1. A GENDA  9:00-9:15Announcements  9:15-9:45Candles Problem  9:45-10:15Candles Problem Discussion  10:15-10:20MTR  10:20-10:35Break  10:35-11:15Introduction to Observation  11:15-11:35Question Types Observation  11:35-11:55Question Types Video Discussion

2.  12:00-1:00Lunch  1:00-3:00Planning for Implementation  3:00-4:00Planning Discussion

3. L ISTENING I NTERVIEWS D ISCUSSION  Ruth’s approach to the interview was more like a classroom approach than Andrew’s. What evidence from the transcripts supports this statement?  Why do you think Andrew might have chosen this particular segment to transcribe for his colleagues?  What questions do you have about what you are expected to do when conducting a listening interview and why are you being asked to do this particular activity with your students?

4. A SKING Q UESTIONS OF S TUDENTS G OALS  Document and reflect on the questions a teacher asks in class.  Explore the intentions teachers have when they decide to ask their students particular questions.  Deepen our understanding of algebraic thinking and the language to the algebraic habits of mind.

5. T HE C ANDLES P ROBLEM  Work on The Candles Problem in your group.  Jot down notes about your algebraic thinking or the strategies you use to solve the problem.  Post your work.

6. T HE C ANDLES P ROBLEM D ISCUSSION  Did everyone in the group come up with the same solution to this problem? Why or why not?  Compare the methods people used to solve the problem. What differences do you note among them?  Discuss how each of these strategies relates to the question, “Why don’t you need to know the lengths of the candles in the last two questions of the problem?”  What evidence of Building Rules to Represent Functions and Doing/Undoing to you see in participants’ work on this problem?

7. MTR—T HE C ANDLES P ROBLEM  What would you like to recall about the different strategies and/or solutions used by your colleagues? Record the approaches and strategies you would like to remember.  What would you like to recall about the algebraic thinking? Record the specific features of habits of mind that you have seen in the different solutions.  What would you like to recall about the different strategies and/or solutions used by your students? Record the mathematical approaches or strategies you would like to remember.

8. I NTRODUCTION TO O BSERVATION  Read “A Three-Stage Cycle”.  We will watch segments of the video and discuss questions after each segment.  As you watch segment 1, take the role of classroom observer, writing the questions you hear the teacher asking.

9. S EGMENT 1  What mathematical ideas did you see emphasized by the teacher in this segment? Refer to the list that you made as you watched as evidence.  What kinds of mathematical thinking on the part of students were evident in the segment? In particular, what kinds of algebraic thinking were evident?

10. S EGMENT 2  What additional insights do you get about what the teacher’s intentions were from listening to the debriefing session after seeing what the teacher did in class?  What does the teacher who did the lesson seem to get out of this debriefing session with her observing partner?

11. Q UESTION T YPES  Managing  Clarifying  Orienting  Prompting Mathematical Reflection  Prompting Algebraic Reflection

12. Q UESTION T YPES O BSERVATION  As you watch the video segment, act as an observer in her classroom, using the Observation Guide.  Note when the teacher’s questions seem to be in response to her perception of how the students are thinking, based on the things the students do or say.  In your group, decide how to categorize each question and circle the question type in the right- hand column.

13. Q UESTION T YPES D ISCUSSION  Did you see examples of questions that elicited algebraic thinking or prompted mathematical thinking in this segment?  Did you and your group disagree about the classification of the particular question?  A teacher’s perception of how her students are thinking at the moment often prompts her to ask particular questions. Did you see examples on the video of the teacher doing this?

14. P LANNING FOR I MPLEMENTATION  With your team member, plan how you will implement Fostering Algebraic Thinking with your group.  Produce a plan outline.

15. K EEP IN M IND …  Keep the professional development seated in the A- HOMs.  Tasks are a medium for the professional development.  Task analysis is important on several levels: -mathematics and algebraic thinking -student thinking -power of the task  Mathematical Thinking Records are an integral part.  Transition to practice is the goal.

16. P LANNING D ISCUSSION  Share your plan with another team.  How have you maintained the integrity of the materials?  What issues have you encountered in your planning?  What issues remain unresolved?

17. F OR T HURSDAY …  Read “Pre-Module Homework” in Documenting Student Thinking, pages i-iv.