Paul Cobb and the MIST Team Vanderbilt University University of Washington

1. A Provisional Agenda for Research on Improving the Quality of Mathematics Teaching on a Large Scale Paul Cobb and the MIST Team Vanderbilt University University of Washington Michigan State University McGill University

2. Purpose • Outline a set of issues that need to be addressed if research is to provide adequate guidance for large-scale instructional improvement efforts in mathematics • Across a large urban district

3. Overview • Preamble: what counts as high-quality instruction • Background: ongoing work as a setting for appreciating the limitations of current research • Proposal for issues that need to be addressed

4. What Counts as Instructional Quality? • Has to be justified in terms of students’ learning of mathematics that is worth knowing • Conceptual understanding as well as procedural fluency • Justifying solutions, evaluating the reasonableness of solutions, generalizing from solutions, making connections among multiple representations of mathematical ideas

5. Research on Students’ Mathematical Learning • Rigorous mathematical tasks • Individual or small group work • Whole class discussion • Teacher presses students to: • Explain and justify their reasoning • Make connections between different solutions

6. Goals for Teachers Learning • High-leverage instructional practices • Planning and conducting productive whole class discussions • Setting up rigorous mathematical tasks • Specific types of knowledge implicated in the enactment of these practices • Mathematical knowledge for teaching • Vision of high-quality mathematics instruction • View of students’ mathematical capabilities

7. Challenge for Districts • How to organize, support, and press for teacher learning across the entire system • What guidance can research provide?

8. Background: MIST Project • Four-year collaboration with four large urban districts – 360,000 students – 2007-2011 • Continued collaboration with two districts – 180,000 students – 2011-2015 • Investigate (and support) the districts’ instructional improvement efforts in middle-grades mathematics

9. Background: MIST Project • High proportion of students from traditionally underserved groups • Limited financial resources • High teacher turn over • High proportion of novice teachers • Atypical in one respect: • Aiming at ambitious goals for student learning and thus for teachers’ instructional practices

10. District Participants • 30 middle-grades mathematics teachers in 6-10 schools in each district • Mathematics coaches • School leaders • Principals, assistant principals • District leaders • Across central office units that had a stake in mathematics teaching and learning

11. Collaboration with Districts

12. Collaboration with Districts

13. Collaboration with Districts • District leaders attempt to act on our recommendations to a significant extent • Become co-designers of district improvement strategies • Participants in as well as observers of the districts’ instructional improvement efforts

14. Collaboration with Districts • Formulating recommendations: Have to address concrete organizational design problems • Occasion to appreciate • The types of problems that district leaders have to address • Extent to which current research can provide guidance – hence this talk

15. Research Goal • Develop an empirically grounded theory of action for instructional improvement at scale • Can inform other districts’ instructional improvement efforts

16. Ongoing Analyses • Initial conjectures about supports and accountability relations • Drew on then available literature • Conjectures informed initial recommendations to districts • District leaders acted on recommendations – opportunity to test and revise conjectures

17. Retrospective Analyses • On-line surveys for teachers, coaches, and school leaders • Video-recordings of two consecutive lessons in the 120 participating teachers’ classrooms • Coded using the Instructional Quality Assessment (IQA) • Assessments of teachers’ and coaches’ Mathematical Knowledge for Teaching (MKT) • Video-recordings of select district teacher professional development • Audio-recordings of teacher collaborative planning time • Student achievement data

18. Theory of Action for Instructional Improvement at Scale • A coherent instructional system: • Instructional materials + professional development + assessments to inform instruction + additional supports for struggling students • Mathematics coaches’ practices in providing job-embedded support for teachers’ learning

19. Theory of Action for Instructional Improvement at Scale • School leaders’ practices as instructional leaders in mathematics • District leaders’ practices in supporting the development of school-level capacity for instructional improvement

20. Research Team Paul Cobb Tom Smith Kara Jackson Erin Henrick Ilana Horn Ken Frank

21. Research Team Jessica RigbyMollie Appelgate Jonee Wilson Adrian Larbi-CherifBrooks Rosenquist Charlotte Munoz Britnie Kane Jason Brasel Brette Garner Seth Hunter Emily Kern Megan Webster MahtabNazemi I-Chien Chen

23. Vision of high-quality instruction: • Small set of high-leverage practices that are potentially learnable in the context of high-quality professional development • Explicit goals for students’ learning • Vision of high-quality instruction • Instructional materials • Component 1: Coherent Instructional System • Instructional materials: • Grounded in student learning trajectories that aim at significant mathematical ideas

24. Teacher professional development • Pull-out Professional Development (PD): • Specific PD designs – promising findings • Grounded in classroom practice – pedagogies of investigation and enactment • Most work in pre-service – have extrapolate to in-service • Teacher Collaborative Time (TCT) • Most researcher-led – potentially productive types of activities • Naturally occurring – characteristics of productive teacher groups • Component 1: Coherent Instructional System

25. Formative assessment systems • Aligned with ambitious goals for students’ learning • Grounded in trajectories of students’ learning • Component 1: Coherent Instructional System • Assessments to inform instruction

26. Goal: support struggling students to participate effectively in mainstream instruction • Component 1: Coherent Instructional System • Additional supports for struggling students

27. Coherent Instructional System • Collaborating districts: fragments of a coherent instructional system • Strengths: explicit goals for students’ learning, vision of high-quality instruction, instructional materials • Challenge: teacher professional development – district capacity • Challenge: TCT – expertise + leadership of meetings – district capacity • Weakness: additional supports for struggling students – not aligned with mainstream classroom instruction

28. Needed Research: Developing District Capacity • Researchers typically assume full responsibility for “building” particular elements • The problem of scale involves supporting districts’ development of the capacity to create, coordinate, and sustain the elements of such a system

29. Developing District Capacity: Sacrificial Offering • Example: co-designing and co-leading PD for coaches with district mathematics specialists • Support the development coaches’ capacity to design and lead high-quality teacher PD • Gradual hand over of responsibility to district mathematics specialists • Overall goal: Investigate how to support districts’ development of capacity to develop and sustain a cadre of mathematics coaches

30. Needed Research: Interrelations Between Elements of the System • Current research typically focuses on the individual elements of a coherent instructional system • Also need to investigate interrelations between various the elements, and between elements and other components of ToA • Which are preconditions for the development of other elements/components?

