An Apprentice in Mastery (Part 1)

In addition to creating a new course this past semester, I also took on another creative teaching endeavor by implementing mastery-based grading in one of my courses for the first time. I’m going to write a short series of posts talking about my approach and my experiences:

  1. Motivation guiding my design (this post)
  2. Implementation of my system
  3. Reflections and moving forward

If you’re reading this, I’m not assuming you have any background in what mastery-based grading is, but I don’t want to spend too much time explaining the various components because they will mostly be revealed through my reasoning and approach. However, it is important that I would describe the key tenets of such a system as (a) assessment and grades are based on the understanding (“mastery”) of learning objectives rather than a traditional numerical scale, and (b) there should be a way for students to have additional attempts to demonstrate mastery.

So why did I want to do something like this in the first place?

  • Giving grades more meaning. When you give a final grade in a course, how does it correspond to what the student actually has accomplished? For example, in a traditional grading system a B could translate to (i) getting everything correct the entire semester but missing a few assignments, (ii) getting B’s on the vast majority of assessments, or (iii) having a wide variety of grades that average to a B in the end. A mastery-based approach treats a course like a license or certification in that you have to demonstrate certain skills to earn the license. Grades then translate to how many of the skills you have demonstrated mastery in and no matter the grade, you will have a tangible list of objectives that you have learned as a result of taking the class.
  • Student mindset. It is always important to attend to students’ mental dispositions and a mastery-based system (in theory) has the ability to make positive impacts on the mindset and anxieties of our students. It is one thing to preach the value of a growth mindset and it is another to align your practices with this value. Allowing students additional opportunities to demonstrate their understanding of learning objectives embodies the growth mindset philosophy of encouraging productive struggle and that learning (especially at the level of mastery) can take different amounts of time for different types of learners. In addition, such a system would hopefully reduce test anxiety where students would know that it is okay to not understand everything at the time of an exam and that they won’t be penalized or judged as inferior for attempting some of the objectives at a later time (and hopefully with additional motivation to achieve mastery).
  • Discourage academic dishonesty. When reading perspectives of others who have utilized mastery-based grading, you probably won’t see this as a reason to employ the system, but I try to be as transparent as possible about my own thought process. In math, homework traditionally counts for 15-30% of your final grade and in my opinion, this only encourages the academic dishonesty that is rampant today (this could be a whole blog post on its own). From a student’s perspective, imagine sitting down the night before a homework assignment is due and not knowing how to do half of it. If the homework is graded for correctness, you would ask a friend for the answers or Google them too, wouldn’t you? For the record, I’m not faulting the student at all for doing this, especially given their stress associated with courses, extra-curriculars, and social life. So academic dishonesty is probably the wrong term, but why use a system that encourages a strategy that is not conducive to making progress towards actually understanding course content? I think it is fair to say that we would like final grades to be (as much as possible) associated with a student’s level of understanding and not the understanding of their friends or people online. We should be encouraging the use of these resources as a means of developing understanding rather than having students feel anxious because they are “cheating” on their homework.
  • Instructor time? In reading perspectives of others, “saving the instructor time” is a commonly cited reason for implementing a mastery-based system, but in my opinion, this isn’t a reason to make a pedagogical change. Yes, as professors we have a lot on our plates and would like to be more efficient, but I would never prioritize this over doing something because I believe it will benefit students in one way or another. In reality, any changes we make will take a lot of time initially and take less time as we gain experience and fine-tune our approaches. I will be expanding on this in one of my next posts, but for now I will say that my implementation this semester added time on the front end in determining objectives, took less time to grade during the semester, and added time in administering retakes.

With these motivations in mind, here were the initial principles I had in mind for designing the structure of my mastery-based grading system:

  • Separating procedural and conceptual thinking. I believe that being explicit about the cognitive demand level we expect from our students is important and I wanted to honor the way in which the mathematics education community differentiates procedural (following steps) and conceptual (displaying reasoning / non-routine problems) thinking.
  • Simple and transparent. The last thing students want is a complicated grading system, especially when it is different from what they are used to, so I wanted to make sure that it was easy to understand how their understanding of objectives would translate to a final grade and that they could see (online) at all times which objectives they have (and have not) mastered.
  • Retake system. This is a key feature of mastery-based grading, so I knew I wanted to incorporate a retake system with a personal goal of trying to find the “sweet spot” of not having too few opportunities for retakes (wouldn’t alleviate the test anxiety issue) and not having too many opportunities for retakes (could take away initial motivation to learn).

I also wanted to figure out a way to incorporate my existing assignments into the system, either as a category or as their own objectives. This is a good time to mention that I did this in a course I had taught the previous two semesters and I think it is much easier to go through the challenging process of identifying learning objectives if you have taught the course before so that you are closer to the content and student outcomes.

In my next post, I will talk about the course, the specifics of the mastery-based system that I created and used, and how the system played out during the semester. Thanks for reading!

The Journey of a New Course

As yet another semester comes to a close, this one was even more special than usual because my vision of creating a new class finally came to life. Considering I assigned my students a final reflection assignment, I thought I’d share my thoughts and experiences as well.

First some background if you haven’t been following along: the goal of creating an entire class on redistricting that authentically uses math in the context of a relevant (and often contentious) political issue was almost two years in the making. In my last semester at UConn (Spring 2018), Adam Giambrone (now teaching at Elmira) and I tried the “let’s throw some things [content] at the wall [students] and see what sticks” approach to teaching this topic which for my money is an underrated approach to education – you don’t always need to have a plan! (More on that later.)

Anyway, upon being hired at Trinity, I was connected to Jack Dougherty who made me quickly realize that my goal of creating such a class was far from a dream, in fact it was exactly the sort of thing the institution wanted and that it had the potential to be brought to life even more through community / government partners. I was also fortunate enough to have the support of my department (Mathematics) who easily could have asked for something more concrete for a new course offering.

