Education ∪ Math ∪ Technology

Month: January 2010 (page 1 of 3)

“Thin slicing” and its effect on educators.

I’m reading Malcolm Gladwell’s book, Blink.  He uses a variety of arguments to show the power of information we can receive from a very small amount of information, and the subconscious ways we make decisions very quickly.  It’s a fascinating read, I highly recommend checking it out.

One point he brings up a fair bit in the first half of the book is the value in making quick decisions based on limited information and how it can both be extremely beneficial for making decisions but that it can also be problematic occasionally.  He calls this process thin-slicing.

First, the power of thin-slicing is that it allows you to make decisions quickly.  You can also trust your instincts when making decisions about directions of programs, assuming you have the expertise in that area.  His book shares some research that shows that people who are experts in their area can make a judgement about their area of expertise in 10 seconds, just as easily as in 2 hours, or 3 days.  The amount of time necessary to analyze a situation and think about a recommendation is very short, with high levels of accuracy achieved in a short period of time.

However there is a darker side to this story.  Unfortunately in areas in which we are not experts, or where there is a great deal of cultural stereotyping, our unconscious decision making can betray us.  The messages which are broadcasted into society subliminally can cause us to make unconscious decisions and snap judgments that betray what our personal sense of morality would lead us to believe.  Essentially, we not only all judge a book by its cover, but we color all of our analysis of the book by the decisions we made when we saw the cover of the book.

Most educators in North America would probably not consider themselves racist but our society sends out messages of racial stereotypes on a regular basis.  We read statistics about how 5% of African American men are incarcerated and recognize that this is much larger than the number of people from any race, and we make presumptions about African Americans.  Of course there are lots of other examples of racial stereotypes in our society, most of which are present on television.  

Now as teachers, we are likely to believe that people are deserving of equality and we almost certainly are not consciously aware of our bias.  If asked, we will say that all of our students deserve equality, and that we should treat them equally.  We may need to give some our students more attention than others because of their individual needs, but we wouldn’t openly treat them differently.

Unfortunately, we cannot avoid making snap judgments about students based on our prior experiences, and the influence of the stereotypes in our society is strong.  These snap judgments will colour all of our interactions with our students and can prevent us from treating them as fairly as we would consciously like to do.  We may downgrade papers from students whom our cultural stereotypes say are supposed to struggle with literacy, or treat unfairly students who may differ in their external packaging (their dress and mannerisms) than their peers.

There is a solution to this problem, or at least a way to make the process of educational evaluation more fair for all students involved.  One of the stories Malcolm Gladwell talks about is how the orchestras around North America and Europe have been transformed by blind auditioning.  Apparently as recently as the 1980s and 1990s, most orchestras were predominantly filled with men, and women had difficulty advancing in this area.  Orchestras recognized this (you have to read the book to find out how they recognized the problem) and began to institute policies that required the gender and race of the musicians to be hidden during the auditions.  In only a few short years, the problem of diversity in orchestras has begun to be solved.

So what can we do as educators? Any time you evaluate student work, make sure the identity of the students is unknown to you while evaluating it.  Have students turn in their work with a number which is matched to their name (randomized for each assignment) and in electronic form to avoid recognizing hand-writing.  After you have read and graded each piece of work, match the numbers to the students and record the grades or feedback.

My guess is that if you institute this policy, you will be surprised on a regular basis of the quality of work that is produced both by your supposed superstars and your weaker achievers.  You will also begin to lose some of your bias as your professional experiences begin to overcome the initial stereotyping to which you have been exposed in society.

Free online education for anyone

Imagine a school without walls and completely online.  Students could log onto any web ready computer, and sign up to join classes.  They could interact via a moderated back channel chat and vote questions to the teacher up or down during live sessions and participate in forum discussions during asynchronous sessions.  Assignments would be handed in electronically, mostly through online individual student blogs.  Assessment of understanding would be tricky in such a system, I’m not totally clear how student work at the higher levels of Bloom’s taxonomy would be assessed.  Perhaps peer assessment mixed with sample moderated by the teacher?

A number of these schools exist already all over the world but they all include one important barrier, registration.  Students have to enroll in the schools, and funding for the school is based on enrollment.  If anyone knows of a K to 12 school which is free for anyone to join and doesn’t require registration, please let me know.  I would like to see a school where anyone at all, anywhere, can join the school without an application requirement.  There might have to be some identity verification, if only to allow the school to comply with federal laws in most countries regarding sex offenders, but that would be it and such information would not be public knowledge.

