A Course in Thinking

This blog post is also a session at Sam Shah's The Virtual Conference of Mathematical Flavors 

In a conference on flavors of mathematical teaching and learning, you could be forgiven for expecting every session to address some version of the age-old arguments about whether there are math people and non-math people, about whether it is better to have a growth mindset or a fixed mindset, or about whether mathematics is the most beautiful of all the disciplines we teach in school.

Which is probably why I feel so hesitant to confess my dirty little secret. In my classroom, I teach mathematics as one of the humanities.

The fact is that math is a human activity. If you are human, you cannot escape it. And what I have come to value the most about the opportunity to teach mathematics is that it has become one of the most pivotal ways in which we transmit the culture and values we cherish the most. For me, some of those values include respect, communication, empathy, understanding, persuasion, civil disagreement, persistence, deep listening, reassessing, and changing one’s mind. Math class gives me an opportunity to share all of these aspects of being human and living together in human culture.

So I’ve rewritten the introduction to my course syllabus to emphasize some of the things about which I feel most strongly — and which I believe are the most powerful and important things I have to share with my students over the course of the next year.

I listen to hear your thoughts.

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This is a course about thinking.

You are here to learn how to think better and to use your thinking to accomplish things in the world.

The essence of thinking is sense-making. To make sense of things, you have to understand them, which means you have to want to understand them. One of our mottos in this class is, You gotta wanna.  This is as important in mathematics as in everything else.

So everything in this class is about making sense of things. In mathematics — as in life — we mostly make sense of problems. If you do not yet know that life presents a steady stream of problems to be solved, you will soon. 

In this class, we happen to use mathematics  as a ground for thinking. I will tell you a secret up front: I don’t actually care if you  ever “use” this stuff ever again or not... so please don’t waste time asking me that question. It is a boring and senseless question. What I care about passionately is that you learn how to think and communicate at a more advanced level than you are capable of right now. 

And that is what we are going to work on.

Thinking better is a set of skills you can actually learn and use at this school. It is the appropriate focus of math class.

Since you are going to be thinking for the rest of your lives, you are going to need to make sense of things you don’t initially understand. And then you’re going to have to persuade other people that your thinking is right. So your goal in this course should be to grow as an active sense-maker who is skilled in using these tools of thinking.

You should also learn to treat your thinking with respect. The mind is a muscle, and this school is a place where we work to strengthen our thinking muscles. That means we need to develop strength, flexibility, and endurance in our thinking — in other words, you need to become a strong thinker, a flexible thinker, and a persistent thinker. You also need to become a good collaborator, which means you need to become a better listener.


While there are no guarantees, I can promise you that if you focus on these goals here, you will do well in this class, and these skills will carry you very far in your life.