This image is an attempt to capture the important stages of doing mathematics. As pointed by other people, **mathematics is not a linear process**, which I am attempting to share via this image. I see analytical reasoning, flashes of insight, and exploratory calculations as the glue that holds these stages of mathematical thinking together.

How do you see the process of "doing math"? Is it possible that what sets mathematics apart from other disciplines is the formalism, and the calculations involved? How does this process compare to other things that we do in life?

I feel the process in math can often be equated to the process in how foreign language is often taught. I think many people find it to be a difficult idea that in math you may solve something in many different ways though it is common in life. Trying to teach students that it is ok to look at something from a different angle is ok. I also insist that they explain their method as well as complete it. It can also confuse other students.

Our math department is trialing two new ways of teaching math this year:

1) students watch teacher produced videos of math concepts for “homework” and then discuss and work their way through problems the next day in class (flipped classroom)

2) the Harkness method (oval discussion table used for inquiry and discussion) is being used so that students can work with each other and the teacher in discussing and solving problems.

The math department head says in his 20 years of teaching, this is the most rewarding and useful way of teaching he has found. The students have done far less homework and are farther ahead academically than they have ever been before.