1. Fellows Meeting 4 Andrew Hickman Regional Mathematics Coordinator, NCESD April 30 th, 2015

2. Purpose of the Fellows 1. To be a part of and support a system that focuses on math making sense for all students. --Leadership in the Extended Community 2. To be a part of a community of learners that focuses on putting the shifts into practice to reflect the CCSS vision both around the student making sense of the mathematics and demonstrating that understanding. –Leadership of Others and Self 3. To deprivatize our practice and take risks in order to facilitate high quality mathematics instruction and experiences students have with the mathematics. –Leadership of Self

3. Why Do We Do Math Together?  “Teaching mathematics required specialized expertise and professional knowledge that includes not only knowing mathematics but knowing it in ways that make it useful for the work of teaching” (Ball & Forzani 2010; Ball, Thames, and Phelps 2008). -Principles to Action NCTM (p.11)

4. MEC 5 Representations

5. Objectives for the Day  Apply your developing understanding of the Teacher Leadership Framework and your skills as a Teacher Leader to Case Stories.  Reflect on your growth as a teacher leader in your role as a Fellow this year.

8. Turn and Talk  How has the book study around the 8 teaching practices deepened your understanding around your vision of mathematics reform efforts?  How has the study impacted your work with your building/district?

9. Facilitate Meaningful Mathematical Discourse Purposeful Questioning Math Practices Think about… What was one thought that resonated with you from either practice? Share out with small group.

10. Facilitating Discourse Simply having students talk does not necessarily advance the mathematical goals of a lesson. o How can the Five Practices (Smith and Stein, 2011), support and facilitate the purposeful exchange of ideas? o Now consider Mr. Donnelly’s lesson… o How does he attend to the 5 practices to facilitate discourse?

11. Five Practices to Support Facilitating Discourse 1. Anticipating student response prior to the lesson 2. Monitoring students’ work on and engagement with the tasks 3. Selecting* particular students to present their mathematical work 4. Sequencing students’ responses in a specific order for discussion 5. Connecting different students’ responses and connecting the responses to key mathematical ideas

12. Facilitating Meaningful Discourse Considering the Levels of Student Discourse: o Which of these practices are under utilized in classrooms? o How can we help teachers become more intentional incorporating these practices?

13. Pose Purposeful Questions o Gathering Information o Probing Thinking o Making the Mathematics Visible o Encouraging Reflection and Justification

14. Questioning Framework Gathering information o Students recall facts, definitions, or procedures Probing thinking o Students explain, elaborate, or clarify their thinking, including articulating the steps in solution methods or the completing of a task Making the mathematics visible o Students discuss mathematical structures and make connections among mathematical ideas and relationships Encouraging reflection and justification o Students reveal deeper understanding of their reasoning and actions, including making an argument for the validity of their work

15. Pose Purposeful Questions Consider the math task for your Grade Band from Digging for Dinosaurs o Review the standards associated with the task you chose o Do the math o Anticipate likely student responses and misconceptions (see Smith & Stein’s practice 1, p. 30) o Create a list of related questions using the framework in (figure 14) o Create a poster with your questions

16. Review Levels of Discourse o What do you see as next steps to see you move along the continuum? o How does this continuum help you think about your work with teachers?

18. Increasing Student Discourse for All Learners Helping students communicate mathematical understanding while constructing viable arguments and critiquing the reasoning of others.

19. Realizing the potential of all our students…  Grouping  Behaviors  Procedures  Accountability  Monitoring

20. Considering Small Groups In linguistically diverse classrooms, unstructured small group and partnering activities continually fail to produce substantive L2 oral language growth. Merely increasing student interaction without explicit, coached language instruction and accountability for application leads to discussions with minimal cognitive or linguistic challenge and negligible academic content. Gersten & Baker, 2001 Saunders and Goldenberg, 2010

21. Graphic Organizers…

22. What do you know about races?

23. A Race Amy and Rebecca are running in a road race. The map, drawn to scale, shows the route of the race: The race consists of four laps of the route and Amy and Rebecca run clockwise along the route at a constant speed. It takes Amy 8 minutes to run a mile. Rebecca takes 12 minutes to run a mile.

