Exploring Statistics

Statistics has never been my favorite subject.  It's inherently fuzzy, and the answers always come in ranges, rather than single numbers.  It's absolutely necessary, though, when we try to measure the world.  Every measurement has some error, and understanding that error requires an understanding of statistics. 

In education, every time we test a student, there is an error in the measurement.  With a single student, and a single score, you have a great deal of uncertainty about that number.  That's inherent in the mathematics around the measurement, regardless of how good the test is.  It's only by combining large numbers of students into a group, or alternately applying a large number of assessments to a particular student, that you can begin to have any assurance that you're talking about anything real, rather than a ghost in the measurement.

Humans are inherently bad about applying our intuition to statistics.  Our languages reflect our philosophical belief that you can apply one number to any quantity.  We talk about my IQ as if that number won't be different if I'm tested again tomorrow, or even given a different IQ test today.  We talk about my height, as if it doesn't change subtly depending on how much sleep I've had, how recently I've stretched, how long I've been sitting in one place.  It's a bit of a joke to print my weight on my driver's license, a number that sticks with me through the decades as it has less and less relationship with my actual being.

Even the kilogram doesn't have the same mass as it did originally.  "The International Prototype Kilogram had been found to vary in mass over time."  Yet our thinking about the things we measure is inherently absolute.

The best thing I can suggest is to study statistics through alternate means.  Don't read a statistics book unless you really need to get some sleep.  Instead, explore the upcoming presidential election.  Nate Silver's 538 blog is fascinating because he tries to answer the question "who will win" and he doesn't take the easy way out, of just guessing randomly, calling it intuition, and hoping nobody notices when you're wrong. 

If you read his posts regularly, you'll understand why even looking at two numbers, the polling number and the "margin of error" is hardly better than just the polling number.  You'll learn how he constructed his model, what factors he decided to include, and how he decided to weigh those factors.  (Hint:  he didn't just guess.  He looked at how each factor correlated with actual results over the course of a century of presidential elections.)  And you will gain the insight he has from all his statistical intuition, developed through years of looking at and puzzling over numbers.  (It often goes like this:  "What do today's polls mean?  I'm not sure.  We need to see more numbers.  But I have a pretty good idea about what was happening last month now, because we have a bunch of data on that.")

Golden mean

I was never that excited about the golden mean (supposedly the ratio in the Acropolis of its width to its height) despite its link to Fibonacci's sequence, which is awesome.  Steven Strogatz explores the golden mean here, especially focusing on its relationship to pentagons and pentagrams.  Devil worshippers and military-industrial complex conspiracists, you're golden.

It's always worth checking out his bibliography.  It will take you to this movie about Fibonacci, which of course pretends that real nautiluses (nautili?) follow the golden mean.  But watch it anyway.

Maybe you aren't unpopular

Steven Strogatz new column explains why your friends have more friends than you do.

Almost everyone's friends have more friends than they do.  Sounds paradoxical?  Mess with your intuition?  That's the signal that the math behind it might just be interesting.

Prezi top 10

Ten(ish) uses for Prezi

1. Provide instructions for a procedure, which students can look at when they want, and at the details they care about.
2. Introducing a new concept, with an overview for everyone, and different levels of detail to provide differentiated instruction.
3. Encoding a learning game.
4. Controlling access to the words, to enforce the timing of reading along.
5. Assign a project in which students create a Prezi that explains how they solved a problem.
6. A group project, in which all the students are able to make their own edits to the Prezi they're creating.
7. Taking another boring powerpoint presentation and making it rotate and scale.  (Of limited use, but something has to be better than powerpoints.)
8. Using the features of Prezi to teach the mathematical concept of translation.
9. Using the features of Prezi to teach the mathematical concept of rotation.
10. Using the features of Prezi to teach the mathematical concept of scale.

Thanks to wildscribblings for this link.  See-through airplanes!  I can't wait.

U of Utah Math Circle

The U has a program for students interested in Math.  It meets Wednesdays 4-6 pm, starting October 10.  Any student who wants to sign up can go to http://www.math.utah.edu/mathcircle/app.html.  It sounds cool to me, and it's free.  WooHoo!

My first Prezi

A presentation about MESA's prosthetic arm challenge.

Steven Strogatz restarts his math blog for the NY times.  This time, he's working through the links between math and ourselves.  This entry discusses the topology of fingerprints and cowlicks.  Woo Hoo!