Today was Day 1 of the Great Online Migration, in which my department moved our entire Winter 2020 semester catalog online through at least March 29, probably through the end of the semester. I've been checking email and in Zoom meetings with people all day, and our faculty have by all indications handled it like the professionals they are. It hasn't been glitch-free but I feel like we are off to a good start in circumstances that are far less than ideal.

One question that we've asked in our department and which I've seen asked in the POD network and other online forums is: How do we administer exams online if there are a lot of calculations involved? I shared a solution on the POD network this morning that I think others might benefit from, so I am writing one of the most nerd-niche posts I've ever done to explain it.

First of all, before getting into details, it's a good idea if you are writing mathematically-intensive exams to move up a level or two on Bloom's Taxonomy and focus on questions that involve application, analysis, and synthesis rather than just remembering and understanding, including mechanical calculations out of context. For example, instead of asking Calculus students to find the derivative of $y = xe^x$ (which can be done easily on Wolfram|Alpha) ask them instead to find the slope of the tangent line to the graph of $y = xe^x$ at $x = 1$. They have to do the same work, but there's a bit of higher-order thinking involved that's harder to fake. Also ask for lots of verbal explanations, and aim the grading more at the quality of those explanations than at the correctness of the computations. This promotes critical thinking and higher-order skills, and it also makes academic dishonesty harder.

The simple student workflow for exams

The most important thing for instructors and students in these times is to keep things as simple as humanly possible, and part of this consists in minimizing change. Resist the temptation to roll out new apps or teaching methods that are not absolutely necessary. I've seen some answers to this question about student work on exams that involves learning an entire toolchain of apps and procedures that just make my eyes glaze over, and I like technology. So in the spirit of keeping it as simple as humanly possible, here's how I handle student work on exams in an online setting. All that's needed from students is a smartphone or tablet and an internet connection.

  1. First, administer your exam online by either emailing it out to students or posting on the LMS.
  2. Second, students open or download the exam and work out the solutions, either on separate pages or on a printout. Either way, they do the work in pencil or pen, just like they normally do.
  3. Third – this is the different part – students scan the handwritten work to a clean, small, black-and-white PDF and upload or email this to you.
  4. Fourth, you open the PDF and grade the work, adding comments on the PDF using a tool that lets you add annotations to the PDF, like Adobe Acrobat, Squid, Kami, Notability, or any of a thousand others. Or you can print the work out and do steps 1-3 – add your handwritten annotations to the printout, then scan to a PDF, and give back to the student.

And of course put the grade in the LMS.

It's very important that students not just take a picture of their work with their cameras, because the high quality of cameras today creates a full-color photo that is often several hundred megabytes in size if not more, and this is larger than many LMS's are able to upload. (Our installation of Blackboard has a file size limit of 100 MB, for instance, and even a low-quality photo will be bigger than that.) And you definitely want to avoid having students email you right before the deadline that "Blackboard [or whatever] won't accept my work".

There are dozens of free or cheap scanning apps for smartphones that use the phone's camera to take photos of a document or whiteboard, then process them so that the angle of the shot is corrected, the photo is cropped appropriately, and the entire thing is turned into a clean, high-contrast PDF that is small in size. My go-to app is NoteBloc; for Office 365 users, Office Lens is a good option because of its integration with that suite of tools.

I wrote the following handout for my hybrid precalculus course that I taught in Fall 2019 that gives step-by-step instructions for students on how to manage this workflow. You can also get to it here. Feel free to make a copy and use it with attribution. Comments are turned on for this document so if you have a question, just leave it there.  

I've used this process for all my online and hybrid courses, and even some face-to-face courses where students couldn't be present for an exam, and it's always worked fine. I like it because it is simple and requires no technology other than what the student probably already has. (I think we're all trying to figure out how best to help a student who lacks reliable access to the internet or a smartphone right now.) The biggest problem is students uploading photos instead of scanned documents despite all the instructions; I just don't grade the work until they send me something that follows directions.

Less simple workflows

There are a couple of other ways that computationally-heavy work could be collected:

  1. Have students type their work up and submit as a PDF as above. LaTeX is good for upper-level courses and experienced students; for others, Word and Google Docs have halfway-decent equation editors that are not great, but which are perfectly adequate for most tasks. And that's all we're shooting for at this time.
  2. Have students use a computer or tablet to handwrite their work with a stylus and submit as a PDF as above. Not a lot of students have such devices, but it's an option for some. Windows people seem to like Drawboard PDF a lot; iPad users like Notability, and for good reason; Chromebook users such as myself as well as Android tablet people tend to use Squid or Xodo. And anybody can use OneNote.

Either way, students create a PDF and then upload it to the LMS or email it to you, as in step 4 above.


The primary message here is that if you want to keep having students do work on pencil and paper and turn that in, you can do so. It takes some tweaking but it's reassuringly similar to the everyday face-to-face practices we are used to – and sticking to what we're used to doing is not the worst coping mechanism these days.