First steps in standards-based grading

I’ve written before about my experience teaching my graduate course this semester, but I haven’t talked about one big experiment I tried: working towards standards-based grading. I started hearing about different implementations of this over the last year or so, and thanks to a Project NExT panel at the joint meeting from Eric Sullivan and Benjamin Braun (links go to their slides), I thought I’d take the plunge.

The idea behind typical standards, specs, or mastery-based grading is to track students’ progress with mastering skills directly, instead of filtered through a weighted average of percentages on assignments. In addition, students have multiple opportunities to improve their work and demonstrate mastery of these skills. Final grades are usually assigned based on how many skills have been mastered.

I didn’t do a full implementation of standards-based grading this semester, but I did get a good start. I skipped the really hard part of this – listing all the learning objectives for my students – because I’d never taught the course before and some of my goals for the class felt kind-of nebulous. This class is algebra for teachers, so a lot of the course is about teaching students to think abstractly, generalize, and write simple proofs. Writing these goals in simple, assessable terms seemed like too much work for a first attempt.

Instead, I started with the easy part of standards-based grading: the actual grading part. I graded each homework problem on a scale of 0-2. A 2 is mastery. Maybe not completely perfect, but it’s clear that the student has demonstrated that they have the skills I’m assessing. A 0 is work that is completely on the wrong track, and 1 is somewhere in between – maybe undeveloped or incomplete, but with a good start. I liked this scale a lot, because it reduces the variance in my grading: if I try to grade a problem out of ten points, the difference between a 5 and a 7 might depend more on my mood than on the actual quality of the work. But the lines between a 0, a 1, and a 2 are almost always clear.

I had a very small class, so I let my students resubmit their work as many times as they wanted. Others put a time limit on resubmissions to prevent a glut of grading at the end of the semester. But the idea is that students can keep refining their work until they are proficient at the skills we want them to learn. And it forces students to learn from their mistakes instead of just shoving a bad grade in the back of a folder and never thinking about it again.

I assigned final grades based on how many 0s, 1s, and 2s students had by the end of the semester. An A was more than 95% 2s, a B more than 85% 2s, C more than 75%. Students knew exactly what they needed to do in order to get the grade they wanted and (most) would resubmit accordingly. One student was terrified that she was going to fail in the beginning of the semester, but after working with her extensively she ended up bringing her grade up to an A.

I have to admit, this was not an unqualified success though. These were graduate students, most of them current teachers with families, so I was very lenient on deadlines. I figured everybody would turn in the required resubmissions by the end of the semester without a lot of hand-holding. That was not the case. If I had this to do over again, I would have been more proactive and made sure that every student knew if they were underperforming.

I will definitely be doing this again for my smaller classes. The simpler scale saved a ton of time and effort, so the re-grading didn’t feel like that much extra work. Next time I’ll even try to align my assignments with learning objectives. I’m also interested to see how undergraduates respond to this method – my guess is that they’ll jump on board a little more easily, but I’m not sure. I’ll report back next year.

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Constructive Summer

The first week after finishing a class I am usually kind of a wreck. I stress through the end, turn in the grades, and collapse into a heap. Then there’s this weird time when I want to relax and recreate, but I don’t quite know what to do without all the responsibilities of teaching. I dream all semester about having nothing that needs to be done for tomorrow, but when it happens, I feel vaguely anxious and at loose ends. So it was a surprise this summer when that didn’t happen at all (not yet, anyway). I feel great! What was different? I think it was that, instead of determining to do absolutely nothing for a while like I usually do, I scheduled a bunch of research related meetings as soon as teaching ended. This turned out to be a great choice.

Often, serious research just sounds too daunting as I finish teaching. Probably because so much of my math research life involves being stuck. Things are going along okay, until I hit a snag. I think I can fix it one way, it doesn’t work, I try something else, it doesn’t work, and at some point I feel truly stuck. Then there is nothing to do but put it aside for a while. Maybe when I pick it back up I get a new idea, but it’s a little scary to pick it up again because I’m so stuck on it.

Skype meeting fun! Me, Katie Haymaker, and Gretchen Matthews in a Skype meeting this week.

Skype meeting fun! Me, Katie Haymaker, and Gretchen Matthews in a Skype meeting this week.

I was willing to jump right in this summer because I actually had a few projects on which I wasn’t totally stuck (yet). The first is a collaborative project in coding theory with Katie Haymaker and Gretchen Matthews, which we’d talked about briefly in person but hadn’t had time to flesh out. Gretchen came to visit for few days right after finals week, and starting with this meeting set a great tone for me. All that energy I had been using to grade papers could suddenly go in to math. This was a brand new project, but we were starting with an existing construction and could get going right away by computing some examples. We all brought different backgrounds to the project, so what was basic for someone would be really interesting and new to someone else. By the time we’d done a bunch of examples, we had some ideas of how a paper could work and realized the kinds of things we still needed to work out. Spending several days together got us through the confusing, unsure parts. We got to ask each other questions that would have been hard to figure out alone but were often very easy for the others to answer. We got to a place where we could really start writing up our work and each add some new ideas. Score one for collaboration with great people who know very different things.



