Ambitions for teaching

In a month and a half, I will be teaching a class for the first time ever. I’ve taken a teaching seminar, and spent the past semester designing a curriculum myself, and listening to experts tell me about teaching gifted students, and I’m terrified. I’m teaching a summer class for gifted high school students that I’m calling Much Ado About Knotting, because nothing is better than math puns. I get to design the entire syllabus myself, write the lecture notes, prepare the TA, and then I will teach, for 6 hours a day, for 3 weeks. Did I mention I’m terrified? Talk about jumping head first in a pool of cold water.

I have a lot of fun knot theory planned out for my students to learn. They will prove Reidemeister’s theorem, study some interesting knot invariants, look at some applications to areas like biochemistry, medicine, and cryptography, and finally we’ll look at my favourite thing: graphs of knots. There will be problem solving, and theorem proving, and some playing with a computer program called KnotPlot. (You should check out the website, it has some of the most amazing pictures of knots I have ever seen). Along the way, students will learn about prepositional logic, equivalence relations, some group theory, some number theory, some mathematical cryptography, and tons of other fun things.

I’m planning on teaching the class using the Moore method modified with think-pair-share. With the Moore method, the instructor only provides students with definitions, and then they get to work out all problems and examples themselves, and present them in class. Since I have the students for full days instead of 3 hours a week, I’m modifying the method to let them work in class. One of the teaching methods we have learned is effective, is think-pair-share. Students get to think about a problem for a few minutes, then pair up and talk about their idea, and finally share them with the whole class.

Everything I shouldn’t do first day of class, from spikedmath.com

I want to use this class to teach them not just a little knot theory, but how to think like a mathematician, and a little about what math is really about. So many of the students I’ve seen in tutoring think that there is just one correct way to solve a math problem, and their job as math students is to memorize that way. This of course leads to major problems when they come across a problem that looks different from the sample examples in the book. I want to show them that math is a set of rules to structure your thoughts, not a set of algorithms. I expect knot theory with me will be quite a shock for students who have spent their lives in an educational system that punishes students for using a different, but equally correct, method than the teacher. Instead, they need to realize that there are many different ways, most of them correct, and each has advantages and disadvantages. I want to teach them to figure out for themselves what is best in a given situation.

Did I say I’m terrified to teach this class? I am, but I’m also excited, and curious to see how many adjustments to my careful plan will be necessary when it meets real life humans. I hear teenagers can destroy the most thought out of plans. I’m also very exited to see what happens this fall when I start TAing a calculus class. I won’t have to jump headfirst into that without teaching experience. And I’ll tell you more at some point about all the exciting ways I want to change my recitations from traditional recitations.