"Exponentially Better"

Dear residents in my little area of the country,

I keep hearing you use the word exponential in reference to a drastic change from one examined point in time to another.  For example, "I slept exponentially better last night than I did the night before."  Or, "My coffee tastes exponentially worse at this Starbucks as opposed to the one on Main Street."

I usually just smile and nod.  As if I understand what you're saying.

But, I really don't.

How do you know the change is exponential when you're only comparing two points?  How do you know it's not linear, perhaps with a steep slope?

To illustrate my point, let's say on Day 1 you rate your sleep as a 2.  On day 2, you rate your sleep as a 4. (I have no idea what these numbers indicate, but you must be able to rate your sleep on some kind of scale if you can make a statement like the aforementioned one.)  Well, then, maybe your sleep pattern, indeed, is following an exponential trend line:

An exponential function:  y=2^x

Or...you could have trend lines such as:

A linear function:  y=2x

A quadratic function:  y=(2/3)x^2+(4/3)

A logarithmic function:  y=2+2.88539ln(x)

And these only represent a few of the possibilities.

So, residents of the great Midwest:  I urge you--be more creative in your comparisons.  Don't assume you need to use the phrase "exponentially better."  Nay.  Why not try something like, "quadratically better," or "logarithmically better"?

Sincerely,

The Picky One

Introverts in the Classroom

I recently watched a TED talk on introverts by Susan Cain.  It was fascinating.  I related to a lot of it.  In essence, Cain says that our society often looks down on introverts.  She recalls when she went to summer camp as a young girl, expecting it to be a time to escape into the imaginary worlds created by her books, while being surrounded by many other girls her age.  Obviously, she was sorely disappointed.  One girl asked her, "Why are you being so mellow?"  As if finding your energy by being alone--as opposed to being with others--was a flaw.

Cain encourages us to let introverts be introverts, because that's when they do their best work.  And for the most part, I agree with that.

In terms of education, Cain argues against continual group work and "pod" seating arrangements. In her closing, Susan Cain says, "Stop the madness for constant group work.  Just stop it."  And receives a flood applause for this statement.

I get a lot of what she's saying, I really do.  And I don't think she's saying, "Stop all group work," because she concedes that most great works require collaboration of some kind.  But, as a teacher, (and may I add, as an introverted teacher) something didn't settle quite right with me.  Maybe it's just hard for me to take advice from people who (I assume) have never taught in the classroom setting. 

So, I'd love to hear thoughts on the following video.  As I said, I think it's excellent.  I'm just trying to digest what it means for me as an educator.

When you have to give him a B