"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

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My students did incredible on the common College Algebra final that all CA students on our campus have to take.  The median for my classes was a high B.  I think that's pretty darn good considering their instructor didn't even know what was going to be on the test.

Here's what kills me.  Even though I had some students do exceptionally well on the final, and--in fact--rather well on tests all semester, I gave out fewer A's than I would have liked.  For example, I had a student whose lowest unit test grade (out of 5) was a 94.  And the kid got a B in the class.

WHY, BOY, WHY??

Because, to do well in my class you have to do more than do well on the tests.  We have homework grades and we have study guide grades (and next semester, we gonna have attendance grades, too, let me tell ya).


Because I'm such a young teacher I have adjusted my grading scale every semester, hoping that one day I'll reach something I like, while still abiding by whatever rules the college has already set up.  For example, when I was a TA, I had to enforce a pretty strict attendance policy.  I had to email every student that missed a class, tell him what he missed, and give him his current attendance count.  Once a student missed more than four classes, I was to drop him.  This was really a lot of work.

So, when I finished grad school, and could structure my courses to my own liking, I went to the other extreme:  no attendance policy.  I thought, "Why make kids come to class if they already know this stuff?"  This really applied to my students, too, as they are concurrent high school seniors who have recently seen every thing College Algebra covers.

And then it hit me.

We are a class.  As in a group.  A team.  We learn from each other, and when someone doesn't show, the group is robbed from the opportunity of learning from that student.  I am robbed from the opportunity of discovering something new about mathematics or about the learning and teaching of mathematics.

Furthermore, I don't want to send the message of, "I don't care if you come to class or not."  Because I do care!  Immensely.


Hence, next semester there will be an attendance policy.  Because I want to teach my students more than mathematics.  I want to teach them life lessons, such as we learn from each other.

And that's why I take other grades into account, too.  Like homework.  I get that not every student needs to do it (but, let's face it--for math, most college students do).  But I want to show them that sometimes in life you have to do things you don't want to do.  And the same rules apply to everyone--whether you're a math superstar or not.


So, that's how someone with a near-perfect test average got a B.  Because he didn't grasp the fact he needed to follow instructions along with everyone else, because the instructions were set up for the benefit of us a group, as a community.

It hurt me a little to submit that B for one of the brightest students I've ever had.


I'm still learning.  Hopefully I always will be...