Lesson Study Summary

Monday - Friday, July 8 - 12, 2013


As of Monday we had three tasks yet to complete in preparation for our run-through on Tuesday: We had to finalize the task language and handout, finish the script for the lesson, and finalize the game we had planned for students to play during the 'practice' portion of the lesson.

First, we attempted to the play the game to see if it was workable. We found the game to be a bit too complicated and relatively ambiguous with respect to the lesson goal.

We split up to fine tune the game, the lesson script, and the language and purpose of the task.


After gathering necessary materials, we decided to give the lesson a quick run through. To decide on who was teaching we drew a name out of a hat. The lucky teacher taught the lesson with the rest of us pretending to be students.

After the run through, we found that we needed to provide more details and reorganize some parts of the lesson. The introductory activity and parts of the lesson task moved slowly. The teacher was in control of the pace of the class at all times. That is, if a student wasn't working with the teacher, he didn't have anything to do. We decided to shift any direct teaching moments to the front of the lesson task to allow students a larger block of time in which to work.

Furthermore, we also decided to add a quick review session on adding and multiplying matrices to insure success during our lesson task. The changes were added into the lesson script and handout.


We taught our lesson to the students at PCHS!


Today we debriefed the lesson and made changes in preparation of teaching the lesson to the Math Camp students on Friday.

Pros: All students were successful in finding the matrices that add or multiply a matrix of coordinate pairs to result in a specific transformation (translations, rotations of 90 degree multiples, and reflections).
The introductory activity was a good scaffold for setting up the lesson task. The tracing paper allowed all students to find points as a result of their assigned transformation.
Students generally wanted to participate in the task and had strategies to begin the task.

Cons: We spent more time than allotted for the lesson activity. As a result, students were not able to adequately debrief the task, nor did they get to participate in the practice game that we had planned. Furthermore, there were little to no assessments outside of unrecorded, formative, anecdotal evidence.

Changes we made in preparation for Fridays' lesson:

  • added a brief 'Do Now' activity that reviewed matrix addition and multiplication as a way to gauge student proficiency with said skill.
  • changed the lesson script to allow for even more self-guided tasks for students (have students read the handout as opposed to reading it for them).
  • changed the purpose of the visual organizer from a space for students to record their work in progress to a place for students to record final thoughts after discussing the lesson task as a whole.
  • due to time contraints (our second lesson will be 30 minutes shorter) we relegated the game to an extension task for students who are done early.
  • added an exit ticket to the lesson as an end of lesson assessment of student learning.


We taught the high school students of PCMI math camp our lesson (V 3.0).

Lesson Debrief

Pros: Task was clear. Everyone knew how to get started on it. More opportunities for student sharing. There was a general expectation that all students were expected to share out. Better scaffolding secured quicker and more thoughtful solutions. There were a lot of "Whys" asked. We have reliable end of lesson assessment data. We stuck better to the time limits.

Cons: The range of solutions was narrower. Some students went off on their own. Last 15 minutes still need to be cleaned up, be more deliberate. We need to allot more time for deeper class discussion at the end of class. Provide more instructions/structure regarding the graphic organizer.

Changes to make:

  • Remove the game. Change extension activity to "How could you use matrices to solve systems of equations?"
  • Revise/add a midway informal assessment to better understand where the final discussion is heading.

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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.