As a mathematics instructor, my two goals in the classroom are for students to deeply understand the assumptions, applicability, and limitations of equations, concepts, and theorems; and to inspire students to be excited about the material. I have always been passionate about mathematics for its ability to solve everything from day-to-day problems to global ones, and I hope to share this excitement with my students. With these two fundamentals, students will excel in future work, both in and out of the academy. A truly inspired student that is able to approach new material and learn it themselves will be successful in any endeavor they take on.
To address the goal of gaining a deep understanding of mathematical concepts, I believe active learning and classroom discussions are necessary. The statements and proofs of equations and theorems can be found in relevant textbooks, but the applicability and limitations of these are hard to find. A technique I employ to encourage this deep understanding is to challenge students, both in class and on assignments, with how they would solve a problem before presenting “the solution” in class. For example, when approaching the topic of conditional probability for the first time, I explain what the concept is and ask how they might approach calculating this utilizing Venn diagrams. We discuss in small groups and as a class, focusing student attention on the assumptions and setup of the problem, and forming connections between course topics. To encourage reflection on the applicability and limitations of concepts, I design assignments and class discussions that necessitate placing these ideas in a broader context. For example, when teaching intro statistics courses I include a module reading and discussing “How to Lie With Statistics” to encourage reflection on the statistical principles we learned, how to use them fairly, and how to cautiously read statistics in the media or academic reports. We discuss statistics reported in current news articles and evaluate their trustworthiness. My students appreciate this broader context and perform better on assessments when I focus on these issues.
My second goal is motivating and inspiring students. My favorite moments in teaching are when the spark in a student’s eye tells me that he has caught some of the passion and energy I exude about my field. To facilitate this inspiration, I need to connect with my students and understand what they want out of the course. When a front row student repeatedly interrogated me about the challenges in translating the steepest ascent method from textbook to practice in optimizing experiment settings, I stepped back to examine his concerns. He was entirely correct – the textbook approach was too vague to implement or deal with complicating challenges. To rectify this, I designed a spreadsheet game that simulated a nuanced, gritty experimental environment. We spent two class periods playing this game in small groups and answering a series of questions to guide them through the design, experimentation, and analysis of the resulting data. Students appreciated the project, one commenting on the course survey “This helped me connect the lessons to a real-life example in a manner that was fun to learn”. In addition, I also find students are much more motivated to work on a fun, silly problem with a story than a dry, generic problem with imagined data. Applied math is fortunate in that problems can maintain rigor yet still tell an amusing story. Why discuss hyperbolic projectile trajectories when you talk about throwing nitrogen frozen pumpkins off a roof instead?
Teaching has always been important to me because I am able to share my passion for mathematics. By demonstrating enthusiasm in the classroom, I am able to make my students similarly eager to learn. One student remarked on the course survey “His enthusiasm and understanding of not just the course material but math and science in general is contagious. Anthony has clearly demonstrated an unprecedented ability to motivate and lead students to success”. In addition, I believe a comprehensive understanding of content, as opposed to simply a procedural one, is crucial to success in any field. I therefore strive for this as a key objective in my classroom. These two traits of motivation and a deep comprehension are commonalities in the teachers I have had that greatly influenced me, and therefore are the traits I hope to emulate in my own teaching.