1. Designing Schools to Support Teachers’ Ongoing Learning Paul Cobb Vanderbilt University

2. Background: US Educational System Decentralized education system 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 100,000 students or more

3. 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 (Richard Elmore)

4. 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 practices

5. Large-Scale Instructional Improvement Projects Focus is typically on teacher professional development Unanticipated “obstacles” Conflicts with other district initiatives Lack of understanding and/or support by school and district administrators

6. Large-Scale Instructional Improvement Projects Flying blind: Little knowledge of the schools and districts in which they are working Reactive: Plans change in response to unanticipated obstacles

7. Large-Scale Instructional Improvement Projects Proactive: Document school and district resources and potential barriers Plan for school and district structures, resources, and relationships that might support 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 supporting the development of high-quality instructional practices School and district support: structures, resources, and social relationships Institutional setting of mathematics teaching

9. High-Quality Instruction Keep one eye on the mathematical horizon and the other on students’ current understandings, concerns, and interests (Ball, 1993)

10. Measuring With a Ten Bar

11. 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]

12. 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].

13. 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.

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

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

16. Demands on the Teacher Teacher adjusts instruction to the students Ongoing assessment of students’ reasoning Non-routine -- a complex and demanding activity Students have to adjust to the teacher Covering instructional objectives + classroom management Teaching a routine activity

17. Demands on the Teacher Deep understanding of mathematics Mathematical knowledge for teaching Knowledge of how students’ reasoning develops in particular mathematical domains Knowing-in-action how to achieve a mathematical agenda by building on students’ (diverse) solutions

18. 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 in mathematics for each school

19. Investigating What it Takes to Improve Instruction at Scale Series of conjectures about school and district structures, resources, and social, relationships Instruments to document the extent to which those structures, resources, and social relationships have been established Investigate interrelations between: Conjectured school and district supports Quality of teachers’ instructional practices Students’ learning

20. Investigating What it Takes to Improve Instruction at Scale Four urban districts High proportion of students from traditionally underserved groups of students Limited financial resources High teacher turn over Most schools and districts clueless about how to respond productively to high-stakes accountability A small minority have reasonably worked out strategies

21. Investigating What it Takes to Improve Instruction at Scale Four annual rounds of yearly data collection Document district strategies for improving middle- school mathematics Document how those strategies are actually playing out in schools and classrooms First year: Baseline data Document change over a three-year period in each district

22. Data Collection School and district support structures, resources, and relationships Audio-recorded interviews On-line surveys Quality of teacher professional development Video-recordings Audio-recordings

23. Data Collection 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. Analytical Tools Extent of teacher networks Frequency and depth of teacher interactions Visions of high quality mathematics instruction Coaches’ practices in supporting teachers’ learning Group and classroom settings Quality of the curriculum Quality of teacher professional development Principals’ direct and indirect instructional leadership practices

25. 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

26. Research Team Paul CobbTom Smith Erin HenrickKara Jackson Glenn Colby Annie Garrison Lynsey GibbonsSarah Green Karin Katterfeld Chuck Munter Rebecca SchmidtJonee Wilson

27. Instructional Quality Assessment Year 1

28. LMT – Year 1 and 2

30. One District as an Illustrative Case Conjectured support structures The district’s improvement plan Analysis and feedback to the district Overall findings

31. Conjecture: Teacher Networks US teachers typically work in isolation Social support from colleagues in developing demanding instructional practices Focus of teacher interactions Classroom instructional practice

32. Conjecture: Teacher Networks Depth of teacher interactions How to use instructional materials Aligning curriculum with state standards Mathematical intent of instructional tasks Student reasoning strategies

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

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

35. Analysis 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

36. Analysis and Recommendations: Teacher Networks Collaboration between isolated pairs of mathematics teachers 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

37. Analysis 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: explicit criteria for selecting lead mathematics teachers

38. Findings: Teacher Networks Online Network Survey All mathematics teachers in participating schools Measure of potential learning opportunities for a teacher Sum of depth of interaction scores across all of the teacher’s interactions

