Reflection On Videotaped Lesson

General Information
For this class I have the chairs arranged in an arc at the front of the room.  My plan is to ‘nudge’ a discussion along with only slight involvement.  I would like the students to reason through things on their own without my leading them too much.  I have set up the camera on a shelf in the back of the room.  Though I hadn’t placed it there with the intention of it being hidden, the students don’t notice that it’s there, and I forget about it until the end of the day.  In the two classes prior to this one these students had completed activities where they researched and explained practical uses of the parabolic shape.  The finished product of this project will be either a parabolic solar cooker or  parabolic microphone.Observation
As  the students enter the classroom they first comment on the chairs as I tell them to get their calculators and have a seat.  One student tries to sit outside the arch of chairs and I ask him to sit up front with the rest of the class and he does.  Once class is settled we watch two short YouTube videos that show a parabolic shaped solar cooker being made and then being used.  After the videos I ask the students how and why the parabolic cooker works.  I ‘play dumb,’ asking for more detail and acting like I don’t understand.  The students begin to get animated with their discussion as they get frustrated with my lack of understanding (quite the role reversal!).  Eventually they explain the concept very thoroughly.  I then ask them for other things we see or use everyday that are shaped like a parabola.  The first thing the students mention is a headlight.  I then act confused by that saying, “Wait, with the cooker you said it took light in and focused it on one spot, but a headlight puts light out; how is that possible?”  It is then a repeat of the events that led to the first explanation.
Once the students have offered a good explanation for the headlight phenomenon, I have a student draw a parabola on the white board that hangs at the front of the class.  I then ask for the students how they would come up with an equation for the parabola.  I ask them what type of equation describes a parabola, they respond correctly that it is a quadratic.  I remind them they had to come up with a quadratic equation for their first project.  They eventually figure out that they would have to identify some points, input them into the calculator, and calculate the quadratic regression formula for the given data.  They argue over the best way to accomplish this, some students get very animated.  They eventually figure out an approach to use and solve for the equation.  This takes until the end of the class period.  They put away their calculators, move the chairs back into place, and are dismissed.

Thoughts
For our last book study, Therese had the desks pushed aside and blankets on the floor.  She had us all take off our shoes and sit down.  It was this approach as well as one of the topics covered in the book that inspired me to do things differently on this day.  The topic in the book that I covered involved making connections in learning to other aspects outside of the classroom in order to help the students remember and apply the knowledge they have learned instead of just memorizing formulas for standardized tests.  In addition to these things I had also been impressed with Dan Meyer’s idea (http://www.youtube.com/watch?v=BlvKWEvKSi8) that we should pull information away and encourage debate on subjects, by using this approach students are more likely to build these connections.
Looking back on this day, I was happy with the results.  There was a complaint from one student, “We had to teach ourselves, you didn’t teach us anything.”  And there were two or three who still didn’t quite grasp what was going on and were just plugging in numbers to their calculators hoping to come up with the right answer.  At this point I am not sure what I would do to improve the experience and outcomes for all students, I am hoping that after having similar classes one or two more times I will get a better idea of what should be done to improve them.  This leads to one of the trickiest parts of the PBL approach; adding scaffolding and structure without it ‘looking’ like traditional classroom structure.

 

