For several years I have run an IBL Euclidean Geometry Course. You can find some of my thoughts about IBL courses in general, and about this course in particular, in other posts on this blog.

An important feature of the course is the *class journal*. I am writing an article about the rôle this plays in teaching students proof writing, so this post will serve as a first draft of my thoughts. I welcome comments and criticism, as that will help me write a better paper, and be a better educator. Also, my digital homey Bret Benesh asked for a blog post about exactly this subject.

As with all of my blogging, I intend to ramble on freely. Buckle up.

## Context

Most the students in my course are in a preservice teaching program that leads to certification for grades 5-12. Most students are getting their first college level introduction to what a mathematical argument is and how to write one coherently.

(This will be changing soon. We are instituting a new course that will explicitly teach proof writing and argument making. Though it won’t be a formal prerequisite, we will advise most students to take that course first. I intend to keep the introductory feel of my course for the time being. I am sure some students can benefit from extra layers of this type of course, and it is simpler to make a course harder than it is to make it more accommodating.)

I run the course as an instance of the *Extreme Moore Method*. So class time is dominated by student led presentations and discussions of their work. They spend a lot of time outside of class finding and constructing arguments. During class meetings, they defend their work, at the chalkboard, to their peers. This is all excellent training for how to work as a mathematician, but it doesn’t cover the skill set involved in carefully writing up results.

As the process of writing is an essential one, and a big part of what characterizes academic work, that needs to happen, too. This is where the journal comes in.

## Basic Set Up

When a presentation is concluded, the student will get feedback from the class about the quality of the argument and its verbal exposition from the discussion that occurs. When the argument, or some portion of it, is accepted as correct and valuable to our class progress, the presenter is responsible for writing up the argument in the form of a short paper. This paper is due by the next class meeting.

This paper then is “submitted” to our class journal. It is refereed, and when accepted, published.

## Details

#### The Submission Process

In the past, students have used whatever word processing system they wish. Most students used Microsoft Word because they are familiar with it. As the course focuses on planar Euclidean geometry, there is not a great need for mathematical symbols, so Word is sufficient. In fact, I like that using Word encourages students to write with English words instead of mathematical symbols. Someone always figures out how to make a figure in GeoGebra, export it, and include it in a Word document, so I let that person be the class expert.

A student paper is expected to conform to the general format and style of a mathematical research paper.

At this point, the first submitted drafts usually come in on paper. In the past I have tried a class wiki, and submission of pdf by email.

#### The Referee Process

At the beginning, I am the sole referee for the journal. I mark up the papers much like I would when reading any other paper, and then make a short referee’s report. These are returned to the author. I try to return them by the next class period.

Of course, all papers are *eventually accepted*. This differs from standard journal practice, but I don’t see how to avoid this.

Some papers require several runs through the referee process. At some point, the changes required become very minor and the paper is deemed as “accepted with small changes” and the next version gets put in the queue for publication.

A few weeks into the semester, students who have proved themselves as competent authors are invited to become referees. Some care must be taken to train the students about how to do this, and some students have to be coached more than others about appropriate professionalism when acting as a referee. I try to monitor this work closely the first time through.

When I have a stable of student referees, the nature of my work changes. I act much less as a referee and more as an administrative assistant—shuffling papers and keeping things moving. Students then are engaged in the work of writing and evaluating writing.

#### The Publishing Process

Every two or three weeks I find enough papers have collected in the publishing queue that I can bundle them together to make an issue of a journal. (Four papers seems to be a minimum.) I have required papers to be turned in as .pdf files, so I can just bundle them together with the LaTeX *pdfpages* package. (I have designed a cover page that I can slap on top of each issue with a little graphic.)

I distribute the journal electronically: it is posted to the course web site. But as a treat, I print a copy of the issue for each author with a paper appearing. I hand these out at the beginning of a class meeting and say congratulations to the authors as I do so.

Students get a kick out of seeing their work in print, so this provides a little reward and motivation.

### To Be Continued:

I promised to go to the local pool with my kids this afternoon, so I’ll just stop writing now. I look forward to your questions and comments. I do plan to write a little more about this issue, so look also for my next post: **The Journal: What About Next Semester?**

I decided I cannot wait until the next post for a couple of questions.

1. How many theorems get published during the semester? It seems like your guidelines (every 2-3 weeks, need a minimum of 4 papers. . .) suggest that you might end up with about 30 published papers by the end of the semester.

Does this sound about right? So the average student would just have maybe 1.5 published papers by the end of the semester? This seems low to me. Is there other homework that is not eligible for publication in the journal?

2. Do you do any sort of oversight of the referees’ work? Do you check to see that they aren’t letting mistakes slip by?

3. How was the pool?

Bret

Brett,

I know you didn’t ask me these questions, but I can’t seen to help myself. I think TJ will forgive me/correct me/expand on anything I say.

Minimum of four papers is when the class is small, like 10 people small. There were about 20 in my section of class (I think) and journals were about 8-10 per issue. I think we were “supposed” to write about 3 papers over the course of the class.

Usually there are about 125-150 theorems in a semester. The first issue might be 4 finished papers, but things accellerate. the last issue sometimes has 15-20 papers in it as students finish up work at the end of the semester.

I do some oversight of the first or second paper a referee works on. At some point, I merely “observe” and only step in when required.

The pool was just OK. The kids enjoyed it.

3 papers is a minimum expectation, and lately I find in that case I am not always sure if that student is supposed to pass… I much prefer 6 theorems or more.

More is better. But miss Crumly accurately represents things I have said to students. (full disclosure: she was a grader for this class once.)