The reason why I want such a school to be free of registration is because I suspect that there would be three distinct types of people interested in such a program.  The first would be high school students looking for an alternative to typical public school.  They might want to register in the program to receive official credit for their diploma.  Another group of students would be supplementing their education in a face to face to school with essentially free support in an online school.  The last group of people, who would probably want the most anonymity, would be the people coming back for a second chance to complete high school, the adult students.

The problems with creating such a school are not trivial.

1.  There is significant cost associated with such a school.  Each teacher involved needs to be paid for their time, and given that the teachers will both have to be experts in trouble shooting connectivity issues and their content area, they will likely cost more than the average teacher.  There’s no reason to run the school if the teaching isn’t excellent and the easiest way to do this is to hire the right people and keep them with the right salary.

2.  Finding the teachers themselves will be difficult.  How many teachers do you know who would substitute time in the classroom (or free time outside of it), have the technical expertise to assist students who are struggling to connect, know their content area well, AND are good teachers.  These are a lot of requirements that need to be met.

3.  Assessing student understanding in a meaningful way would have to be well thought out.  One of the most time-consuming tasks teachers have is assessing student understanding.  Obviously, in an online format, it would be easy to handle any of the lower level skills.  In fact you’d probably see these kids tested more often on the easy to test stuff, but figuring out ways to assess the more difficult to assess would require some work.

4.  Actually being connected live in such a way that everyone feels like they have an equal opportunity to participate would be extremely difficult. I recently participated in an Elluminate session using webcams for viewing the presenters, and the audio and video were awful, I quit after a couple of minutes.  Now, I’ve used Elluminate before successfully, so it was just the set up of these particular sessions.

5.  Becoming part of the school and connecting has requires vastly different access points.  We’d have students attending part-time from a public library to little 5 year old students who are just learning how to use a computer.  We’d have to differentiate the access to the system so that it was easy enough that anyone could participate.

Fortunately, I believe these problems have solutions and that if a team of dedicated teachers and administrators worked together, we could solve these problems.  Education is a right for everyone and it is our society’s responsibility to provide it.  Unfortunately, as we know, not everyone has the access to the high quality education we all desire for our children, so I think we should step forward and provide it.


What could 3D do for language learning?

So I’ve had a thought about the direction of language learning.  I’ve been experimenting with 3D interactive worlds (specifically OpenSim), which are programs which let people interact with each other real-time in 3D.  Pretty cool stuff.  This is already being used to help people learn languages as many of the 3D servers offer the ability to communicate with each other via voice and text.

There are a couple of problems I can see with doing this activity with students in a class.  The most important problem is that it is extremely difficult (or expensive) to find a real human being that speaks the language you want to know and who has the time to interact with your students.  It can be incredibly difficult to find an entire classroom’s worth of people willing to interact with your students one on one.  Certainly the online nature of the 3d world makes this easier to manage, but still it almost certainly does not happen in most classrooms (although some languages teachers are adopting Skype successfully).

The second problem is the lack of control you have over what happens during the conversation.  Unless your language learners are somewhat advanced, they will probably struggle to communicate effectively with a native speaker, especially early on in their learning.  You also don’t know if they will cover the content you want to cover, or if their conversation even becomes completely off topic or even inappropriate!

Technology has come a long way recently. There are already chat programs which do reasonably well in conversation, especially if they are limited to a specific known topic area.  3d animation is amazing with highly realistic facial animation and human-like gestures, just check out the movie Avatar.  Voice recognition is improving in leaps and bounds every month with some big players (like Google and Microsoft) putting a lot of money into development and again this technology works better when the bounds of the conversation are known.

Imagine we combined these three technologies together.  Students could then be lead through a carefully arranged conversation including, most importantly, the context of the conversation.  All of the subtle cues and body language we use to learn languages can be programmed into the simulations so that students get as close to a real life experience as possible.  Programs of study could be designed for all levels of language learners, allowing for extremely differentiated and customizable instruction for every student in your class.  Instead of having to carefully plan an online session, your students could interact any time from any computer with sufficient power to run the program.  It would also be a fair bit of a fun for the students and hopefully end up engaging them at a deeper level than revision exercises from a textbook.

