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.

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 ( 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.