levels of copying: I get to write down my notation, and also it forces me to be more structured. Because when I write down my notes, the notation has to be the same on slide 2 and slide 15. So, if I realize I need more letters or something that makes it clearer, then I don’t have to go back in the middle of the lecture and fix it. I have to fix it before I go into the classroom. It makes a presentation crisper, and you really leave room for the students to think, hopefully more about what’s being presented, and ask the right questions. Like “Why does this work?” or “How does it work?” and not get stuck on the rote copying down to paper.

I think it also falls on the instructor to add something to the slides. Because if all you do is come in and read your slides, well then, there’s really no reason for students to come to class. I think you as an instructor have to provide a reason to come, actually you have something more to say, you can make it an interactive experience, if the students are to come in, they can ask questions, get more background and more depth as they want it.

It is information transfer, but if it’s information transfer all the time, which happens when you write on the board, it’s a very slow way of transferring information, then there’s no space to step back and maybe look at the bigger picture. I really want to create an environment both in the classroom and in the entire class where people have time to think.

What data, observations, or feedback from students have you received regarding your approach?

There’s really nothing that’s better than showing the students maybe a movie of the actual physical phenomena, then show a solution of the differential equation over time as a movie, then compare the two. You can see that the model is capturing the real physics, so you have a movie of a water droplet falling into a bucket, taken with a high-speed camera, you can see the waves going out. And then, next to that, you can show a solution of the wave equation which is supposed to model this, and you can see that it fits pretty well. So those are the kinds of things that I bring in. I can really show solutions and I can show the physical world at the same time. That’s something you can absolutely not do on a blackboard.

I feel that whenever I have a good demonstration like that it really captures the students. It’s easy to drift off when you’re discussing the theory or maybe you’re proving something and it gets a little technical, and after I do something like that, if possible, I like to pull in one of these examples and animation because it captures the minds of those students that drifted off during the technical details, and brings them back into the class.

How does the feedback you've received match up with your observations and/or expectations for the impact and success of your approach?

It’s hard as a student to absorb the information at the rate it’s coming—I didn’t do it when I was a student. So you always have to go back and think about it. By providing more physical examples and the big pictures and showing what the solutions look like in sort of a dynamic fashion, I’m hoping that I’m giving the students something to cling on to.

Even if they don’t have all the details they have a gut feeling for what’s going on. I’m a very visual person myself, so if I have a gut feeling for what it looks like, then I can fill in the details. It’s much harder, at least for me, to go from a collection of details, and then putting together the big picture, and I think most people are like that. It’s easier to go from generalities to details than the other way around.