Through the help of Jack and Megan Hartline (who both do an amazing job organizing and supporting Trinity’s Community Learning Initiative) I was put in touch with various local professionals who had some connection to redistricting or politics and voting in general. This led me to a government employee (who would prefer to remain anonymous) who is simply incredible and whose knowledge and passion further inspired my own. Our first meeting is when my vision started to feel real for the first time.

Ok so I had a government partner supporting my vision and the course was quickly approved by the school – with the Political Science and Public Policy & Law departments even counting it towards their major! – and my passion for the topic and for education were always there, but creating a class from scratch isn’t easy. To be honest, up until the beginning of this semester I had nothing prepared beyond a list of potential topics, an idea for the final project (having them redistrict Connecticut as authentically as possible), and some materials I developed and used for a 2-3 week unit on the topic in my general education “Math and Politics” class.

Back to not having a plan…here’s the thing: It wasn’t that I didn’t know what to do and it certainly wasn’t laziness. For me part of education is being responsive to your audience and I wanted to gauge the mathematical and political science background of my students and use that to guide my instruction. This was especially important because this was my first time teaching a subject area outside of math or education and I had no prior experiences to rely on to somewhat estimate the level of the students.

As you might imagine, this “approach” led to a lot of late nights making lecture slides, handouts, readings, etc. I always joked with the students that twice a week I felt like one of them working on a class presentation assignment. Creating a course organically and in real-time is not something I would recommend (especially when you have two other preps in the same semester) but it did keep me very close to the content and to current events. On that note, thanks to the state of North Carolina for providing excellent content for this class!

What ended up happening is that effectively all of my course content was front-loaded into the first eight weeks (out of 14) of the semester. At that point I think both myself and the students (we affected each other) sort of “ran out of steam” when it came to content. There were definitely a few other related topics I could have covered, but I’m confident that I covered all of the crucial content and in a way that the students successfully grasped.

At the same time, I was communicating with various stakeholders to create and schedule the authentic learning experiences that I believed were absolutely essential for the course. Managing these logistics takes time and naturally forced these experiences into the second half of the semester, but I think this worked out because students went into the experiences with a strong foundational knowledge of redistricting policy and the associated mathematics.

What experiences am I referring to? In addition to two excellent guest speakers in the first half of the semester, there were three experiences I was able to put together and add (in my and the students’ opinion) incredible value to the course. First, I’m extremely thankful for the Caliper Corporation that generously gave my class a license to the software program Maptitude for Redistricting, which is the actual program used by a majority of the states. Thanks to Cheryl Cape and others in Information Technology, we were able to put together a “Redistricting Lab” in the library for students to grind away and act as independent redistricting commissions to propose a new State Senate map for Connecticut. There were certainly challenges and a learning curve for all of us in operating the software, but it was more than worth it for the authentic experience and the ability to empower students as some of the most qualified individuals for future redistricting in any state.

Second, I can’t thank State Representative (and Chief of Staff to Trinity’s President) Jason Rojas enough for leading a behind-the-scenes tour of the State Capitol and Legislative Office Building. While the focus was not directly on redistricting, so many students reflected with incredible positive feedback about the experience and how it humanized the people working in the government. And it’s not every day you get a chance encounter with the Governor!

Third, I was hoping that students could get an even more personalized meeting with elected officials involved in the redistricting process both to add anecdotes that I or any reading wouldn’t be able to provide and to humanize the process as well. Fortunately with Jason’s help, I was able to have smaller groups of students meet with two former Democratic Speakers of the House (Chris Donovan and Brendan Sharkey) and a former and current Republican Minority Leader of the House (Themis Klarides and Larry Cafero). I am thankful for each of them giving some of their time to our class and I was personally involved in two of the four meetings and I know I learned so much more from them than in researching my lecture slides.

I want to clarify that this class isn’t about me. Anyone can have an idea or vision for a new course but without interested and engaged students it’s simply not possible. This is a good time to mention that registering for this new class was by permission only and that the initial interest of my 22 students (from an initial cap of 19) actually did carryover throughout the semester. I can only imagine our collective attitudes toward education if all of our classes were this way.

With that being said, I do want to share a couple of personal anecdotes. First, I don’t have any formal background in Political Science (I completed half of a minor as an undergraduate!) and I never pretended that I did. I joked that I was a “Math professor masquerading as a Political Science professor” and it was no secret that the advanced Political Science majors were more well-spoken about the field in general than I was. And that’s ok! There’s something to be said about learning together and using our unique knowledge as individuals to advance our collective knowledge. As for my own knowledge, I certainly noticed a shift as the semester progressed. Thanks to the students, the guest speakers, the legislators, and hours of research in preparing lecture slides and activities, I noticed myself transition from someone who is knowledgeable and interested in redistricting to someone who is an expert in redistricting (particularly in the context of Connecticut).

My final takeaway: In looking back, I’m proud of what I was able to provide my students both in terms of content and experiences in my first attempt at doing something like this. It’s really amazing to think back to an initial vision and realize everything that contributed to its reality. Thanks to my experiences and my students’ input, my head has been spinning at all of the tweaks I can make to improve this class when (not if) I teach this class again. I firmly believe that this type of class represents something we should do more often in education, but clearly it’s not easy. Most importantly, we can’t do this alone. It takes (a lot of) communication and collaboration with others at your institution and the right people in your community. It takes others to trust and support your vision. It takes the right students. It takes the Supreme Court making a key ruling two months before the semester (just kidding, but it does help). It takes a belief that math truly matters. And finally, it takes a commitment to the philosophy that the sharing of perspectives and experiences are at the core of education.

For more information about the course content, see my page about the course.