Continuous Everywhere but Differentiable Nowhere

Today was a really hard day, because it brought back a lot of the emotions that I had when doing my student teaching. Those days were long and exhausting, and I remember that every little thing affected me. 
In those days, I took every student comment to heart. A student got upset after getting back a quiz [...]

I was sad that Polaroid stopped making their film. Now I have an amazing substitute: Poladroid. Check it out.

 
Yes, I did in fact spend about an hour today converting all these digital photographs into polaroid photographs. (I loved every minute of it.)

In MV Calc today, we were learning about arc length. In 3D, if you have parametric equations defining a curve, you can find the arc length by calculating: 

I asked them to calculate the length of this curve, which will repeat itself, over and over and over:

If you graph it, it looks like this (it’s a [...]

In my (non-AP) calculus class last week, I was teaching my students about continuity of a function. Before we started, I asked them what continuity was, and students in both sections started their answer by saying “well, it’s when you draw a function and you don’t have to lift your pencil.” Some spoke of holes [...]

This year I’ve decided to be a faculty representative on the Student Faculty Judiciary Committee (SFJC).
I’m sure I must have talked about SFJC before, because I went a lot last year. I was called in to answer questions about some cheating incidents that happened in my class, and I went in as an advocate [...]

As you probably know, I’m teaching Multivariable Calculus this year, and I came into the course with a vision: a collaborative, problem-solved based class, where students aren’t motivated by exams and grades, but rather by the challenge of thinking for themselves. 
(Of course, getting really great, full-of-personality students helps too!)
The problem sets seem to be working [...]

In my classes this year, I’ve been really concertedly trying to emphasize that students need to really understand concepts and explain ideas in written form clearly. Today I’m faced with a conundrum about how students are connecting concepts with the problems we’re doing. 
On my Algebra II quiz, I asked:
Explain — using complete sentences and proper [...]

One of the students in Math Club recently put his own twist on the age old hat question: Assume you have people, each of whom has a red or green hat put on them. They each don’t know what color hat they have on. However they can look around and see everyone else’s hat.
After [...]

Even though I was sick — aching and tired — I survived our Parent’s Night last week. I think it was pretty successful, even though I was foiled a few times by parents who tricked me into talking about their children. (I keep a general policy not to talk about individual kids at these events; [...]

I woke up feeling under the weather today. As the day went on, I felt worse. I’m going to bed sick. Of course I would get sick for the first time this school year… the night before parents night.