What’s amazing is that the technologies to implement this are very close to becoming a reality.  Within 2 or 3 years, all of the component technologies to make this work will be mature enough to produce a software package which is stable enough to release into the classroom environment.  Hopefully with a little bit of work on the administrator’s interface, a typical non-techy language teacher could set up their own simulations for their students.

The future language learning looks very bright, although maybe in 10 years we won’t need to learn other languages because the technology will be so advanced that all of our phones will include universal translators.


My first semester as a teacher – part 9

…continued from here

Yes, I sold my soul to the administration of my school.  In exchange, I got to keep my job.

Well, actually how it worked out was this.  We had a special department meeting about a week before grades were due in which it was discussed that if our students did not pass our classes at a high enough rate, that it was clear we were inadequate teachers and maybe wouldn’t be asked to come back next year.  We were even told that about 60% of our students should pass our courses overall, that was the "expected" number in our school.

Whoa!  Wait a minute, I thought, that’s not going to happen!  I have one class where I don’t even have 60% attendance for the year, how am I going to make these students pass?  Am I going to be fired if they don’t pass?

I went back to my classes and made sure they were all aware where they stood in terms of homework.  We had sessions during class time when the students were encouraged to "work on" (read copy from each other) their missing homework assignments from earlier in the year.  All of my students got a full 20% participation score!  Almost all of them had 20% for handing in all of their homework!  I was getting there.  But wait! In NYC students need 65% to pass, not 50%.  Fortunately we did have a few tests from the year, and I did some quick math.  Let’s see 65 – 40 = 25 points.  Okay my students need 25 points to pass.  I shared the math with the students.  That meant that they needed to make up 25 points from the 60 points the tests were worth, which meant that anyone who had 42% or more overall on their tests could pass the semester.   Oh, and anyone who achieved at least a 60% was bumped up to the magic 65%, the rest were moved to either 50% or 55% depending on whether I felt they were trying or not making any effort at all.

Whew!  That worked out to about 70% of the students in my two strong classes and about 30% of the students in my weakest class.  I felt a bit guilty but decided that the attendance rate was poor enough in that class that I would be forgiven for the poor grades.  Besides, I’d carefully kept my phone call log from the semester with the several dozen phone calls I’d attempted to make to encourage my students to come to class.  That should cover me.

What sickens me about this experience now is that I was encouraged by the administration to be much more concerned about the numbers of students passing and my job security than the quality of work I was doing.  As long as my students pass at that magic 60% or greater mark every year, I felt like I was okay, I could keep working in the school.

Actually doing report cards in New York city was very easy.  Incredibly easy, I’ve never had it so easy since.  Every teacher gets bubble sheets from the school, with one row for each student in each of their classes, and carefully filled in the bubbles for the percentage grade, and then choose between 2 and 3 appropriate comments for the students, which were also selected by filling in bubbles.  Lots and lots of bubbles sheets, that’s what I remember from grading in NYC.

The end of the semester soon came.  I handed in my bubble sheets and looked forward to a fresh start.  I had survived a semester teaching in NYC.  I had developed some friendships which have lasted since.  The students had come to give me some respect and I had learned a tremendous amount about to survive in Brooklyn.  My life would never be the same.  Since New York I’ve had the confidence to face anything, and this experience will always stay with me.  I’ve lived and taught in 3 other countries and although I miss friends and family from those countries, only the city of New York do I truly miss itself.

Maybe we should be aiming for computer programming instead of calculus in Math?

I read an article one time which questioned why we choose calculus to be the top of the math pyramid in school.  Basically, most of the mathematics students learn once they master the basics aims toward preparing the students to take calculus at the end of K-12 school.  The article I read suggested that statistics instead of calculus should be at the top because it is much more practical to real life than calculus is.

We deliberately choose calculus to be at the top because we want our society to produce more engineers and scientists.  This helped produce a generation of engineers and scientists.

However, although engineers and scientists are still needed, the US Department of Labor predicts that neither engineers nor scientists will be in the fastest growing jobs in the future.  They have predicted the 30 fasted growing jobs in the United States and there is something interesting about the list.  5 of the jobs involve the use of computers.  Jobs number 25, 24, 23, 4, and 1 all include the significant use of computers in a highly technical fashion.  In fact all 5 of these jobs require computer programming skills to some degree.

So I propose that we make computer programming skills should be at the top of the list.  This way we will be preparing our students for careers in the future rather than the careers of the past.

