Thursday, October 31, 2013

superpig to the rescue


I finally sat down at my desk at 5:00pm and had time to think for the first time.  I sat just breathing for a moment and let the meetings and the papers and the classes and the sheer craziness of the day wash over me.  I looked across my desk to one of my favorite things.  This silly purple pig was a prize won by my students last year for selling magazines as a fundraiser for our school.  They earned Superpig because I asked them to do it.  I had never won a pig before and these students tried extra hard just so I could have him.  Groups that won the pig were entered in a pig race.  Superpig got last place last.  
 
I love this pig.
 
Whenever I am feeling a little down, I turn on Superpig and his snorting shuffle always makes me laugh.  He reminds me that I work in a wonderful place with amazing students and dedicated colleagues, and no amount of crazy will ever change this. 
 
I really needed Superpig to cheer me up.  Batteries practically dead, he gave me what he had and I am grateful.
 
Tomorrow I will begin again. 

 
video

can I borrow a calculator?

Day 3 of Spirit Week was an exciting one.  The day's events included the annual Powderpuff Football game.  Our junior and senior girls faced off in flag football, the boys acted as coaches and cheerleaders.  I have mixed feelings about this event always.  I am a huge fan of the idea of supporting our female athletes.  In fact, the crowd was quite large and plenty rowdy.  But of course our boys always push the limits of parody wearing matching short shorts with words emblazoned across the rear.  They did lead the fans in rousing cheers and even created some interesting pyramids and lifts. 

The game was rough and close with several tackles rather than simple flag pulling.  The seniors led at the half 13-12, but the juniors came back to score one more time.  In the the end, the juniors upset the seniors, 18-13. 

As I walked toward the parking lot, I thought about this event and listened to the kids talking.  "This was the best game ever," proclaimed one male cheerleader.  "That was so much fun," another junior raved excitedly.  My own junior cub and coach told me the class plan was to "win everything."  I am sure a bunch of seniors have other ideas, but the rivalry is clearly on.

There were a couple of minor injuries and a possible torn ACL in our starting softball catcher.  I wonder whether she will think it was worth it if she can't play this spring.  I saw her this morning, frantically hopping around in a knee brace looking to borrow a calculator to take her math test.  Gears shifted, she is already back in student mode.

I'm not sure I have any deep and meaningful revelations today.  Instead I am reminded that youth are resilient, gender stereotypes are persistent, traditions are powerful, and worry is wasteful. 



Wednesday, October 30, 2013

now I've heard everything

Homecoming week:                     Day 2 - Benjamin Button Day

I never saw the movie or read the book, The Curious Case of  Benjamin Button, but my understanding is that he is both old and young in the story.  Our students were instructed to dress as a child or a senior citizen.  Those dressed as toddlers wore footie pajamas and carried stuffed toys.  Those dressed as seniors wore bathrobes and slippers, plaid suits with high water pants, or house dresses.  A few had canes, spectacles, and powdered hair, walkers, or wheelchairs. 

The net result was that students mostly came to school in their pajamas.

I was going to write a treatise on our cultural stereotype of senior citizens, but then a student stopped me in my tracks with the following question.  

"May I go to the restroom?  I think I have my diaper on backwards." 

You can see how this week gets out of control by Friday...

Photo Credit

Tuesday, October 29, 2013

mirror, mirror

On Monday we began spirit week, a five day celebration of school spirit.  I will attempt to chronicle some of the events of the week, but to be fair, there's no way to describe the inevitable, escalating spiral into chaos.  Most days I make a run at getting something done, but by the end of the week, there's little I can do but laugh and enjoy the ride.  The students are happily enjoying their school, their friends, and being young.  I am going to indulge in two of the three.

Monday:  Dress up as your alter-ego day.  The students are interpreting this as dress as what you are not.  Thus far I have seen students dress as cowboys, goth girls, members of various athletic teams, skaters, nerds, their parents, hippies, rockers, rappers, the opposite gender, and a host of characters that I don't recognize.    

