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Regarding a proposed implementation of standards-based grading
As suggested by Jojo last Monday, our summer pilot study of SBG might assess each standard as follows:
We would count anything that's 2 or 3 as mastery, but for the "A" and "B", we would use the 3 scores to distinguish them from the the "C" students.
I would support using this version for courses such as MATH 181, where D and F have the same implications for enrolling in the sequel. In a standalone course like MATH 110, I would use a 5 point scale (0,1,2,3,4) so that college credit might still be earned for "D-level" work. While some four-year institutions might not grant college credit for a D in MATH 110, at least the public universities in this state are required to transfer all credits in a lump sum if the applicant has earned an associate's degree.
One might visualize a student's demonstration of mastery by plotting a step function, with standards as unit intervals on the x-axis and the scores for each standard represented by the height of a bar. Since this pilot study is taking place in a calculus course, why not specify the thresholds for each letter grade using integrals of such a step function f? For instance, find the integral of f*x[core]+0.5*f*x[non-core] where x[S] is the indicator function for set S. Possible thresholds for the various grades would then be almost identical to the usual mapping between numbers and letters.
On a slightly different topic, one of the challenges I faced this semester had to do with shoehorning the reflective learning component into the SBG grading scheme that I tried out in MATH 110. I designed three prompts loosely based on the standards I wanted to assess, and hoped that my students' reflections could be mapped onto these standards. When the submissions came in, I had trouble reconciling my desire to incentivize creative exploration with the SBG mantra of counting only the best instance of a skill being demonstrated. In the case of my math students, counting the best instance of an assessed standard would result in their homework grades overwriting even the most disappointing ePortfolio reflection.
This realization highlights the difficulty of using multiple assessment types in an SBG classroom. On the one hand, we want to make sure our students are comfortable expressing their knowledge in a variety of situations, not just on their strongest type of assessment. On the other hand, SBG asks us to meet the student where they're at, giving greater weight to the assessment where they've done the best.
In a calculus class it's not too difficult to incentivize homework completion, since at this point in their college careers the students are aware that they can't learn passively any more. Hence SBG can be implemented using only one type of assessment (in-class quizzes or tests). In classes that rely on two or more assessment types, however, the end-of-semester gradebook reconciliation can be a daunting exercise in reevaluating priorities.