Coaching for Math GAINS Peel Co-Teaching Project Anchor Session #2

1. Coaching for Math GAINSPeel Co-Teaching Project Anchor Session #2 April 1, 2010

2. Reviewing our Norms • Start and end on time. • Contribute to a safe learning environment that encourages risk taking; be kind. • Listen actively; speak fearlessly. • Invest in your own learning and the learning of others. • All electronic communication devices off except during lunch/break. • Suffering is optional!

3. Overview of the Morning • Welcome • Responding to Feedback • How well have you been listening? • Sharing your journey • Mathematics as a social activity • Is your locker open? • Common Questions … consolidating questions for parallel tasks

4. We were listening … • Working on open & parallel tasks • Time to dialogue and plan with colleagues • Logistics … how do we make it work? • Opening up my classroom to others • Purpose of Math GAINS project • Ministry perspective • Peel perspective • What the research says • Making sense of the "Big Ideas"

5. Peel Perspective - Math GAINS Project Facilitated co-teaching activities to promote job-embedded professional learning opportunities related to supporting the implementation of the ongoing priorities and initiatives of the Peel District School Board These include, but are not limited to the following –

6. Peel Perspective - Math GAINS Project • Transformational Practices • School Success Planning • Differentiated Instruction • Cross-Panel Connections • Student Success / Learning to 18 • Transitions (Grade, Panel, Course) • Report Card for Student Success • Alternative Programs

7. Research Foundation for PD Context • Providing sufficient time; • Engaging external expertise; • Engaging teachers in the learning process; • Challenging discourses; • Providing opportunities to interact in a community of professionals. Math GAINS • Eight release days; • Math Coach; • Teachers working together in school teams and working cross-panel; • Rethinking our approach to teaching math; • Co-planning days, anchor sessions and debriefing after demonstration lessons.

8. Research Foundation for PD Content • Different aspects of content are integrated; • Clear links made between teaching and learning and student teacher relationships; • Assessment is used as a focus; • Sustainability of improved student outcomes. Math GAINS • Big ideas, questioning, group work skills and problem solving; • How we teach math impacts on how well students learn and we can connect through more engaging tasks; • Formative assessment using open and parallel tasks; • Students can continue to improve.

9. Research Foundation for PD Activities • Content and activities aligned; • A variety of activities needed; • Professional instruction sequenced; • Understandings discussed and negotiated. Math GAINS • Developing then trying open or parallel tasks; • Different tasks, grades and strands covered; • Modelling, co-planning then teaching • Active discussion with colleagues of what works for students.

10. Research Foundation for PD Learning Processes • Substantive change is difficult; • Some new understandings are consistent with current thinking and some are inconsistent; • Teachers can learn to regulate their own learning. Math GAINS • Trying questions together; • Some tasks are similar to what we have done before, some are a new approach, with support see what works for students • Begin to use questioning in other lessons if it supports student understanding.

11. How well have you been listening? • We spend a great deal of time talking about questioning. • How effective some of our questions will be, really depends on how well we listen to our students. • The more we listen … the more our role will evolve from "Stand & Deliver" to …

12. Impress Me! • As you watch this video, please consider the following questions: • How does the participating teacher describe her usual classroom practice? • What is new/different for the teacher and her students in this lesson? • How do the students respond to the lesson approach? • 4. What observations/reflections does the teacher share in the lesson debriefing? • 5. How does your co-teaching experience compare with this example?

13. Self Reflection A big idea of co-teaching is to reflect on your current classroom practice, whatever that may be, and ask: “What can I add to my practice to help students understand the concepts I am teaching more deeply?” “How will I know if my changes are having a positive impact on my students?”

14. Sharing Your Experience • Each person in your team will go to a different location. • With the other people at your location, form an inside/outside circle. • Each "inside" person will start. Choose one question to ask from the following list. Take turns.

15. Sharing Your Experience • What was the focus of the lesson that was co-planned? How was the lesson delivered? What was the most valuable feedback from the debrief? • How did your students react to the lesson? How did they feel about all of the observers present? • The biggest surprise of co-teaching is … • A change in your practice that has resulted from your involvement in the GAINS project is …

16. Math as a Social Activity As you watch this video clip, record the steps the teacher takes to create the learning environment he wants for his students.

17. Break Time!

18. There are 1000 lockers in the long hall of the Peel District High School. In preparation for the beginning of school, the janitor cleans the lockers and paints fresh numbers on the locker doors. The lockers are numbered from 1 to 1000. The Locker Problem

19. The Locker Problem … continued • In your family of schools team, identify 3 people who will act as observers. • The remaining team members will work on the problem in "the fishbowl". They may divide themselves up into smaller groups if they wish to. • Send one of the observers to the materials table to collect the forms they will use to record their observations.

