On the recommendation of Jesse Stommel, I’m reading this paper about grading student writing by Peter Elbow, and I’m trying to figure out what it might say about my own grading practices. First, let me say that that the problems of grading writing may be qualitatively different that the problems of grading mathematics. Mathematics has this wonderful and horrible right/wrong duality in it, and it is often set up as an objective arbiter. Emotions and opinions don’t come into mathematics grading, because how can they? It is always true that 2+2=4, and it is never true that 2+2=0 (except of course if you are working mod 4, but that’s just me being an obnoxious mathematician). I suppose that is the true truth if you are either machine grading, or are grading with no “partial credit.” But that is almost never true for me, because I don’t think that the most important thing about a solution on an exam or in homework is the final answer. The process is far more important, and gives me more clues about what the student is thinking and what they have learned. Add to that the fact that I typically give projects and other more subjective assignments for at least part of a student’s grade, and the situation gets quite muddled. And of course I accumulate a large list of quantitative measures during a semester and combine them together in an arbitrary way that I determine at the beginning of the semester, with each grade making up a certain percent of the final grade. All of that is the say: mea culpa, I may need a better theoretical framework here.

Right away the paper grabs me, then with the discussion of the difficulty and unreliability of grading, and even more with the wall it puts up between teacher and student. As Elbow says on the first page, “Students resent the grades we give or haggle over them and, in general, see us as people they have to deceive and hide from rather than people they want to take into their confidence.” I’m in, but what do I do?

Elbow recommends using minimal grades, like pass/fail or strong/satisfactory/weak. He recommends this for low stakes writing, and I could see it working perfectly for low-stakes assignments. In fact, I rarely grade homework. Most is graded on completion only, or if I actually want to provide feedback I use a 0-2 or a 0-3 scale. But really, maybe the words work better (only what do I write in my gradebook?). Elbow says that we can judiciously increase the number of levels in higher-stakes situations if we want, still without resorting to the eight levels of the traditional letter grades with pluses and minuses. Honestly for a test, this would be harder for me than what I already do. I tend to grade student work on each problem using a rough rubric that tells me how many points to give what kind of work — I might subtract points for certain kinds of errors, or give a certain number of points if the student made a correct start to a problem. So when grading is done, I have a bunch of number to add up, and presto, I have a grade! And arguably that grade gives me an idea of how well they were able to demonstrate their knowledge on that particular test. Moving to a more fuzzy system would be more work for me, but I can still see some advantages. I would likely still grade in much the same way, but I’d have a less fiddliness over the small numbers of points, with all questions being strong/satisfactory/weak. Then I have to think of a way to get the exam assessment overall.

Elbow can help here again, and maybe help with my poor Excel gradebook. He suggests to look at all of the grades in aggregate. Say you have a lot of low-stakes grades. Doing “satisfactory” on all of those might be a B, and then looking at the smaller numbers of higher-stakes pieces could pull that B up or down. Being a math person, that screams out to me to make up a formula, and you again get into the whole problem with grades. Wouldn’t a narrative evaluation simply be better and more nuanced, allowing me to say to a student “You did great with all of the lower-stakes pieces, but once the stakes were raised, you struggled to show your competence and understanding.” Then the student and I could both think about why that was. Perhaps the higher-stakes assignments required putting more concepts together, or maybe the pressure negatively impacted the student’s ability to think and communicate clearly.

Elbow advocates for portfolios, which I think are a good idea, but I have only occasionally used. He also discusses the use of contracts for grading, which I think I last encountered in high school. I could see contracts being a way of being up-front in my manipulation of students, as Elbow suggests. In doing so, I could clearly spell out my expectations for behaviors associated a passing grade. My only question there is what happens if the student has all of the behaviors associated with passing, but still doesn’t learn the material? What if they still can’t do any math? Honestly, I don’t think that really happens, at least not if I choose the right behaviors. But I worry about whether I have a clear leg to stand on if criticized for this kind of grading practice. Is it “rigorous enough?” Don’t I want students to come out of the class with some products, rather than just a process and effort? I think what I am struggling with is the student that just does the motions as they go through my class, appearing to really engage without really engaging. I suppose that such students pass through my classes all of the time, and there is no fool-proof method for bending them to my will and forcing them to engage in the ways that I desire. And when I put it that way, perhaps there shouldn’t be. Maybe the real problem is in trying to manipulate students into doing what I want them to do at all.

