Month: November 2012

Explore, Conjecture, Test, Prove.

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A spider web in Kakamega forest. Good accompaniment for a mathy post?

I’m spending the afternoon grading student papers from the Foundations course, and realizing that it might have helped to separate out the process of mathematics a bit more.  We gave them a take-home assignment to write up a proof that we discussed in class, in detail.  The issue is, though, that our classroom discussion included a lot of exploration and kind of side-conversations, which have worked themselves into the submitted proofs in interesting (in the not-great sense) ways.

There’s a great course in the Budapest Semesters in Mathematics program called ‘Conjecture and Proof,’ which combines a proof-writing class with a problem-solving class.  (But it’s really focused on the problem solving.)  In Foundations we’ve been striving to get across the importance of rigor and proof, while teaching basics of proof-writing and techniques of proof.  Inevitably, though, such a project has to be mixed with some problem solving alongside: students need to write proofs that they haven’t seen before, and that involves solving problems.  So we’ve ended up a bit reversed from the C&P structure, which places a lot more emphasis on the problem-solving than the proof writing.  (And I feel a bit like we’re falling on the wrong side of history in this sense…)

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Crescent Island

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Uma Kambhampati wanders near some giraffes.

Elizabeth came into town on Thursday, which has been really fun!  On Saturday we took a trip to Crescent Island, on Lake Naivasha.  It’s where the film Out of Africa was filmed way back in 1985.  There weren’t any animals living on the island, though, so they shipped in a bunch of charismatic megafauna: zebra, gnu, Thompson’s gazelles, antelope, and, yes, giraffes.  There aren’t any predators to thin out the herds, so the island, while small, is really packed with animals.  And they’re pretty tame: one just walks around amongst them, no big deal.

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Election Day (US Edition)

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With Fulbright Scholar Erik Nordman and his wife Jen at the US Embassy’s election party.

I spent the morning of Wednesday, November 6th at the residence of the US Ambassador, where a big election-viewing party was taking place.  There were maybe three hundred people at the event, all told.  I went with a couple great Fulbrighters, leaving our hotel at 4:30 am to get to the residence at 5.  Of course, our travel calculations included time for traffic, which for some reason wasn’t bad at that hour, so we actually got to the show a bit early.

It was a very nice morning!  The party featured a mock-vote, which resulted in 166 votes for Obama, 44 for Romney, and 1 write-in vote for Hillary Clinton.  The crowd included lots of people working at the Embassy; I met people from USAID, the CDC, and the consulate, amongst others.  There were also around thirty or so secondary students who had been invited, along with some law students from the University of Nairobi who were very friendly.  And yeah, lots of free coffee.

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Teaching programming… Without computers.

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Blue vervets are probably one of the most photogenic species of monkey.

At the main maths camp this year, we had five different topic areas that we structured the camp around.  All of them used computers in a big way, except one: Programming.  The justification for this was that we had really nice, user-friendly programs for illustrating ideas in statistics, geometry, and so on, but actually throwing the students into a programming environment would almost certainly be too overwhelming.  A significant number of the students had never touched a computer before, and really taking them into a code environment seemed a bit of a stretch for people still figuring out the idea of a right-click.

That’s not to say that good computer tools don’t exist; just that we haven’t managed to review them yet.  (MIT’s Scratch, for example, looks well worth checking out.)  Furthermore, given the time-scale we were working on, I think there was a lot of value in separating the programming concepts from the physical object of the computer.  This makes the concepts available in a larger context than the computer, which, as a maths camp, we were eager to do.  The idea of setting some basic rules from which we can extrapolate is a basic idea of mathematics.  Getting across the idea of the need for precision was also of key importance.

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