Random crap

I had perhaps a single contiguous hour to put toward work on Linear this morning, along with a few minutes scattered here and there amidst the hours that went into helping the Calc III folks study for their exam tomorrow I spent much of that time brainstorming in-class activities, and coordinating them with the stated learning goals to which they correspond. It's really starting to come together: on the back of a page from a desk-sized office calendar (October 2005, I think) I made a table linking each activity with its stated learning goal, together with suitable assessment/evaluation methods and resources needed to pull it off (thank you, Fink!). It'll make great office art.

I'm about halfway through my 14 stated learning goals, and I'm finding that many of the goals are to be addressed and assessed in similar fashions. For instance, I find myself writing "hands-on exercises" and "research journals" and "final projects" quite frequently...I'm hoping this is a symptom of a well-planned battery of feedback and assessment methods and not just a lack of creativity on my part. ("Gee, I dunno how I'm s'posed ta tell if they're learnin' that...garsh...")

I'm also finding that it's hard to design in-class activities without linking them to a specific topic. I have dozens of content- and subject-specific activities in mind, but I find it difficult to distill from them a general essence that would allow me to sort them into meaningful larger units: it's those overarching categories (corresponding to given learning goals, for instance) for which I'm having a hard time finding labels: "what activities will help develop develop analytical skills? I don't know what you'd call them, but they look like this in the context of eigenvectors: ..."

There have been a few activities that seem sufficiently flexible to be applicable in a number of different instances. For instance, expository dialogues might come in handy in helping students to ensure deep knowledge of foundational material: if they have to plan how to teach it to each other, chances are they'll understand it better. And "What if...?" exercises will be a great way to get students used to the idea of generalization: "what if we didn't assume the system is first order...?" This is the kind of probing question I'll ask folks to expound upon in journals as well.

I also spent a good amount of time looking for confidence-building activities, in order to address the stated learning goal of "achieving confidence in carrying out a large-scale research project in mathematics." (This goal falls under the Human Dimension component of Fink's taxonomy.) I found some promising exercises on several websites dealing with improvisational acting (not surprisingly), one of which reminded me of the fantastic parlor game, Werewolf. I also found some great large-group math games. I think that by taking part in math games which are not specifically linear algebraic, which do not even necessarily have a "mathy" feel to them, some students who are less sure of their math skills might be convinced to leave their apprehensions behind and feel more comfortable in doing math with and in front of others. (The Math Forum's game Toss and Sort seemed one of the most promising.)

Meanwhile, our Learning Circle on Fink meets for the last time tomorrow...I'm going to miss this group! Of course, I'm sure we'll all stay in touch on the topic (those of you who read this, leave a comment, let me know you're out there!) and will reconvene to share the thoughts and actions which have come of this particular meeting of the minds. The adventure's just beginning!