Photo credit: Michael 1952

Elbow also suggests being explicit about criteria. I tend to have rubrics when I grade project work that spell out what I am looking for, and Elbow’s minimal grading would make this easier and less rigid. I could also give criteria on exam problems, or I could split up into multiple criteria. In a calculus class exam problem I might be looking for the method of solution, setting up the solution in a reasonable way, and executing that method including getting algebra correct. I could be clear about each of these criteria and evaluate each problem on each criteria.

Part of what makes grading hard is being the person that holds the power of judgment, and that’s just part of being a teacher. The power is mine to hold and negotiate, since I have to write down a letter grade at the end of the semester. I want to use student assessments in a way that is helpful to the students, and to determine letter grades in a way that doesn’t create excessive distance between me and the student, or between me and the task of judgement. Honestly, right now I use my grading system as a very long arm that allows me to avoid the uncomfortable position of judge. I don’t really determine the grades — a lot of numbers determine the grades, and I have very little to do with it. I can hide behind those numbers. I can even advocate for and advise students about how to beat those numbers, ignoring the fact that I’m the one writing down that letter grade. Once again, it all comes down to the relationships in my classroom and how I navigate them and engage with the students, and I can see that I have some work to do here.

# Accomplishments and Regrets in 2012

With 2012 coming to a close, I’ve been thinking about my year. I am proud of a lot that I did this year including

• My application for a Radcliffe Fellowship: I wrote a good application and was brave enough to apply
• My application for promotion
• Taking the first steps for my Liberation Math website (http://liberationmath.org)
• The amazing connection I have had with my spouse this year
• The way I talk to my kids about anything and everything
• The great talks I gave and connections I made at conferences, workshops, and invited talks this year
• The connections that I had this year with both my parents
• Getting a 529 set up for kids for college and setting up regular contributions
• Solving my long-standing digestive issues! Figuring out that I have SIBO was transformative, and I have made great strides in fixing my problems. Woo hoo!
• I had a paper accepted to a sociology journal (the paper is in press at Rationality and Society), and I’m a mathematician!
• I had great connections with students in many of my classes and I feel good about a lot of the teaching I did this year.

Climb Ev’ry Mountain (Photo credit: Wikipedia)

I also have some regrets:

• Not pushing the 529 out to grandparents so they can contribute
• Not being proactive enough in setting up solo time with my mom
• Losing the connection with dad for a little while because I stopped calling him
• Getting angry at my kids and not wanting to stop getting angry and be a grownup
• Not doing something like yoga or meditation to restore and center myself
• Letting myself get away with not connecting deeply with my students
• Not blogging regularly enough
• Not attending to how my net worth is growing (or, um, not growing)
• Not dreaming big enough about liberation mathematics (but I’m working on that now!)
• Spending my energy treading water and distracting myself rather than really digging in (busy bee trait)

I have started to work on setting up dreams, plans, and goals for this upcoming year, so I may blog about those in the coming week. A lot of my energy is going to putting up content at my new site Liberation Math, so come visit me there!

# Math Exams

I gave exams this week, which means that both my students and I are in emotional turmoil. My calculus students struggled to complete the exam in time, which isn’t typically true of my exams, so I need to compare this year’s exam to last year’s. I did have a worry as I was writing it that it was a little long, and I should have listened to my gut! The exam I gave in abstract algebra didn’t seem too long for the students, but I know students struggled. Now I have to grade all of the accumulated exams and have the usual emotional baggage. I feel disappointed in myself and in the students. I doubt myself. I question my fitness for teaching. I get angry at the students for not trying harder, and I even get angry at them for making mistakes. I feel hopeless about the class and about the possibility of any forward progress at all. Dreary and gross stuff that I really don’t even want to admit.

Exams are a situation of artificial pressure. Exams are weak on authentic importance. These exams are only important because I will use it to write down grades for the students. The grades are important to me because they give me a way to assess my class and the students in it, determining whether individual students and the class as a whole met the objectives of the course. The grades are important to the students because they want good grades in order to stay in school, keep scholarships, look good to others, be attractive to employers, and meet requirements of a program or major. Note that none of those things involve student learning. What I want to do in my life is to help students understand and use mathematics, to be powerful with math. A test can only do that as an accidental outcome. A test might help me to assess if I have helped students, but the only way for a test to help with learning is if the pressure of the test helps students to put forth more effort, or if, when faced with a bad test outcome students make a change in their learning habits or approach.

But I have seen first hand what happens when students aren’t having tests — the majority of them don’t push themselves to work. Maybe students are addicted to tests, and thus we are all addicted to this unpleasant experience. Maybe I’m addicted to tests because I have developed too few other methods for helping students to motivate themselves. In any case, I don’t know what to do about it, so I keep giving tests.