Designing Schools to Support Teachers’ Ongoing Learning

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 ImprovementProjects • 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 ImprovementProjects • 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 ImprovementProjects • 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. 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]

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 Cobb Tom Smith Erin Henrick Kara Jackson Glenn Colby Annie Garrison Lynsey Gibbons Sarah Green Karin Katterfeld Chuck Munter Rebecca Schmidt Jonee Wilson

27. Instructional Quality Assessment Year 1

28. LMT – Year 1 and 2

29. 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. Findings: Teacher Networks • 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