I have really enjoyed our discussions of Specifications Grading. I have learned a lot from it, and I have enjoyed the conversations (which I will continue to engage in). I particularly want to thank Theron Hitchman, Robert Talbert, and Andy Rundquist for helping me think through this. I feel like I kept asking the same questions, and everyone was very patient with me. In this post, I will post the answers I eventually came to to those questions.

My conclusion: my grading is going to become more like specifications grading, but I am not going to fully use it. I want to give my students specifications on how to do a good assignment; that is a great idea. But one of my specifications absolutely has to be “the mathematics is correct”—I cannot live with less than that.

But putting a correctness requirement in the specifications is problematic. Here is how Nilson introduces specifications (page 57, all emphasis is her’s):

For assignments and tests graded pass/fail, students

have tounderstand the specs. They must knowexactlywhat they need to do to make their work acceptable. Therefore, we have to take special care to be clear in laying out our expectations, and we cannot change or add to them afterward.

The problem is that the point of mathematics classes is arguably to teach the students when mathematics is correct and when it isn’t. This is obviously a huge simplification, but it would be ridiculous to expect students coming into a mathematics class to already know what is correct—it is our job to help the students learn this. As such, I think that it is not in the spirit of Nilson’s specifications grading to include a correctness specification (the same may be true of requiring that writing be clear).

Now I do not think that Nilson’s book was written on stone tablets, and Nilson herself has suggested that it may need to be modified for mathematics. I am happy to adapt specifications grading to make it work, but there is another issue: the tokens.

Viewed one way, the tokens are a way of allowing students a chance to reassess. I like that thought, but I can’t help but to view things the opposite way: tokens are a way of limiting reassessment chances. [Late edit: I think that specifications grading is a huge improvement over traditional grading, since it allows for reassessments. I just think that there are already better grading systems out there for mathematics courses. Thanks to Theron Hitchman for reminding me that I should say this.]

So we have a correctness specification that students do not understand, and they will not receive a passing grade if the work is not correct. Yet they only have limited chances to reassess due to the token system. So here is the situation I fear:

- A student comes to the course without knowing how to create correct mathematics.
- The student is given an assessment that says they are required to write correct mathematics to get a passing grade.
- The student, still in the process of learning, turns in an incorrect assignment and receives a failing grade on the assignment.
- The student uses a token to reassess; they may or may not get the mathematics correct on the reassessment because mathematics is hard. Maybe the students needs to use a second token to re-reassess.
- This process repeats 3–4 times until the student is out of tokens.
- The student never gets to reassess again, and therefore does not learn as much.

This is very similar to the reasons why Robert Talbert is considering moving from a PASS/FAIL specifications grading system to a PASS/PROGRESSING/FAIL system, where a grade of PROGRESSING is allowed to reassess without costing a token.

Here are a couple of other modifications that could avoid this:

- Give students a lot of feedback-only assignments prior to the graded assignments to help students learn what it means to be correct.
- Give students
*a lot*of tokens so that they can get the feedback they need.

But if I give a lot of feedback-only assignments, why not give students credit it they demonstrate mastery? And if there are a lot of tokens, I think you may as well just allow an unlimited reassessments—you will probably come out ahead, time-wise, because you will not need to do the bookkeeping to keep track of the tokens (my opinion is that it is probably better to give unlimited reassessment opportunities over a PASS/PROGRESSING/FAIL system, too).

One clarification: when I say “unlimited” opportunities for reassessment, I do not literally mean “unlimited.” For one, the students will be limited by the calendar—there should not usually be reassessments once the semester ends. I am also fine limiting reassessments to class time, and not every class period needs to be for reassessment.

So I think that it is unfair to require a student’s mathematics be correct to pass an assignment, but then limit the number of reassessments. This is why I am not going to use specifications grading in my mathematics classes (I will just take some of the ideas of specifications grading and graft them onto accumulation grading).

That said, I like the general idea, and I would likely use it if and when I teach our First Year Seminar class. This is the class that Nilson mainly wrote about in the book, and I think that specifications grading could be fantastic for that class. But not for one of my mathematics classes.

Questions for you:

- Is there a way that we can break down the “correct” specification so that the student can know it is correct prior to handing it in? This is reasonable for computational questions (use wolframalpha!), but I don’t see how to do it any other type of question.
- Are there alternatives to the “lots of feedback-only assignments”/”lots of tokens”/”more than two possible grades” solutions to the issues above?