I’ve been meaning to write a post about my standards-based Linear Algebra course for months, but the hectic schedule of the semester has kept me away from this task until now. Today was my last “content” day of Linear Algebra — we have two more classes remaining, one for a test day and another for a re-assessment day. This seemed like a good time for me to take ten minutes to gather some thoughts about how the semester went.

**Standards List for Linear Algebra**: https://www.overleaf.com/read/kycvnvzdvksw (Availablle on Overleaf, which is awesome and I can’t recommend enough)

**What Went Well: **We ended up having 20 standards this semester. This is a little more than one per week (our semester has 16 instruction weeks). Overall, I think this was a good number of standards to have, and I’m happy with how they turned out. I tried to group them again by “Big Questions” to have a reference frame of what it is we’re trying to do in the course. Oddly, we tackled “Big Question 5” last (on inner product spaces), but I kept it numbered like that because of the textbook we are using. My basic idea was to come up with a Big Question for each chapter. For some stuff, this worked well (e.g., eigen-everything) but for other stuff we didn’t cover a whole lot (e.g., determinants).

I think I’m doing a better job of the sales-pitch aspect of a standards-based course. Many of my students expressed to me at various times that they really appreciated the ability to improve on past performance and that they were under less stress than in a traditional class. In a recent class meeting, a student wasn’t happy with the performance on the last quiz, and exclaimed, “Oh, thank goodness we have an exam on this soon!!!” [I asked the student for permission to share this quote.] I think this is one of the best things about my SBG courses — students really want to take an exam just to show what they know, whether that means showing mastery of current material, or showing mastery of material they struggled with earlier in the course.

My SBG approach definitely has some pros and also some cons, but the way it has shaped my interactions with students has always been a huge positive. Even with the sticky details that need to be cleaned up from this semester, I can’t imagine going back to a traditional grading scheme.

**Room for Improvement**: This semester was a little odd because we lost several days because of weather. Tropical Storm Hermine hit us, and we lost almost a week because of Hurricane Matthew. The re-shuffling of the academic calendar created a speed-bump that I never really recovered from. I hope next semester our calendar runs much more smoothly.

In particular, I am wondering about how I can improve in three areas. First, I want to expose my students to more applications of the material we are learning. I felt rushed all semester (related to shuffling of course calendar, maybe?) and so I didn’t ever feel like I had time to fit in cool applications, or videos on where people use this stuff “in the real world,” etc. A colleague teaching the same course required students to do group projects on applications of linear algebra & I believe the students presented them to the class at the end of the semester. This seems like a great idea, but I’m always nervous about assigning group projects because I remember how much I hated doing them as a student. It’s something I should consider more.

Second, all of my course standards are weighted equally. This has served me well in Calculus II and in other courses. But in Linear Algebra it became a little tricky, because part of what I was aiming to do was to have my students attempt to write proofs of mathematical statements. (The only mathematical background required for entry into my course is Calculus I, and that is for “mathematical maturity” as opposed to content reasons.) So some of my students were concurrently taking our “Introduction to Proofs” course, but others weren’t taking this course and won’t need it for their major. In general, my idea was to ask them to prove elementary results they had already seen in class. The problem I encountered is that a “**write a proof**” standard is really tough. How do I let them have multiple attempts? Is it okay if they end up never being able to prove stuff about, say, matrix inverses, but they can prove stuff about, say, subspaces of a vector space?

One idea I’ve had is to have the students keep a “Proof Portfolio” and grade it as either “complete” or “not” at the end of the semester. I’m sure there’s some specs-based approach I could implement for this, but I haven’t worked out what it would look like yet.

Third, trying to put together all my course materials on the fly is hard. All of the time, I was working on: Plans for class, writing exams, writing quiz questions, writing reassessment questions, putting together online homework, meeting with students for several hours a week outside of class, updating the list of standards regularly… I would admonish my summer-month self that I should do more of this “in my free time” before the term begins so I’m not under such a time crunch during the semester. But I am not great at this because I like building a course as it goes, as I see how the students are responding, as I see how the pace of the course unfolds, etc. Having to get all this done ahead of time would probably help me out a lot, but it’s tough to do. Thankfully some of my stuff from this semester can be re-used when I teach Linear Algebra next semester.

My ten minutes are done so I have to move on to the next task on my queue! I hope to add more later.

Thank you. I don’t do SBG exactly, but I do let students retake quizzes in my office (more than 1 retakes usually allowed) and tests at a prearranged time when they all can do it. So they get two chances on tests.

For proofs, I required 3. There was one on each of the 3 tests (which could be retaken once). And there were 2 more on the finals. So there 10 total for them to attempt. The ones on the final might come from early material, but were likely harder than the ones on Test 1. The 3 best proofs counted as one test.

Hi Kate,

I’m currently looking into SBG and it seems to be a wonderful way to track student learning. However I’m wondering, how do you keep track of your students’ frequently changing scores on each of the standards? I saw the screenshots of your gradebook that you posted, but are you constantly making new copies of it to keep a record of older scores?

Hi Francesca. Basically, I have one gradebook, and for each standard there are three columns since I’m using the scheme that the current score is the average of the last two attempts. So I have a column for (recent attempt), a column for (prior attempt), and a column for (current average). Once a student re-attempts a problem, I just delete (prior), move over (recent) and recompute (average). So I am constantly deleting old data from my gradebook.

This seems like it would be a lot to keep track of, but in reality it isn’t too bad. 🙂

Wow, thanks for the immediate reply! I’m co-facilitating a workshop this week on grading for faculty at Boston College and am using excerpts from the Calculus II syllabus you posted (and encouraging everyone to visit your blog!) as a case study for them. I expect some questions about tracking grades and other practical matters, so having your response will help.