Long day. Full day.
I got to campus by about 7:30 so I could take care of some bureaucratic matters and get ready for the "reboot" of my MATH 179 Ethnomathematics course. My intent today was to transition smoothly from the textbook by Marcia Ascher we've been using to guide the course so far to Stanislas Dehaene's (about the relative merits of these books I blogged yesterday).
That we did: we spent about half an hour talking about least common multiples, primes, and relative primeness. These concepts all come up in understanding Mayan calendar. Though some of the students were shaky with the concepts at first, they all seemed willing to engage them, and moreover the concepts are more concrete than many of those we've worked with so far this semester (like Marshall Islander stick charts and months based on Jupiter's moons). This concreteness helped students get a grip. We even dished a bit about Gauss's formula for the sum of the first n natural numbers and the conjectural infinitude of twin prime pairs.
The smooth slide into Dehaene that I'd hoped for came with an exercise I'd put together to test one of the points Dehaene makes in Chapter 4 of his text (which students are to read for next Tuesday): people who grow up with either English (13 of the 14 students present today) or French (the remaining one of the 14) as their native language have difficulty in remembering any series of more than seven or eight randomly generated digits shown to them 20 seconds previously. All 14 students were successful at remembering five, six, or seven digits, and at eight people started to falter: two students failed to get all eight, and several more failed to get nine. No one remembered ten correctly.
Incidentally, native Cantonese speakers can generally manage 10 without difficulty. If you'd like to know more, read Dehaene's book.
I felt renewed energy in class today. I'm looking forward to seeing what the students think about the reading for next week.
From Ethnomathematics I went straight to my colleague Louise's LANG 120 (our first-year composition) course, where I was guest-lecturing on the subject of writing in mathematics. Louise hoped that I could expose the students to some of the conventions of mathematical writing, partly in order to demonstrate that many of those conventions, and the criteria by means of which the quality of writing can be measured, are not all that different from those of academic writing in general. I think I succeeded in this to some extent. It was a lot of fun! It seemed like a good class, with some very outgoing and eager students.
In Calc II I (boy, that looks weird) tried out a new format for the students' quiz. Rather than offering a collaborative quiz (as the last few have been), and rather than making the quiz a fully solitary activity, I gave the students a brief "consultation period" in the middle of the exercise. The students had several minutes to get a start on solving the problem posed to them, and then I allowed them roughly two minutes to confer with one another in whatever way they wanted to, sharing ideas, checking their answers against each others', etc. This period over, they returned to solo work before submitting their quizzes. My theory was that this format would help students in much the same way "think/pair/share" exercises help them: the initial brainstorming and groundwork is done on a solo basis, but then conference with their colleagues helps to refine their initial thoughts as they take shape.
I can't tell how people felt about this, or if it had a noticeable effect on performance on the quiz. (The students did pretty well, making, for the most part, the errors I'd expect them to make. Nothing out of the ordinary.) Only one student offered feedback on the format on the quiz itself, indicating that she felt it threw her off more than it helped her.
If you're in my Calc II class, how do you think it went? If you're not in my Calc II class, how do you think you'd respond to this activity? Would it help you? Hinder you? What up? Feedback, please!
Thursday, February 24, 2011
Long day. Full day.