*By Dana Ernst*

When I first started using inquiry-based learning (IBL), grading/assessing students caused me the most anxiety. When it comes to grading, I always feel like I am trying to solve an optimization problem. I want to maximize useful feedback to students and data to justify grades while minimizing the amount of time it takes for me to do the grading. After some trial and error, I’ve settled on a method that I feel is both effective and efficient.

One key component of my approach to IBL
is to get students to the board to present their proposed
solutions/proofs as much as possible. In my upper-level proof-based
courses, the student presentations form the backbone of what we do
each day in class. In my calculus courses, the student presentations
play less of a role, but they are still an important part of the
structure of the course.

In most cases, students are presenting
material that was assigned as homework. In the past, I allowed
students to freely annotate and/or modify their work during the
presentations. One problem with this, however, was that it was usually
impossible to tell what work a student had done prior to class. Certainly, in some cases, I was giving credit to students for
work they did not do. For a brief time I experimented with collecting
student work prior to the presentations, but this also bothered me since I felt the advantages of giving students an opportunity to learn
something by comparing what they had done to what the presenter was
doing outweighed the disadvantages.

Then

__Clark Dollard__(Metro State University) suggested having students use colored felt tip pens to annotate their work during class. I remember dismissing this idea as silly, but a couple months later I decided to give it a try. It's such a simple thing, but it has had a big impact!
Here's my current approach to using the felt tip pens. If students are presenting material from homework that the class will ultimately turn in for a grade, the students in the audience are allowed to annotate their work, but only with one of the felt tip pens that I provide in class. Each day, I bring a box full of a variety of colored felt tip pens. The purple pens are the most popular and no one ever chooses the red ones. Students are encouraged to annotate their work as much as they want with the colored pens. Their grade on the assignment will not be impacted by what they write with the felt tip pen, but rather their grade is a result of what they had before they entered class.

Having students use the felt tip pens enables me to discern what students had done
before class. Moreover, students are encouraged to reflect in the
moment on their work, not days later when I return it. I have nothing
other than anecdotal evidence to support this, but I strongly believe
that adoption of the felt tip pen approach has changed how my students annotate their work. Not only are
the annotations different, but I can also tell that deep reflection
is occurring. At the beginning of each semester, it's clear that a
few students think that the idea is silly, but feedback from students
(both in person and on anonymous course evaluations) has been
extremely positive.

On a selfish note, the felt tip pen
approach also allows for speedy grading. Since we’ve already
discussed each of the problems in class, I don’t feel compelled to
grade the work for correctness. Instead, I use a ✓-, ✓,
✓+ scale, which makes the
grading of the homework lightning fast. All that matters is what the
student had done

*before*class.
In addition to
the homework that is presented in class, I also assign an additional
weekly homework assignment whose purpose is for students to reflect
on the previous week’s presented homework. Each week, students are
supposed to turn in two problems (from a subset of my choosing) that
were presented during the previous week. These weekly assignments
are supposed to be carefully written, and since this is the second
time that students are working on the problems, the grading goes
quickly, but I also feel comfortable grading them harshly. One
significant advantage to this approach is that it forces students to
revisit their annotations. In fact, I believe that having

*both*the daily and weekly homework is key.
If you want to learn a little bit more
about my felt tip pen approach,

__check out the slides__from the "Effective and efficient grading for an IBL course" talk I gave at the__2012 Legacy of R.L. Moore Conference__in Austin, TX.
## 7 comments:

Very interesting. I have students do the same in my high school math classes. However, I have a difficult time getting them to use something different from the writing utensil they did the assignment in. Perhaps using a provided felt tip pen will do the trick. Sometimes I have trouble getting students to write ANYTHING about the problems we discuss in class, even though they know part of their grade is based on checking. Any suggestions?

Dana, I like the felt-pen idea and the targeted weekly homework very much. It will force them to look at their mistakes and reflect on that. I think many of my students don't improve as much as I want them to is because they don't treat their mistakes as valuable assets.

I have a question though on your grading. If there are two students who did the same amount of work before class (some correct ones and some incorrect ones), but one student annotate a lot and write down a lot of comments and the other students don't write anything. Do you differentiate their grade at all?

Xiao

I tried this in two of my classes (one with 24 students, one with 12 students). This is what I did:

1) They took out their homework as if to submit it.

2) I wrote problem numbers on the board.

3) They wrote their names next to whatever problem about which they felt comfortable.

4) I picked presenters from the names on the board; had them stow away all writing utensils; gave them new marking pens (various colors as Dana described - though not felt tip as I was concerned about the ink bleeding through).

5) The students I picked explained what they did for the problem to the class. Any time they looked at me, I gestured to the rest of the class. (I was trying to hide in the back of the room.)

6) After each presentation, I added fine tuning comments or clarifications if there was a debate going on and they didn't seem to be getting anywhere.

7) After all presentations, they turned in their work. (The group of 12 felt attached to their work so took pictures of it before turning it in.)

Grading times for the big group: 5 computational exercises each (*24 students) took about 10 minutes from when I sat down until when I got up again. 4 word problems for the same group took around an hour. I think I like reading what they write too much to just skim what was written down. Most of the time, my comments on what was turned in were minimal as I had already commented in the classroom.

Hope this helps!!

Amanda

Christine, thanks for your comment. I hand out the felt tip pens at the beginning of class and when we are discussing/presenting problems (which for me is pretty much the whole class period), the students are only allowed to use the felt tip pens. In this case, I don't have any trouble getting them to use a different writing instrument. Perhaps I should pay more attention to how I sell this to the students, but I don't have any trouble getting them to play by the rules and to actually annotate their work.

Xiao, great question. My approach in calculus is slightly different, but for the rest of my classes, I treat the felt tip pen annotations as a layer on top of their original work. I can't actually pull this layer off, but I pretty much ignore it when assigning a grade. I thought about doing something more elaborate. If you cook up a way to tweak this approach, I'd love to hear all about it. Also, since we've just discussed most or all of the problems, I pretty much just grade for completion. That is, I don't look at the details of their original work. However, I don't give them full credit for just doodling under a problem. They have to write something that is an honest attempt at the problem.

Amanda, thanks for the details. Love it!

What do you do about Amanda's concern about bleeding? I have the same one. Do students only write single sided?

Grace

Kathleen, the pens I use do not bleed through, but there are probably some brands that might. Any colored pens will do the job. I probably went with felt tip pens the first time because they were cheaper. My students generally use both sides of the paper.

There is an added bonus to this method. The students now leave more room for comments on their paper as they know that they will want to write follow up remarks after they are "finished" with their homework. I was pleasantly surprised when I saw this occur.

They also have grown attached to some of the pens. One of my students really really wants the orange pen and will plead with his classmates for the right to use that particular pen. Some students bring their own colored pens. I allow it so long as I can see that they are not using the same pen that they had used on their work previously.

Amanda

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