24. Sharing Individual Solutions P-24 1.Take turns to share your individual work with your partner(s). 2.Share the notes you made on how you might improve your work. 3.Listen carefully to each other, asking questions if you don’t understand. 4.Use the Build on an Idea Card and Ask a Question to guide your conversation.

25. Joint Solution: Making Posters-Talk Through P-25 1.In your group, agree on the best method for completing the problem. 2.Produce a poster that shows a joint solution to the A Race task, that is better than your individual work. 3.State on your poster any assumptions you have made. 4.Give clear reasons for your choice of method.

26. Sharing Posters-Talk Through P-26 1.One person from each group get up and visit a different group. 2.If you are staying with your poster, explain your work to the visitor, giving reasons for your choice of method. 3.If you are the visitor, look carefully at the work, asking clarifying questions to help you to understand the method used. 4.Discuss whether or not the method described on the poster is similar to the visitor’s method. 5.The visitor is to write on a post-it note, suggestions on how the work could be improved.

27. Sample Responses to Discuss: Sally P-27

28. Sample Responses to Discuss P-28 1.Read each piece of sample student work carefully. 2.Use the E.L. Achieve Discussion Cards (Build on and Idea and Challenge and Idea) to understand what Sally, Diane and George’s mathematical thinking. 3.Take turns explaining your thinking to your partner. 4.Listen carefully and ask clarifying questions. Use the Pose a Question Card to frame your questions. 5.Provide feedback to each of the three responses using the discussion cards.

29. E.L. Achieve Discussion Cards Support Your Thinking- Secondary Math Simple Academic Language The solution is reasonable because… Look at the data / pattern / structure. I see… My method / strategy for solving this problem can also work with / to / for …

30. E.L. Achieve Discussion Cards Support Your Thinking- Secondary Math Solid Academic Language  The solution demonstrates / shows that / is evidence that … because …  Based on the data / pattern / structure, I see / reason that…  My method / strategy for solving this problem can also be applied to / used for ….

31. E.L. Achieve Discussion Cards Support Your Thinking- Secondary Math Sophisticated Academic Language  Although I estimated …., my solution is reasonable because…  Based on the rule … I can reason / justify / that … because…  Because …, I can generalize the that the method / strategy for solving this problem applies to …

32. Exploration and Extensions…  How did the use of the E.L. Achieve Cards and other graphic organizers help support critiquing the reasoning of others?  How might you utilize a teaching tool such as the E.L. Achieve Cards and graphic organizers?

33. Case Story Discussion CSTP

34. Learning Through Case Stories  Read the Case Story “Overwhelmed and Underappreciated”  Consider what you know from the Teacher Leadership Framework that might connect to the Case Story – either in evidence provided or lack thereof.  Annotate your thoughts within the article or on scratch paper.

35. Learning Through Case Stories  How do you and don’t you see yourself in this dilemma?  Where does this dilemma ‘live’ in terms of the five areas in the Teacher Leadership Framework (could be multiple areas)?  Where do you see evidence of the teacher leader employing specific knowledge, skills and dispositions from the Teacher Leadership Framework?  What from the Teacher Leadership Framework might assist this teacher leader in managing this dilemma?

36. Set-Up: Circle of Viewpoints  Brainstorm a list of players in this dilemma – in other words, who is part of the system described in the Case Story?  Each person in your group takes on the role of one of the players identified in your brainstorm

37. Circle of Viewpoints  Use the Circle of Viewpoints Routine to re- examine and discuss the Case Story.  Going one at a time, each group member contributes to the following three prompts:  I am thinking of this Case Story from the point of view of…  I think…  A question I have is…  Repeat with the next group member until you’ve gone all the way around the whole group.

38. Reflections & Next Steps  After using the Circle of Viewpoints routine, what new ideas do you have that you didn’t have before?  What implications or realizations did you have for your own work as a fellow in reading this Case Story?  What are your next steps?

39. I used to think…Now I think…

40. Things to consider  Returning and New Fellows Applications available April 9 th ; close May 13 th. New Fellows will be announced May 22 nd.  Homework listed on your agenda

41. End of Year Wrap Up!  Lets work together to wrap up the Fellows work this year!