This is a continuation from my previous post.
I have been unhappy with grades in general (I cannot believe that I cannot find a link to a previous post where I complain about grades). However, grades at my school are not going away any time soon, so I am working on improving them this semester.
Here are my major complaints about how grades are typically done in math classes:
- They are not informative. What does a “C+” or “73%” tell you about what you need to improve upon? It tells you roughly “how much you know,” but not “what you know.”
- Grades are designed to be incentives, but they incentivize the wrong thing. A student who does poorly on a quiz is actually better off (prima facie, at least—and our students often never get past this stage) ignoring the material on that quiz to concentrate on learning the material that will be on the next quiz.
- I cannot find the source, but one math department chair lamented that his students could get a major in mathematics without every getting a problem correct in his/her four years at college (e.g. you could get 7/10 on every problem and get a degree).
I suppose that one advantage that our current system has is that it allows us to easily rank students according to “ability.” I have doubts as to how effective this is, but—regardless—I do not see a good pedagogical reason to rank my students. It gives neither them nor I information about how much mathematics they know.
Here is my solution (with lots of help—see the bibliography above):
- I listed the content of the course into “topics.”
- Have frequent quizzes. This has the advantage of making assessment more familiar and less scary.
- Each quiz question is graded and (essentially) recorded individually. There are only two possible grades: “Acceptable” and “Incomplete.”
- If a student gets an “Incomplete,” he/she must either get a similar problem correct on a later quiz OR come to my office and have a make up quiz. There is no limit on the number of redos (save for the time limit of “end of the semester”). There is no penalty for missing a quiz question (except that you have to make it up later).
- The questions are split into two types: “skills” (e.g. taking the derivative of ) and “concepts” (e.g. demonstrating understanding of where the definition of the derivative comes from).
- The students need to get an “Acceptable” for each skill topic three times; once this has been done, he/she can skip all later questions concerning this skill topic.
- Similarly with concept topics, but they only need to do it twice.
- A student earns a C for the course if he/she gets “almost all” of the “skill” requirements met.
- A student earns a B for the course if he/she gets “almost all” of the “skill” requirements met and roughly half of the “concept” requirements met.
- A student earns an A for the course if he/she gets “almost all” of all questions requirements met, “almost all” of each topic requirements met (so he/she must have no weaknesses), and do a project.
There will be a quiz once per cycle (roughly a week), as well as “team quizzes.” These team quizzes are done by choosing one member at random (once they feel they are ready) to do the quiz for the entire team. If the chosen person gets it correct, all students in the team get credit. Otherwise, all students on the team will have to redo it at some point (which they would have to do anyway).
There are other details. For instance, students are only allowed to redo one problem outside of class each day (for my sanity), there will be a midterm and final averaged in (for political reasons), but this is the gist.
I have been working on this post for two weeks. I am going to post it now;I wish I could spend more time on it, but I need to get on with my life.