I think it's a worthwhile exercise to consider what you are not.  I was interested in how this day would turn out, as I think there is some potential here for offense as we dive into stereotypes.  What we are and are not is sometimes a matter of genetics, more often a matter of choice.  Others can often clearly see who we are, simply by considering our dress, our words, and our behavior.  But what does it say when we choose one aspect of ourselves and highlight that it is specifically what we are not?  I think it begs the question, why is this what you are not?  


I dressed as normal.  The kids asked me what I was.  I replied "not cool."  I don't think they got it... 

Photo Credit


Monday, October 28, 2013

truth... with a side of bacon

Teachers are actually people. 

I know that seems like a ridiculous statement, but I think people forget sometimes that we are just like everyone else most days.  We don't have superhuman abilities to manage teeneagers.  We don't have endless patience.  And we definitely have lives, friends, and family.  Our weekdays revolve around our school and our students, but I just want to mention one thing to all those readers out there, be you parents, students, colleagues, or friends.  

NOT EVERYTHING IS ABOUT YOU.

I see my students everywhere in the Orlando area, in restaurants, at concerts, in the grocery store.  I remember one student looking in my cart, and asking in a stunned voice, "You eat bacon?" 

Yes...  yes I do.  I've also been having a decade long on-again, off-again love affair with Swedish Fish.  I do a lot of things that students and parents don't know about.  I have interests and friends unrelated to my career.  I have my own children and some days they drive me nuts.  They drive their teachers nuts sometimes too.  And I know this will shock you, but I'm not a superhero.

So I'm asking you, dear reader, to cut teachers a break.  We have bad days.  We lose our temper.  We are sad and happy, excited and exhausted.  And all this means that not every day is a perfect day for us or for our students.  We are truly sorry for those days.  But we keep coming back because we believe that maybe for one kid, maybe for your kid, we can make a difference. Even on a Monday morning, we come back to try again, because we love our disciplines, our students, and our schools.

And bacon...  I for one definitely love bacon.

Photo Credit

Friday, October 25, 2013

surf's up... the solution

I think it's easy for people that love math and have studied it for years to quickly grasp mathematical ideas and solutions, simply by reading them.  To those with passions in other disciplines, reading about how to do a math problem may be both unsatisfying and a challenge.  I am going to try to explain the solution to the surfing problem without any fancy math terms or formulas.  The answer will be a little less precise, but I hope to give you some insights in how to think about the problem  You can tell me if this makes sense.

Here's the question again: 

The Surfboard Store sells Special Surfboards that
are so carefully made that only 1 in 1 thousand
is bad. The store tests all Special Surfboards
using a test that is 99% accurate. If you buy
a Special Surfboard that tests bad, what is the
probability that it really is bad?

Start with the first sentence:  One in a thousand surfboards is bad.  Let's look at a thousand surfboards.  How many are actually bad?  I hope you said 1. 
 
 
The next sentence says that the test is 99% accurate, meaning that 1% of the time it misidentifies a surfboard....  so in the remaining 999 good surfboards, 1%  or about 10 will be identified incorrectly as bad when they are really good. 
 
 
Thus we have 11 surfboards identified as bad, but there is only one surfboard that is actually bad in the bad group.  1/11 is roughly .09 or 9%.
 
Thus the probability that a surfboard identified by the 99% accurate test as bad actually is bad is only about 9%. 
 
 
What makes this idea important in my mind is less about the calculations and more about the counter intuitive nature of the solution.  When we hear that a test is 99% accurate, we tend to think that it must be absolutely correct.  

There are interesting implications when we apply this idea to politics.  There are life-changing implications when we consider this idea in the context of medicine. 

Statistics is an incredibly important and largely misunderstood discipline.  Math teachers have an important responsibility in addressing this problem.  I'm not sure we are doing the job very well. 

I welcome your comments on this problem's explanation and on statistics in general.
 

Thursday, October 24, 2013

surf's up

What if I tried to teach you some math?  I know, a word problem...  the most dreaded thing in all of mathematics.  Let's make it about probability, one of the most misunderstood and difficult things for folks to master.  Wanna try?