Now we will still end up producing engineers and scientists because there is a huge overlap between the mathematics required to master calculus and the skills required to master computer programming.  We will end up producing a lot people who are totally capable of programming a computer.  Students who do not end up completing the stream will still end up having a very good understanding of how a computer works, which is obviously going to be an advantage in the future anyway.

I suspect that the current stream of math would end up diverging just after algebra.  It would end up involving a lot more number theory and logical reasoning and a lot less graphing and physics based mathematics (except for the stream of students interested in game programming).  I don’t know that students would find this much more interesting, but at least it would pretty easy for them to use the math they were learning and use it in direct applications involving their favorite technological devices.

Maybe kids might enjoy math more? 

My thoughts on Malcolm Gladwell’s Outliers – The Story of Success

I just finished reading Malcolm Gladwell’s book Outliers.  It was very cool, I knew a lot of the information provided in it but some of the things had a fresh perspective and were collected in one place.

He starts off with an observation, which I’ve known for a long, long time (from even when I was in school) that kids whose birthdays fall immediately after a cut-off deadline in our society are way more successful than the kids who are near the other end of the spectrum in that area.  Suppose a child is born in January, and the age limit for a sport is 10 years old with a cut-off of January 1st.  The kid born in January will be nearly 10% older than a child born in December if the season starts in December.  At that age, there is a huge advantage to being slightly older, some of the 10 year old kids will even be starting puberty and could be much larger than their peers.

Of course if you look at school themselves, the same problem exists.  Each school has a date they choose, usually somewhat arbitrarily, which determines whether or not they accept students into the school.  In this case a student who is deemed too young has to wait a year, and the students who are just before the cut-off end up starting school almost a year younger than their peers.  Can you imagine how much of a difference this makes?  This results in a 20% age difference between the students on one side of the date to students on the other side.

The solution Malcolm suggests, which makes sense to me, is to create multiple dates during the year for these cut-offs and run simultaneous systems along side each other.  Instead of everyone starting school in September for example, students would start in one of 3 or 4 streams during the year.  You wouldn’t need very much more money to support this system since the number of students wouldn’t change, but it might make a much more equitable system.

There are a lot of areas which Malcolm decides are problems.  He points out that cultural differences and differences in how people of different socioeconomic status react to setbacks and communication are even larger barriers to success.  His argument is pretty complex, but I can see his point.  One example of this is in measurement of reading scores.  If you measure reading scores during the course of a year, kids tend to make about the same amount of progress during the year.  It’s the summer vacations during which the poor kids tend to fall behind the richer kids.  Apparently their school experiences are pretty similar, but what happens outside of school can be quite different.  Over time, these differences tend to amplify.

The solution here is to make the summer vacations shorter.  I know it’s not a popular move for teachers, we really like our 2 month vacations.  We can get course work done, finish building our house, all sorts of projects.  Take this away and you will definitely decrease the quality of life for teachers.  That being said, the improvement on the quality of life and equitability of our system would be dramatically improved.

For the rest of his argument, I strongly suggest reading his book.

My first semester as a teacher – part 8

…continued from here

As the Christmas break loomed in front of me, I began to finally feel more confident in my teaching.  I had more classes which seem to run smoother, not many more, but a few.  A lot of these things though, in reflection, I really don’t think had to do with me.

First, in November our school’s cap on suspending students was lifted as we’d had our annual Title one attendance taken.  Students who were extremely disruptive, even dangerous in the school were now out of school on long holidays.  This meant that my classes were smaller, and that the most disruptive students were generally gone.  It’s not fair for those students, but it made it a lot easier to manage the other 90%.

The second thing that happened is that my 10th grade students decided to declare a truce and finally admit defeat.  They were neither going to make me quit, nor make me cry in class.  I found out from one of them that they had successfully made 3 teachers quit the year before I started and were going for a 4th.  This revelation actually made me feel better, I realized that some of their misbehaviour was deliberate and intended to destroy my self-confidence.  Why did I feel better? Mostly just because it wasn’t entirely due to my bad teaching.

And my teaching was bad.  I mean, you probably remember your first year, it was horrible.  You did everything wrong!  We all did.  We lacked the experience necessary to do our jobs right.  In some schools, the students are forgiving and will even make an effort to help you out.  In others, such as the one I was in, the wolf pack instinct kicks in and the students go for your hamstring.

