Digital Grading Follow-Up

Back in March, I wrote a post called “Want Some Free Red Pens?” on my dream for digital exam grading. In my ideal world, I’d remove all the paper from my office entirely. Having only digital copies of exams would be splendid since I could get a lovely potted plant to put in place of my institutional-looking filing cabinet. Last semester, I did accomplish my goal of grading an entire set of exams without using any non-digital ink. Now I finally have the time to tell you how it went.

The exam was for our “Introductory Calculus” (MATH 120) course. It was the third exam of the semester and I had about 30 students enrolled. I gave the same exam I would have otherwise — it wasn’t an online test. If you’re really interested, you can find a copy of the test here. I photocopied it like usual, and my students took it like usual. I did choose 1-sided copies over my usual preference for double-sided to help with the scanning task.


  1. Write, photocopy, proctor, collect exam. Alphabetize exams by student lastname and remove staple.
  2. Scan exams to PDF files using department’s Xerox machine; export as e-mail attachment to myself.
  3. Use husband’s perl script to “pull apart” multi-exam PDF file into 7-page segments. Rename files “lastname-exam3.pdf”. Transfer each file to iPad and open in GoodNotes.
  4. Correct each exam, save graded copy as “lastname-exam3-done.pdf”, compile exam grades, and upload grades onto our LMS.
  5. Use LaTeX’s “pdfpages” package to combine each annotated exam with a very thorough “Solution Key” (with comments, hints, suggestions, etc) at the end. Send each student an e-mail containing their exam’s feedback with the Solution Key & notification that official exam grade is available on LMS. [This was done to avoid FERPA issues about sending graded assignments, or grades themselves, over e-mail.]
  6. Save un-graded exams in my filing cabinet in case any student wants to pick theirs up. (As it turned out, no one did.)

Here are the things I did like:

  • No crayon marks! No spilled orange juice! No paper shuffling! No page flipping! No running out of ink! Grading at home with a toddler is a tedious process, but being able to get in eight minutes of grading while also providing parental supervision was fantastic.
  • Forced Solutions. By giving every student a full Solution Key, I was able to write things like “See Remark on page 5” instead of re-writing the same paragraph of comments over and over again. Also, I didn’t have to feel guilty about printing thirty copies of said Solution Key, and I knew each and every student had been given the chance to see the solutions. (Usually, I upload the Solution Key to our LMS, but not every student bothers reading it, which is weird.)
  • Grading was Fast! During the “active grading” phase, I think it went faster than grading on paper. I didn’t have to spend time turning pages. I could Copy-and-Paste similar remarks from one test onto a different test. Because I didn’t need as much physical desk space to spread out, I was able to get in five minutes of grading here, four minutes of grading there, and so forth, so I think I was able to return the exams sooner than I would have otherwise.


  • Hello, Copy Room. With about thirty students and a 7-page exam, the scanning task involved around 200 pages. It turns out that our Xerox machine does not like it when you ask it to scan anywhere near this many pages at once. After trying to scan 8 exams at once (56 pages), the Xerox’s “brain” would get hung up mid-process and a machine reboot was necessary. After this happened twice, I realized that I could only really scan 28-pages at once. So I set up four exams, pressed “SCAN”, and waited three minutes; lather, rinse, repeat. Four exams taking three scanning minutes meant about half an hour in the Copy Room I would have liked to spend elsewhere. (Thankfully, this wasn’t a total time loss since I could work on other tasks while the copy machine whirred.)

    A colleague let me know that elsewhere on campus, there exists a better copy machine that could handle this type of task more easily. But, accounting for walking to-and-from time, I am not sure this would have taken any less than thirty minutes anyhow.

  • Returning Exams. It had been my plan to use the LMS’s “Dropbox” functionality to return the exams. Unfortunately, I lost over an hour of my life trying to get this to work — without any success whatsoever. We use a Desire2Learn product, and after consulting back-and-forth with my Instructional Technologist, we concluded that you cannot return graded work unless a student has submitted ungraded work first.

    In other words, there is no way for me to return a PDF file to a student unless and until they have uploaded a (potentially blank) PDF file to me. So, basically, there is a way to “reply” to an uploaded student document, but there is no way for me to “send” a student an uploaded document first.