This is a problem offered to our students this week in the monthly Florida Math league contest.  Lots of schools across the state participate.  Not many of our kids got it, but surely you are smarter that a high school student, right?? 

The Surfboard Store sells Special Surfboards that
are so carefully made that only 1 in 1 thousand
is bad. The store tests all Special Surfboards
using a test that is 99% accurate.  If you buy
a Special Surfboard that tests bad, what is the
probability that it really is bad?

Think about it a while and put your answer in the comments here or at the forum where this is posted. (or you can message me if you're shy) I will try to explain the answer tomorrow. 

Tuesday, October 22, 2013

fold, spindle, and mutilate

This weekend I went to an Florida Council of Teachers of Mathematics (FCTM) math conference and heard one of my all-time favorite presentations.  I've been to literally dozens of conferences in my career, so calling this a favorite really means it was great.  The session was led by Jean Adams, a "born again" teacher who joined the profession in her forties.  She is dynamic, energetic, and still in love with the job. 
 
Jean had a lot of ideas, but we spent most of the time  building foldables, something I've never much been interested in.  They feel kind of artsy, something that I do not do well.  They require a little bit of 3-D visualization, at least at first.  This is definitely my weakness.  I looked around the room and everyone seemed to be getting it but me.  I felt like I arrived late to a party. And not in a fashionable kind of way. 
 
The good news is that I do know students need to learn in a wide variety of ways and foldables are a great means of engaging the kinethetic learner.  Like any good teacher, I realize that even though I don't learn this way, I know a good thing when I see it.  Foldables are definitely a good thing.
 
Jean had us build this review foldable for AP Calculus.  It's a jam-packed full of calculus goodies.  I can't wait to share it with my students this spring! 
 
You can get the foldable for free here.  You need to sign up for teachers-pay-teachers.
 
You can check out Jean's website for more great ideas here.

What do you think of foldables? 

Monday, October 21, 2013

things you might not know

It's a Friday and when I walk into class, 12 of my 17 students are absent.  Some are on an art field trip to the Salvador Dali Museum, others are at Epcot touring the French-speaking pavilions, a third group is on a forensics trip, and the rest are at a college meeting with a rep from FSU.

My planned lesson no longer possible, I scramble into lateral reinforcement mode.  All teachers know this place.  Our best laid plans in shambles, we throw something together that helps the students practice whatever we have been studying with a little more depth. 

Before we start, I ask the remaining five students to teach me something they know about that I might not. They get to take on the role of teacher, and I become the student.  It's an interesting exercise for everyone.  Here's what I learned, although I make no promises as to the veracity of this information. 

  • When rowing, one should activate body parts in the following order:  legs, back, arms
  • Johnny Cash burned down a national forest by crashing his car into a tree and leaving it there
  • Our weight-lifting coach, Mrs. Miller, has mastered the death stare and when she trains it on you, be very afraid
  • Monkey's guitarist Mike Nesbitt's mom invented liquid paper.
  • When scuba diving, nitrogen builds up in the bloodstream, causing a feeling of intoxication 
Your turn.  Teach me something...

Photo Credit

Friday, October 18, 2013

isn't it romantic?


Somehow it became a thing for our students to ask each other to dances in very cute, creative, and public ways.  "Hey, you wanna go to the dance with me?" just won't cut it.  One of our football players got some help from his teammates to ask a volleyball player to homecoming.  Perhaps romance isn't quite dead yet. 

Thursday, October 17, 2013

pirates, skateboards, and leeches

Our school runs on a modified block schedule.  This means that two days per week we see only half of our students for 80 minutes.  On one day we see periods 1, 3, 5, and 7 and on the next day we see periods 2, 4, and 6.  Teachers are actively discouraged from lecturing or testing for 80 minutes.  Instead they are encouraged to engage students in new ways, to build lessons that take advantage of the extra time to creatively do many things or just give one thing the time it needs to be done really well.
 

There's no coffee in my building and in a brief stroll across campus yesterday, I saw so many wonderful things.  