39. Findings: Teacher Networks

40. Controlling for size of math department: Math teachers in Districts B and C participate in interactions of greater depth than those in District A Scheduled time for teacher collaboration Will compare by department and by grade level Types of activities in which teachers engage Math coaches Ties with coach influences depth of interactions

41. Findings: More Accomplished Others - Math Coaches District B: School-based math coaches District policy: Support learning of all math teachers The extent to which the coach is central in teacher networks

42. Findings: More Accomplished Others - Math Coaches Teachers perceived the coach: to be a good mathematics teacher able to support them Described interactions as useful in improving their classroom classroom practice

43. Findings: More Accomplished Others - Math Coaches Principal able to describe how coach should support teachers in some detail Support all teachers versus weak teachers Scheduled time for coach to meet with math teachers as a group – emphasized the importance of the meetings Co-participated on improving instructional practice – more likely to seek advice from coach outside meetings

44. Findings: More Accomplished Others - Math Coaches Principal shared responsibility for supporting teachers’ learning with the coach Attended mathematics department meetings Observed classroom instruction frequently Ongoing discussions about quality of mathematics instruction and teachers needs

45. 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 reasoning can be supported

46. 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

47. 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)

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

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

50. Analysis 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 Support alignment between Curriculum and Instruction, and Leadership Brokers between district leaders and principals

51. Analysis 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 or learn from expert teachers

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

53. Conjecture: Mutual Accountability School leaders hold mathematics teachers accountable for developing high-quality instructional practices School leaders are accountable to mathematics teachers (and district leaders) for supporting teachers’ learning

54. Conjecture: Leadership Content Knowledge Enables school and district leaders to: Recognize high-quality mathematics instruction Support its development directly Organize the conditions for teachers’ ongoing learning (Stein & Nelson, 2003)

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

56. Conjecture: Leadership Content Knowledge Distributed across formal and informal leaders Lead mathematics teachers Accomplished teachers as informal instructional leaders Principal instructional leadership involves recognizing and capitalizing on mathematics teachers’ expertise

57. District Plan: Mutual Accountability Professional development in instructional leadership for all principals In classrooms observing instruction for two hours each day Use developing understanding of (content-free) high-quality instruction to: Assess quality of instruction and give feedback to teachers Organize school-level teacher professional development Develop school improvement plans

58. Analysis and Recommendations: Mutual Accountability Most principals do not view themselves as instructional leaders Most principals are spending only limited time in classrooms 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

59. Analysis 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., arrange 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

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

61. Analysis and Recommendations: Mutual Accountability Generic classroom observation form Promotion of innovative teaching methods Redesign observation form to reflect district vision of high-quality mathematics instruction

62. Findings: Principal’s Visions of High- Quality Mathematics Instruction PD for principal instructional leadership in all four districts Overall improvement from Year 1 to Year 2 Generally not in conflict with districts’ goals for instructional improvement Form view rather than function view Bad news: Communicate expectations for and press for high-quality instruction

63. Findings: Principal’s Visions of High- Quality Mathematics Instruction Principal PD in District D Distinguishing between high- and low-cognitive demand tasks Distinguishing between high- and low-level enactment of tasks based on: Classroom observations Student work Giving feedback to teachers Developing school improvement plans for mathematics instruction

64. Findings: Coordination Between District Administrative Units District leaders’ view instructional improvement as a process of: Supporting others’ learning Disseminating information about desired practices and pressing for compliance Extent to which mathematics specialists viewed as a valued resource

65. Findings: Coordination Between District Administrative Units Relationship between “the line” and technical assistance departments Discourse of: High-stakes accountability Instructional improvement Supporting others’ learning Disseminating information and pressing for compliance

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

67. Policy and Learning Policy Local, state, and national policies intentionally designed to influence teachers’ classroom practices Mathematics education Professional development and instructional materials intentionally designed to influence teachers’ classroom practices

68. Policy Research The outcomes of specific policies The process by which particular policies are implemented No position on what high-quality instruction looks like

69. Mathematics Education Students’ and teachers’ learning Classroom in an institutional vacuum

70. Learning Policy Formulate and refine policies by building on research on learning and teaching Frame instructional improvement as a problem of organizational learning for schools and districts