# In math courses with writing requirements, how should large papers be graded fairly?

In a course I am teaching this semester, I am required to have my students write a large (6-12 page or so) paper worth 40% of their grade. Many other colleges have courses with similar requirements, e.g. a capstone major course involving writing, or a history of mathematics course, etc.

Where papers are required in a course, how can they be fairly graded? My concerns are:

1. How much emphasis (if any) to place on correct grammar/spelling/formatting
2. How much emphasis to place on good exposition vs mathematical rigor (which are, of course, not contradictory goals)

My concern is that I am not trained as an English teacher, and my students are not taking an English course. However, the paper should be readable. What has worked in your experience?

• I would advise minor focus on grammar/spelling. Formatting I think depends more on what you want them to know. Maybe make it count for 15% at most. I'm not sure what should be focused on for the second. – ruler501 Apr 7 '14 at 18:40
• I suggest putting more attention on avoiding ambiguity than an English teacher probably would. I also suggest looking at the Paul Halmos article How to write mathematics. Although this article is directed towards a different group than your students, if you haven't looked at it in a while you may not have realized that much of what is said can be modified to fit your situation. – Dave L Renfro Apr 7 '14 at 20:24

Set up a grading schema, awarding points for grammar, spelling, correct use of the technical terms. Central should be points for correct, logical overall structure, and enough explanations to lead the reader from one step to the next.

You can publish the grading schema for their guidance, and perhaps write up an example of how their work should look like. A few, short, examples of wnat not to do (a rambling stretch of algebra with no explanation whatsoever, another one with totally redundant comments like "now we add 1 to $n$ to give $n + 1$." Im' sure in a term or two you'll have hairraising exampĺes enough to distill into more "don't do this" texts.

There are lots of texts on how to write mathematics around, I like Knuth, Larrabee, Roberts' "Mathematical Writing a lot, or Chang's "How to write proofs: a short guide" should be required reading.

If this is their first collision with this, make up a "test drive homework" (for, say 5% of the grade) asking them to write up some of the proofs in class (or asigned "randomly" from a pool of not-so-briliantly-written texts), to be graded as the 40% requirement, so you can fling zero grades around at leisure when it goes "for real."

For a "writing in the disciplines" course, which it sounds like this is, think about what it means to be a writer in this discipline. For a writing in mathematics course, I'd expect writing of a quality that could be published in a mathematical journal. This means that, yes, I would expect proper spelling/grammar/punctuation/formatting. But primarily I'd expect clear exposition of the mathematics being presented, and mathematical rigor.

Does your school not have guidelines for grading in the "writing in the disciplines" classes? Since this is probably a graduation requirement it would make sense for the school to specify what its goals are for students upon completion of your course. Use those goals to guide your grading.

In all cases, provide a clear rubric to the students.

I assume that in addition to grading students on their mathematical writing, you are expected to teach the students to be good mathematical writers (and not just assign a paper and expect them to figure it out). The pointers that others have posted here will be helpful. In the course of teaching students to be good writers of mathematics, you will naturally touch on the points that end up in your rubric. So students should have a good idea of how to achieve the goals you set for them in the rubric.

Good luck!

I do not have precise, practical advice for how you should grade, but my comment will hopefully be of some general value.

What, specifically, do you hope your students will develop over the course of your class? My advice would be to keep this closely in mind and make that the focus of your grading. Ask: to what extent do the papers demonstrate the essential aspect of our class?

It will, of course, be helpful to the students to know what you're focusing your attention on when you are grading. So, let them know what you will be paying attention to, and give them a rubric if you can. That way they can put their effort into showcasing how they have coherently learned the subject matter.

The overlap of your content and ELA, of course, is in comprehensibility and coherence. It is possible for the paper to fail to communicate; if you are unable to decipher points of the paper, then they have not merely failed in an ELA sense. So, technically, grading them on their ability to make a coherent argument and express it clearly still falls well within your class. They can only succeed if they were able to express their ideas effectively, even if they break some ELA rules along the way.

However, this doesn't prevent you from marking up any ELA problems you happen to notice as you are grading. While it may not be part of their grade consideration, and it need not be something you spend additional time on, you can probably provide some useful ELA feedback to them. You may note that there are grammar problems, that spelling is an issue, that there is a problem with the coherence from paragraph to paragraph, etc. These comments can be useful to students even if a grade is not dependent on them.

Cheers!