1. Analyzing Shifts in Teacher Discourse and Mathematical Knowledge for Teaching Nanette Seago WestEd

2. Examine what it might mean to learn mathematical knowledge for teaching (MKT) through the analysis of two sets of PD video of teachers’ pre-post discourse (same facilitator, same PD curriculum, different teacher groups). Focus of the Session

3. Turning to the Evidence Project* *This work was supported by the National Science Foundation under Grant No. 0231892. Any opinions, findings, conclusions, or recommendations expressed here are those of the authors and do not necessarily reflect the views of the National Science Foundation. Nanette Seago (P.I., nseago@wested.org) Lynn Goldsmith (P.I., Lgoldsmith@edc.org) Research Questions: What do teachers learn by participating in professional development that uses classroom records and artifacts? What aspects of their learning do teachers apply to their classroom practice?

4. Examine & engage with the PD materials Define Mathematical Knowledge for Teaching Examine & analyze two sets of pre-post teachers’ discourse (two different PD settings) Discuss implications for leaders of PD Agenda for this session

5. The PD Materials  Videocase centered  Modular  Sequenced PD curriculum  Learning and Teaching Linear Functions Session 1 Session 2 Session 3 Session 4 Session 5 Session 6 Session 7 Session 8

6. Growing Dots 1 Lesson Task At the beginning At 1 minuteAt 2 minutes Describe the pattern. Assuming the sequence continues in the same way, how many dots are there at 100 minutes? For any number of minutes?

7. Sample Solution Methods 1 dots = t(4) +1dots = 4t + 1 where t = number of minutes At 2 minutes # of min = # of dots in each of the 4 “arms” # of min = # of squares; 4 dots(vertices) in each “square” 1 “Arms” Method“Squares” Method

8. We drop in Situating the Video Segment Within the Lesson

9. Video Segment Questions What important mathematical issues arise for the teacher and students within this segment of classroom interaction? Kirk Linear Functions context Danielle & James Whole class

10. Shifting our Attention: From Classroom to Professional Development

11. Mathematical knowledge required for teaching that is different from other mathematics-intensive professions such as research mathematics, engineering, or financial modeling. MKT emerges within core activities of teaching such as:  Figuring out what students understand  Analyzing methods and solutions different from one’s own, determine their adequacy and compare them  Unpacking familiar mathematical ideas, procedures and principles in ways to make them more accessible to students  Choosing representations to effectively convey mathematical ideas  Figuring out student errors  Designing and modifying mathematical tasks Mathematical Knowledge for Teaching Ball & Bass, 2000

12. PD Group 1 Context:  24 middle school mathematics teachers  Large urban school district  Session 1 of Learning and Teaching Linear Functions Foundation Module  Large group discussion of 1st video clip  Teachers have worked on and discussed the mathematics in the dots problem Session 1 Session 2 Session 3 Session 4 Session 5 Session 6 Session 7 Session 8

13. Predict  What might teachers tend to in the video?  What might they not tend to?

14. Video Focus Use the MKT worksheet to focus on: –What are the teachers talking about as they analyze the video segment? –What core activities of teaching are teachers working on?

15. Session 1 Video Clip

16. Video Focus Use the MKT worksheet to focus on: –What are the teachers talking about as they analyze the video segment? –What core activities of teaching are teachers working on?

17. PD Group 1; Session 8 Context:  Five months later: Session 8 of Learning and Teaching Linear Functions Foundation Module  Teachers have revisited and discussed the mathematics in the dots problem  Large group discussion of 1st video clip Session 1 Session 2 Session 3 Session 4 Session 5 Session 6 Session 7 Session 8

18. Video Focus Use the MKT worksheet to focus on: –What are the teachers talking about as they analyze the video segment? –What core activities of teaching are the teachers working on?

19. Session 8 Video Clip

20. Video Focus Use the MKT worksheet to focus on: –What are the teachers talking about as they analyze the video segment? –What core activities of teaching are teachers working on?

21. PD Group 2 Context:  6 middle school, 3 high school mathematics teachers  Medium-sized urban school district  Session 1 of Learning and Teaching Linear Functions Foundation Module (October)  Teachers have worked on and discussed the mathematics in the dots problem  We drop in on the large group discussion of 1st video clip Session 1 Session 2 Session 3 Session 4 Session 5 Session 6 Session 7 Session 8

22. Video Focus Use the MKT worksheet to focus on: –What are the teachers talking about as they analyze the video segment? –What core activities of teaching are teachers working on?

23. Session 1 Video Clip

24. Video Focus Use the MKT worksheet to focus on: –What are the teachers talking about as they analyze the video segment? –What core activities of teaching are teachers working on?

25. PD Group 2; Session 8 Context:  Five months later: Session 8 of Learning and Teaching Linear Functions Foundation Module  Teachers have revisited and discussed the mathematics in the dots problem  Large group discussion of 1st video clip Session 1 Session 2 Session 3 Session 4 Session 5 Session 6 Session 7 Session 8

26. Video Focus Use the MKT worksheet to focus on: –What are the teachers talking about as they analyze the video segment? –What core activities of teaching are teachers working on?

27. Session 8 Video Clip

28. Video Focus Use the MKT worksheet to focus on: –What are the teachers talking about as they analyze the video segment? –What core activities of teaching are teachers working on?

29. Implications As leaders of professional development, what has this session raised for you in terms of:  Teacher learning of MKT?  Facilitating the learning of MKT?