Wednesday, February 09, 2011

Confusion and confidence

Lately in all of my classes I've been using a variation on the classic "three-minute theme" low-stakes writing activity in which I ask students to write three things about a reading or a class discussion or a course in its entirety:

1. What one topic are you most intrigued about, or want to know more about, right now?

2. What one topic are you most confused about right now?

3. What one topic are you most confident about right now?

Each of these prompts has a particular purpose. The first helps students identify their interests and better understand why it is they might find our coursework appealing. This interest and appeal translates into motivation to keep working at the course. The third prompt has much the same effect: by reflecting on a topic she feels confident about, a student is likely to say to herself "yeah, I can get this! I'll keep at it, and sometime soon the rest will come just as easily." Meanwhile in the reflection needed to respond to the second prompt the student will identify areas on which she may need to focus extra effort.

I'm calling this activity "Intrigue, Confusion, and Confidence," for obvious reasons. I've already used it several times this term to help my MATH 179 class focus their discussions, and I just used it a half-hour ago to help me figure out where it is my Calc II students are feeling good about themselves...and where it is they might need extra work.

What are the students feeling good about?

Numerical integration: 18
Finding volumes (using disks/washers or cylindrical shells): 13
General integration: 6
Riemann sums: 2

What are they feeling not-so-good about?

Finding volumes: 13 (general: 5, cylindrical shells: 4, disks/washers: 4)
Work and other physical applications: 6
Numerical integration: 5
Setting up integrals: 3
General integration: 3
Visualization (drawing): 1

It's worth noting that we've just today wrapped up our discussion of numerical integration, so those topics may appear more frequently because they're fresh in mind. They're also not quite as complicated conceptually as some of the other topics we've covered. I find it interesting that as many people are fine with volumes as are iffy about them; this complication makes it difficult to give any specific prescription for study or review. I'll put together some additional practice problems for people to tackle tomorrow after the quiz.

If you're one of the students in my Calc II class and you're reading this, do me a favor: take five minutes to go to the comments section and let me know if this brief exercise at the end of class today was helpful to you...and if so, why. I appreciate it!

By the way, the two most entertaining comments, both about areas of confidence: "Rotating functions around axes is SUPER FUN! [accompanied by a Bundt-pan shaped volume of revolution]" and "That thingy. Can't think of process name. [accompanied by a sketch of a vase-like object suggesting a disk-method volume-finding question]"

1 comment:

Jack Derbyshire said...

The process is incredibly helpful; although I can't specifically explain why. I suppose it gives me the feeling that you're taking into account where I'm struggling or where I'm succeeding, and altering your focus in lectures accordingly. Most professors lecture, give quizzes, homework and tests, and then let individual students struggle silently through their most difficult aspects of study.

Who knew democracy was so effective?