Mapping the Math: Using Concept Maps to Learn Controls Theory

by Jeremy Adams, Chemical and Biomolecular Engineering

Teaching Effectiveness Award Essay, 2020

Dynamics and Control of Chemical Processes is the final content-driven course in the chemical engineering curriculum and has a reputation as one of the most mathematically intense courses in the major. In the class, students are taught fairly complex mathematical concepts that are needed to understand and design control systems for chemical processes. While the lectures focus on the theory and mathematics behind process control, the GSI-led discussion sections spend more time learning and practicing computational techniques required to model process dynamics and control. I soon noticed that many students, while able to perform the analytical and computational techniques needed to complete assignments, struggled to put these techniques in the context of the broader engineering goals taught in the course. Simply put, I found some students were learning how to do the math without fully understanding why or when to do the math.

About four weeks into the semester, as the complexity of math required to complete the assignments was rapidly increasing, I encouraged my discussion section to take a step back. At the beginning of the discussion section, I had the students complete a fifteen minute exercise where they brainstormed what they think are the four most important topics covered in class so far. They were then instructed to arrange these topics in a concept map, drawing arrows between words to show how they view the relationships between these topics. I gave them suggestions such as arranging the topics sequentially to show how one leads to the next, as well as arranging the topics in a tree-like model to show how some topics are categories of a broader concept. After about five minutes of sketching these concept maps out, I asked the students to share theirs with a neighbor and justify their arrangement. I then asked for a few volunteers to come to the board, draw their maps, and explain their thinking to the rest of the class. While doing this, I kept my comments to a minimum while facilitating discussion among the students. I stressed that there are many valid ways to approach learning Controls Theory, and itâ€™s reasonable that people would arrange the topics in different ways.

I repeated this exercise again during the final weeks of the semester as the students were preparing for the final exam. This time, I allowed them to pick the six most important concepts of the course rather than four, as more content had been covered. Through these exercises, students were challenged explicitly to think about how the skills they were learning, both theoretical and computational, were interconnected. Most importantly, this exercise promoted visual learning, a style of learning often overlooked in courses that depend heavily on mathematics. In addition to being more accessible to students who favor this mode of learning, I believed this would provide a new lens for understanding the course content.

Overall, I found this activity to be well-received by the students in my section. In the midterm evaluations that I administered, a majority of students were satisfied with taking the time in section to do these types of activities. Furthermore, the second time we did the activity there was much greater participation. Students were more likely to come up with thorough justifications for their concept maps, and were more eager to share theirs with the rest of the class. This suggests some students became more comfortable with examining the concepts taught in the course, holistically. Additionally, the final projects in the course involved designing a process control system, requiring students to connect the individual concepts learned throughout the class into a cohesive analysis and report. The success most students had in completing their final projects suggests a strong understanding of how the individual concepts learned throughout the class must be synthesized in the design of chemical process control systems.