Lecturing vs Active Learning

I have just finished my first semester teaching an active learning class (of Calculus I). This means that every day when students came to class, I sorted them into groups of four and gave them worksheets to complete. The worksheets guided them through that day’s material, helping them discover the concept and practice examples. I would facilitate the worksheets by answering questions and discussing students’ solutions at the board. Having taught many lecture-style classes, I see how active learning has some pros and some cons by comparison.

Pro: Students get to know each other better. By working together every day, students are more likely to build partnerships and friendships, which not only helps them when they need someone to study with, but also enhances their college experience.

Con: Their mathematical writing is sloppier. I do very little writing at the board, so students don’t see many examples of how solutions should be written precisely. (If they check the posted worksheet solutions online after class, they’ll see typed versions of the work, but I know many students don’t do this.) Some students are mis-remembering notation from their high school math classes, and passing it along to their classmates.

Pro: They get to discover and develop most of the concepts themselves. The worksheets are designed to help students form an intuitive idea of the lesson (e.g. where the limit definition of the derivative come from) and then helps them prove it to themselves. This provides deeper learning than when they passively take notes, and is more likely to stick with them into the future.

Con: We cover less material in class. On the surface, we have covered the same number of sections in the textbook as when I teach a lecture-based class; however, students often have to finish the worksheets at home because there isn’t enough time in class. The “deeper learning” provided by the worksheets comes at a cost that the students have to pay with extra time after class. This time is in addition to what they spend doing homework and studying for assessments.

Pro: Students receive more consistent feedback on their work. Every day, I collect the worksheets, grade one of them from each group, and return them all by the next class period. This way, students are receiving feedback in class every day, either on their own worksheet or on the worksheet of a group member. (The worksheet answer within a group are very similar in general.) They also receive verbal feedback during class as they ask questions to me and their group members. This helps them to correct misunderstandings every day, not just after the weekly quiz.

Con: Administering the course takes up more time. This one surprised me. I expected active learning to be easier on my time than it has been. Before every class period, I have to compile the worksheet, work it myself, tweak any pieces I don’t like, and print it. After class, I have to grade the worksheets, enter grades online, and post the worksheet with solutions online. Each of these is a small task, but the time adds up quickly. It seems like, when I teach this active learning course again in the future, it will take almost as much time to administer each lesson as it does now; there are few tasks that don’t have to be repeated, and even the worksheets will need to be altered now that I have experience working with them once. I don’t mind the time commitment, but it could be prohibitive to someone teaching three or four courses this way.

Ultimately, I think a mix of lecturing and active-learning may be the best approach. I love to see my students working together and having those “Aha!” moments, but I also love explaining a difficult concept to them and pointing out the techniques that will help them solve a certain type of problem. Next time I teach Calc I, I’ll be excited to find the right balance between these two styles.