The third thing that happened during the semester, which always makes me sad when I think about it, is that kids started dropping out of school.  My M$AA class (see an earlier post for the reference) started with 17 students by the beginning of the year.  There was another similar class with 17 students as well.  The second semester they combined these two classes, and by the end of the year I had 6 students who were still attending school.  6 students out of 34!  The only advantage to this was the students who were still attending actually had SOME interest in learning and were more willing to participate.  One of these students passed the state exam with a reasonably strong score for our school (he ended up in the honors stream the next year) and 3 others barely passed.

Finally, I think my teaching improved a bit.  I started to experiment with a larger variety of activities.  I used the time I had with my 10th grade students in the computer lab more wisely.  My classroom management was better, etc… I finally had enough experience with my students that I was angry less often when they were disruptive.

Of all of the things which I do miss from my time in NYC, I am certainly glad I’m not angry all the time anymore.  I used to spend at least an hour each school day angry at someone or just the system in general.  I shouted at students in frustration, and even at coworkers.  I was often very unpleasant to be around.  Since I’ve matured and the teaching I do is in a much more student friendly environment, I am almost never angry not even when students are deliberately trying to antagonize me.

Life was starting to become bearable.  That was until I sold my soul to save my job.

final part

Reflection on using Activexpressions for the first time

I used clickers in the classroom for the first time today.  For those of you who don’t know, a clicker is also known as a classroom response device, and is used to collect immediate student feedback.  Students have a small device, it looks like a remote and on your computer you have a hub of some sort for collecting responses wirelessly from the students, and some software on the computer to process this data as well as display the questions.  You ask a question, it gets displayed on an LCD projector, the students answer the question, and you can post the results very quickly.  The whole process takes under a minute, and can take as little as 15 seconds once the students understand how to use the clickers.

The clickers I’m using come from a company called Promethean, they also produce an interactive white board (IWB).  Their clickers are designed to work with their interactive white board software and when you use the installation CD for the hub it installs their IWB software.  I have to say, I wasn’t very impressed with the license for their IWB software.  It only allows a single use and can only be legally installed on one computer.  This means that if you want to share the clickers between teachers, you need to purchase multiple copies of the software.  However, we only have 1 class set of clickers so we will never actually be running one copy of the software at a time.

The installation failed halfway through, it seems it requires a very specific copy of the Macromedia Flash installer.  I tried 4 different versions and none of them worked.  I cancelled the installation of Flash and the rest of the installation went through smoothly.  It was very strange, since of course I have Flash installed on my computer.

Once you actually start using the devices, the first thing that needs to happen is that each device needs to be registered to the hub.  This process took some time, and has some definite flaws in it.  First, you really need to name each device as you register it.  We tried to number all of the devices as we were registering them and we discovered that the internal number changed once we registered it, UNLESS we named the devices with numbers.  Pretty painful, I can’t imagine a non-techy trying to set up these devices.

Creating questions for the students to do was relatively easy, but a bit too slow to do on the fly.  Tomorrow I’m going to test the "question-less" questions, which are ideal for asking verbal questions and getting student feedback and take a lot less set-up.  If you want to have the students answer complicated written questions, my recommendation is to set up the questions in advance and use the multiple-choice or short-answer versions.

Once we were set up, the questioning part worked fairly well in two classes and really didn’t work well in a third class.  My 10th grade class and my IB Year 2 class took to the clickers fairly easily and participated with them well.  My 9th grade students struggled using the clickers.  Some of them were great, but some of the students pretty refused to try them.  I’m hopeful that in the long run the clickers will help this class participate more, but it was not an auspicious beginning.  

We tried a wide variety of different types of questions.  All of the questions are pretty easy to set up but each question requires it’s own screen, so right away I realized that formal assessment through the clickers would be pretty difficult.  Students definitely found answering the multiple choice or true/false questions easier to answer, the text response questions should be limited to at best very short answers.  Trying to enter mathematical expressions on the clickers is tremendously painful and should be avoided at all costs.  Given my recent exploration of the iPhone device, a proper keyboard on the clickers would be ideal, using old style phone texting through a number paid is pretty painful now.

Once the class is over, you can export the results.  If you want to use them again and analyze them, you need to export the results.  I tried to save my flipchart, hoping the results from the questions would be saved as well, and it turns out they are removed.  Unfortunately this means I lost all of my results from today, but the good news is that I won’t make that mistake again.  I probably should have read the manual first, but there wasn’t a paper one included in the set, just one on a CD.  I couldn’t imagine a teacher popping in a CD to read the manual, so I worked out how to do everything without it.