  • Photo teacher Ryan Bowden was zipping down our driveway on a skateboard to assist our students in learning to photograph motion.  
  • Fortunately he did not spook the horses invited to campus by art teachers Kym Moreland-Garnett and Irina Ashcraft as they encouraged our drawing classes to expand their skills. 
  • Georgia Parker greeted her students dressed as a flight attendant and handed out boarding passes in a student recreation of the opening of "Lord of the Flies."  This time students invented their own characters and wrote about what would happen during and after that fateful flight. 
  • Speaking of crashes, a crash in the physics lab meant Mike Arney's students were exploring the difference between the theoretical and experimental acceleration of falling objects.  (It turns out they are not the same)
  • Outside on the quad, Susan Lilley's students recreated a scene from "Much Ado About Nothing" as a pirate adventure complete with costumes. 
  • In Lali DeRosier's Animal Diversity class, students spent the morning studying the behavior of leeches, positing that they would be attracted to heat.  One student told me he had a "bad leech." 
The good news is that I didn't have to try hard to find great things happening.  Teachers given the time and encouragement to bring learning to life will do so eagerly and in amazingly unexpected ways. 

This makes me want to take a lot more coffee breaks...


Photo Credit

Wednesday, October 16, 2013

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
 

Tuesday, October 15, 2013

it's all talk






Conversations I had yesterday at school












  • How cancer has impacted our lives and school.
  • Why our geometry teacher is so awesome. 
  • Why the senior class and their parents are so stressed out.
  • How we might use homework more effectively. 
  • Why you should use your brain AND your calculator to answer questions.
  • What to expect on the PSAT.
  • Why our government is having problems.
  • How to be more successful on the next test.
  • Why we should start a new TEDTalks type club on campus
  • When we can have the next meeting of Mu Alpha Theta.
  • Where is the best place for sushi.
  • Who is responsible for helping the middle school math teachers.
  • Why am I still at work.
  • What is for dinner.
What did you talk about? 

teacher pay

Ask any teacher and she'll tell you it's never been about money.  If you want to keep her coming back day after day, it's just this simple.  Why not make a teacher's day?
 
Thetruffles are optional.

 

Monday, October 14, 2013

your comments are appreciated


This past week was the end of the quarter and at midsemester we take the time to not only give students grades but also write comments on their progress this far.  Student grades are posted every two weeks, so there are really no surprises, but this practice continues on.  It is definitely a time-consuming process.  I often wonder if the parents read what we write.

Here is a sample:

John is off to an uneven start in Geometry. He completes assignments consistently and seems to have a reasonable understanding of the ideas we discuss, but he is not always able to translate that into performance on tests and quizzes. I have asked John to see me to discuss his mistakes, but I have not seen him lately in study period. It is likely that a little time reviewing with me before the next test would go a long way toward ensuring that he has the details mastered. John is quiet in class and only speaks when called upon. I would love for him to take a little initiative and start putting his work on the board and volunteering to answer questions. The more he engages in the class on a daily basis, the more he learns. John has plenty of potential, and I look forward to his efforts in the coming weeks.

Friday, October 11, 2013

technological marvels


Technology is changing at light speed and the human ability to change with it is in a race to keep up.  My colleague, Jen Baselice, assigned an innovative project to her students.  She got some interesting results.  I welcome her thoughts as today's guest post. 


So I had this idea to have the 7th graders create "review websites" after our unit on solving one-step equations and inequalities. I had a few reasons for doing this:

1) I needed some time to work during an especially busy week. 
2) I wanted them to use technology for a project.
3) I REALLY wanted them to learn how to find appropriate and helpful study resources online and figure out how to organize these sources to share with someone else.
4) And last but not least...I REALLY REALLY wanted them to grade each other.

So I created this project, gave them the time to work on it, and then gave them the time to evaluate each other's presentation and websites based on a set of criteria. They were so cute! They are so strict with each other!! Some of the comments they made included:
 
"Add bullet point lists and embed a link in text to make website look more organized"
"Very well rehearsed. One of the best I've seen and they knew what they were taking about"
"Needed a little more rehearsing, but we liked the videos and the layout of the website. Great job!"

