I haven’t shown Vi Hart in class, mostly because I only discovered her last May or June and haven’t gone back through the archive yet. I have shown some TED talks – Arthur Benjamin has one on squaring which is good for a snowy day, while Hans Rosling and Peter Donnelly are great for statistics.

I’ve got a Mythbusters clip too for scatterplots (um… this looks like a copy of it: http://www.youtube.com/watch?v=P1wEowdfRdw ). It’s brilliant because I get to ask why time is on the vertical axis (answer: because it was actually their dependent variable, they were controlling distance) and whether the line actually goes perfectly through all the points Adam lists (answer: it doesn’t, the three points aren’t perfectly collinear). Mythbusters have also tested the Monty Hall Problem experimentally, nice for probability.

]]>The film “Between the Folds” (Netflix, not Youtube) is a real beauty; I’m showing it, in sections, in Geometry this year.

Thank you for your posts! ]]>

http://www.cut-the-knot.org/ctk/NatureOfProof.shtml

The most important point in the description, for me, was the idea of transfer. Students weren’t just memorizing definitions and proofs created by Greeks over two millennia ago. They were utilizing the IDEA of precise definitions as axiomatic constructions to reach logically sound deductions. And they were doing it without any formal geometry at all!

The real point to mathematics (aside from the fact that it’s absolutely critical for anyone in a scientific or technical job), is that it helps us make sense of the world around us using the power of abstraction and generalization.

]]>I like to think geometric proofs allow students to fit some organized structure to creating a compelling argument, or conclusion. They wouldn’t just show up in court to dispute a speeding ticket with the defense of “I wasn’t going that fast, really” or “The cop should have pulled over the guy who passed me a mile earlier” as their crutch. I would hope they would more carefully plan the steps necessary to having the ticket dropped. I apologize for the sketchy analogy, but I think a court case offers up so many tie-ins to making a defense for an argument, which is one of the critical components I see in geometric proofs–defending each step of the process and justifying those steps based on previous, similar circumstances.

Maybe try my idea for a week: if a student has a genuinely perplexing question, write it on the board and seek out a resolution to it. I just did a blog post on UPC/barcodes based on my own curiosity of how they worked, but it armed me with a wealth of knowledge when a student happened to ask about it last spring. That post is available here:

http://scottkeltner.weebly.com/1/post/2012/09/remainders-not-just-the-rest-of-the-story.html

Pardon the “Top Gun” references. It sets the scene well when talking about remainders to refer to military time, though.

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