Teaching with Technology Portfolio: Teaching Philosophy
I was sitting in my office on a sunny July afternoon when Carrie told me, “I prefer math… I’m really more of a math person,” while talking about her summer courses. She may not have realized it, but that was an important moment in her life.
I met Carrie 7 months earlier; she was a student in my differential equations class. I asked to meet with her after I noticed she had made some mistakes on the first homework. That assignment was written to assess my students’ prerequisite knowledge. I do this for every class in order to address gaps early and set my students up for success. When we met, she told me, “I’m just not a math person.”
My philosophy is that everyone is a math person. Mathematics is just a formalization of how humans naturally solve problems. I explained to Carrie that struggling in a past math class does not mean you are bad at math. It does, however, mean that you have some gaps that need to be addressed, which requires work.
I communicate two things to my students: (1) learning math means a lot of practice and (2) mistakes are an important part of that practice. My first class consists of a powerpoint presentation that summarizes my philosophy on learning math and explains how this philosophy informs my class structure. Essentially, it translates to daily practice, fast feedback, and an opportunity for the student to make revisions—daily practice solidifies the knowledge, fast feedback quickly indicates when review is needed, and revision means the grading system accounts for improvements over time.
There are many ways in which I can set up such a structure, but, as someone who is particularly concerned with increasing diversity in mathematics, it is a priority to me that I create a system that works for a variety of cultural and socioeconomic backgrounds. Explicitly, I try to accommodate students who
don't want to be anonymous,
do well with structure and consistency,
enjoy learning in a collaborative environment,
are afraid to make mistakes,
work multiple jobs, and
struggle to afford their textbooks.
I address these issues in the following ways
I learn my students’ names. I find it spooky that college students can interact for days with people who do not know their name. I worry that this is an unhealthy experience. Students should be acknowledged as individuals and I try to do just that. Even when the course is over, I say hello when I see my students around campus and catch up whenever possible.
To keep a consistent learning schedule, I assign homework after every lecture and make it due in the following one. My homework schedule develops the important habit of reviewing material between classes. Though this is a lot of work, my students always respond positively. Littered throughout my student reviews is the phrase, “Everyday homework sucks, but it works!”
I reference the work and ideas of my students to foster a collaborative environment. When we discuss problems, I will say phrases like, “Let’s use Matt’s idea,” or “Becky made a great suggestion.” This encourages creativity, it turns lectures into collaborative problem-solving sessions, and it helps my students know each other better. Within a few weeks, my students naturally form study groups with classmates.
My homework assignments are worth few points, my written feedback is constructive and supportive, and students can revise any assignment. If homework assignments are worth few points and revisions are allowed, then mistakes will not significantly impact one’s grade. Furthermore, I write supportive and corrective feedback, which help my students better assess their learning. Supportive comments praise improvement and creative thinking. Correcting comments differentiate between minor mistakes (like calculation errors) or conceptual ones. If it is minor, I circle the area where the mistake occurred and write, “careful!” If it is conceptual, I write a detailed clarification of the concept. All this combined normalizes mistakes.
I avoid quizzes. Homework can be practiced when a student is intellectually prepared for the material. For students who work, this makes a huge difference. The stress of their jobs can often spill over to their academic life and it’s important to have some flexibility.
I do not rely on a textbook whenever possible. Instead, I treat it as a supplement and write lecture notes that are self-sufficient. If I am ever concerned that something may be unclear, I type up materials that clarify a concept and distribute them.
With this set up, I can accommodate both intrinsically and extrinsically motivated students, both collaborative and competitive students, and students anywhere on the financial and the learning autonomy spectrum. Semester after semester, my student reviews confirm that this system works for them.
Although my approach works well, I am always looking to improve. I have taken Stanford’s course How to Learn Math and Penn State’s Course on College Teaching. I also run a weekly discussion group that analyzes research on mathematics education. Most importantly, I ask for feedback from my students by sending out anonymous surveys. Everything I learn, I incorporate whenever possible. My approach to teaching is similar to the system I use on my students: constant study, feedback, and revision.