Fall 2010 Reflection #3

For our last book study, Therese had the desks pushed aside and blankets on the floor.  She had us all take off our shoes and sit down.  It was this approach as well as one of the topics covered in the book that inspired me to do things differently the next time I taught.  The topic in the book that I covered involved making connections in learning to other aspects outside of the classroom in order to help the students remember and apply the knowledge they have learned instead of just memorizing formulas for standardized tests.  In addition to these things I had also been impressed with Dan Meyer’s idea (http://www.youtube.com/watch?v=BlvKWEvKSi8) that we should pull information away and encourage debate on subjects, by using this approach students are more likely to build these connections.
The next day in class I pushed the tables to the back and arranged the chairs in an arc at the front of the room.  I know from past experience that even a simple changing of the seating chart will often have the effect of ‘resetting’ things in the classroom and gives you a chance to make a fresh start.  By removing the tables altogether I hoped to increase this effect.  Also in my plan was drawing out a conversation, biting my tongue and allowing my students to stumble through the process of figuring things out, and generally trying to ‘stay out of the way.’  I started out by showing a couple videos of parabolic shaped solar cookers, which they are designing and building for this project.  I then asked for a volunteer to draw a parabola on the board.  I then asked how a satellite dish works.  After the first couple of standard quick answers, I just piped up to ask for details, asking them to explain in greater detail, pretending not to understand.  This seemed to work as they got more and more excited and finally moved beyond the, “That’s just the way it is” answers and started to really reason things out on their own.  The prior class they had researched practical uses of the parabola so this wasn’t just sprung on them with no prior knowledge.  Next came the tough part.  I asked the students how they could come with an equation that describes the parabola that was drawn free hand on the board.  This took the most amount of lip-biting on my part.  I did my best to just provide gentle ‘nudges’ here and there.  I reminded them of times they took data and created parabolic equations from it.  Slowly the students started dissecting the problem.  They drew a graph over the parabola, took points, and created an equation.  Throughout this whole process they argued over the best ways to proceed and why.  After this I gave them a two problem worksheet to do on their own that was the same type of problem they had done on the board.
Reflecting back on this I was happy with the results.  There was a complaint from one student, “We had to teach ourselves, you didn’t teach us anything.”  And there were two or three who still didn’t quite grasp what was going on and were just plugging in numbers to their calculators hoping to come up with the right answer.  At this point I am not sure what I would do to improve the experience and outcomes for all students, I am hoping that after having similar classes one or two more times I will get a better idea of what should be done to improve them.  This leads to one of the trickiest parts of the PBL approach; adding scaffolding and structure without it ‘looking’ like traditional classroom

Fall 2010 Reflection #2

That is the question I ask myself time and time again.  Do my students really understand the concept we just covered?  Do they understand the point of a project?  Are they just pushing buttons on a calculator and hoping the correct answer is displayed?  One of the goals of the Project Based Learning approach to teaching is that the students develop a true understanding of what is being covered.  A big complaint by teachers that otherwise love the idea of PBL is that there is just not enough time to cover all of the information that will be on the End of Course test.  Well, when the children actually understand how to apply the information that is covered, they can reason their way through problems that weren’t specifically covered.  However, I hardly ever able to ascertain if they have truly understood the information.
What I’ve always done in the past is to include essay questions on each test and the occasional quiz.  I always tell them to “pretend you are explaining this to a 7th grader in pre-algebra.”  In other words, I want them to explain using plain language, not trying to write big fancy sentences that throw back vocabulary words (often incorrectly).  I encourage my students to go home and explain to a parent what they have done in class.  If they are able to explain something, that generally means they understand it.  Also, sometimes taking the moment to think about something enough to be able to explain it will cause an ‘a-ha’ moment when the proverbial light bulb comes on.  I myself have experienced this when helping students with advanced subjects.  When I look at problems which I haven’t seen since college, as I explain them I suddenly develop a new understanding.  I have caught myself more than once saying, “Oh, that’s why we did it that way!”
What I think I will do in the future is to use worksheets with diagrams where the central idea and supporting concepts are listed and the students fill in the rest.  Like a fish bone diagram, or a center balloon with ideas coming off at all sides.  Maybe I’ll start out with things even more elementary, and slowly raise the bar, fill in less and less, until they start with just a blank diagram that they fill out.  Hopefully this will help me arrive at my desired results.  We introduce a new project (of Mr. Sears design) next week.  If I am unable to try this then, I will do so when we begin my next project in November and see if it results in more complete projects.

