Forum Spring 2000: Metaphors, Mathematics, and Myers-Briggs

Metaphors, Mathematics, and Myers-Briggs
or How I Learned To Love Chaplin and Venn
Joanne Munroe
Whatcom Community College, Bellingham, WA
(jmunroe@whatcom.ctc.edu)

After reading articles - by Betty Field, in particular - and links online to the Labyrinth and the Forum which discuss interdisciplinary approaches and problem-solving, I was intrigued to find a "community" of teachers who wrote about classroom simulations, with an emphasis on problem solving, and the use of metaphors to speak of mathematics. The exchanges which juxtaposed metacognition, games, and the diversity of learning styles and, which framed some of the success stories in terms of Myers-Briggs analyses, moved me in a way that is hard to describe. (The best that I can say is that it got to my "teacher's soul.") The call for papers and the assumption that current research would "lay the groundwork" for the "Maricopa Learning Exchange" proposed, encouraged me to join the dialogue. I think I share your vision.

For me, flexibility, passion, and a playful tone in the classroom are indispensable. In terms of flexibility, I have found that using a Myers-Briggs-type indicator to identify learning styles and then using the results to fit projects to a particular "mix" of students, not only works well for me, but helps my students to accommodate one another. The passion is the easy part. With each student who understands dialectical reasoning, with each student who says "I thought I was stupid because I couldn't do math, but I'm not and I can," with each student who comes to the blackboard to "teach" a problem to the rest of us, I feel the "life" in the classroom and the thrill we teachers get when we are "in the zone." Inevitably, when I'm "in the zone," the students experience the joy, the delight, and the incredible fascination that mathematical patterning holds for me, and they want to "know how to get that."

For some of my colleagues, creating a playful atmosphere in a logic course is an oxymoron. Yet, if I were to identify one element that makes the integration of mathematics across the curriculum easy and successful, it would be that I approach mathematics as art, as language, and, fundamentally, as radical free play. Inspired by the Steve Martin play, Picasso At the Lapin Agile (1996), a marvelously witty look at twentieth century theory, in which Picasso and Einstein use napkins and pencils in a duel over which of them is most creative and which of their creations is most "beautiful," I try to show the students how to "bring a beautiful idea into being." In teaching them the "closed system" of deduction and the value of an algorithm, I have first worked to convince them that the structure, the pattern (confirmed or violated), is the baseline of what Keith Devlin (1994) has called the "sense of the simplicity, the precision, the purity and the elegance" from which we derive the creative and aesthetic aspects of abstract thinking and, ultimately, the incongruities which give us humor. The works of John Paulos, especially Mathematics and Humor (1980), encouraged me to use incongruity theories, jokes, and humor, in general, to teach the often confounding and unpalatable elements of counterintuitive thinking: the necessity of logic, patterns, rules and proofs.

I had such success with using Paulos' ideas to teach Venn diagrams, and I was so inspired by the works of Keith Devlin and Reuben Hersh, that I began to use musical notation, choreographer's notes, and Renaissance art (vanishing point/perspective) to help my students recognize the nature and vitality of abstract reasoning. The most controversial innovation I introduced was a lecture/practicum on mathematical "patterning" and proof in which I introduced brilliant timing, exquisite "choreography," and identifiable incongruities in a clip from Charlie Chaplin's City Lights. In my opinion, "the patternŠpatternŠconfirmation" and the "patternŠpatternŠviolation" sequences helped some students see, for the first time, what we mean when we speak of forced inferences.

In that same lesson, I told the students the story of "Theseus and the Labyrinth," and I asked them to hold on to the Chaplin images as though they were Ariandne's thread. Intriguingly, we made unprecedented headway with the propositional calculus problems we had been investigating. It seemed that all that we had needed was a common reference point, an intersubjective "thread" that we used together to negotiate the path. Then, we had it, and whether it was the patterning or the moments of laughter we shared, as we moved toward the intersection of horizons, the mood was lighter. The tension was gone. The passion was there. We all saw it. We all had it. The problems were play.