hero worship

Consider a question like, “How many pairs of shoes do you own?”  I am guessing most people in the U.S. would answer somewhere in the neighborhood of two to thirty pairs of shoes.  According to the Daily Mail, the average woman in the U.K. owns nineteen pairs of shoes but wears only seven.  But that’s not important.  What I want to talk about is the woman that owns two hundred pairs of shoes.  She is unusual by almost any standard and statisticians would call her an outlier.  Outliers are pieces of data that alter the outcome in significant ways, so much so that sometimes statisticians throw them out on the grounds that they are not reflective of the general population.  Outliers are impactful.  We can decide how much impact we want them to have.

So there.  You learned a little statistics.

Now consider this movie plot.  An experiment in a lab causes a spider to become infected with a radioactive virus.  The spider then bites a man.  The man dies.  The spider dies.  End of story.  Not much of a story is it?  No one tells this story because it is both predictable and unexceptional.  No one cares about the story where Peter Parker dies.  But we love the story where Peter Parker becomes a super hero.  Spiderman is unusual.  He is an outlier.

Our deep worship of and fascination with the outlier is culturally entrenched.  Everyone loves the story of a person that overcomes incredible odds to excel.  We also watch the fall of our heroes played out in the media with glee. 

So how does this relate to education?

It seems love of the outlier colors our every desire, our every

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decision.  We want our schools to “pull themselves up by their bootstraps” no matter the budget or the challenges of poverty, violence, and health that the children face.  We demand that teachers meet every child’s needs, differentiate every lesson, overcome every setback, because that’s what Jaime Escalante and a few other teachers somehow managed to do.  We envision our schools and our teachers as somehow able to work miracles and fix what has taken decades to break.  And we don’t even apologize for our expectations.

Part of what's hamstringing education today is the demand for outliers.  Heroes do things faster and better, and so do our best schools, teachers, and students.  But this cannot be the expectation.  We can certainly use excellence as a model, to use awesome as inspiration, but in the end, to expect it from everyone is not reasonable.  There's a reason why everyone cannot be an outlier.  Outliers are rare.  Heroes are rare.  Demanding more does not make a hero. 
 
On the flip side, I think it’s perfectly o.k. to want these things, to hope for a hero. But hope is not a plan.  I am a math teacher.  My job is to teach kids math, assuming they want to learn, and they had breakfast, and they didn’t have a fight with their boyfriend, and they can concentrate for more than a minute, and.. and… and…  If I’m lucky, in the process of teaching math, I might just stumble into some lessons of hard work, compassion, leadership, overcoming adversity, and helping others. 

That’s it folks.  That’s a good day. I’m not a hero.  I’m a teacher.  If you want me or my school or these kids to be heroes, to be outliers, you’re going to have to help.  And by help I don’t mean inventing more hoops for us to jump through, more tests to take.  I mean putting your time, your money, and your wisdom where your mouth is. I mean actually doing something to help schools, teachers, and students.

Does your school have the supplies and computers it needs to be successful?  Do your school’s teachers have the time and training to do the job well?  Do your school’s students have the tutors and one-on-one attention they need to be successful?  No?  So what are YOU going to do about it? 

What if I expected YOU to be an outlier? Hey hero, how does that feel?

 

TEDTuesday: the best stats you've ever seen

This talk from Hans Rosling is one of my all time favorites.  I always use it in my Leadership and Service course when we talk about service projects in the developing world.  But it is truly a beautiful illustration of statistical data.  It simply turns what could be a complicated set of numbers into a fabulous explanation of change over time.  Truly incredible! 

pants on fire

Consider this gallop poll from October, 2012, just a few weeks before the election.  What conclusions would you draw from looking at the graphic?  Does it seem like Romney has a good lead?  Does it seem Romney is pulling ahead?  There's a lot of unanswerable questions in this graphic that are really important if you want to understand what the data is telling you.

First what is the sample size?  Is it 20 people or 1000?   
How were people polled? Registered voters, likely voters, random folks?
How sure are you of your results?  What if I said the pollsters were 80% confident?  What if they were 99% confident?

All of these questions are important and because you don't know the answers, the pollsters can draw whatever conclusion they want from the data.

Here's what I mean.  What if the accompanying text told you  that 1000 random registered voters were surveyed.  I hope that would make you more confident than if 20 people in Chicago were selected.  It is Gallop, so let's assume those 1000 random, registered voters are guaranteed. 

