Teaching Philosophy

Mathematics is an important subject and a careful selection of mathematics courses should be an integral part of most if not every university curriculum. Here I reflect on some of the ways I organize my course, my style of teaching through problem solving and the methods I use to make the education process enjoyable for my students.

Planning for the course

A badly structured course will throw students off track and the confusion caused will keep them from focusing on actual mathematics. I keep my students informed about the goals of the course and expectations I have from them.

For example, on the first day of classes I inform students about the overall work-flow, class policies, exams, homework and other technicalities. I also get an idea regarding the mathematical background of my students and formulate some problems that they will understand, find interesting, yet unable to solve using prior knowledge. I present those examples and explain briefly how the course will assist them in finding a solution. All this helps keeping students focused and removes lingering doubts regarding the purpose and usefulness of the course. This way they stay motivated and feel less like a captive audience.

Teaching method: Promoting an interactive classroom

My goal is to make the teaching process less of a lecture and more of a conversation. I make sure to learn the names of my students and their majors. This helps a lot with breaking the ice and making them comfortable asking questions in the class.

Students comes with varying amounts of background knowledge and at times one may feel intimidated or inferior to their peers. As an instructor, it is my duty to discourage such feelings by making it clear that no math question is a stupid question. In my class it is natural for students to ask multiple questions on the same topic.

This method of teaching is well liked by students and I quote from my end of semester evaluation: “Whenever any of the students asked questions in class, he always tried to answer the questions fully until they were well understood. If the student who asked still did not understand, he would rephrase it in a different way or connect it to something else that would clear up any blurriness. This really helped me a lot.”

Motivating and teaching through problem solving

When introducing a concept, sometimes, I start with a carefully crafted example and encourage students to work on it using prior knowledge. I work with them and demonstrate how we have arrived at the edge of our understanding
and a new idea is necessary to solve the problem. Then I introduce the new concept and show them how it helps in solving the problem we previously failed to solve.

This way a student not only appreciates the true value of the concept but also learns to identify problems where such a concept is applicable. I have had a lot of success with this teaching method when introducing Laplace transforms in my differential equation class.

Once again I would quote from the evaluations: “…. I really enjoyed my time with him and could seriously listen to the guy talk for hours. He urged students to truly think critically and understand the mathematics behind the operations performed to solve differential equations. (A lot of the WHY in addition to the HOW) ….”

An anecdote: A new way to make problem solving fun!

Here is an anecdote about a variant of the above ‘teaching through problem solving’ method and how it turned out to be an effective, engaging and entertaining teaching tool.

This happened while teaching college algebra. We were trying to rationalize the denominator of a fraction like 1/(√3 −√2) and the technique involved multiplying the numerator and the denominator by the conjugate of the denominator. I suspected that the students were memorizing the algorithm rather than understanding the underlying concept. So I told them that if they could rationalize the denominator of 1/(6√3 −6√2), they can skip the next quiz. I informed them that they have the background knowledge for the problem.

I did not believe that they would try very hard and solving it would honestly require them to understand algebra at a depth beyond the expectations of the course. But I could not have been any more wrong. I started receiving emails right away claiming a solution and as I suspected, they multiplied the numerator and denominator by (6√3 +6√2). I explained why this was not correct but it did not deter them. I received about 60 emails and often multiple emails from the same person. I could see them inching closer and closer to the solution.

Eventually some students were able to solve the problem and lot came close. This single problem taught them how to work with fractions, surds, appreciate the importance of formulae and yes it taught them what rationalizing the denominator actually means. That was a significant portion of the entire syllabus!

Office hours

I encourage students to come to my office and even tell them to use my office hours and space to do regular homework. This not only helps them get their work done faster but gives me an insight into how they think when solving problems. I often use this feedback to improve my lectures and problem sets.

I often use office hours as a platform to promote healthy collaboration by encouraging students to work in small groups. I also use office hours to teach students that mathematics is a ‘skill’ which like any other skill can be sharpened with practice. I give carefully designed problem sets to specific students if I feel that they are intimidated by the subject. As they practice, they get better and this helps them to get rid of their fear of mathematics.

Promoting a respectful learning environment

Students in modern universities come from different backgrounds, have different goals in life. The reasons for which they have decided to take my class can vary wildly. Neither do I judge my students based on their prior knowledge of mathematics, nor do I think it is appropriate to mock those wishing to pursue careers requiring less direct knowledge of mathematics.

My job as a mathematics teacher is to show them the beauty of this subject, share some of the enjoyment that comes from solving problems and talk about how it will be useful to them in future. I stay focused on my job and make sure every one who takes a class with me is shown proper respect in the classroom and in my office from me, their peers and my fellow teachers.

Conclusion

My experience has opened me up to several aspects of teaching. Some I listed above, some I didn’t and I believe there are many more that I am yet to discover. Being a mathematics educator can be challenging and one needs to be industrious in overcoming obstacles. When I am able to come up with a way to help an individual student or device a new strategy to introduce a concept to the class, I find it to be an oddly satisfying experience.