Teaching Philosophy
Teaching Philosophy
Math is not a spectator sport. When I read a mathematical text, research article, or watch an instructional video, I work alongside it by performing example calculations, verifying logical steps, solving problems, drawing pictures, and generally exploring the ideas with which we are being presented. This process allows me to both assess and develop my understanding. That is, if I want to truly know what is being presented, I must actually do the math. From this, a guiding principle emerges which drives all facets of my instruction: students learn best by actively participating in mathematical activity. Through active learning strategies, a flipped classroom model, and individualized support, I cultivate an environment where students feel empowered to learn mathematics by doing mathematics.
In-class mathematical activities are the cornerstone of my active learning strategy. For example, take the “Designing a Highway” activity that I use in my Multivariate Calculus course. This activity accompanies the section on curvature and places the student in the perspective of an engineer that must decide what curve to use for a highway off-ramp. The initial and terminal segments of the curve are orthogonal lines, but these must be connected through an intermediate curve. While a circle may seem like a good choice for this intermediate connection, the students pull from the material presented that week to analyze the curvature function of such an arrangement and find it is discontinuous. They are asked to consider the real-world implications of discontinuous curvature and conclude that a continuous curvature function is preferred. The Euler spiral then comes about as a natural solution to the problem. In many of my courses, I utilize activities like this one that engage my students in this process of investigation, analysis, and discovery. These activities also encourage my students to collaborate with one another in class and discuss mathematics. These discussions allow stronger students to deepen their understanding by explaining the concepts to eachother, and it allows struggling students to address weak points in their understanding and ask questions that they may not feel comfortable asking in front of the entire class. Finally, the in-class activities allow me to develop a more personal connection with my students as I meander through the class to mediate arguments, address unresolved questions, and help them work through the activity. I find my students not only develop a deep understanding of the material, but also they develop their ability to communicate, problem solve, and work as a group – skills that will help them succeed beyond the classroom.
To allow more time for in-class activities, I began practicing a flipped classroom model which the MAA Instructional Practices Guide describes as a “pedagogical model in which first contact with new ideas takes place in the individual space rather than in the group space, and the group space is repurposed to focus on active learning and creative application of those ideas.” My students make contact with ideas through instructional videos, reading assignments, and - to make even the individual space as active as possible - “guided notes” which prompt the students to respond to conceptual questions and work out examples found in the videos and text. The biggest challenge here is to make sure my students are engaging with the material before class. The guided notes help, but I have also experimented with “group quizzes” which are administered during the first class period of the week and have found some success with this strategy. My strategies for effectively running a flipped classroom are under regular development and improvement based on student feedback, peer observation, and discussions with colleagues that share a similar approach to instruction.
As example of how I respond to feedback to develop a more effective course,
I assessed the effectiveness of the guided notes assignments by turning to student feedback in the course evaluations. The feedback was mixed. In my Discrete Mathematics course, I saw positive comments like the following:
“Guided Notes were from book and in-class lecture questions,
so they were a great tool for in-class note taking and out-class participation.”
While others responded with something more like this:
“The guided notes that are required feel too much like busy work. I’m aware it is supposed to prove my understanding of the material, but the problem sets should already be enough proof I feel.”
The second comment revealed that I was not explaining the purpose of the assignments satisfactorily – they were never intended to “prove” an understanding of the material. Giving clearer descriptions both in class and in our learning management system, Brightspace, allowed me to more effectively communicate the purpose of the assignments and reduce the number of students that felt like it was “busy work.” It also led me to reevaluate how much I was asking of my students in the guided notes and encouraged me to experiment with group quizzes as an alternative strategy. While constructive criticisms found in student evaluations drive the development of my courses, the positive feedback also lets me identify my strengths as an instructor. For example, a student responded to the question, “What do you feel are the instructor’s strong points,” with:
“Dr. O clearly had a strong understanding of all topics discussed, and was prepared to answer questions regarding the importance of the course, and was able to clarify difficult topics.
Dr. O also utilized brightspace and email well, and was always quick to respond and assist.”
This revealed the value of the student-instructor interaction I was providing both in class and remotely. To the same question, a student wrote:
“He is extremely down to earth and understanding.
He feels friendlier than just any other professor.
He has a clear love of his work and it’s contagious.”
In these, my strengths are discovered: clear explanations of difficult content, connecting with my students on an individual basis, and sharing my passion for mathematics.
The active learning strategies I apply allow me to showcase these strengths by changing my role from a “keeper and presenter of knowledge” to a “learning guide.” Through advancing my instructional design, like transitioning to a flipped classroom model, experimenting with new strategies, and adjusting my methods through student and peer feedback, I regularly improve the effectiveness of my instruction. In doing so, I work toward the goal of sharing my passion for mathematics, and by sharing my passion, my students are inspired to do mathematics. After all, the value of their meaningful participation in mathematics goes beyond the classroom: they become better learners, they are empowered to learn, and, through this, they are set up to succeed in finding and developing their own passions so that they can find success in life.