by Sandy Irani
Professor at University of California, Irvine
I teach Discrete Mathematics at UC Irvine. Although many professors shy away from teaching lower division courses, I really enjoy reaching students early in their undergraduate careers. In addition to teaching a subject that I love, I also have a chance to impact students’ academic work habits based on my experiences.
Looking back, while I loved college, I do have some regrets about how I managed my time. I did sometimes skip class(!) and then had to cram in the material at the last minute. At some point, though, I realized that the students who took away the most from their undergraduate experience were the ones who showed a sustained effort throughout the semester. The best way to learn a subject in a deep way is to engage with the material repeatedly over time. It’s a bad habit to let an idea that you don’t understand slip away. It’s much better to address a confusing topic and conquer it early on — particularly since course material is usually cumulative! Understanding one idea will likely shed light on more ideas presented throughout the course.
One of the features that I love about teaching from a zyBook (and a big part of why I decided to dedicate so much time to writing one on Discrete Mathematics) is that it helps me enforce these good learning habits with my students. I require one or two sections of the zyBook to be read before every lecture. I believe that it’s better for the students if they work through the material only a day or two before the class on a particular topic. The fact that the zyBook material is interactive really forces the students to engage in a way that they wouldn’t have to if they were just passively reading. I can use a set of questions to lead them through an example that they figure out in small steps, and then present the general rule after they have some intuition for the underlying idea.
The fact that most of the students have read and thought about the material before class enables me to use class time more productively. I can spend less time introducing basic ideas and more time on extended examples. I can also get a feel from their reading results as to which concepts they found particularly challenging. I have noticed that I get more questions in class when I teach from the zyBook because students have had a chance to formulate their questions in advance.
I hope that my students see the benefit of preparation before coming to class and that those habits carry over into their other classes. Ideally, students will carry this philosophy of sustained engagement with them as they continue learning throughout their time in school and beyond.