AGENDA

9:00-9:15 Announcements

9:15-9:45 Candles Problem

9:45-10:15 Candles Problem Discussion

10:15-10:20 MTR

10:20-10:35 Break

10:35-11:15 Introduction to Observation

11:15-11:35 Question Types Observation

11:35-11:55 Question Types Video Discussion

12:00-1:00 Lunch

1:00-3:00 Planning for Implementation

3:00-4:00 Planning Discussion

LISTENING INTERVIEWS DISCUSSION

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?

ASKING QUESTIONS OF STUDENTS GOALS

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.

THE CANDLES PROBLEM

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.

THE CANDLES PROBLEM DISCUSSION

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?

MTR—THE CANDLES PROBLEM

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.

INTRODUCTION TO OBSERVATION

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.

SEGMENT 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?

SEGMENT 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?

QUESTION TYPES

Managing

Clarifying

Orienting

Prompting Mathematical Reflection

Prompting Algebraic Reflection

QUESTION TYPES OBSERVATION

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.

QUESTION TYPES DISCUSSION

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?

PLANNING FOR IMPLEMENTATION

With your team member, plan how you will implement Fostering Algebraic Thinking with your group.

Produce a plan outline.

KEEP IN MIND…

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.

PLANNING DISCUSSION

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?

FOR THURSDAY…

Read “Pre-Module Homework” in Documenting Student Thinking, pages i-iv.