Rebooting the final exam

Rebooting the final exam

It's almost final exam season for a lot of us. As that time rolls closer, it makes me think about something wonderful that happened during the pandemic in 2020: A lot of faculty just opted out of traditional final exams. We took a look at our students and at ourselves, ran the cost/benefit analysis of having a traditional final exam, and simply said — You know what? It's not worth it. And it turned out fine. When I was department chair last spring I encouraged our faculty not to give traditional final exams; I myself did not give a traditional final exam once I was back teaching last fall. To date and to the best of my knowledge, the number of complaints or bad situations that this has led to, is zero.

Based on some of the discussions I've been involved with lately, it seems like many faculty want to go back to traditional final exams this time. Whether that's just simply forgetting how well things went not having traditional final exams, or an outgrowth of the pernicious desire to "get back to normal", I'm not sure. But we'd all do well to continue the reverse pilot program we started in 2020 and re-envision what a final exam could be, if indeed we do them at all.

Why do we give final exams? I'm not the first person to ask this question by a long shot. There seem to be three main schools of thought on this.

  1. To ensure that students do daily work.  The idea being that any student can do well on short-term, limited-focus tasks like weekly quizzes or homework, but only a student who has really consistently applied themselves through the semester can do well on a final exam.
  2. To serve as a focal point for pulling all the threads of a course together. All those limited-focus tasks are, well, limited in focus; whereas a final exam is a chance to have all the concepts of a course together in one place, perhaps the only time when this happens.
  3. To boost students' grades or to punish students with grades. The thought goes that if you enter into the final exam session with a borderline D or C grade, then the final exam can pull it up to a C or B. It's actually a gift! But it goes both ways, because students who aren't really prepared will have their grades adjusted downwards, and rightfully so, by a bad grade on the final.

Reasons #1 and #3 go together and are equally flawed, although reason #1 is at least somewhat understandable (whereas #3 is just appalling and should never be espoused by a professional educator). The reason #1 doesn't work, is because of the prevalence of false negatives and false positives in traditional points-based grading systems. You have students who really have shown consistently good work during the semester who may just have a bad day at the final exam (exponentially more likely now during the pandemic). You also have students who have never really shown excellence on anything, who for whatever reason can pull off a miracle on one exam; nobody believes that this one exam outweighs the body of work that the student has created during the semester, but their grade gets boosted anyway.

And note that if you are using a mastery grading approach, reasons #1 and #3 are no longer sufficient reasons to have a traditional final. As I've used mastery grading, I've realized that my students are reviewing older concepts on a constant basis through revisions and retesting. By the time we get to the end, any information on their mathematical skill from a traditional final would be redundant with of the mountain of data they've provided me already. There's just nothing to be gained from having a traditional final.

Reason #2 is the only one of these that makes sense. A final exam has the unique ability to have students make cross-course connections and provide a 40,000-foot vantage point on the entire course experience. If you're going to give a final exam at all, this should be the purpose for it. But a traditional final actually doesn't usually do this; in my discipline of mathematics, a traditional final doesn't make connections at all but rather is just a grab bag of problems to work, that come from all over the course but just sit aside each other, and the conceptual connections between them are left to the reader.

So I'd like to propose that all of us this semester, if we are giving a final exam at all, give one that is quite non-traditional, that has as its sole purpose to prompt students to make explicit connections between ideas in the course and articulate just what the course was all about.

Here are some ideas for what your students might do on a final exam like this.

  • Create a mind map of the course or a portion of it. Use a tool like LucidChart or MindMeister to make a connected map of all the concepts from the course, or a single chapter from the book.
  • Write a new catalog description for the course. The university has decided to rewrite the entire course catalog and has contracted you to write the description for this course. It has to be brief, but interesting and list the major topics that are covered and why we're covering them. You have 200 words. Go!
  • Write a letter to an incoming high school student who will be taking the course next semester. A kid from your high school is taking this course in the fall and has written you to ask what it's all about and what they need to know. Reply to that kid with a detailed overview of the course, written in the right tone (encouraging, optimistic) and pitched at the right level.
  • Write a short essay about: What are the main ideas of this subject, and how do they all connect together? For example in Calculus, the main concepts are the limit, the derivative, and the definite integral. That produces three different possible connections between those concepts. What are they?
  • Write about their metacognition. What did you learn about failure in this course? What did you learn about problem solving? About using technology to learn math? About managing your time and commitments? About how to learn things?
  • And perhaps the best final exam item of all: Leave one piece of advice to the next round of students taking this course. I asked this of my Calculus students last fall, and their replies were overwhelmingly wise and detailed. They were so good that I wrote them up and published them here. I had my Calculus students this semester read these in the first week of classes and they've been a focal point of discussion all semester.

The benefits of this kind of final exam are numerous. First, there's almost no chance of cheating or plagiarism because these items are compelling to students and involve them on a personal level. The items are also simple, although not always easy, so there's a low threshhold for getting them done and a low likelihood of making a catastrophic error. They are also a lot easier to grade than traditional finals; they are actually engaging and you find yourself wanting to grade these. And maybe most importantly, they actually produce something of value for the student, namely a solid idea of the big picture of what they just accomplished.

This isn't just advice – it's what I did in the Fall and will be doing again in this time. This is the final exam I gave to my Calculus class. You'll see it's a mix of the questions I listed above with a few more I didn't list. I added an additional wrinkle that on any of the items on the exam, students could submit written work or a video on FlipGrid. Those videos were the best idea I had all semester. In my mastery grading system (syllabus here), students' base course grades (A/B/C/D/F) are already determined coming into the final exam; the only impact the final exam has on the course grade is to potentially add a "plus" or "minus" to that base grade. (You are free to copy or modify this exam if you want; just give attribution according to the Creative Commons license.)

If you've already committed to giving a traditional final exam, one way that you can work in a non-traditional exam into your plans is to replace some of the items on the traditional exam with some of the ones above. Or, give students a choice between the traditional and non-traditional final exams along with a different weighting system if you don't want the non-traditional one to count as much. (If your traditional final is 20% of the course grade, offer the nontraditional one at 5% of the grade and shift the other 15% to more traditional assessments. Students are opting into this so it's their choice.)

Robert Talbert

Robert Talbert

Mathematics professor who writes and speaks about math, research and practice on teaching and learning, technology, productivity, and higher education.