This month's topics:
Pigeon math in the New York Times"Stumped by Math? Ask a Pigeon for Help" was the headline in the December 23 2011 issue of the paper. James Gorman reporting on a report published that day (Science 334 1664: "Pigeons on Par with Primates in Numerical Competence" by Damian Scarf, Harlene Hayne, and Michael Colombo, all at the University of Otago, New Zealand): "Pigeons have now shown that they can learn abstract rules about numbers, an ability that until now had been demonstrated only in primates." In the reported experiments, pigeons were trained to peck at images of one, two and three objects in increasing order. "It may have taken a year of training, with different shapes, sizes and colors of objects, ... , but all that work paid off when it was time for higher math." From the Science report: "Subjects were then tested on pairs of numerosities drawn from the range of one to nine. The pairs were one of three types: familiarfamiliar (FF) pairs contained two numerosities drawn from the training range, familiarnovel (FN) pairs contained one trained numerosity and one novel numerosity drawn from the values four to nine, and novelnovel (NN) pairs contained two novel numerosities." The pigeons performed above chance on all three tests. The team compares pigeons' performance with that previously recorded for monkeys, and speculates about the evolutionary history of this ability: "Our results suggest that, at least with respect to numerical competence, pigeons are on par with primates and are well perched [sic] to inform us about the selection pressures and neural structures required for abstract numerical cognition." Of ants and basketball players
The Khan Academy in the math classroomThe front page of the New York Times business section for December 8, 2011 showed photos of a teacher and a student at the Summit school in San Jose: "Jesse Roe ... can use the teaching software to monitor the math progress of students like Cheyenne Grant, 14, right." The Times reporter, Somini Sengupta, explains that the software in question is an experimental hybrid: material from the Khan Academy's playlist of short, ultrafocused math lessons is blended with traditional classroom instruction. The students are all working at various Khan minilessons on computers networked to the teacher's; the teacher can check individual students' progress and intervene if a student seems to be stuck or to have become distracted. Sengupta also gives us a glimpse into the mind of Salman Khan, the 35year old innovator who "has become something of an internet sensation" with his YouTubehoused lectures (which "got their start six years ago when Mr. Khan needed a way to help a cousin catch up on high school math." ) She tells us that, when Salman was in school, "Math became his passion. ... He came to see math as storytelling. 'Math is a language for thinking,' he said, 'as opposed to voodoo magical incantations where you have no idea where they're coming from.'"
Tony Phillips 
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