Paul Cobb Vanderbilt University ICME 11, Monterrey, Mexico, July 2008

1. The Challenges of Scale: Designing Learning Organizations for Instructional Improvement in Mathematics Paul Cobb Vanderbilt University ICME 11, Monterrey, Mexico, July 2008

2. Purpose • Illustrate a way of conducting research studies that aim to inform the ongoing improvement of mathematics teaching and learning at scale

3. Background: US Educational System • Decentralized education system • Long history of local control of schooling • Each US state divided into a number of independent school districts • Rural districts with less than 1,000 students • Urban districts with more than 100,000 students

4. History of Failure • The closer that an instructional innovation gets to what takes place between teachers and students in classrooms, the less likely it is that it will implemented and sustained on a large scale

5. Limited Impact of Research on Classroom Practice • Supporting students’ learning of central mathematical ideas • Instructional materials • Teachers’ instructional practices • Supporting mathematics teachers’ development of high-quality instructional practice

6. Large-Scale ImplementationProjects • Focus is almost exclusively on teacher professional development • Unanticipated “obstacles” • Conflicts with other district initiatives • Lack of understanding and/or support by school and district administrators

7. Large-Scale Implementation • Flying blind: Little knowledge of the schools and districts in which they are working • Reactive: Plans changed in response to unanticipated obstacles • Proactive: Anticipate school and district structures that might support mathematics teachers’ ongoing improvement of their instructional practices

8. Map Backwards From the Classroom • Research on high-quality mathematics instruction • Demands on the teacher • Challenges of developing high-quality instructional practices • School and district support structures

9. The Swing of the Pendulum • Student-centered approaches • Celebrate students’ discoveries and methods as ends in themselves • Teacher-centered approaches • Focus on conveying mathematical ideas to students

10. Transcending This Forced Choice • Keep one eye on the mathematical horizon and the other on students’ current understandings, concerns, and interests (Ball, 1993)

11. Measuring With a Ten Bar

12. Measuring With a Ten Bar • Edward: I think it’s 33 [points to where they have marked 23 with the three cubes] because 10 [iterates the smurf bar once], 20 [iterates the smurf bar a second time], 21, 22, 23 [counts the first, second and third cubes within the second iteration]

13. Measuring With a Ten Bar • Edward: Ten [iterates the smurf bar once], 20 [iterates the smurf bar again]. I change my mind. She's right. • T: What do you mean? • Edward: This would be 20 [points to the end of the second iteration].

14. Measuring With a Ten Bar • T: What would be 20? • Edward: This is 20 right here [places one hand at the beginning of the “plank” and the other at the end of the second iteration]. This is the 20. Then, if I move it up just 3 more. There [breaks the bar to show 3 cubes and places the 3 cubes beyond 20]. That’s 23.

15. Measuring With a Ten Bar • Measuring as a sequence of separate units • Measuring as the accumulation of distance

16. Classroom Discourse • Not sufficient to show how measured • Also have to explain why measured in a particular way • Measuring structures distance into units

17. Demands on the Teacher • Deep understanding of mathematics • Mathematical knowledge for teaching • Knowledge of how students’ reasoning develops in particular mathematical domains • Skill in pursuing a mathematical agenda by building on students’ contributions

18. Improvement in Instructional Practices • Students have to adjust to the teacher • Teaching routine • Covering instructional objectives + classroom management • Teacher adjusts instruction to the students • Ongoing assessment of student reasoning • Non-routine -- complex and demanding

19. Background: US Educational Policy • No Child Left Behind Policy • Standards for mathematics learning • 50-80 standards per grade common • Assessments at the end of each school year to test whether students are achieving these standards • Primarily procedural skill at expense of conceptual understanding • Yearly student achievement targets for each school in mathematics

20. Framing Instructional Improvement at Scale as a Research Issue • Series of conjectures about school and district structures that support teachers’ ongoing learning • Instruments to document the institutional setting of mathematics teaching • Extent to which the conjectured support structures have been established

21. Research Plan • Four urban districts • High proportion of students from traditionally underserved groups of students • Limited resources • Most districts clueless about how to respond to high-stakes accountability • A small minority have reasonably worked out strategies

22. Research Plan • Document district plans for improving middle-school mathematics • Six middle schools - 30 teachers • Four rounds of yearly data collection • First year: Baseline data • Document change over a three-year period in each district

23. Data Collection • Institutional setting of mathematics teaching • Audio-recorded interviews and surveys • Quality of teacher professional development • Video-recordings • Quality of instructional materials • Artifact collection • Quality of teachers’ instructional practices • Video-recordings of two consecutive classroom lessons • Teachers’ mathematical knowledge for teaching • Student mathematics achievement data

24. Add Value to Districts’ Improvement Efforts • Feed back results of analyses to districts • Gap analysis -- how district’s plan is actually playing out in schools • Recommend actionable adjustments that might make each district’s improvement design more effective • Design experiment at the level of the district

25. Research Team Paul Cobb Tom Smith Erin Henrick Kara Jackson Chuck Munter Sarah Green John Murphy Karin Katterfeld Lynsey Gibbons Glenn Colby

26. One District as an Illustrative Case • Conjectured support structures • The district’s improvement plan • Findings and feedback to the district

27. Conjecture: Teacher Networks • US math teachers typically work in isolation • Social support from colleagues in developing demanding instructional practices • Focus of teacher interactions • Classroom instructional practice • Depth of teacher interactions • Mathematical intent of instructional tasks • Student reasoning strategies

