Partially Ordered Thoughts

Last week, on a beautiful Friday afternoon before Spring Break, I was teaching my applied combinatorics students about generating functions. We’ll see some of the more powerful things next week, but last week we were focused on the number of integer solutions to an equation in a small number of variables. This is a recurring problem in our class: first we saw it with binomial coefficients, then we saw it with inclusion-exclusion, and now we’re seeing it with generating functions. To make the material less abstract, we were discussing the question in terms of fruit baskets. (You want to make a fruit basket with apples, oranges, bananas, and peaches in it. The number of apples must be even, there must be at least two oranges, there can be no more than six bananas, etc.) Read more »

I firmly believe that for effective teaching and learning in a class, you need two-way feedback. That means that not only do I give the students feedback, but they also get to give me feedback. Georgia Tech, like most places, have a standardized end-of-term course survey. However, I want to be able to fix things on the fly. To do this, I implement a quick midterm survey through our course management system. I provide a modest incentive to the students to take the anonymous survey (free credit for a reading assignment or three clicker questions), and this time I got a phenomenal response rate. (The survey really is anonymous since our course management system can record a score in the gradebook for taking the survey without attaching a name to the responses.) Read more »

We’ve already covered the fact that I write long course policy documents. The Spring 2010 Applied Combinatorics (MATH 3012) Course Policies and Expectations are seven pages long. Last time I taught this course, they were four. However, last time I wasn’t doing as many different types of assessments and wasn’t using much active learning in class. This time, I had a lot of explaining to do up front. Inspired by Maria Anderson’s post over at Teaching College Math, I decided to get my students to actually read at least part of the course policies by crowdsourcing them. Read more »

On to the next step of the course design process. This entry will finish building the stool that is my course design. First, let’s review where we’ve been. We looked at the situational factors, which are sort of the ground upon which we build the course. The first leg was the course goals, which established where the course is going. Next up was assessment, since we need to figure out if the students have reached the goals. What remains? How on earth do we get the students to succeed on the assessments we’ve so carefully planned? We need to map out teaching and learning activities for each of our goals. The next (fifth) step is to do what Fink calls “integrating the component parts”, which I think we can look at as putting the top on the stool and making sure it sits level. This is really a key part to a successful course design, since, for example, if I wrote a course goal that’s at the evaluation level of Bloom’s taxonomy but just lectured to the students and didn’t give them a chance to practice and then gave test problems that were at the application level (or lower!) to assess if the students met the goal, I’d be pretty hopeless. The assessments need to actually check what the goals are trying to get and at the right levels; the teaching and learning activities need to help facilitate students getting to meet the goal and succeeding on the assessments. This doesn’t mean hand holding or teaching to the test, it just means that we can’t expect students to magically make the leap from understanding to synthesizing without help through the steps. Read more »