  • Big File Sizes. One has to be careful about writing too many GoodNotes comments. GoodNotes didn’t do a great job of compressing the PDF file size, and our LMS refused to allow me to send any file over 2MB in size as an e-mail attachment. Some of the exams were over this limit (too many comments) and others weren’t. To be fair, I am not sure if this is more annoying because of GoodNotes or more annoying because of our LMS. I also don’t know if GoodNotes has gotten better at saving from a GoodNotes document to an annotated PDF and keeping the file size smaller.


In the end, I don’t know if I’ll try this process again anytime soon. The biggest time drainers were the Xerox scanning & learning what didn’t work. If I were to do this again, I might investigate a better scanning technology. I would certainly ask my students to submit a blank PDF file to the LMS Dropbox, so I could “grade it” and instead return to them their graded test papers. My students really liked having a digital copy of their tests — it meant that when final exam week rolled around, they didn’t have to dig through their course materials to find their test. So, maybe I will revisit this idea sometime in the future? I’ll let you know if I do.

The Pregnant Mathematician Continues Teaching, Probably

Recent Events
During the month of June, I’m teaching our “Introductory Calculus (Math 120)” course. We meet five days a week for 145 minutes, with a total of twenty class sessions running June 5th through July 2nd. Our final exam will be held on Wednesday, July 3rd. A few days ago, my very compassionate students expressed interest in knowing the probability their final exam would be cancelled due to an unexpectedly early birth of my daughter. I’m sure their inquiry was based solely on concerns for our health and not at all from them hoping to escape the intellectual challenge of a cumulative final exam!

Also recently, my husband and I went on an “Expectant Parents Tour” of the hospital where I will be delivering. Our son was born in November 2010, but at a different hospital; this time, I will be delivering at a hospital that was still under construction then! Since they have recently opened their doors, their NICU [Neonatal Intensive Care Unit] is still a “Level 1” facility. This means that they are certified to care for healthy infants born at 36 weeks or later (measured from LMP) or 34 weeks gestational age (i.e., since conception). Infants who are born with complications, or who are born before 36 weeks, are usually transferred to another local hospital. It turns out that reaching “Week 36” of my pregnancy and having lots of calculus final exams to grade will coincide perfectly.

Some Probability
While on our tour, I started wondering about the chance that I would go into labor early enough that it would affect my summer class. Not only would this be an unfortunate inconvenience for my students, it would also mean that I would probably have to deliver at a different hospital since I wouldn’t be at 36 weeks yet. What’s the chance this happens?

First, I should point out that I’ve had a relatively uneventful pregnancy — thankfully, both my unborn daughter and I have been in excellent health (if not a little grumpy from having to share the same circulatory system and oxygen supply). Second, my son was born within a few days of his due date, a little on the early side. Third, I’m not carrying multiples, nor am I expecting any major complications as my due date approaches. So we will just assume that this is an average pregnancy as far as the medical issues are concerned.

One of the things I talked about in my original “Pregnant Mathematician” post was how due dates are calculated using Naegele’s rule. Also, there was a rather large (n=427,582) study done in Norway [See Duration of human singleton pregnancy—a population-based study, Bergsjφ P, Denman DW, Hoffman HJ, Meirik O.] that found the mean gestational length for singleton pregnancies was 281 days, with a standard deviation of 13 days.

Let’s assume a mean of 281 days and a standard deviation of 13 days. What’s the chance a woman goes into labor 251 days or earlier (corresponding to 36 weeks)? Notice that 251 is about 281+(-2.31)*13, so giving birth prior to 36 weeks means you’re about 2.31 standard deviations away from the mean. By the Empirical Rule, I know this would be quite rare: There’s less than a 2.5% chance!

We can use Wolfram|Alpha to compute the exact probability. Our input is the command “CDF[NormalDistribution[mean, stdev], X]”; in this case, we are taking mean=281, stdev=13, and X=251. Wolfram|Alpha returns a result of 0.0105081, meaning there is about a 1.1% probability that I will give birth early enough to impact my current students.

It’s Gonna Be How Hot?!!

According to tomorrow’s weather forecast, the heat index here will reach 110 degrees tomorrow. This is miserably hot for everyone, but especially if you’re pregnant. Although my actual due “date” is in the first few days of August, I’m sincerely hoping that the birth occurs sometime in July. August heat in South Carolina is no joke! Wolfram|Alpha comforted me with its computation that there’s about a 41% chance I will give birth before I have the opportunity to be pregnant in August.

