For many years we have taught an introduction to logic as one of the first two units in Honors Geometry. Typically we present a single set of symbols and a single set of rules of inference, keeping everything consistent so as to avoid confusing students any more than necessary. (Some confusion is necessary. See my post of October 13.) But this year I decided to give an assignment that expands this consistent set by asking the students to consider a slightly different point of view. The idea is to step back and force a broader view of what we’re doing, so that students can see the forest and not just the trees. One way to do this is to look at other trees, such as a slightly different set of rules of inference. The big picture will remain the same, but some of the details will vary. I am hoping that this assignment will accomplish its purpose with a minimum of fuss, since I picked an alternative point of view that doesn’t differ very much from ours. (I could have used Hofstadter’s, taken from my all-time favorite book, or Henle & Tymoczko’s, from another book I like a lot, both of which I did when I taught at BU Academy, but that would require much more of a time commitment than we have at Weston. We’re just spending one day on this.)
The additional perspective will probably clarify matters for some students and confuse matters for others. The real question is whether I can arrange things so that the first group learns something from the experience while the second group is at least not harmed by it.
We do something similar at the end of the year, when we look at non-Euclidean geometries as an antidote to the “truth” of Euclidean geometry. Stay tuned for a post on that topic in June.