Back to the basics

I'm feeling a bit less stressed-out than I was this afternoon when I put together that last post. A good run always helps me out.

While handing back exams in both my morning and afternoon Calc I sections today I brought up the idea of using portfolios as a means of assessing student learning in mathematics courses. This idea was couched cozily inside of a conversation about the shock of receiving a "bad" grade on an exam (as some of the students no doubt experienced today). "I hate having to grade y'all," I told them. "I'm more and more opposed to grading in general, and to the simplistic distillation that goes into assigning a single letter grade to such a Gestalt as the sum-total of a student's learning activities throughout an entire semester."

There were many nods of agreement when I described how I'd like to be able to supply them with all of the same feedback I give them already...without the numerical rankings, the stigma-making marks that say "she's more highly-ranked than he is."

"I'm not going to do it this semester, since it wouldn't be fair to any of us, you all or me, to change the system midway through. But I'm seriously thinking about it for future semesters."

More nods of agreement. I'm convinced that students are not against this.

But if I were to move to portfolios, the first question would be, What goes into those portfolios? Clearly students would be asked to submit materials of various sorts that purport to demonstrate mastery of course learning goals. Ultimately, then, the question becomes twofold: What are the learning goals of the course? and What course activities (projects, exams, written assignments, homework assignments, etc.) would be sufficiently rich to demonstrate clear mastery of the learning goals selected?

As I reminded my 280 students today (quite forcefully, I hope), when you've got no idea what to do, you go back to the basics. In 280 in particular and in mathematics in general that usually means you'll want to take a long, hard look at the definitions. In course design, it means you'll want to take a long, hard look at the reason you want the students taking your class in the first place.

My current learning goals for Calc I (as stated in this semester's syllabus) are as follows:

1. Be able to explain to a peer the concepts of limit, continuity, and derivative.

2. Demonstrate how basic problems in physics, engineering, chemistry, and other fields can be couched in math terms using mathematical models.

3. Be able to follow confidently the course of a simple proof.

4. Be able to perform and properly interpret derivatives.

5. Demonstrate (through informed question-asking) a healthy skepticism regarding mathematical and scientific arguments.

6. Demonstrate how to approach a (not necessarily mathematical) problem effectively by breaking it down into smaller problems, arguing by analogy, and applying other basic problem-solving techniques.

I think it's clear that mastery of some of these would be very difficult to assess using "traditional" assessment instruments. While (1) and (4) could be got at with a well-designed traditional test, assessing (2), (3) and (6) would require a more robust (and likely highly nonstandard) project of some sort, and (5) would require something extremely atypical...maybe a dialogue of some sort, or some other "creative analytic practice" (to use Laurel Richardson's term).

Of course, the above learning goals are merely my own...I'd love to see what students could come up with for learning goals of their own. Maybe I should ask them? Yes, I think I shall.

Clearly there's a lot of thinking left to do, on many persons' parts.

For now, I'm off to eat dinner. I hope that if you read this, you'll reflect on it for a moment or more and offer me a few thoughts of your own in the comments section.