Fall 2010 Reflection #1

I miss the comfort and security of my own classroom.  I had helped start the New Tech program at my former school and was its unofficial spokesperson.  My room looked more like a corporate conference center than a classroom.  I generally wore jeans every day and had an easy going manner with my students.  Getting out of my comfort zone has been a challenge, but it has also forced me to take a step back and look at how I do things.  It is kind of like my approach to teaching motion in physics.  There are a lot of “everyday” words that are used in physics, but have different meanings than their usual use.  To break the kids free of this confusing trap, I set problems on a different planet.  Change the setting and they are forced to think.  Get me out of where I am comfortable and I am forced to think a lot more about the things I do.   This deeper look at what I do, what works and what doesn’t, and how I deliver material is in line with my research for the summer.
I was intrigued this summer by Vygotsky’s definition of scaffolding and how it should be used to provide just enough support for the student to reach the next zone of proximal development (ZPD).  As a project based learning teacher, this is an idea I employ every day.  Ideally I should be providing the little steps that allow the students to see where they are going and how to get there.  When I first started with the New Tech program I had only been teaching a year; in a way this was good as I had no old ingrained practices to break, but in a way this was bad because I was unable to pick up on the subtleties of their excellent training.  When I learned about scaffolding I saw it as worksheets and traditional classwork, and that is how I treated it.  In a purely practical sense this idea is not entirely incorrect.  However, it can be so much more.  Now that I’ve had time to think and have educated myself on the art of teaching I am starting to take a deeper look at the possibilities.  Working with Mr. Sears has helped me move this research from the purely academic to the practical classroom setting.
I am lucky to be working with Matt Sears.  Not only is he a former DPS teacher of the year, the New Tech advocate for his school, at the head of the STEM movement in NC, a Fulbright scholar, and a former Keenan teaching fellow (this list could go on for a while), he is also in his fourth year of being a project based learning teacher.  When I was the only math teacher in my New Tech program, I used to drive to Durham and observe Mr. Sears for my own personal professional development.  Having somebody of his caliber and experience to bounce ideas off of and receive criticism from has been truly wonderful.  It only took about a week to convince him that I would not take such criticism personally.  I also quickly realized that he had no problem with my asking him to explain why he was doing certain things.  Although many people use this as a more polite/passive aggressive way to criticize, I truly just want to understand his thought process and why he does things certain ways, and he has no problem with that.  I have been able to study his approach to scaffolding, and it has been an eye opener.
Just in the first few weeks of working in Mr. Sears classroom has made me realize that I panic way too easily.  I worry when it seems like kids aren’t understanding something and rush in way too soon to explain.   This goes against the idea of inquiry based learning.  Some of my scaffolding is way too structured; sometimes a standard math worksheet is a good thing, but there are other ways to get the kids to understand new concepts.  They need to be allowed to struggle a little more, the main thing we have to do as PBL teachers is make sure they stay on task.  As long as they are working with their group, brainstorming ideas and talking about the problem they are probably on the right track.  Sure, an occasional nudge/hint is needed but don’t give away too much.  Not only is this bad for their understanding of the current problem, it also sets a precedent.  Students will begin to think they need not do anything or work as hard as they ought because they will know that I will swoop in and bail them out.
Another thing that has made this collaboration especially effective is a result of a random event.  Four days before the beginning of the school year, Mr. Sears’ classes were switched around, instead of the anticipated Geometry courses, we were to teach Algebra II.  Mr. Sears had just the week before became a father and was swamped, I had a project; actually the first one I ever created as a New Tech teacher, that was made to be the first Algebra II unit.  Watching another teacher run a project I was VERY familiar with and seeing their approach/receiving their criticisms has made the collaboration even more effective than I had anticipated.  I get to hear his thought process and also get a chance to observe as he teaches and better see what is working, what isn’t, and why.
Working in this environment has made me realize that I need to put interaction with fellow teachers high on my priority list when I return to “my own” classroom.  Receiving critical input not only on broad unit plans but also on the day-to-day processes whenever possible is too helpful of a teaching tool to ignore or just give lip service to.