CapitalistImperialistPig

Yet another commission concludes that American kids suck at math. This one sounds more sensible than most: The sharp falloff in mathematics achievement in the U.S. begins as students reach late middle school, where, for more and more students, algebra course work begins,” said the report of the National Mathematics Advisory Panel, appointed two years ago by President Bush. “Students who complete Algebra II are more than twice as likely to graduate from college compared to students with less mathematical preparation.” The report, adopted unanimously by the panel on Thursday and presented to Education Secretary Margaret Spellings, said that prekindergarten-to-eighth-grade math curriculums should be streamlined and put focused attention on skills like the handling of whole numbers and fractions and certain aspects of geometry and measurement. They seem to be trying to steer a middle ground between the currently popular "discovery" math ideas and old fashioned computation: The ...

Bert and Dave were cruising the streets of DC, Dave at the wheel. Bored, Bert reaches into the glove compartment and pulls out a map. "Hey Dave," he says, "this is a map of DC inside the beltway." He looks at it for a couple of seconds, crumples it up, and tosses it out the window. Not being a litterbug, Dave screeches to a halt, and gets out of the car, muttering. Bert is undeterred. He too jumps out, runs over to the map, whips out a Ben Franklin and says: "I will bet this fifty hundred bucks that there is some point on this map that is exactly above the point in the City that it represents." Should Dave take the bet? UPDATE: As Wolgang noted, this is the fixed point theorem of Luitzen Egbertus Jan Brouwer. (In this case implying that any continuous map from a disk (say the inside of the beltway) to itself has a fixed point). In session 10 of Conceptual Mathematics the authors deploy the map theory they have taught us so far to prove Brouwer...