When I taught stats, the first day I would ask students which was most likely to kill you in the US: a poisonous snake, a vending machine, or falling out of bed? Students mostly chose the poisonous snake. Others figured it wouldn’t be the obvious choice of the snake, but they couldn’t decided which of the other two would be more dangerous. It turns out that 7 people die a year from snake bites in the US, vending machines kill 13 people each year and falling out of bed kills 450 people annually. Students couldn’t believe it and some even accused me of lying. I then asked which was more likely to a child: a gun in the house or a swimming pool in the backyard? Again, they were shocked to find that children are 100 times more likely to die from drowning in their pool than be shot by the gun in their house. I use this to introduce the class because I told students how important the study of statistics is because we need mathematics to make sense of everything around us because we usually do a very poor job as humans. As I taught this past week, I started to see this at work in my class and thought about how it’s possible some people may not like mathematics because it defies their logic.
At the beginning of the week, students were asking me all about the probability of a choosing a perfect bracket to win the $1 billion from Warren Buffett and Quicken Loans. I showed them how there are 9,223,372,036,854,775,808 possible brackets. We then did the math to find, if every person in the world could fill out a bracket every 3 minutes, it would take about 7,291 years to complete all the possible brackets. Business Insider then posted an article saying that, if you used some knowledge about the tournament, there were more like 128,000,000,000 possible brackets. At this rate, each person in the world would only have to fill out 17 brackets to cover the more likely possibilities. You are 730 times more likely to win the Powerball jackpot. Some students in class then claimed I was wrong. This couldn’t be. There was no way it was that difficult to have a perfect bracket. The math defied their logic.
As long as we’re talking about Powerball, I’d like to bring up something I heard months ago when the jackpot was over $400 million. While buying a ticket, I heard another person say, “I won’t play now, too many people are playing. I’ll wait until it goes down and not as many people are playing. Then, I’ll have a better chance of winning.” That isn’t true. If they chose the winner by putting every ticket-buyer’s name in a hat and drawing one out, then that man would be correct. I didn’t bother explaining this to him though, it would have defied his logic.
Currently in class we are studying volume and I showed students this video made by Dan Meyer. In the video, he takes two normal 8.5″ x 11″ sheets of paper and rolls each one into a cylinder. One he rolls vertically, the other horizontally. He then pours popcorn into each one to see which would hold more. When students were asked which held more or if they held the same, almost all students said they would hold the same. Their explanation was that it was the same sheet of paper, which would then result in the same volume. Some even talked about how height and radius would change, depending on which way you rolled it, so the volume wouldn’t change, just the dimensions. We then found the volume of each and students claimed that somehow I was lying to them or had tricked them. One student even said I switched out one of the pieces when they were finding the volume of the other. Even after we did the math, they couldn’t believe that the two had different volumes. The math defied their logic.
My wife and I recently watched “White House Down” and I probably felt the same way students do in my class as I watched it. There are so many things in the movie that defied my logic. In fact, my wife says its hard to watch movies with me because I point out all of the unrealistic flaws in any movie. But, it’s possible that I’m the one that wrong and the movie is logical. I mean, I did just see a book on Bigfoot in my school’s “non-fiction” section.