Fostering Algebraic Thinking

1. Fostering Algebraic Thinking • October 26 • December 1 • 6-hour Assignment • after Session 2 • January 20 • Presented by: • Janna Smith • jannas@esc5.net

2. Agenda 8:30-8:50 Housekeeping and Updates 8:50-9:50 Analyzing Student Work 9:50-10:00 BREAK 10:00 -11:00 Staircase Problem/Discussion 11:00-11:30 Examine TEKS 11:30-1:00 LUNCH 1:00-2:00 Listening Interview Video/Discussion 2:00-2:15 BREAK 2:15-3:15 Carnival Bears Problem/Discussion 3:15-3:30 Homework Assignment

3. Housekeeping • Cell phones • Restrooms • Vending Machines • Breaks

4. Analyzing Student Work

5. Each person choose 1 sample of student work from chosen activity to share with your group. • Choose a piece that you think will provoke discussion • A piece in which the student thinking is not clear to you • A piece that shows a link of thinking about the problem that in some way seems atypical • A piece you believe nicely represents features of the habits of mind • Number the student work 1, 2, 3. • Use Student Work Analysis Sheet to jot down features that strike you, what you infer from the features you noticed, and alternative inferences about the students’ thinking. • Discuss findings in small group

6. Mathematical Thinking RecordQuestion 3 • What would you like to recall about the different strategies and/or solutions used by your students?

7. Break

8. Staircase Problem • Work alone or with 1 other person to complete the Staircase Problem. • Keep track of your thought process and the strategies you try as you work. • Spend no more than 30 minutes on the problem.

9. -Discussion Staircase Problem • Did everyone in the group come up with the same solution (or partial solution) to this problem? Why or why not? • What mathematical methods did you use to solve the problem? • In what different ways did the habit of mind “Building Rules to Represent Fxns” show up? • Within the group members’ approaches to this problem, do you see any evidence of Doing/Undoing?

10. -MTR Staircase Problem • Write your reflections to Questions 1 & 2 of the Mathematical Thinking Record for the Staircase Problem

11. Group Process Discussion • How does the way the group works help you develop a spirit of inquiry and ask questions about algebraic thinking or the teaching of algebraic thinking? • How could the group do this better?

12. Examine TEKS • You have been provided TEKS for Grades 5 -12 • In groups of 2, examine the TEKS for grade levels 6-12 and record the TEKS that are covered by the Staircase Problem (5th grade teachers can look at 5th grade TEKS, too, if they choose). • Come together as a table and record your findings on chart paper

14. Listening Interview • Watch the video segment “A Listening Interview”. • This video shows a group of 7th graders working together on the Postage Stamps Problem (worded somewhat differently). • As you watch the video, listen to what the students say, both to one another and to themselves. Try not to worry about them getting the “right” answer. • Thought processes—how the students’ solution evolves • How students’ written answers compare to the ideas you find in their discussions leading up to the solutions.

15. Listening Interview Discussion • As a group, complete the “Listening for a Thought Process” discussion questions • Discuss as a whole group • What steps do the students go through to develop the rule that it is possible to make all numbers above 23? • If you had tried to answer these questions by just looking at the written work students turned in, without having heard what they said, which questions would you have been able to answer?

16. Break

17. Carnival Bears Problem • Work alone to complete the Carnival Bears Problem. • Keep track of your thought process and the strategies you try as you work. • Spend no more than 30 minutes on the problem.

18. -Discussion Carnival Bears Problem • Did everyone in the group come up with the same solution (or partial solution) to this problem? Why or why not? • Compare the strategies that different people used to reach their solutions. • In what different ways did the habit of mind “Building Rules to Represent Fxns” show up?

19. -Discussion Carnival Bears Problem • Within the group members’ approaches to this problem, do you see any evidence of Doing/Undoing? • Did you see evidence of “Abstracting for Computation”? • How might you use the different solution methods you have discussed to address this question: What happens if there is an unequal number of bears on each side?

20. -MTR Carnival Bears Problem • Write your reflections to Questions 1 & 2 of the Mathematical Thinking Record for the Carnival Bears Problem

21. Homework • Read Article, “Conducting Listening Interviews” • Conduct a listening interview with a group of 3 students completing the “Carnival Bears Problem”. • Shoot a video or take pictures of the activity, write a summary of the experience, and produce a transcript of an excerpt of the interview (typed in MS Word) of the listening video. • Save the video/pics to a cd, dvd or a flash drive and bring it with you to our meeting January 20th. • Also print a summary of the interview and a transcript of an excerpt of the interview (typed in MS Word) to bring with you on January 20th. The description and the transcript can be on the same document. • Your transcript should be a short excerpt of the listening interview that represents issues related to students' algebraic thinking, or Habits of Mind. • In your summary, include: • Grade level of students • Your experiences with this activity • The Habits of Mind of the students that were most apparent to you and why.

22. See you January 20th! Janna Smith jannas@esc5.net (409) 923-5488