Teaching Philosophy

Dr. Carol JVF Burns

If you live in a tiny house, then you will come to understand the possessions that are essential to your life. If you want to get at the essence of an idea, try to express it in one sentence. The process of distilling often vast information to decide what earns the right to occupy that small space is incredibly valuable.

So, what would be my one-line teaching philosophy? On continued reflection, I keep returning to a statement that has been my compass as a parent:

If everything you do is done with love as the basis, then you can make a lot of mistakes, and things will still turn out okay.

To adapt it to teaching, interpret ‘love’ in a broader context—to include respect for individuality and belief in each person's ability to learn and grow. This simple statement gives me the courage and flexibility to explore, providing comfort that a sometimes unexpected result is okay.

There's a lot of mathematics out there—and many ways to travel through it. I take my role as a guide very seriously. Some groups have time only to glance through the windows; others have the luxury to poke into shadowy crevices. I always want to do more than just meet expectations—I want to give a glimpse of perhaps unexpected beauty and a deep understanding of culture. I want those on the journey with me to want to return for more.

For almost three decades I have been refining and adjusting my teaching. However, certain concrete realizations of my beliefs have proven themselves so universally effective that I would never teach without them, and I will explore some of these here:

Each person has an obligation to give back to the world, and part of life's journey is in discovering and developing those unique talents to be shared. By giving to those in need, we receive the rich gift of being needed.

When I explore mathematical ideas with others—be it in the classroom, one-on-one, or via the web pages I present to the world—then I find deep happiness. The ongoing search for more effective ways to communicate mathematical ideas gives meaning to my life, and my lifelong endeavor is to keep at it.