Is it Worth 12 Hours to Grade a Test?

Feeling a bit better after two months of recovering from the flu while juggling three preps, BTSA, and other teaching tasks, I took a moment to pen the kernel of the following for my Facebook friends.  Sharing an expanded version now with those who follow my blog.


The two charts below depict my AP Calculus AB students’ performance (N=35) on a cumulative test covering second semester topics: 1) integration techniques; 2) applications of integration; and 3) separable, first order, ordinary differential equations.

The first chart depicts scores as a histogram using 10% bins.  The second chart shows scores using my rating scale spanning categories from far below basic to advanced.  These correspond to letter grades of F through A, respectively.  My cut scores break at 15% intervals from 40% to 85% corresponding to far below basic to advanced, or F to A.

The results include distributions of the total score as well as sub-scores for Integrals, Applications of Integration, and Differential Equations. The overall average was 47%. High score was a 95%; low score was an 8%.  I am not pleased with the results; however, I am not surprised.  I do wish I knew how best to motivate these advanced students to invest more time in their studies; it seems the majority of them are so accustomed to minimal effort out of class based on earlier successes in mathematics that they simply do not know how to do so in an advanced course like calculus.  A few have simply given up, which takes more time and energy from me to get them to re-engage.

Test #7 Distribution 1 Test #7 Distribution 2

It took 12 hours to score this test, as I needed to read the written work from 700 problems for maximal partial credit. As you might imagine, that is a considerable investment on a teacher’s part for one course (aka prep); I have two other preps. It is very worthwhile if students are investing significantly in their preparation for a test, and their learning, but not so much otherwise. I’ve asked my students to please consider this as they progress in their education.

BTW, the overall score is the only score that counts towards their grade at present. At some point, I will compare each of their sub-score percentages to earlier test scores to replace those that are higher, which helps late bloomers. I’ve also suggested that students look at their sub-scores and use them to guide subsequent studying for the course and AP Exam.

Let’s hope they do so!

About Dave aka Mr. Math Teacher

Independent consultant and junior college adjunct instructor. Former secondary math teacher who taught math intervention, algebra 1, geometry, accelerated algebra 2, precalculus, honors precalculus, AP Calculus AB, and AP Statistics. Prior to teaching, I spent 25 years in high tech in engineering, marketing, sales and business development roles in the satellite communications, GPS, semiconductor, and wireless industries. I am awed by the potential in our nation's youth and I hope to instill in them the passion to improve our world at local, state, national, and global levels.
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3 Responses to Is it Worth 12 Hours to Grade a Test?

  1. Dave says:

    The kernel is in the ear but the ear does not hear. Yes, they are in this class because they have had success, but at a much lower level of difficulty with vastly different expectations. Many West Point students had similar rude awakenings their first month of classes. part of the “AP for everyone ” syndrome. All i can think of is explaining that this is how college Math is for non liberal arts students and that if you show progress, come to class, and do your work I will give a grade no lower than 80 ( if that’s OK with you ).

    Next year or in the selection process for next year you may proceed differently. Feel better; The Yankees played West Point on Saturday. Might be a tough year for both of them.


    • In some ways, I was fortunate as a plebe. I bombed my placement test (either fell asleep during Beast sitting in the air conditioned auditorium in Thayer Hall or forgot all my math since I last took math as a sophomore in HS or some combo thereof), so I ended up in MA100, or “rock math.” That allowed me to regain my math skills and “get” calculus, as I ended up in seat 01, section 01 by the end of each semester afterwards.

      I plan to give no less than a C- letter grade (55.1%) if students put in effort, which is difficult to tell at a certain level. Not sure about the 80% / B-, which occurs at 70% with my cut scores, as some have much lower than a 40%. I can rationalize the C- easily, less so the B-.

      One of my classmates went to the exhibition game. It sounded like fun was had by all.

      Your comment re: USMA cadets is intriguing. Sounds like the voice of experience to me…


  2. Stephanie says:

    12 hours? I admire your perseverance! I don’t know how you find the time — when I was teaching there was just no way (in between lesson planning and grading) that I could have spent that amount of time on grading. I used a lot of online tests that graded instantly, which makes me think I cheated a little bit — many of my colleagues were spending their weekends grading, but I needed some “me” time 🙂
    Thanks for sharing!


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