I’m also going to assume my chances of a July delivery are even higher than this, since human gestation doesn’t exactly follow a normal distribution. While a measurable percentage of moms give birth two or more weeks early, nearly none give birth two or more weeks late. By that point, OBs usually induce labor because of declining amounts of amniotic fluid and concerns for the health of the newborn. I’m going to take this and a “fingers crossed” approach and assume that a July birthday is at least 50% possible.

[There’s a name for such a distribution; I thought it was a truncated normal distribution, but that doesn’t seem to be quite right. The statistician who told me the term isn’t in his office at present! Anyone know what it’s called?]

Postscript: Dear Students,
Regardless of when I deliver, I can assure you that your calculus final examination will occur as scheduled. I know lots and lots and lots and lots of people who really enjoy torturing unsuspecting college students with tough calculus exams, and it would be easy for me to cajole one of those people into proctoring your test! So, don’t fear: You will certainly have the opportunity to demonstrate all the calculus you have learned this summer & feel proud of your scholastic achievement upon completing our course — including its final exam. 🙂

The Pregnant Mathematician Drinks Coffee

In our math department’s faculty lounge, one can often find a liquid-y substance some people refer to as “coffee.” This designation seems questionable to me, so instead I have opted for a Starbucks prepaid card. I don’t drink a lot of coffee, but I do have one cup in the morning.

According to Starbucks, a tall (12 oz) cup of Pike Place Roast contains about 260mg of caffeine. Personally, I prefer the Blonde Roast, but I haven’t found its nutritional data. One of my students inquired at Starbucks and the barista told him that the Blonde Roast contains more caffeine per ounce than the others; apparently, since it is less roasted, less caffeine is lost during the roasting process, leading to more in the final product. I wonder if this is true.

How long does caffeine hang out in your body?

Wikipedia reports that the biological half-life of caffeine in an adult human is around 5 hours. The half-life of a substance is the amount of time required for half of the material present to metabolize. In other words, if the half-life of caffeine in your system is 5 hours and you consume 260mg of caffeine at 8am, then five hours later (at 1pm) we would expect 130mg of caffeine to remain in your system — provided you haven’t consumed any more caffeine since your morning coffee.

The half-life of caffeine in your system is related to lots of factors: Your age, your weight, what medications you’re taking, how well your liver is functioning, and whether or not you’re pregnant.

Maternal Caffeine Consumption & Half-Life
It turns out that if you’re pregnant, the half-life of caffeine increases quite a bit. In other words, it takes your body longer to metabolize caffeine. Today’s quick search yielded these few medical studies that agree about this:

According to Golding’s study, by the 35th week of pregnancy, the half-life of caffeine increase to a high of 18 hours. (For comparison, the Knutti et al. study cites a half-life of 10.5 hours during the last four weeks of pregnancy.) Since I am not yet in my 35th week of pregnancy, let’s assume the half-life of caffeine in my body is 12 hours. How is this different from my (assumed) non-pregnant state, when its half-life is only 5 hours?

Suppose I consume a Pike Roast Tall coffee at 8am that contains 260mg of caffeine. What time will it be when only 50mg of caffeine remain in my system? When not pregnant, it would take my body about 11.9 hours, so by 8pm less than 50mg of caffeine would be found in my system. Meanwhile, a half-life of 12 hours means it would take my body 28.5 hours — that’s over a full day!

We discussed this calculation as part of my PreCalculus course a few semesters ago. One student, who was usually rather quiet and didn’t ask many questions, raised his hand. He asked, “So, Dr. Owens, what you’re telling me is that to save money on Starbucks coffee, I should get pregnant?” Laughter ensued, and I assured my students that getting pregnant as a cost-savings measure was really not an optimal strategy.

As far as the risk to maternal and neonate health, the American Congress of Obstetricians and Gynecologists concluded “Moderate caffeine consumption (less than 200 mg per day) does not appear to be a major contributing factor in miscarriage or preterm birth” in 2010 [1] [2].

My Conclusion: Okay, it’s probably best if I limit my caffeine intake while pregnant. But I also have to think about my overall happiness and my enjoyment of life — as far as caffeine goes, today’s science seems to imply that my occasional Starbucks habit is a net positive (happiness minus risk), even when taking into account its expense (increased work productivity minus $2 per cup).