In the movie, A Beautiful Mind, John Nash (Russell Crowe) explains the Nash Equilibrium by discussing the probability of picking up a girl at a bar. If all the guys go after one girl, he says, their probability of landing a date is low.Â If they work in concert, and selectively avoid the most attractive girl, their probability of getting a favorable date increases. A friend of mine once voiced a simpler explanation,Â “…you don’t go after the cheetah.”
I bring this up because of a book I’m reading about how randomness influencesÂ our lives more than we realize.Â Â The book, by Leonard Mlodinow, is called The Drunkard’s Walk.Â In the book, Mlodinow uses a number of real world examples to explain concepts of probability and chance.Â As it turns out, randomness is a rather difficult thing to manufacture, yet its presence pervades our daily lives.Â The “Drunkard’s Walk” is not just a catchy title, but actually refers to a mathematical term for random motion like the “…paths molecules follow as they fly through space, incessantly bumping and being bumped by, their sister molecules.”Â The problem with randomness, that Mlodinow points out, is that our brains aren’t really wired to understand it or take it into account in our decision making.Â Our human brains are programmed to seek order, find patterns, and make decisions accordingly.Â This programming certainly helps us learn new things, but it can also lead us to misinterpret many things in our lives.Â We sometimes see patterns where there is only randomness, and interpret something as random when it actually had a high level of probability.Â Factoring probability into our decision process changes one’s outlook and can be used to our advantage – like the chances of Nash and his buddies landing a date (the basis of Game Theory).
Because we aren’t wired to think this way, intuitively, it can certainly lead to errors in student assessment for teachers.Â It’s a lot easier to misinterpret the results of data than you might realize, especially on multiple choice tests (i.e. – high stakes testing).Â I guess this is why my grad school professors were always harping about authentic assessment.Â Though results from authentic assessments can also be misinterpreted I try to incorporate them into every unit I teach.Â If students can apply something they’ve learned to a real-world project, then I feel pretty comfortable that they’ve genuinely learned something.Â With only a traditional assessment, students may have just gotten lucky or memorized a bunch of facts, but not really learned anything.Â Does the student who got 100% on the vocabulary test really use those words in spoken or written works?
Getting lucky through a series of random events isn’t always a bad thing.Â I met my wife because my chemistry lab partner in college was her roommate.Â Had her roommate and I not been paired up, I doubt I would have ever pursued a “cheetah” like her :-).Â More recently, while visiting my parents home in Iowa, my dad told me about the book on randomness he’d just finished.Â A few days later I met my student teacher for the summer – a former engineer who decided to become a teacher.Â That same day, I received an email from an alternative energy guy I’d worked with earlier in the year.Â This all occurred while I’d been mulling over what to do with my summer school math class.Â By the end of the day, I had it pretty well mapped out – Game Theory, Toothpick Bridges, and Wind Turbines.Â Â Pictures to follow soon.