28. Conjecture: Key Resources for Teacher Networks • Time built into the school schedule for collaboration among mathematics teachers • Access to colleagues who have already developed relatively accomplished instructional practices • Concrete exemplars of high-quality instructional practice

29. District Plan: Teacher Networks • 1-2 mathematics teachers in each school receive intensive mathematics professional development • Lead mathematics teachers • Facilitate biweekly or monthly teacher study group meetings

30. Findings and Recommendations: Teacher Networks • Quality of professional development for lead teachers high • Does not focus specifically on teaching underserved groups -- English language learners (ELLs) • Additional professional development for lead teachers on: • Teaching language in the context of mathematics -- ELLs

31. Findings and Recommendations: Teacher Networks • Collaboration between isolated pairs of mathematics teachers in some schools • Typically low depth • No opportunities for lead teachers to share what they are learning in most schools • Common planning time for mathematics teachers • Additional professional development for lead teachers on: • Process of supporting colleagues’ learning • Organizing the content of a study group’s work

32. Findings and Recommendations: Teacher Networks • At least one mathematics teacher in each school with a sophisticated view of high-quality mathematics instruction • Principals selected teachers for additional professional development • District policy: criteria for selecting lead mathematics teachers

33. Conjecture: Shared Vision of High Quality Mathematics Instruction • Instructional goals -- what students should know and be able to do mathematically • How students' development of these forms of mathematical knowing can be supported

34. Conjecture: Shared Vision of High Quality Mathematics Instruction • Coordination between district administrative units • Curriculum and Instruction • Leadership • Research and Evaluation • English Language Learners • Special Education

35. Conjecture: Shared Vision of High Quality Mathematics Instruction • Occupational groups: Mathematics teachers, principals, district mathematics specialists, district leadership specialists, … • Differences in: • Responsibilities • Practices • Professional affiliations (and professional identities)

36. Conjecture: Brokers • Participate at least peripherally in the activities of two or more groups • Can bridge between differing agendas for mathematics instruction

37. District Plan: Shared Instructional Vision • Curriculum Cabinet -- heads of all district units + area superintendents • Professional development in instructional leadership for all principals • Vision of high quality instruction -- not content specific • Intellectually-demanding tasks • Maintain the challenge of the tasks as they are enacted in the classroom • Compatible with district goals for mathematics instruction

38. Findings and Recommendations: Shared Instructional Vision • District leaders: Inconsistent visions + not specific to mathematics • Form rather than function views • Area superintendents participate in mathematics professional development with lead teachers • Broker between district leaders and principals • Support alignment between Curriculum and Instruction, and Leadership

39. Findings and Recommendations: Shared Instructional Vision • Principals: Not specific to mathematics • Form rather than function views • Teachers: At least one mathematics teacher in each school with a sophisticated view of high-quality mathematics instruction • Few formal opportunities for principals to draw on teacher expertise

40. Findings and Recommendations: Shared Instructional Vision • Principals share leadership of mathematics study groups with leader teachers • Principals gain access to mathematics expertise in their schools • Broker between mathematics teachers and school/district leaders • Legitimize work of lead teachers • Lead teachers can focus on content-specific aspects of study group activities

41. Conjecture: Mutual Accountability • School leaders hold mathematics teachers accountable for developing high-quality instructional practices • School leaders are accountable to mathematics teachers for supporting teachers’ learning

42. Conjecture: Leadership Content Knowledge • Enables school and district leaders to: • Recognize high-quality mathematics instruction • Support its development • Organize the conditions for continuous learning of school and district staff (Stein & Nelson)

43. Conjecture: Leadership Content Knowledge • Principals require a relatively deep understanding of: • Mathematical knowledge for teaching • What is known about how to teach mathematics effectively • How students learn mathematics • Teachers-as-learners and effective ways of teaching teachers

44. Conjecture: Leadership Content Knowledge • Distributed across formal and informal leaders • Lead mathematics teachers • Accomplished teachers as informal instructional leaders

45. District Plan: Mutual Accountability • Professional development in instructional leadership for all principals • Spend two hours in classrooms each day • Use developing understanding of (content-free) high-quality instruction to: • Assess and communicate about instruction • Organize school-level teacher professional development • Develop school improvement plans

46. Findings and Recommendations: Mutual Accountability • Most principals do not view themselves as instructional leaders • Most principals are spending only limited time in classrooms • Inconsistent messages from district leaders -- not aware that district leaders expect them to be in classrooms • District leaders need to communicate expectations for what it means to be an instructional leader clearly and consistently • Hold principals accountable for supporting mathematics teachers in improving their instructional practices

47. Findings and Recommendations: Mutual Accountability • Most Principals have developed form rather than function views of high-quality mathematics instruction • Feedback to teachers focuses on surface level features of instruction (e.g., arranging students in groups) • Most principals are not organizing school-based professional development for mathematics teachers • No supports for principals as instructional leaders beyond professional development

48. Findings and Recommendations: Mutual Accountability • Area superintendents provide guidance on: • Providing constructive feedback to teachers • Organizing school-based professional development • Principals participate in at least a portion of mathematics professional development with lead teachers • Principals share the leadership of mathematics study groups

49. Findings and Recommendations: Mutual Accountability • Generic classroom observation form specifies “promotion of innovative teaching methods” • Redesign observation form to reflect district vision of high-quality mathematics instruction

50. Summary • Teacher networks • Time for collaboration • Access to expertise • Shared instructional vision • Brokers • Mutual accountability • Leadership content knowledge