Talbert was right; I was wrong.

I was thinking about specifications grading over break, and I came to realize that Robert Talbert was right and I was wrong.

My particular complaint about specifications grading for mathematics classes—that it is unrealistic to expect students to be able to judge that their work is mathematically correct—still holds. But Robert came up with a very slight modification that I was too quick to write off.

Robert’s solution was to move from two possible grades per assignment—PASS or NO PASS— to three: PASS, NO PASS, and PROGRESSING. The idea is that you can create all of the specifications you want—including whether the work is mathematically correct—and grade according to whether students have met the specifications. The one difference is that you split your specifications into two groups. The first group contains the specifications that students can easily check themselves, such as “There are no spelling mistakes” or “All variables are defined prior to use.” Failure to meet any of these specifications leads to a grade of NO PASS.

The second group of specifications are ones that students cannot necessarily judge for themselves, such as determining whether the work is mathematically correct. If a student satisfies all of the specifications in the first group but misses any in this group, the student is assigned a grade of PROGRESSING for the assignment (the student receives a grade of PASS if she meets all of the specifications).

The only difference between NO PASS and PROGRESSING is how easily students can re-do the assignment. If the student receives a NO PASS, the student needs to spend a token to re-do the assignment; a student who receives a PROGRESSING may re-do the assignment without any cost.

I initially did not like this system because I thought it simply added the complex token system on top of allowing unlimited re-dos—I preferred simply letting students do an unlimited number of re-dos. But I have changed my mind. I now think that raising expectations on specifications that students can easily evaluate themselves is a completely reasonable thing to do, and penalizing students for simply not doing it does not seem so unreasonable.

The benefits are that students get in the habit of evaluating as much of their work as they possibly can, I get to grade higher-quality work, and the students get used to creating higher quality work. The costs are implementing the mildly complex token system (although keeping track shouldn’t be too hard) and some potential loss of goodwill after penalizing students. But the higher quality work argument wins in the end for me.

I am rather pleased at Talbert’s plan, because this gives me the grading plan for proof-based classes that I am looking forward to (I think that I am planning on sticking with accumulation grading for the non-proof classes).

So—thanks, Robert. I am sorry I didn’t realize how good your plan was right away.

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6 Responses to “Talbert was right; I was wrong.”

  1. TJ Says:

    All of this makes good sense.

    But I want to push you in one particular place. This is not exactly a thing about grading, but I think it is important.

    The primary thing I want my students to learn is to know when they are correct. That is, they should know when things are really settled and the mathematics is fine, and when they are not there, yet.

    I believe that unless we give students an opportunity to practice this crucial skill, they will not develop it. EVER. So, I don’t tell students when they are correct. Instead, I ask questions. Sometimes they are pointed questions about the material intended to refocus on an idea. But more often, I like to ask one of these:
    “So, are you done? How do you know you are done?”
    “So, what is wrong with that? If anything, how do you fix it?”

    That second one can only be asked of students who are in a really comfortable place, so I ask the first one more often.

    If you are always the one who decides what is correct, class will always be, at some level, “satisfy the crazy professor.” But if you make it the student’s job to decide when things are done, class can be about “How do I figure this out?”

    • bretbenesh Says:

      I am with you about pushing them in the class, although I am not very good at it (any tips, beyond the questions you wrote above?).

      However. . .maybe we _should_ be talking about grading. How about a gradual-release-of-responsibility-thing like this: for the first 2/3 of the semester, we go with the PASS/NO PASS/PROGRESSING grading system above. For the last 1/3, we go back to PASS/NO PASS, and the students are now expected to judge whether things are mathematically correct for themselves (we let them know that this switch will be coming from the first day)?

      I think that this still might be a little severe, but I think it could be modified into something good. Here are two advantages:

      1. Students, who will know that they will be responsible for determining whether the mathematics is correct, will be trying to learn how to determine if something is correct from the first day of class.
      2. Students will have an incentive to start work earlier rather than later.

      One possible tweak that would make me feel better: the first 2/3 happen as in the post, in the last 1/3 the students only get one PROGRESSING per assignment. That is, the students can get feedback on what they did wrong once, but the second submission must be correct (otherwise the student has to use a token to get a third submission).

      One more thing that I will be blogging about: I have been reading Creating Self-Regulating Learners by our friend Nilson. I think that a lot of what is in that book could help, such as having students write pre- and post-assessments of how correct they think the math is. If their pre-assessment is incorrect, their post-assessment would have to address what went wrong in their pre-assessment.

      What do you think of this? Do you have ideas?

      • TJ Says:

        First, i should say that I am only successful at the change of responsibility in my Moore method classes. In my linear algebra class I try, but it isn’t great. And in my liberal arts course I only nudge this way with the tiniest steps.

        Even in my more method classes, it takes a few weeks until the students get it. In that time we do a lot of talking about what we find convincing and why. Eventually, a common standard for rigor comes out.

        I recognize that grading will be an important part of how this works in my other classes, and I am leaning on you to show me the way there.

      • bretbenesh Says:

        ” I am leaning on you to show me the way there.”

        I was afraid you were going to say that.

      • Joss Ives Says:

        I really like the idea of changing the amount of responsibility that the students have over the term. Another possibility is that instead of moving from the the three-tiered to the two-tiered system at some point in the term, you could gradually remove the things that qualify them for the PROGRESSING category.

      • bretbenesh Says:


        I think that that is a great idea. When I wrote it, I thought that “doing correct mathematics correctly” might be the only PROGRESSING-eligible item. But I could see that it might be smart to start with most everything in there. For instance, I could see that it might take a week or two to learn what “define all variables” even means.

        Thanks, Joss!

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