The response from the students was extremely positive from my 10th grade class, and moderately positive in the other two classes.  The students generally liked using the clickers.  One student asked if "we could use these every class."  The 12th grade students had a more reasoned response, questioning if the value of the clickers was worth it, and one wondered if they could spend the money elsewhere more wisely.  One huge complaint from all of the students was the time it took to enter responses via text.  I think I’ll avoid the text responses, unless I use extremely short responses (like numeric responses).

So far it’s gone fairly well, we’ll see if the process improves over time.  I’ll also need to introduce the clickers to more staff members, so far just myself and one other staff member are testing the clickers.

Problem based learning in math

How does problem based learning work anyway?  According to Wikipedia, "Problem-based learning (PBL) is a student-centered instructional strategy in which students collaboratively solve problems and reflect on their experiences."  To me this means, choose problems which will reflect your curriculum and which students want to solve.

Implementation of this in mathematics can be tricky for some topics, even contrived.  If you find yourself really stretching to make a particular concept or unit fit PBL, don’t use it, use some other strategy instead.  However for almost all topics finding a real-life problem, which the students think is interesting or at least has application in their life, is relatively easy.  This is a chance for we mathematics teachers to stretch our creative muscles but it is really important that the problem chosen is either something the students have a direct interest in, or something that they can see someone in their society needing to solve.

The model I use for PBL is this; I describe a problem that exists in our world and needs solving on a regular basis, and I give the students a starting place for solving the problem, then I guide the students through the solution (giving different amounts of advice depending on the understanding of the students). At the beginning of the year the problems are quite regimented, by the end of a school year some students can solve problems mostly unguided.

My objective is to choose problems which ideally weave many different areas of mathematics (or other subjects) into the problem itself.  For example, students were given an assignment to try and decide what the best possible choice of cell phone plan is in the Metro-Vancouver area.  The solution to this involved using linear functions to model the individual cell phone plans, graphical analysis of those linear models to try and determine the best plan for any given number of minutes, algebra to determine the exact number of minutes when different plans intersect, and of course, lots and lots of research into different cell phone plans.

As the students progress through the problem, I can feed them some ideas on how to proceed.  Different groups require different amounts of guidance, and the final product the students produce can vary greatly within a class.  I often find I teach a bunch of related skills to a problem at the beginning of a class, then let the students find the connections and decide how to use the skills during their project.  Most of the time if a given skill is useful, the students find a way to incorporate the use of that skill unto their solution of the problem.

Many of the authentic learning experiences I described in an earlier post can be turned into problem based learning.  You can review these projects and then think of ways you can find problems of your own to use.

My first semester as a teacher – part 7

…continued from here

There were some really bright moments during my first semester too.  I remember the first time my grade 10 class was completely silent.  They actually quieted down and we working away diligently on one of my many worksheets that year, and then one student blurted out, "Oh my god we are quiet! I can’t believe it!" and broke the spell.  It was really nice while it lasted though because I felt like it was possible to feel successful.  I don’t know, but for some reason in my first few years as a teacher, I felt that silence in a classroom was critical to being successful, I’m less convinced now.

I also remember when one of my students who was extremely challenged learned something new in my class.  He was actually a nice kid but very disobedient because he was always bored.  He towered over me at 6 foot 4 inches and was in the 300 pound range, so he was physically intimidating.  He struggled a lot in school, and by the age of 21 had amassed 0 credits in high school.  His big accomplishment in math in my year?  Realizing that the symbols shown to him in a math question were instructions to do something.  I was so proud of him when he told me in class his discovery and the pride in his voice was evident.  Sometimes the small things stick with you.

There was also the time we played Math Jeopardy in class with my really low achievers and at the end of the class one of the students said, "I really learned stuff today!  Let’s do this again tomorrow!"  and two of the other students agreed with her.  Almost all of the students participated nicely and I really felt like I had engaged the class.

When my 10th grade students asked where I was going to be going for the Christmas holidays, I felt pretty good about that too, because it meant that despite their misbehaviour, they were curious about me.  Curiousity about a teacher in NYC is pretty close to respect in my books.

I also had a couple of laughs although not in front of the students when I could help it.  As part of a game, I asked the students to guess which city in Canada I was going to be visiting during the holidays (the correct answer was Vancouver).  One of them said, "Winnipeg?" then "Toronto?" and I was pretty excited, these kids knew their geography!  Unfortunately another student said, "Connecticut?" and it was all I could do to keep from laughing out loud.