What if you knew that the margin of error was plus or minus 4%?  What conclusion would you draw about the October 15 poll?  I hope you can see that if the error could be 4%, then the October 15 poll was pretty much a statistical dead heat.  What if I told you the margin of error was plus or minus 2%?  Then you might conclude that Romney was ahead on October 15. 

The sneaky part is that Gallop and anyone using this poll can actually make both of those claims by manipulating how confident they are with the result.  If they are 99% sure of the result, then the margin of error is a whopping 4%.  If they are only 80% confident, then Romney takes the lead.  And the average reader will never know the difference.

So why am I talking about these ideas?  Well, I am teaching my statistics students this information right now, but more importantly, in these kind of political scenarios, where races are fairly close, it is possible to make the numbers say anything you want them to simply by manipulating the sample size and the level of confidence you prefer.  This means that a particular media source can literally call a winner in any close race simply by bending the statistics.  And this explains why two polls can have completely different results. 

I'd like to think that the media is acting with integrity when they report on polls, but to be fair, recent events lead me to believe otherwise.  If you really want to use mathematics to call political races, I would lean toward Nate Silver's blog, FiveThirtyEight.  The man is a statistical genius (yes I have a mad crush on him), and he correctly predicted nearly every race in the 2012 election.  For the sake of harmony in my own life, I'm going to head there during the next election and consider his efforts the most credible source for predicting results.  Then I can skip all the hot arguments on Facebook. 

rolling the dice

At the start of school a colleague asked me, "Can you use these?" and handed me a box of dice.  They weren't regular 6-sided dice.  They were crazy dice with 8, 10, 12, or 20 sides.  They were a dozen different colors, beautiful and unique.  I spent some time thinking about them and considering whether I could use them to help students learn something about probability.  I asked my students, "How can we figure out if any of these dice are 'loaded?'"  Together we built a project where they rolled the dice many times and attempted to determine whether the dice were loaded, whether a certain number came up more often than was statistically likely. 

Each student chose two different die and calculated the theoretical probability of each roll.  Then they rolled the pair 300 times and calculated the experimental probabilities.  Finally they commented on whether they thought any differences were significant.

In hindsight, I probably should have waited until later in the year when we study how to determine the statistical significance of differences in data, but I am pretty satisfied with how this went.  We got a chance to practice using excel, the students did something they'd never done before, and I got to take advantage of a lucky windfall. 

This is what I love about teaching, the opportunity to take a chance, try new ideas, and evaluate their effectiveness.  I encourage my fellow teachers to go ahead and roll the dice. 

Just for fun, consider a pair of dice, one with 8 sides, one with 12.  If the sides are numbered 1-8 and 1-12, what is the probability that you will roll a lucky 7 on this pair of dice? 

(The probability of rolling a lucky seven on a pair of six-sided dice is about 16.7%)

we need to talk

xkcd.com #385

Today in calculus class we were playing a game to determine the "Supreme Awesome Student of 4th Period."  Several students were absent and someone noticed that there was only one female student in class.  In fact, only 20% of that particular section are female.  In my other calculus section, 45% of the class is female. 

One student commented as a "joke" that women aren't good at math anyway.  Of course I set him straight, but it got me thinking about the most visible academic role models in my students' lives, their teachers.  I did a quick survey of my school's faculty and got the following results.  You can see a listing of all of our faculty at our website. 

Department	% Female	% Male
Math	83%	17%
Science	58%	42%
Social Science	40%	60%
English	55%	45%
World Languages	81%	19%
Fine Arts	60%	40%
Computer Science	50%	50%
Physical Education	50%	50%
Entire School	61%	39%

It turns out roughly 60% of my school's faculty are female.  Women constitute at least half of every department except social science.  These are quick numbers.  I made no effort to weigh the difference between a part-time and full time member of a department.  Some members of our faculty teach in two departments, and I have no idea whether these numbers are typical of private 6-12 schools like mine or private or public schools in general. 

Today's class got me thinking about the fact that a student in our school would make such a statement despite the fact that 83% of the math department faculty are women, and he himself has never had a male math teacher at our school.  (I checked)  I also wonder about the conclusions our students draw about academic work and the career paths they might pursue based on the role models that surround them. 

I think there's a lot to think and talk about in this event.  I welcome your thoughts. 

An interesting SciLog blog post:  Math is a Girl Thing

XKCD credit