Changing Math Education

I want to share the following 3 min video of Arthur Benjamin explaining how mathematics education in our school systems should be changed to centered around statistics and probability.

Arthur Benjamin's formula for changing math education | Video on TED.com




In his talk, Arthur Benjamin discusses how all mathematics taught in school are based on a pyramid, on which calculus rests on the top.  While calculus is definitely an extremely important part of mathematics, the majority of people will not use it during their lifetime.  However, statistics are used on a daily basis by all people.  Thus, his idea is to reconfigure the pyramid of mathematics so that statistics and probability rest on the top.

       

“There are 3 kinds of lies: lies, damned lies, and statistics.”

“There are 3 kinds of lies: lies, damned lies, and statistics.”

                                                                        - Benjamin Disraeli

I'm sure at one point or another you've heard how statisticians can wield statistics to their will and make them say anything.  This is true.  However, all people need to know how to spot truthful statistics, and how to spot those that have been manipulated.

Dishonest statistics was the topic of conversation one evening when a good friend and firefighter was in town visiting from New Zealand.  He mentioned how he read a study about how dangerous firefighting was.  However, the way they portrayed the statistics in the study was misleading.  Yes, firefighting is a dangerous endeavor.  The question is, just how dangerous is it?  I looked up a few statistics in the US to examine this.

In 2008 there were 1,148,850 firefighters.  Of these, 79,804 (7%) were killed or injured in 2008 due to firefighting.  

A first thought upon reading this may be, "Wow, if I become a firefighter there is a 7% chance I will die . . ." This is simply not true.  On its own, this statistic is misleading.  Before you go conducting analyses to predict whether or not your firefighting days will result in survival, let's examine this statistic in a bit more detail. 

First, the idea of "killed or injured" stands out to me.  There is a big difference between the two.  Let's examine this a little further and separate the deaths from the injuries.  Of those 79,804 who were killed or injured, only 104 of them were killed, and 79,700 were injured. This corresponds to less than 1 out of 10,000 (1/100th of a percent) who were killed on the job in 2008.  Are you rethinking your dreams of fighting fires now?

While we're here, let's just examine this one step further, for the sake of honesty.  Of those 104 who were killed, 42 of them were career firefighters, and 54 were volunteer. This corresponds to less than 4 out of 100,000 career firefighters who were killed on the job in 2008.  

Is firefighting dangerous? Of course it is! I'm not trying to demean the bravery and hard work of the many men and women who dedicate their lives to saving lives.  However, let's not make the numbers into something they're not. After all, we statisticians are not liars, we are wielders of truth.

Data Source: National Fire Protection Association

  

Some People Don't Like Statistics?

When I first meet people and I tell them I'm a statistician, 90% of them respond with a comment about how difficult stats was or how much they hate the subject. I'm amazed at how many people think they don't like statistics. From watching the news, to calculating how long it will take you to get to work that day, to deciding what to eat for breakfast, statistics are part of everyone's everyday life. So what I want to know is, what's NOT to like about statistics?

Picture this, your alarm goes off in the morning and you’re still tired.  You determine that you can press the snooze button twice before you absolutely must get out of bed in order to make it to work on time.  How do you know you can press the snooze button twice? You know that because you know it will take you 30 minutes on average to shower and get dressed, 10 minutes to take your dog out and feed him, and 45 minutes on average to get to work, provided there isn’t any rain, snow, or traffic accident.  Sound familiar? You planned your entire morning out based on statistics.

Before you run out the door, you glance back and forth between the apple, the pastry, and the cereal.  The apple would be the healthiest choice, or perhaps the cereal provided it’s not loaded with sugar, but that pastry sure smells and looks delicious! How do you decide what to eat for breakfast? Statistics.

For those of you who are sports fans, have you ever tried to predict which team will win the big game? Played fantasy football? Filled out an NCAA March Madness bracket? How did you decide who would win the game, or which players to select? More statistics.

What about those of you who are homeowners; did you ask your real estate agent for comps for other homes in the neighborhood you reside in? Did you look at the previous sales prices for your house, previous real estate taxes, estimated monthly bills, and average price per square foot? All statistics.

For those of you who were students at one point or another, have you ever converted your homework score into a percent correct score? It’s nice to know that you answered 17 out of 20 items correctly, but knowing that you answered 85% of the items correctly is more meaningful.  By doing this you’re calculating statistics. Did you ever get a test back and ask your teacher what the class average was?

So you not only like statistics, and calculate them on your own, but now you are even asking other people for them?!  So what you’re telling me, is that you like statistics! That’s not a question, it’s a “fact” (a word seldom used in statistics).