Mathematics is the abstract language we use to describe nature. At the same time, we can employ such language to solve very practical problems. When teaching, I want students to learn how to properly apply mathematics to tackle real-world problems that could positively impact theirs and others’ lives. Through projects and case studies, students can have a first-hand experience in using computational methods to investigate and explore fascinating questions in physics, chemistry, biology, or engineering. In this way, students appreciate the beauty of mathematics understanding the importance of its applications.
I believe the best way students learn is from diligent practice. I center my lectures on examples and exercises. Whenever possible, I integrate theory and computer programming during class time. I use tutorials to make sure that every student has the necessary prerequisite to be successful in my classes. My experience with this student-centered learning approach suggests that in this way students can truly master the content of the course.
During my lectures, I try communicating that mathematics can be fun. Once, for example, I used a modified version of the SIR model for describing the spreading of an infectious disease to simulate a zombie apocalypse. By connecting pop culture with ordinary differential equations, student not only found the topic relatable, they had fun in the process.
Whenever possible, I prefer assessing my students orally. In small classes, oral examinations are an effective way to understand whether a student has completely mastered the content of the course. During oral evaluations, students can correct their mistakes and demonstrate their problem-solving skills better than in written tests. Unfortunately, in large classes, this form of evaluation is not practical. In this case, I use projects and written reports to evaluate student learning. Students are given the option to submit a draft to receive feedback prior to their final submission. For this and similar assignment, a rubric is used to set up the grading criteria and help maintain an objective evaluation of student’s work.
Course evaluations are usually available only when the semester is over. However, because their feedback is important to assessing how well their learning is progressing, I give my own evaluation forms during the semester. This process helps adjust my teaching style so that I can plan classroom activities to be more effective. For example, in a class where I was using a flipped method, I noticed that most students were not sufficiently prepared to solve the in-class computational exercises I had prepared. Using the student feedback, I was able to turn this around, changing the structure of the class, guiding them through the theory before the practice.
Advising and Mentoring
I had the chance to mentor both undergraduate and graduate students. One of my best experiences was with Luca Barbarotta, a MSc student who approached my Ph.D. advisor because he was interested in working in cardiac mechanics. I encouraged him to explore a new muscular contraction mechanism using the computational framework I was developing at that time. As I left my Ph.D. institution, he was hired to keep working on such a project. We kept meeting regularly and I was able to advise, guide and support him remotely. Eventually, he developed a novel model and his results are now published in a high-quality international peer- reviewed journal (IJNMBE). He also continued his career in cardiovascular modeling entering a doctoral school in biomedical engineering at the University of Eindhoven.
Becoming an effective instructor is a life-long learning experience, and, for this reason, I continue to expand my toolkit of teaching techniques by participating in conferences and teaching events. Learning new teaching methods enables me to engage students in a way that increases their curiosity and knowledge.