 
Hilarious!!
 
They said they really enjoyed this project because they enjoyed trying to create a study resource for other students. They also said they enjoyed grading each other.
 
They did say grading was the "hardest part.

You can find a link to a couple of these websites here and here.



**Jen and I have had a number of conversations about this project in terms of it's value to our students, whether everything we do in school needs to be graded, and the impact of having students grade each other. 

It is awesome that 7th graders can easily create functioning websites with not a lot of training.  This kind of project was pretty much unimaginable 10 years ago and very difficult even 5 years ago.  The pace of technological growth and student interaction is staggering. 

I would love to hear about other people's innovative projects.


Jen teaches Prealgebra and Algebra II this year, is the Coordinator for Professional Development, and is working on her Specialist Degree in Educational Technology at the University of Florida.  You can contact her at baselicej@trinityprep.org

Thursday, October 10, 2013

law of the jungle


During 3rd period a colleague uses my classroom to teach a class.  I usually head to our cafeteria to work, as it is empty and quiet in the mornings.  Our middle schoolers come in for lunch right at the end of this period on Wednesday.  This Wednesday I was at a table in the back and when the bell rang I was right in the middle of a project, so I kept on working.  In the back of my mind I could hear the kids filing in, getting food, talking, laughing. 

Finally I finished typing and closed my computer.  I was amazed to find that all the chairs at my table were filled with 6th graders, busily settling in to eat.  I looked up and there was one more standing next to the table staring at me as if to say, "Dude, you're in my seat."

There were a dozen empty tables available, but this one was their's.  Even after all these years kids stake out territory in the school cafeteria.  Middle school is ever the jungle. 

In the face of hungry 6th graders, I felt lucky to get out alive.

Image Source

Wednesday, October 9, 2013

risky business


One of the things I try to foster in all my classes is a willingness to take risks.  We learn most when we fail and then correct our mistakes, and every day I try to allow students to share their work in the hopes that if they make mistakes, we can collaboratively correct them.  There's no penalty for getting a problem wrong during class.  Students only lose if they make mistakes on assessments. If I can fix their mistakes in class, they are far less likely to mess up on a test or a quiz.  And a lot of times they do things well, and I can give a lot of positive, public feedback for that.
 
Some students buy into this right away.  They put their work up on the board, and we immediately can see how far along in a problem they got or where they made the fatal mistake.  The ability to proofread each other's work is no less vital in math than it is in any writing course.  I am confident that seeing another person's work is integral to learning.  Students come to understand that others think as they do and that there is more than one road to a solution.  But still they are hesitant.

They tell me they are embarrassed when they make mistakes.  They freeze and mumble and cannot explain their work or their problems. 

"I don't get it," is the phrase of the day. 

Teenagers are the consumate risk-takers in so many ways.  They take physical risks in playing sports, riding skateboards, and surfing.  They take social risks by dressing in unique ways, playing music in public, drinking, and taking drugs.  They take emotional risks when they ask a date to the prom or have sex.  These are pretty big risks with significant potential consequences. 

But asking them to take intellectual risks is completely different.  Apparently forcing them to make a mistake in public is a much bigger deal than I imagine.  And it's the thing they really need to be doing.

I don't get it. 

Photo Credit

Tuesday, October 8, 2013

going old school

Last week I came to work and our computer network was down for a little while.  Our campus is wireless and most teachers don't even have the cables to plug into the network or their projectors if needed. 

 We keep and do everything online these days, from attendance to grades, powerpoint lectures to collaborative activities, online homework and textbooks to email.  

When I first started as a teacher, we put a note on the door for attendance, we lectured and wrote problems on the board, handouts were run on the mimeograph, homework was done in notebooks and handed in, grades were kept in a gradebook and calculated with a calculator or by hand, and we communicated by telephone or snail mail.  
 