21. The Locker Problem … continued • Explore the problem in your groups. Various manipulatives are available for use from the materials table. • Record your findings on chart paper. • Be sure to explain the mathematics that will justify why your answer is correct.

22. The Locker Problem … continued When the school's 1000 students return from summer vacation, they decide to celebrate the beginning of the school year by working off some energy. Student #1: opens every locker. Student #2: starts at locker #2 and closes every 2nd locker. Student #3: starts at locker #3 and opens or closes every 3rdlocker. This process continues ...until all 1000 students have entered the school. Which locker doors are open once every student has arrived?

23. Consolidation of the Locker Problem • Life in the Fishbowl observers share their observations with their team members • Presentation of Solutions  a math congress

24. Parallel Tasks Revisited Focusing Our Lens on Common Questions

25. Possible Lesson Goals • Find the distance from a point to a line segment AND / OR • Apply the geometric properties of circles, midpoints, line segments, and perpendicular lines to the real world

26. Consider this example: The diagram shows the locations of Katie’s, Krista’s and A.J.’s homes.

27. The Parallel Tasks OR Option 1 A. J. and Krista want to meet somewhere that is equally distant from each of their homes. Where could they meet? Option 2 Katie, Krista, and A. J. want to meet somewhere that is equally distant from all three of their homes. Where could they meet?

28. Possible Tools • GSP • Grid paper • Rulers • Soft measuring tapes and/or string

29. The Solutions Option 1 There are actually many solutions to Option 1. All the points on the perpendicular that meets the middle of the line segment between A.J.’s and Krista’s house are equally distant from each house.

30. The Solutions Option 1

31. The Solutions Option 2 There is only one solution to Option 2. Students need to find the single point at the centre of the circle that passes through all three of the points representing the locations of the homes.

32. The Solutions Option 2

33. Meeting Student Needs • The first option allows students the opportunity to apply their knowledge of lines to solve a real life problem. • The second option allows those students needing a challenge the opportunity to apply their knowledge of lines and circles to solve a real life problem.

34. Other Variations • Choose points with positive coordinates for students who struggle with integer calculations, and points with negative coordinates for those who do not. • Choose points with whole number coordinates for students who struggle with fractions or decimals, and fractional coordinates for students who do not.

35. Common Questions Whichever task the students complete, the teacher could ask: How did you find the meeting spot? Is there another way to solve the problem? What tools did you use to help you? Is there more than one possible meeting spot? How do you know? How could you verify your meeting spot is equally distant from all three homes?

36. Principles to Keep in Mind • Parallel tasks need to be created with variations that allow struggling students to be successful and proficient students to be challenged(consider common studentstumbling blocks when creating your tasks). • The tasks and common questions should be constructed in such a way that will allow all students to participate together in follow-up discussions.

37. Consolidating Questions Consolidating questionscan be used to tie big ideas together at the end of a lesson or activity. Common questionscan serve asconsolidating questionswhen the main activity of a lesson has been a parallel task.

38. Your Turn! There are six different parallel tasks at your table. • Work in groups of 2 or 3. • Choose a task. • Solve the problem. • List student stumbling blocks that might be addressed by offering each choice. • List common questions that could be asked of all students at the end of the task. • Record your work on chart paper, and post according to tasks.

40. Welcome Back! Effective teaching involves risk taking … by both the teacher and the student.

41. Overview of the Afternoon • Connecting Big Ideas with Expectations and Lesson Goals • Consolidating Questions • Time to Practice & Share • 4. A Few Words About Logistics • 5. Group Communication: SharePoint

42. Relationship among Expectations, Big Ideas, & Lesson Goals Topic Big Ideas Expectations Goals 47

43. Relationship among Expectations, Big Ideas, & Lesson Goals Sometimes you can reframe the big ideas for your topic. For example, a trig big idea might be: 48

44. Relationship among Expectations, Big Ideas, & Lesson Goals Limited information about a periodic relationship can sometimes, but not always, reveal other information about that relationship. 49

45. Or… When a relationship appears to be periodic in nature, then it is appropriate to consider a trigonometric function to model the relationship. 50

46. Relationship among Expectations, Big Ideas, and Lesson Goals We will use the Posing Powerful Questions Template (PPQT) as a tool. 51

47. An Example … Lesson Title: Grade/Program: 7

48. What Big Idea is being Addressed? Most likely BI 4 53

49. List the Big Idea(s) … Lesson Title: Grade/Program: 7

50. Create Your Lesson Goal Lesson Title: Grade/Program: 7