Editing mathematical writing

As I mentioned in a previous post, I’ve been assigning large-scale collaborative writing projects in my mathematics classes. I’ve had my topology students write a textbook for their class, and this semester I’ve been doing the same in my discrete mathematics class. As I mentioned in that post, the approach has been very successful, but…

How I teach topology: an inquiry-based learning approach

Recently I’ve had a number of people ask for more information about how I teach topology. I’ve taught it five times using a “modified Moore method” or “inquiry-based learning” approach. I’ve modified it each time, trying to work out the bugs. I think it is pretty successful now. Context. At our college all math majors…

How do you place incoming mathematics students?

Our department is looking for a better method of placing incoming students in mathematics courses. Currently we have a placement exam that determines whether a student should begin in a calculus I course or in a calculus/precalculus hybrid course (our lowest-level math class). The exam consists of 25 precalculus questions. It does a pretty good…

Parametric curve project for multivariable calculus

I’m teaching two sections of Multivariable Calculus this semester. Each class has 3 hours of lecture and a 1 hour 20 minute lab each week. Last week the students were learning about parametric equations. So in lab I wanted to give them some hands-on experience with 2-dimensional parametric curves. Their assignment was to create a…

Using wikis in mathematics classes

Wikipedia describes a wiki as a website that allows the easy creation and editing of any number of interlinked web pages… [Wikis] are often used to create collaborative websites, to power community websites, for personal note taking, in corporate intranets, and in knowledge management systems. I have used wikis in three of my classes: two…

Showing two expressions are equal: stop the madness

I know that most you who read my blog teach mathematics at either the high school or college level. I’d like to ask you a question (at the end of the post). It is about how our schools teach students to show that two mathematical quantities are equal. This has bothered me ever since I…

Thoughts on teaching induction

I don’t plan on doing this very often, but I thought I’d re-post one of my earlier blog posts—one that I wrote a year ago, when I had many fewer readers. Now is an appropriate time for me to re-post it because I am currently teaching induction in my Discrete Mathematics course. Enjoy. In their…

Kindergarten mathematics

This is a call for help. My son’s kindergarten teacher has invited parents to come in and talk about their careers. I’d like to go in and talk about math. I’d like to have some interactive hands-on mathematics activities for the kids to do. I also want them to be activities outside the typical kindergarten…

Flashlights and conic sections

Recently, Ξ over at the 360 blog wrote about hyperbolic light (which was inspired by the article, “The Shape of Lamp Shade Shadows” by Kenneth E. Horst, The Physics Teacher, Volume 39, March 2001). They were looking at the pattern of light on the wall emitted by a desk lamp with a cylindrical lampshade. They observed that the…

Students as Facebook friends?

I’ve been on Facebook for approximately six months. I resisted for a long time, but caved in eventually. While there are many things I dislike about Facebook, it can be an interesting trip down memory lane (As Lev Grossman wrote in Why Facebook Is for Old Fogies, “son, we’ve lost track of more people than you’ve…

How to use KnotPlot

As I’ve mentioned before, I’m teaching a knot theory class this semester. I’ve been playing around with KnotPlot, a powerful piece of software for drawing and working with knots. I want my students use it, but it has a somewhat unintuitive interface. So I’m trying to write up a list of easy-to-use instructions for them. The…

Calculus and sustainability

I saw a number of interesting talks while at the Joint Mathematics Meeting last week. Hopefully I’ll find the time to write about some of them here. One of the presentations that got me the most excited was the minicourse that I attended, Educating about the state of the planet and sustainability while enhancing calculus,…