When the network goes down now, everything goes down, and teachers are forced to fall back to the old methods of teaching, chalk and chalkboard, although only a few of us even have that anymore. Most of us use whiteboards and dry erase markers 
 
It's not a far stretch for me to just stand there, make up problems, and lecture as I did for years.  When it's just me, the students, and a piece of chalk, teaching is completely different.  It's performance art.  There are no videos, no interactive games, not even a filmstrip.  Whether or not a student buys into a concept like "factoring" depends solely on my ability to teach, to market math in compelling and exciting ways.
 
My long years of teaching make going old school no big deal, but some of my colleagues are in their early twenties.    There's never been a day when they didn't have a computer, a smart phone, a projector at the ready.  I'm an old dog and have had to learn a lot of new technology tricks.  Can our new pups learn a bunch of old teaching tricks? 
 

Sunday, October 6, 2013

sometimes I get a good feeling...


My colleague sent me this picture in an email, the perfect combination of two of my passions, exercise and math...  so I tried it with my students. 

We did the moves to Flo Rida's "Good Feeling"


 
Start the video and try it!   

After that 5 minute interlude, I gave them a calculus quiz that included the following question.  Can you solve it? Maybe our "dance" helped a little.
 
Our assistant principal walked by while we were dancing.
Yes, I'm still employed...   


Thursday, October 3, 2013

opportunity knocks


A colleague, Lali DeRosier, said something at the beginning of the year, and it has stuck. 
 
 
"You just have to keep giving students chances." 


Lali doesn't penalize students for skipping homework.  Instead, she rewards them if they do it.  Before tests, she posts powerpoints to help them review and hides answers to extra credit test questions in the powerpoint.  Students who study the powerpoint not only learn more and do better on the test but also earn the added reward of "secret information" that helps them excel. 

What is powerful about this philosophy is that it does two things.  First it helps students learn that there are consequences for both action and inaction.  Doing nothing and doing something both have consequences. 

But better, it allows students to make different choices and experience a different outcome.  They get to try on the "study hat" and the "don't study hat" and see what happens.  They can fall down and fail and then pick themselves up and try something different. 

In the world of hard knocks, we sometimes only get one chance to answer the door.  But these are kids and this is school and our job is to teach, not just once, but over and over, until it sticks. 

"You just have to keep giving students chances." 



Lali DeRosier is a smart science teacher.  If you'd like to learn more from her you can follow her on twitter @lalsox or read some of her writing here or here

Wednesday, October 2, 2013

double stuff


I grade AP Calculus exams in the summer for a week.  It's a festival of math nerds, and if it weren't for the grading, would be my favorite vacation.  As such, it's plenty of work, but still a lot of fun.
 
One of the things I am able to do is take note of national trends in how students think about calculus.  We grade thousands of papers and the data is overwhelmingly obvious in some cases.  The past two years, a particular concept has been tripping the kids up.  It's called the chain rule, and the calculus aficionados in the world will recognize that it is a simple rule by which we are able to take the derivative of composite functions.  I teach this idea in early September and use oreos to illustrate the concept. I think the kids grasp it pretty well. 

Yesterday we were doing SAT prep, an activity the students dread, and we also had oreos.  Now don't panic.  There is absolutely no calculus on the SAT.  But the oreo eating was an opportunity to reinforce an idea in a new context, an opportunity to talk about the chain rule for just a minute while in the middle of something else, thereby making a new link to the idea.  I'm talking about building memory and helping kids encode ideas successfully.  It turns out, the more links we have to ideas, the more likely it is we are going to remember them.  

Memory formation is a reasonably well-understood process in the brain, and although we don't know every detail of the brain's functioning, any teacher worth her salt has a pretty good grasp on how to help kids learn and remember in her particular discipline.   

Yesterday's oreos were not an accident.  Repeated exposure over time improves memory retrieval.  If I have the time, I can create a well-planned class where each activity is useful and most every minute is utilized.  That's what teachers do all day, every day, and why we get so upset when some random person off the street thinks they can come in and do it better. 

Random Guy thinks this was a waste of time. 
Concerned Mom wishes I didn't give her baby sugar.  
Joe Student unknowingly had his brain manipulated.  
Visiting Principal didn't see any calculus. 
You know different.



If you want to know more about memory, you'll find a decent discussion here.