Mathematical Communication

A letter sent back in time

As last year was winding down, I realized that the kids I ended up with at the end of the year were very different than the kids I began with. I thought about where they were on the first day, and how much they had learned in the intervening months. Not only did I have to get used to them and their quirks, learning differences, personalities, but they had to acclimate themselves to my course, my personality, my quirks, my method of presentation.

And so, in the last week of classes, I asked each student to type a 1 page (double spaced) letter to themselves 9 months ago. I asked them to give themselves advice on how to succeed in this course. Things they know now which they wish they had known then.

And they gave me some pretty awesome reflective letters, full of advice useful to my classes this year. Instead of me telling them that doing their homework nightly is important, or that cramming at the last minute doesn’t work, they now have it from the horses mouths. From those who were forged in the crucible of my math class.

advice-for-algebra-ii-students

advice-for-calculus-students

What’s great about these documents, read in their entirety instead of just the snippets I provide here, is that I get glimpses of my class — and the way I am as a teacher — through the lens of a student.

After talking with my colleagues, I decided not to foist this upon my students in the first few days. There is too much information flying around and it’s too potentially useful to be flung into the “first day crud” pile. Better to wait two or three weeks, when they’ve had a chance to get to know me and my class, and I get a chance to know them and their class. Then I’ll have two or three histrionic kids read a few pieces of advice.

For students, by students.

A Mathematician on Mathematics

I want to share with you an article I found on ArXiv written by mathematician Steven Krantz for mathematicians on mathematics in the larger university context. [Paper on ArXiv; or get it here.] It’s a good read for mathematicians, yes. It makes a convincing charge that the isolationist tendency of mathematics (specifically the individuals, the departments, and the profession) can’t remain so. But it’s also a really good read for high school math teachers who want to know what professional mathematicians do, how they think.

Abstract: We consider the question of how mathematicians view themselves and how non-mathematicians view us. What is our role in society? Is it effective? Is it rewarding? How could it be improved? This paper will be part of a forthcoming volume on this circle of questions.

A choice excerpt to get you interested:

When we meet someone at a cocktail party and say, “I am a mathematician,” we expect to be snubbed, or perhaps greeted with a witty rejoinder like, “I was never any good in math.” Or, “I was good at math until we got to that stuff with the letters—like algebra.”

When I meet a brain surgeon I never say, “I was never any good at brain surgery. Those lobotomies always got me down.” When I meet a proctologist, I am never tempted to say, “I was never any good at . . . .” Why do we mathematicians elicit such foolish behavior from people?

Krantz first came on my radar when I was writing a research paper on rhetoric in Wolfram’s A New Kind of Science. To this day, I have not forgotten his review of that book: the most vicious piece of academic writing I’ve come across. Ever. Krantz knows how to pack a wallop, with rhetorical aplomb. (Plus, I agree with almost everything Krantz had to say damning Wolfram’s book.)

A Scholastic Journal for High School

The high school I teach at has a student-run newspaper, yearbook, literary and art magazine, and even a foreign language publication! One germ of an idea that I had months ago has recently become something I have gotten passionate about pursuing: an online academic journal. (Open source journals exist.)

Seriously.

Think about it. Students pour their heart and souls into research papers. Okay, let me rephrase: some students pour their heart and souls into research papers. These papers are usually only read by their teachers. I think having a yearly, online academic journal for my school could really be a blessing for students and teachers alike.

My vision:

5-8 students and 2 faculty members will be the editors of the journal, which will initially be published once a year. Upper school students will be encouraged to submit year round any non-fiction pieces they’ve written and are proud of. This includes research papers for classes, papers they’ve done for independent studies, or excerpts of their senior theses. I would expect that most of the papers would come from English or History or Art History classes, but I think that research papers are written in both the Chemistry and Bioethics classes. Also, students working on investigative problems in Math Club could submit. Basically any non-fiction piece written by a student would be eligible for submission.

From the student perspective, the journal provides an outlet for students to shine, and showcase work that they’re particularly proud of. Plus, it feels good to have good work acknowledged. It’s too often that we forget to praise the good, and so often that we focus on the bad.

From the teachers’ perspective, an academic journal could act as a pedagogical tool in at least four different ways:

  1. Teachers could recommend that students submit their papers when they have done a particular stellar job. Positive reinforcement does the trick, yet again.
  2. It could also act as a way to get students who did well on a paper to ask themselves “how can I make this better?” before submitting to the journal. It sets a higher bar of expectation for students.
  3. At the same time, creating an archive of strong research papers could provide a set of exemplars that a teacher could direct students to. (“If you are wondering what a strong and narrow thesis statement looks like, see this paper written by StudentX on Invisible Man.”)
  4. The editors’ discussions over which papers to admit and to reject will not only expose student work to people other than the student and the teacher, butit will also force a critical analysis of student work. In other words, the discussion and scholarly debate that will revolve around this publication itself will be a great learning experience

Lastly, this type of journal, allowing non-fiction pieces from any department, would be the first glimmers of cross-disciplinarity at my school, where departments are independent islands which each reign supreme.

Certainly there are kinks that need to be worked out. But to me, in my vision, the benefits far outweigh the costs [1].

[1] This is intended to be a bit of an exceedingly weak pun, because actually, the monetary cost of the journal is negligible, since it will be an online journal.

Update: After reading this post, I really want this journal (if it ever comes to fruition) to have its name change with every volume!