Had a interesting geometry class today. Somehow we dealt with a.) how to deal with mistakes, b.) the relevance of geometry to art and interior design, and c.) what actually is a "bug?"
The top photo is from a page in my nature journal on which I discovered I had misidentified a bug. A few weeks ago, in this same building, we had found a live Box Elder Bug crawling on the stairway. We were having a warm spell so some of these bugs that often spend winter "hibernating" in the walls decided to come out for a stroll. I took a few photos and posted them on this blog under "Birds and Bugs." Later, when I decided to enter this event in my journal, I accidentally used a drawing of a similar bug, a White-crossed Seed Bug, as a model. Note the similarity to the Red Milkweed Bug. Later, when I reviewed my earlier blog entry, I realized I had the wrong bug. So, today, after looking over some articles on the Box Elder Bug and my own photos, I painted a Box Elder Bug and explained the correction. Drawn in this way, dorsal view, the bilateral symmetry is obvious. Also, the parallelograms I used as background of the top paintings were the subject of today's geometry lesson. The problem was, more or less, graph the following four equations on the same co-ordinate system. y = x + 5, y = x + 10, x = 5, and x = 10. We actually had some "greater than's" and "less than's" in there somewhere, since the lesson was ultimately about graphing inequalities. I placed the colored shapes behind the bugs just to make the page more colorful.
We talked for a while about mistakes. In typical high school math classes, the answers are in the back of the book. Students never get to try to solve problems that haven't already been solved. Students don't learn how to make hypotheses or to take mistakes in stride. In science, we tackle problems that haven't yet been solved. One has to be ready for mistakes, hypotheses that don't pan out. I try to simulate this in math by giving the students open-ended questions. For example, give them a drawing of a regular polygon and ask them to work as a group and list as many "facts" as they can about this figure. Their lists get surprisingly long.
Finally, we talked for a bit about what actually is a bug. When the term is used loosely by lay people, it can refer to most any arthropod, insect, spider, centipede, millipede, etc., and sometimes even worms and slugs. To a biologist, a true bug is a member of one order (subdivision) of insects, the Hemiptera. This is one of the larger orders of insects, topped by beetles, butterflies, and flies. The backs of most of them are shield-shaped, and when I was a kid we called many different species of them shield bugs.
I'm nursing a sore throat and getting sleepy, so I'll postpone any further comment, and proof-read this tomorrow a.m.
Next morning: corrected a few typos and have to add this - When I looked up Red Milkweed Bug and clicked on "images" I got a mixture of photos of Red Milkweed Bug and Red Milkweed Beetle! Two different orders of insects. They're both red, but are quite different in most respects. "Mathematics seems to endow one with something like a sixth sense." Charles Darwin.
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