31. Developing District Capacity: Sacrificial Offering • Example: co-designing and co-leading PD for school leaders • School leaders press for instructional improvement • Coaches support teachers in meeting those expectations • Investigate development of aligned support and press for teachers’ improvement of their instructional practices

32. Mathematics Coaching • Finding: Teachers’ improvement of their instructional practices depends crucially on their access to colleagues who have already developed accomplished practices • Three of our four districts: Small proportion of accomplished teachers • Critical role of coaches as more accomplished colleagues

33. Mathematics Coaching • Design and lead pull-out PD • Work with groups of teachers during TCT • Current research + our findings indicate importance of leadership/expertise in TCT • Support teachers one-on-one in their classrooms • Build on pull-out PD and work in TCT

34. Current Research on Coaching • Provides little guidance on: • Types of activities in which coaches might engage teachers • Coaches practices as they enact these activities • Supporting the development of a cadre of accomplished mathematics coaches • One of the collaborating districts: four years of sustained professional development for coaches • Only slightly ahead of the teachers they were expected to support

35. Needed Research: Delineating Goals for Coaches’ Learning • Develop testableconjectures about potentially productive coaching practices • Working with groups of teachers: • Draw on studies of researcher-led and naturally occurring PLCs • Kazemiand Franke: Potentially productive activities • Horn: Press teachers of key issues

36. Needed Research: Delineating Goals for Coaches’ Learning • Working with teachers in their classrooms: • Draw on research on teacher learning and professional development • Points to importance of modeling and especially co-teaching • Observation/feedback at specific points in teachers’ development • e.g., Tuning their enactment specific practices

37. Needed Research: Delineating Goals for Coaches’ Learning • Important to explicate the forms of knowledgeabilityimplicated in the enactment of proposed practices • Researchers do not typically report what they needed to know

38. Needed Research: Specifying Forms of Knowledgeability • Mathematical knowledge for teaching (MKT) • Additional candidate: an envisioned trajectory for teachers’ learning • Classroom management • Student engagement • Teacher questioning • Informs decisions about which aspects of practice to work on with teachers

39. Needed Research: Designs for Supporting Coaches’ Learning • Both settings: • Draw on very limited literature on coach PD • Extrapolate from work on teacher learning and teacher PD

40. Needed Research: Test and Revise Designs for Coaches’ Learning • Design experiments to: • Test and refine conjectures about supports for coaches’ development of target practices • Assess in terms of improvements in: • Coaches’ practices • Quality of teachers’ classroom instruction • Student learning

41. Coach PD: A Sacrificial Offering • MIST & District Math Leaders collaboratively plan for upcoming session Coach PD Session • MIST views video-recording of pilot PD in light of goals for coaches’ learning • Coaches lead PD with pilot group

42. School Instructional Leadership • Standards-based reform: Principals and assistant principals increasingly expected to act as instructional leaders in specific content areas • Manage instruction rather than manage around instruction

43. Current Research School Instructional Leadership • No consensus on what school leaders need to know and be able to do in order to be effective instructional leaders in mathematics • General content-independent characteristics of high-quality instruction • Observe instruction and provide feedback • MKT, student mathematical learning, high-quality mathematics instruction, teacher learning • Coach mathematics teachers

44. Findings • Interviews – vision of high-quality mathematics instruction (VHQMI) • Form rather than function views • Consistent with teachers’ accounts of the feedback they receive from school leaders • Extensive professional development • Focused on general, content-independent characteristics of high-quality instruction

45. Initial Findings • General characteristics of high-quality inquiry-oriented instruction • Too abstract – not able to connect to concrete instructional practices • MKT, student mathematical learning, high-quality mathematics instruction, teacher learning • Beyond the capacity of most districts

46. Needed Research: Delineating Goals for School Leaders’ Learning • Develop testable conjectures about potentially productive school leadership practices • Justify in terms of: • Direct support/press for teachers’ learning • Indirect support – developing conditions for teacher learning

47. Current Bets • Identify and capitalize on instructional expertise in the school • Observe mathematics instruction and provide feedback • Participate in teacher collaborative time (TCT) • Support coach to support teachers’ learning

48. School Leadership Routine School Leader And Coach: Quality of Individual Teachers’ Instruction + How to Support Instructional Improvement + Jointly Plan for Teacher Collaborative Time Attend Teacher Collaborative Time Observe Classroom Instruction Meet with Mathematics Coach

49. Needed Research: Delineating Goals for School Leaders’ Learning • Important to explicate the forms of knowledgeabilityimplicated in the enactment of the proposed practices • Vision of high-quality mathematics instruction • Observing instruction and giving feedback • Identifying and leveraging instructional expertise

50. Needed Research: Designs for Supporting School Leaders’ Learning • Extrapolate from work on teacher learning and teacher PD • Vision of high-quality mathematics instruction • Distinguish between high- and low-rigor tasks • Distinguish between strong and weak enactments of specific high-leverage instructional practices