Another project I’ve worked on this summer is an expository paper, arising from an email I got a few years ago from a friend’s mom (old blog post here, follow up here). She was asking a question about passing quilts in her quilting group. This simple question led me to learn a lot about a certain kinds of Latin squares. I’d been thinking about this for a few years and finally had started a paper in the fall (again, with my colleague Katie Haymaker), but we just hadn’t had time to do anything with it for months. By the time teaching ended I was just really looking forward to it. This is my first expository paper, and it is fun to work on because I have found that I can’t really get stuck! There is investigation, organization, and writing, but there is no way to go into a mathematical black hole. Unsolved problems are just another section of the paper. Score one for expository papers.

This is the row-complete latin square modeling the above quilts.

This is the row-complete latin square modeling the above quilts.

Finally, I spent several days working on a long-term project with friends in Colorado. I had been pursuing a particular line of thinking for the last year or so, proving small lemmas and inching closer to proving a conjecture that we had made. One of my collaborators did yet another literature search, and we started reading some new papers. We made some great strides in understanding! We also discovered that our conjecture had already been proven by others. This could have been discouraging, but it fact it was great that we found this out. First of all, our conjecture was totally true! Score one for us! Also, I would have spent many more hours following my same line of inquiry, never realizing that we could just move on to the next stage of the project. Of course, that stage is hard, but hey, at least we still have all summer.

Here’s what I’m taking away from all this:

  • Doing research at the beginning of summer can be really rewarding, even though it might seem daunting after a long and difficult semester.
  • Again, I am reminded that collaborations really work for me. They are the most fun way for me to do math.
  • I should always have at least one project that I can actively work on. By “actively work” I mean compute examples, write background, something concrete that doesn’t require me to have some enormous idea to make any progress at all. That way I can always pick up this project when everything else sounds too hard.
  • Expository papers can be a good way for me to organize learning new math. Nobody has agreed to publish our expository paper yet, so it may have no real payoff-towards-tenure, but it was still really fun to write and gave me a great sense of accomplishment.
  • If I can’t figure out what to actually do on a problem, it can pay off to keep searching the literature relentlessly. Maybe somebody has already solved this awful part of the problem.

This has been an excellent math summer so far. However, just so I don’t give the wrong impression that I gave up on my dream of doing nothing productive: I have also binge-read five wonderful novels, watched two full seasons of 30 Rock, listened to a lot of music (including some old Hold Steady albums, hence the blog title) and gotten some massive bruises roller skating with my sister. I have still been collapsing into a non-mathematical heap; just for smaller periods. Hooray for summer!

My summer reading so far!

My totally non-mathematical summer reading, so far.

Any thoughts on the best parts of an academic summer, or the best ways to use it?

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Graduation (1 of n)

Many of the Hood College new faculty cohort.

Many of the Hood College new faculty cohort.

The year flew by, and my first commencement as a faculty member is over. We sat in the hot sun in our hotter robes as the Hood College Class of 2016 paraded across the stage. I hadn’t taught many Seniors this year, so most of the faces were unfamiliar, but it was fun watching the students beaming as they shook the college president’s hand. What I didn’t expect was all the students wanting photos with the department after the ceremony. It was really touching to see how much they valued my colleagues time and patience. And luckily the clouds had moved in a bit by then so nobody passed out from the heat.

When our students complete a math course at the 200 level or higher, they receive a button that represents the class. They’re simple and a little corny, but the students love them. A lot of these buttons live on student backpacks for years, and then get worn on their robes or mortarboards at graduation. It’s a nice symbol of the progress they made during their time here, and it really livens up their regalia.

One of our students with her impressive collection.

One of our students with her impressive button collection.

This wasn’t the most productive semester of my career, but I hit a good number of my targets. I applied for and received an internal grant to do summer research with two undergraduates – ambitious freshman I had all year for their calculus sequence. We’ll begin working in June, and I’m sure I’ll be posting about that later. I’ve never guided any undergraduate research projects before, so it will be a learning experience for all of us. I got accepted to some other summer programs that I’m really excited about – one for inquiry-oriented curriculum, and one for developing online interactive resources. I chugged away at a couple of papers and one’s starting to get close to the finish line. I implemented standards-based grading in my graduate class, which was wildly successful with some students and much less so with others. I dipped my toes into helping at my MAA section meetings, and got nominated to a few committees, both on campus and in the wider mathematical world. And I was on a couple of masters student committees. Pretty much checked all the expected boxes for my first year.

I’m thinking about all this not because I’m independently reflecting on my year like everybody says you’re supposed to. We have a short annual report due soon, in which we all have to express our accomplishments as eloquently as possible and explain our goals for the future. It’s not nearly as big an undertaking as a mid-tenure review, and these reports should help me organize myself once that time comes, so I definitely see the value. It’s also nice to see how much I really got done all in one place, especially after what felt like a somewhat lackluster semester. I think a lot of us focus so hard on the goals we didn’t meet that it’s easy to ignore the ones we did. I can’t say I’m thrilled about the paperwork, but I am glad my institution requires us to brag as hard as possible about ourselves at the end of every year.


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