I’ve been asked for my thoughts on how my semester teaching a three-week sophomore-level linear algebra course went, particularly to answer the question: “Is mastery grading a reasonable system to use during a minimester?” The course ran daily for about three hours each day (so the equivalent of one regular week of class per day). For me, mastery grading is tangled with my use of a active pedagogy called Team-Based Inquiry Learning, so this post will address both.
Briefly, my mastery grading system tracks evidence of student understanding of 24 course standards. Students may earn up to two checkmarks per standard by submitting a completely correct solution for a relevant exercise, via daily quizzes (with at-home revisions allowed for very minor errors, but they still must resubmit a completely correct solution). Grades are determined purely upon the number of mastery checkmarks earned during the semester.
Also briefly, Team-Based Inquiry Learning is a carefully scaffolded sequence of activities designed to have students discover as much of the mathematics as possible on their own. This includes a readiness assurance process to bridge the gap from (perhaps forgotten) prerequisite material, and each activity is discussed in teams (or one team in the case of this small class) before responding via multiple choice or a written solution on a vertical whiteboard.
Less briefly, more details can be found on my course syllabus here: https://prof.clontz.org/classes/2019/05/ma237/.
More briefly than anything, here’s my bottom line. All five students passed with a C or better (possibly B or better depending on how their finals turned out), and none of my students reported any complaints about the course structure to me, so I would highly recommend the use of active learning and mastery grading to any instructor of a mini-semester mathematics course.
Student Reactions
I’ll begin with some student reactions I gathered this morning. These should be taken with a grain of salt: I only have five students this semester, and I asked them for their feedback in person just moments before their final. I’ll get the anonymous evaluations sometime this fall; if those indicate any feedback drastically different from what I write below, I’ll update this post.
When asked for their general feedback on how our “team-based whiteboard activities and checkmark-based mastery grading system” supported or conflicted with the three-week mini-semester, the responses were entirely positive.
- Students appreciated that I gave daily mastery quizzes that allowed them to add checkmarks to their progress report. This gave them incentive to keep up with the daily grind of new material.
- They remarked that the format was the reason that every student had perfect attendance (with the slight excpetion of one student who was an hour late due to a flight delay). It wasn’t said directly, but I suspect the subtext here was that they would not have felt encouraged to attend class daily without the daily quizzes to improve their grade, or if the class was just three hours of me talking at them.
- Students specifically mentioned that they really appreciated being kept engaged in the course via multiple choice activities and working out problems on the whiteboard together. While ungraded multiple-choice activities may not seem very deep, I should emphasize that the point of these is not to find an answer, but the discussion that leads to the answer. I made a (faux) big deal about not confirming their thoughts until they committed to a specific choice, allowing them to come up with many of the big ideas of the course on their own through discussion of my questions.
- Students suggested that they learned more in this intense three-week format than they would have over fifteen weeks. I suspect this is a product of mastery grading, which gave them daily opportunities to either prove mastery, or recieve my feedback on how they could improve on each standard assessed.
Adjustments and Non-Adjustments
I did not run the course exactly how I would have run a fifteen-week semester, but I also probably didn’t change as much as you might think.
First thing to note is that I didn’t change anything about the TBIL active learning materials that I coauthored with Drew Lewis, even though they were designed for a 15-week course. I usually spend two 50 or 60 minute periods each week on covering material via those activities; so instead I just spent about two hours each day this semester covering the same material, with the rest used for assessment of mastery.
Since I had only one team, I didn’t have to spend time leveling weaker teams to catch them up with the stronger teams. Also, the team I had this semester was stronger than average. This probably helped: I actually covered all the core material for the course in this way using only 12 days of class (e.g. the time I’d have during twelve weeks of a normal fifteen-week semester). The rest of the time was used for covering applications of linear algebra, additional time for assessing mastery, and review.
I usually offer “office reassessments”, and did this semester at first. These are untimed reattempts to master standards that I stopped asking about on daily quizzes, available on a limited basis to students who were active in the course and who showed me that had done some limited homeowrk.
However, after a full three hours each morning, I found the students weren’t super interested in returning after lunch for more assessment of their linear algebra skills. So I asked them if they’d rather I just offered “requiz” opportunities, where they completed the same requirements, but instead of an untimed attempt in my office hours, they would be given an additional exercise for that standard to be completed during the usual quiz period. They said they’d prefer that, so that’s what we did. I ended spending less than an hour all semester in “office hours”.
Even still, I had far less requests for reassessments/requizzes than I usually do during a semester. I suspect this is because that a common reason for reassessment is distraction from other classes (e.g. a big exam) that cause a student to punt on preparing for certain standards at certain times. This isn’t an issue during a minimester where the students shouldn’t be taking more than one course.
I definitely provided a larger percentage of in-class time for assessment than I usually do in a semester (which also probably impacted the reduced need for reassessments). Partially this is because I could due to the rapid progress of my team of students. But even still, I would often let students go 15 minutes early because they had blown through the material, so with a larger class or a class that needed more of my direct support I’d keep that ratio of in-class assessment time. Since I used mastery grading, assessment isn’t a burden. It’s either an opportunity for practice, feedback, and reflection, or it’s an unloading of burden because they were able to demonstrate mastery and check off something on their progress report.
Conclusion
Well, I wrote it at the end of the introduction. :-) For some added context, my wife works at an elementary school, so there’s added incentive for me to teach during May rather than June or July. But I think the semester was a huge success regardless, and I hope to offer the course again next May.