In the reflection and revision phase of the adapted Lesson Study cycle, the teachers participated in video clubs (Sherin and Han, 2004) during study group sessions where they watched and discussed short video clips (1-4 minutes) from each other's enactments of the lesson. 

• The research team selected the video clips to be shown during the study group sessions using the criteria developed by Sherin, Linsenmeier, and van Es (2009).   This framework rates the windows into, depth of, and clarity of student thinking displayed in the video. 
• The research team created the transcript of the students' interactions and added captions to the videos.
• The research team made copies of the students' work to distribute during the video club.
• The research team viewed the video while discussing the students' thinking in relation to the mathematical task. 
• Through this discussion and sharing their own experiences implementing the lesson, the teachers were able to investigate how students' approached the task and in what ways the task engaged their prior knowledge. 
• Teacher proposed edits and adjustments to the lesson based on their observations.
• The project had teachers engage in a Lesson Study Cycle for each concept twice over two years.  After the first cycle of reflections and revisions based on what was observed during the video clubs as well as their own experiences teaching the lesson, the teachers proposed revisions to the lesson for the second lesson implementation.  In the second year, teachers participated in video clubs using videos from the implementation of the revised lesson and discussed changes to their lesson based on their observations of students' thinking.

Based on their noticing of students' thinking and prior knowledge during the video clubs, the teachers identified three ways that they wanted to modify the original student worksheet as well as their implementation of the One-Point Perspective Problem. 

• Launching the Problem (Can be used with any Student Worksheet)

  • Photo in Perspective - In the first implementations of this lesson, there were not many contextual launches.  From the video club, the teachers concluded that the students were having difficulty differentiating the measured height of the trees on the paper versus what the trees represent in real-life.  The teachers decided to address this misconception through the launch of the problem.  One idea was to show students a photo of a street with building that they were familiar with and discuss how the buildings further away, while if you measured them on the picture would be shorter, in real-life, the students knew that building was taller than the buildings closer in the photo. 
     
  • Video of a Racing Video Game - In order to address the same misconception as the photo, other teachers decided to launch the problem by showing an online video of someone playing a racing video game.  This launch highlighted that as figures in perspective became closer to the camera as the car drove by, the peoples' heights were not changing, but their image got larger as they moved closer to the camera.
     
  • Create your own One-Point Perspective Drawing - Several teachers decided to have students create their own one-point perspective drawing as a way to launch this lesson.  This launch took significantly longer, but students in these classes developed a better understanding of the vocabulary of "vanishing point" and "perspective lines" as well as developed an intuitive understanding of what made a perspective drawing "look right".

• Student Worksheet - The Diagram Page 1

  • No Perspective Lines Under Trees - Teachers observed that some students struggled with the lines under the trees that did not connect corresponding points, so these lines were removed for the second implementation of the lesson.  Student Worksheet Option 3

• Student Worksheet - The Diagram on Page 2 

  • Creating a Basketball Hoop - The original student worksheet had students drawing a second tree, however, the teachers observed that there were too many lines for the students to consider and create with the trees.  So the teachers adapted the lesson to create a basketball hoop instead. Student Worksheet Option 2
     
  • Creating a Street Light - The teachers noticed that students didn't recognize the outline of the basketball hoop for what it was, and it still had a signifiant number of lines for students to copy, consequently, teachers proposed changing the basketball hoop to a street light. Student Worksheet Option 3

• Student Worksheet - Coloring Corresponding Parallel Lines

  • Highlighting Corresponding Parallel Lines - During the implementations and video clubs, teachers noticed that students were not understanding the full definition of a dilation, and that included that corresponding lines were parallel.  In order to accentuate this portion of the definition in the lesson, the teachers added a question asking students to color corresponding lines from the two dilated figures. Student Worksheet Option 3
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Go to Next Step:  Investigating Curricular Materials