Tag Archives: incongruity

Classroom Improvisation: a favorite moment from my teaching

I used to teach a research methods class that appealed particularly to students writing Masters and Doctoral theses. My students came from several different disciplines, and from all over the world. What they had in common is that they were all facing the terrifying prospect of having to do an extended piece of original research, and then to write what would be by far the longest research paper—a book, really—that they had ever produced. They were wonderful students to teach, because they were dedicated to making the world a better place, and because fear concentrates the mind wonderfully and made them very motivated to learn.

The class was a three hour seminar, and because three hours of talking can be deadly, I always had the students do something that took them out of their seats and got them using a different part of their brains. On this day, I had hung large pieces of paper around the wall. Each page had a different question or caption, and I asked the students to move around the room and write something on each sheet, in response to the question posed. One page said “The thing that scares me most about doing my research is…,” another said “What I most want to accomplish with my thesis is…” One said “A picture of me as a researcher.” This was the one I most enjoy, because the social sciences, which I teach, are so often entirely verbal and text driven. One of my favorite things to do with students in my classes is to use pictures, Lego, hands on exercises, and other things to get them out of a purely text-and-talking mode.

After the students were finished, I walked around the room, commenting on what they had written on the flipcharts. My last stop was the chart of self-portraits. In the bottom left hand corner was a little cartoon of a pig with wings, surrounded by the legend “when pigs fly” and “a snowball’s chance.” I knew who had drawn this one. I’ll call him Joseph. He was an engineer from a developing nation in Africa who was here in Massachusetts to get a doctorate, and his passion was the recycling and redesign of electronic products to prevent environmental harm. He was new to the US and homesick for his family, but determined to do well. He was struggling more than his fellow students, who had all been in their respective degree programs longer than he had. I had already spent considerable time with Joseph outside of class, at his request, because he was so concerned about whether he could do well in the course and had so little confidence in his ability to understand.

All the drawings showed students who were frazzled, at sea, overwhelmed, but Joseph’s was ostensibly the most hopeless. Although I didn’t look at Joseph when I pointed to his drawing, I could feel him tense as I began to speak. He had not signed his drawing, and I didn’t say whose drawing it was, but watched him out of the corner of my eye. I said “This student is afraid of not being able to do what he has set out to do. He thinks he will succeed only when pigs fly. Well, I have news for him. Pigs don’t fly, and they will never fly.” I could feel, rather than see, Joseph sagging into his chair as I spoke. “But the good news is, that although pigs cannot fly, there are other things that they can do very well. Pigs are great at hunting for truffles, which they detect through careful searching and dig out of the ground, like precious gems. Research is a lot like hunting for truffles—pursuing and finding gems of insight in a vast field of dirt. So for all of you, if you are a pig, don’t try to fly. It won’t work. But do what you do best—do what you are good at, and what you are passionate about, and you should be a good researcher.”



Filed under creativity, learning

Crocheting Hyperbolic Planes

A hyperbolic plane is a mathematical object. I first made its acquaintance through the work of Daina Taimina, author of Crocheting Adventures with Hyperbolic Planes. The photograph in the previous post is of a crocheted hyperbolic plane I made this past summer.

Taimina’s book won the Diagram Prize for Oddest Book Title of the Year for 2009 (the prize was originally conceived as a way to avoid boredom at the annual Frankfurt Book Fair, and has been awarded annually for more than 30 years.) In her blog, Taimina writes, “Best of all, in The Booksellers announcement I liked what Mr. Bent said about my book:

I think what won it for Crocheting Adventures with Hyperbolic Planes is that, very simply, the title is completely bonkers. On the one hand you have the typically feminine, gentle and wooly world of needlework and on the other, the exciting but incredibly un-wooly world of hyperbolic geometry and negative curvature. In Crocheting Adventures with Hyperbolic Planes the two worlds collide—in a captivating and quite breathtaking way.”

Mr. Bent’s reaction to the book was mine as well. I was drawn to the paradox, the incongruity. I had no interest in math, and really no interest in crochet either, but the idea of the book stayed with me. I don’t recall how I first heard of the book, but I think it was before the award was announced. Perhaps my brother, Nat Kuhn, who has a Ph.D. in Mathematics (his dissertation adviser William Thurston–winner of the Fields medal–wrote the introduction) told me about it. I know I bought a copy in the Winter of 2010 for my students in the Olin College of Engineering extracurricular “Fiber Arts for Engineers.” Then in September 2010, Taimina spoke at the Common Cod Fiber Guild at MIT (fiber guild? a bunch of knitters at MIT? Absolutely!) Of course I had to go.

At her talk, Taimina answered the question you are probably asking too: what IS a hyperbolic plane? Her simple and accessible answer is more or less as follows: an orange is a surface of constant positive curvature; a banana has both positive and negative curvature; and a hyperbolic plane has constant negative curvature. Imagine the ruffled edge on a leaf of kale, my personal favorite hyperbolic vegetable. Or the ruffles found on other natural things, such as some seaweed or the inhabitants of the coral reef (the inspiration for the Crocheted Coral Reef, an effort sparked by Taimina’s work.) These real life objects, of course, are not perfect models of the mathematical ideal–but they bring us close, and are lovely inspirations to mathematical inquiry.

In spite of all this inspiration, it was not until this past February that I finally decided to try my hand at hyperbolic crochet. I bought some cheap fuzzy synthetic yarn at a local big box store and set to work. The directions in the book were fairly minimal, and minimal is all you need–if you already know something about crochet. I struggled with my yarn, and soldiered on, but as I did my misgivings grew. What was I doing wrong? What was I doing right? I had no idea. I didn’t even have much idea about how to get help. At last I came up with the idea to go to drop-in night at my local independent yarn store, and I did get a little lesson on how to crochet. Finally, the penny dropped when I went to an hour-long workshop on “crocheting a hyperbolic dishcloth” (yes, you read that right) at Common Cod’s spring Fiber Camp. Thanks to Rachel, my teacher, who helped me see the light. My skills are still extremely rudimentary, but they are good enough to allow me to churn out the hyperbolic planes at the rate of one every week or two since March! Thank you, Daina!

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Filed under fiber arts, mathematics