The two chapters on which I here reflect deal with informal writing.  The Gottschalk & Hjortshoj chapter starts by comparing informal writing to the rehearsals one in the arts may undertake before a performance in front of an audience.  If we think of a pianist this person does not just play in front of an audience without being prepared.  Hours upon hours of practice, rehearsing the material, improving one’s ability and so forth must precede the performance if one is to do well at it.  They paint the same scenario for athletes and actors as well.  Writing, they argue, is no different.  We cannot expect a solid performance (a high level writing assignment like a research paper) if we do not prepare students through practice (informal writing assignments, exploratory writing, drafts and so on).  Yet, they argue, we often do leaving both the instructor and the student frustrated.  I think they make a very valid point.  In fact, I argued something somewhat related in my class two days ago.  A few students expressed difficulty with the homework problems.  After we reviewed some I suggested that they go home and pick a few out of the book to do on their own for practice.  What resulted was a brief conversation where they explained that their hatred/fear of math kept them from doing extra problems (they stuck only to what was assigned, collected and graded) and where I explained that those who struggle most need the most practice.  It was interesting and eye opening.  We, of course, like what we are good at and because we like it we do more and more of it which makes us get better at it and like it better.  Rarely do we invest the same amount of time and effort into something that frustrates us, makes no sense to us, challenges us.  Though in mathematics (and elsewhere I presume) being able to work through frustration, to stick to a problem over an extended period of time, and to relish in the challenge are what make for successful students.

In my own teaching both at the high school and college level (though I admit more so at the high school level) I have tried to incorporate writing into my classes.  I saw some of the types of informal writing from the texts mirrored that which I had tried in my teaching.  At the high school each of my students had a math journal.  We kept them in a file cabinet in the classroom.  The students wrote at times freely, at times responding to a writing prompt of mine and at time answering specific questions.  Every few weeks I picked a number of them to go through and read and commented on a certain number of their entries.  They received a grade for the journal but mostly for keeping at it and doing it.  I found that giving a precise grade was difficult but really valued the ability to have ongoing conversations with students, to see how they were thinking about the material and i think students (with time) came to enjoy writing.  Initially every year I was met with resistance.  The usual “this is math class – why are we keeping a journal?” came out year after year and sometimes those protests lasted all year but more often than not the vast majority of students came to value their journal and the opportunity it represented.

At the college level I ask each of my students to write a letter introducing themselves to me as their first homework assignment.  In addition they are to write about the experiences with mathematics over the course of their lives.  I have found these to be very enlightening.  Students at times spell out what supports they might need to succeed in class, they speak about how they view the subject, how they view themselves in light of it and their goals for the course (from “I’m taking this because it’s required” to “I hope that I understand and even like math after this because right now I don’t”).  I also learned that this writing eases the worry of some of the students that are weaker mathematically (or else view themselves that way).  A student 3 semesters ago came to me after class.  She explained that she was a visiting students from Queens college and that she had already failed pre-calculus twice.  She said she thought a new school might help and how worried she was about failing again.  She thanked me for asking her to write the letter saying it gave her the belief that I really cared about the students, would tr my best to support their learning, and valued the experiences they had with the subject in the past.  In the end she passed the course mostly because of her persistence.  She came to office hours often, attended tutoring, studied often, asked questions and so on.  I wonder how much of that was a result of believing she might have a chance this time?  Or that she was somehow valued in class?

I have also tried having an online discussion in my class last semester but a lack of structure rendered that quite the failure.  Students’ posts were less and less thoughtful with time as my expectations for what should be included were sorely lacking, I am afraid.  I also had no way of counting the work they did with that and many students took that as an invitation not to participate.  I really would like to do this again but in a more structured way.  I am thinking of presenting math class scenarios to my Math 271 class who are all prospective teachers and having them respond to these scenarios online so that each week we have a discussion about one of these.  I have to think it out a bit but I think there is much potential there.  In fact, I think the Bean text highlighted why my efforts failed.  The expectations were not made clear, examples of good posts were not included, and a reward for completing the task not put forth.  In this respect I am most appreciative to Bean for including the “Explanation of Exploratory Writing for Students” (pp. 101-102) where he shares a handout used by a professor to explain to students what type of writing to submit.  The lengthy directions include (1) a clear definition of what is meant by journal writing (the “What” of the assignment), (2) the reasons for such writing (the “Why”), (3) explanation of how to go about the assignment, (4) an example, (5) answers to frequently asked questions.  More and more these readings are reminding me that directions, instructions and clear expectations affect the work submitted as much as the students’ ability to do the work does.

Also by reading the Bean chapter (especially the 25 ways to use informal writing in a course) I see how simple it is to include some informal writing in class.  I don’t really mean to say that it is simple or that one need not think through how best to do so.  What I mean is that we at times push away changes to our pedagogy  because it’ll require too much work, time, effort, etc.  However, some of these ideas can be implemented easily, without adding too much to one’s work load and in a way that weaves the writing into the course without it feeling like an add on.  If nothing else it made me think of ways I can use some of these techniques.  I like the metaphor games and extended analogies.  In mathematics these would be great to highlight the similarities and differences between two problems.  Sometimes students can do a problem (say find the midpoint of a segment when the segment’s end points are given) but if slight modifications are made to the problem (given the midpoint and an end point of the segment find the other endpoint) it becomes impossible.  Using the metaphor games as informal writing students can begin to analyze problems that while related are different in some way and doing so may help them better learn the material and be able to deal with related problems.

The generic exploration tasks for an argument addressing an issue (p. 114) seems useful to me too.  In fact if we add to the title “through mathematics” that fits right into the idea of mathematics as a tool for analyzing, exploring, arguing about social life, etc.

Well, I am off now to actually modify this very task a bit for use in my course this fall.