• Professor of Mathematics Annalisa Crannell
Associate Dean of the Faculty, Professor of Mathematics



Office: Old Main 113

Perspective Math:
the first course 
First Year Seminar: for instructors of Mathematics of Art

1. Things my students see  

- A Summer assignment asking them to read, respond to, and draw a diagram of what is happening in Plato's Allegory of the Cave, and 
The Syllabus, including

  •  A list of supplies to buy
  • The weekly schedule
  • The list of one-page papers

2. Some things that might be helpful to instructors of math and art

Grading writing and grading art are two things that math instructors don't often do.  Here are some of the tools I use that help me do each.

    Grading the writing projects.
    Grading the art projects.


Grading Writing

1. My teaching-writing Philosophy

I try to structure my assignments so that each new assignment encourages students to work on a new skill (the first paper focuses on correct, descriptive language; the second focuses on developing a thesis, etc.).  But more importantly from the point of grading papers, I want to teach students how to proofread their own papers before they hand them in to me.

Therefore, I try to comment as minimally as possible on the specifics of their papers, and instead to comment on the process and structure.  For the 1-page papers, I do this by attaching a half-page checklist to each paper.  I make most of my comments on this checklist; the comments on the actual paper mostly illustrate/support the comments I make on the checklists.  For the longer papers, I have a 2-sided rubric on which I comment extensively.

2. How I construct the checklists

Each checklist begins by repeating the criteria that I presented in the assignment.  Theoretically, this teaches my students the value of reading and addressing the assignment.  Over the years, I have revised both the assignments and the checklists so that I can easily comment on (or even head off) common difficulties that the students have.

Each checklist ends with a set list of writing skills I care about (Use active voice!!) and a list of bad writing habits that particularly irk me (misplaced modifiers).


The Grading Checklists

As with my art rubrics, each checklist repeats the information from the assignment, and there are several to one page (so print them out and cut them up before using).


Grading the Art Projects 

Grading art projects in my Mathematics of Art Course


Grading art is not like grading math: a drawing is not exactly “right” or “wrong” in the same way that a math problem is. I give feedback and then assign grades using the two-step process below, which tries to address both the artistic and the technical aspects of each of the pieces.

1. The Critique

On the day that the students turn in their art, we begin class by taping the artwork to the wall and doing a “critique”.  (Art studios usually have cork-lined walls just for this kind of exercise/feedback).  I look at all the pieces first, and then direct the students to certain aspects that are done particularly well, or that posed particular problems for students.    I’d say things like,

Notice how these three students each got the bottom line of the doorjambs just right.  That’s great attention to detail.
In this drawing, Sarah attempted to draw a checkerboard floor, but it seems like she wasn’t quite sure where to put the next line.  That’s a tough problem, and we’re going to be thinking about this together later today.
You’ll see some students put a lot more effort into this assignment than others did.  Please remember that these drawings should take 1-2 hours each -- and if you don’t spend that time, it shows.

Then I send students around to look at each other's work.  The first stage of the feedback process is done.

2. The Grade

Then I collect the artwork and photocopy it.   It is for THIS reason that I require my students do their sketches on a uniform-sized sketchpad (9 by 12 works well). I will draw on the photocopy to vet the work for mathematical accuracy – for example, I’ll extend lines that should go to a vanishing point but don’t, or I’ll draw an X to verify that the middle of a word is where it should be.  I attach the small (usually quarter-page) checklist that contains the criteria for the artwork; the number of checked “yes” items determines the grade – for example, 7 out of 10 points, or 6 out of 10 points.  I try hard to have the checklist correspond to the initial assignment.

The checklist allows me to combine technical comments (that is, to assess whether students can correctly draw an object in 1-point perspective) with aesthetic judgments. Obviously, I have a little more leeway in judging creativity, beauty, and neatness.  But overall, students see this as ``fair" --  the sloppy students saw the really, really nice art on the wall in class, and they know their work wasn't as good.

Notice that the students turn in one piece of paper and get three pieces of paper back:  their original art (unmolested), a marked-up photocopy, and the checklist.  

The Grading Checklists


As with my writing rubrics, each checklist repeats the information from the assignment, and there are several to one page (so print them out and cut them up before using).