I am teaching probability and statistics, a course for first-year students, for the first time this spring. I have been struggling with how to grade the students.
This course is unusual in that there is only a little mathematics in the course (we throw in all of the probability that we can, but it is still mainly statistics). This requires that I think like a statistician, which is new and somewhat painful.
It also makes designing a course more difficult. I have the basics of what I want to do, but—as mentioned above—how to grade the students is the most difficult part. I want to stick with an SBG approach, but I was not sure how to set up the standards.
In calculus last semester (and other courses in previous semesters), I had a general format of: “if you can do the basic skills from the course, you will get a C. To get a grade higher than C, you must demonstrated some conceptual understanding.”
I realized as I was brushing my teeth last night that this is completely and utterly backwards.
I want my C students to understand the concepts of the course, but not necessarily be able to do the computations and symbolic manipulations. My B students should, in addition to understanding the concepts, be able to do many of the computations and symbolic manipulations. My A students should, in addition to understanding the concepts, be able to do all of the computations AND demonstrate that they can do some self-guided work.
Here is my rationale for requiring understanding the concepts to get a C:
- I am convinced that the concepts are easier in most college-level mathematics courses—students are better at drawing tangent lines on graphs of functions than they are at finding the equations of tangent lines.
- The students who need the calculation and symbolic manipulation skills are the ones who are going to continue taking more mathematics (and related) courses. I am guessing that C students are less likely to continue taking these courses.
- Computers can now do much of the calculation and symbolic manipulation, although the user has to understand the concepts to correctly enter the information.
- Most importantly, the concepts are the most important part of the course! I want to explicitly encourage students to focus on the concepts—I don’t want, say, a calculus student to be able to get an A in the course by only having good algebra skills (a colleague yesterday complained to me about such students; I view this as a flaw in the grading system).
I am not happy about having this completely backwards, and I feel bad for my previous students. But I am happy that I now understand what I want.
The tough part is designing assessments that isolate concepts. But that is part of my job, and I find it fun to come up with such questions.
How can this be improved? Am I wrong about this?
(image is “LED Light Bulb” by flickr user Wade Brooks, Creative Commons License)