On Grading

Oliver Knill

Grading is maybe one of the least liked parts of the teaching profession. It is therefore often delegated away to teaching assistants or to automated grading systems. That impression is even stereo-typed in movies. In the movie ``Help, I shrunk my teacher", an initially unpopular teacher is shown, who likes to grade which obviously is weird)!
See this page for some math related clips about this movie.

I actually would like to make the point that grading gives great insight to a teacher. Doing the grading personally opens a direct insight how students work and solve problems. It is important however that the students write by hand and not just fill out forms or boxes online. Also a type writing system hides a lot of the insight.

We see that also when looking at personal notes and initial drafts of scientists writing papers or books. Handwritten initial drafts reveal a lot of information on how the mind struggles to solve a problem and which parts were difficult. This is often distorted in the actual paper or then textbooks which write about it. Some who have studied the works say of Einstein are surprised how helpless this great scientist first was when working on general relativity. Obviously, there had been important math (Pseudo Riemannian geometry) which had been missing. One knows today that Einstein got assisted there by mathematicians like Marcel Grossmann.

Of course, there is the time issue. I have been lucky to be able to allocate a lot of time to teaching and so also to grading (as I'm not in the publish or perish mill) and one has to understand that not everybody has. But I would like to make the point that it is not only the grading, the assessment and valuation of work done by students which matter, reading original work by students is actually part of what I would call ``pedagogical explorations" or even ``pedagogical research". As teachers, we are in interested in not only assessing the work of the student but also in assessing the work of ourselves. Of course there are the course evaluations but we all know that they are often just a popularity contest and have sometimes little to do on how effective the teaching was.

Hitting difficulty in a course is not easy. If the assignments and exams are too difficult this can also discourage and frustrate. If the assignments and exams are too easy however, then the entire thing becomes a joke and the gap between what one needs to know for more advanced courses and what is actually known gets so large that one hits the wall right after having taken the course. I believe that we have a good tool to figure out how effective problems are and that this is by doing part of the grading. I have never taught a course myself where I had not been doing some grading and it was always highly enlightening (even so one often feels that the time doing that could be used for better purposes).

Here is a video showing the grading process during summer 2020. It was filmed for a Life in a day contribution 2020:
At the Harvard Summer school (I teach the multi-variable course since 2002 every time, this is 19 times so far), I always grade all exams personally. (2002 was a joint teaching, where we also graded together). Grading had always been a wonderful way to assess how well things have been understood and what part of the course has transferred. This summer 2020 semester was different, as 115 students were in the class which is more than usual 60-70.

Technology actually makes grading even such an amount quite smooth as one does not have to shuffle around papers. I get the paper by email, import it to the ``notability" app, grade with the pen and when finished, send it back to the student. The grading can be done everywhere, even outside in nature (which is a challenge with lots of papers and wind blowing) or while watching additionally a movie (of course a movie which one has seen lots of times already so that one does not have to spend CPU time there). The above video shows the process.

Of course, grading needs time and also requires the problems to be written in a way that they provide information about the thinking process. But it is a multiple times more valuable than surveys which is usually the way to probe how students learn. For me, it is not the grading time but personal consultation time.

Seeing the work of students in real and all of it, even the multiple-choice problems (one can clearly see patterns even there) allows to gain a lot of insight in how students learn and is of unimaginable value, much more than any theoretical mumbo jumbo about pedagogy or ``learning" or shifting the load to automatic grading systems (which is the fast food of teaching). Unfortunately, in these times, with remote teaching the personal or small group interaction with as many students (not with video but in real) was out. This had always been even more valuable in all classes I have taught the last 30 years. That information was not possible this summer, but talking during office hours over video was not a bad substitute. (It will never replace personal interaction however).

Just as an additional benefit from doing the grading on our own and not through automated grading systems is that these systems harvest all information. It is clear that the process of transferring higher education from universities to corporations has sped up considerably during 2020. We do not know where this ends but it is not hard to predict that even higher education will survive as such as all is sucked up by external entities.

Posted: August 13, 2020