don't drum up the men to gather wood,
divide the work, and give orders.
Instead, teach them to yearn
for the vast and endless sea.
"The Wisdom of the Sands" (1900-1944)
The mechanics of taking a college math course are very much like building a ship. There is a long list of tasks for students to do, from attending lectures and office hours to completing homework and studying for exams. I am not just a taskmaster, making sure my students complete their work. I am a mariner, freshly returned from exploring the vast body of mathematics. My strength in the classroom is that I am a mathematician teaching mathematics. Students can witness my enthusiasm for mathematics. I try to bring that enthusiasm to them, to get them excited about a subject I love.
My classroom is my workshop and my students are apprentice mathematicians.
- Mathematicians do many computations and prove other's claims for themselves. Where possible, I minimize the amount of time I am at the front of the classroom lecturing. Students should be actively engaging with concepts, spending most of class time doing an activity or working with problems.
- Mathematicians communicate. Students need to practice effectively conveying their ideas to others. In my classroom we work in small groups and practice being precise. To be precise orally, students and I brainstorm good math language and critique examples of imprecise descriptions. We strive to be precise when writing. Because mathematics is a foreign language in its own right, we practice writing the same statement in different notations. We practice precision visually. When drawing, we clearly label each aspect of our picture and provide enough data points to make our meaning clear.
- Mathematicians look for patterns and make conjectures. In discussion, students use their knowledge as the scaffolding to learn something new. I want students to escape the fear of "saying something stupid." I encourage them to conjecture based on evidence. We work towards proving our claim or finding a hole in our reasoning.
The world of mathematics is sublime, an intimidating object of immense beauty. I love exploring it and strongly believe every student deserves a taste of this ocean, even if all they ever do is build a ship on its shores.