Partially Ordered Thoughts

I’ve been tweeting a lot during these first 3+ weeks of school, but blogging has fallen by the wayside. This is my attempt to remedy it during a rare lull in my activities this month.

Clickers in Precalculus: My excursion into using clickers (namely InterWrite’s PRS, Georgia Tech’s chosen classroom response system) has gone very well. It’s amazing how engaged my students are at 0805. With a different course, one might be able to argue it’s because students who take classes at that time are morning people. However, this is the only section of precalc being offered this term, so that’s not a factor. I pre-planned the clicker questions for the first six sections of the text, and I’ve found that was good for allowing me to have time for other things in the first two weeks or so. However, I don’t think they were the greatest questions. I was more concerned with writing clever clicker questions than setting up a good sequence of questions. Since my supply of pre-planned questions has run out, I’ve been writing questions during the day before class, and I think it’s working better. I have a better feeling for what the class needs and how long questions will take, which is important. I’ve also become much more cognizant of the sequence of questions I give in class. Fortunately, the students have bought in pretty well, and I got positive feedback from the one complainer on how I’ve adjusted since my initial supply of questions ran out. She wanted me to lecture more, while keeping PRS questions, but I really think that the incorporation of peer instruction is important.

Lengthy course policies: I’m pretty happy with my comprehensive set of course policies, and the students seem to be navigating it OK. I spent too much of the first day (as in all of it) covering the policies and expectations, which I think was overwhelming. I did do a group scavenger hunt of sorts through the document, which helped, but I know I could’ve done a better job of setting the initial tone of the course.

Documented problem solving and peer feedback: The idea here is to help the students learn how to show their work, draw good figures, explain their use of variables, and explain their steps using complete sentences. This has gotten off to a rough start, but I think we’re making progress. My initial plan was that the students would take 15 minutes to solve a problem in groups and then exchange feedback with another group. Turns out they weren’t very swift at solving the problem. I adapted pretty well, however. I decided that they’d have to finish the problem outside of recitation and bring it in the following week to exchange feedback. That went better, by and large, although things still aren’t perfect. The peer feedback was decent, but it left a bit to be desired. The strangest thing here was how two very similar but differently-worded questions could elicit strikingly different responses. The two problems I assigned are the set-up portion of typical optimization problems students struggle with in calculus. The second problem went reasonably well, with students generally producing the correct function. However, in the first problem, roughly 3/4 of the groups latched onto the part about the base having side length 10 and never produced a function for surface area. They saw that and immediately determined the box was a cube and ignored everything else. However, in the absence of that sort of information, they knew what to do. I’m still baffled by how this happens, but it has definitely taught me that I need to think about how I write problems in the future. Maybe a part (a) and a part (b) would have helped them figure out what I was looking for? I guess we’ll see as we go forward.

What I’ve learned about students: They are not taught how to read and follow directions in primary or secondary school. They are also incapable of following verbal directions. I think they’re getting better, but it’s a slow, painful process. I was also astounded to learn that they don’t know how to install software on their computers (among other computer literacy skills one would assume students at the Georgia Institute of Technology would have).

In a new personal record, I have a fully-developed course policies and expectations document two weeks before classes start. (You might call it a syllabus, but since the proper definition of syllabus doesn’t include all the information I put  in my course policies, we’ll agree to call them course policies.) This will take us through the last four steps of Fink’s 12-step model of course design. First up, we have step 9, which concerns grading. Normally, like most mathematicians, I’m a weighted average sort of guy, aiming to have the final worth twice the weight of a single midterm. However, with all the things I’m planning to incorporate this semester, I decided that using a point accumulation model would be more appropriate. I hope that I don’t later decide this is a mistake, but I’m pretty confident that I’ll be happy with it. Those who want to suffer through the details can consult Table 1 in my course policies and expectations. The pie chart below tells pretty much the whole tale. (The miscellaneous category is participation, note-taking assignments, and reading assignments.)

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In Fink’s “Intermediate Phase”, he says the idea is to take the pieces we’ve already developed (goals, feedback and assessment plans, and teaching and learning activities) and form them into a coherent whole. As I’ve previously mentioned, I feel like Fink ran out of steam after dealing with his “Initial Phase”, and this phase isn’t always clear in what it’s trying to say. Or maybe the book suffers from a malady that is unfortunately not uncommon in this type of book: the author has a common sense point to make but wants to make it sound more complex, and therefore blathers for multiple pages. It’s hard to tell if the ideas here are underdeveloped or just muddled, so I won’t try to decide which it might be. There’s also a possibility that this is one of those areas where those of us who teach in highly-structured disciplines full of dependencies miss the subtleties that those who teach in other disciplines have. This post discusses my journey through steps 6, 7, and 8. 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 »