designing schools to support teachers’ ongoing learning paul cobb vanderbilt university
TRANSCRIPT
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Designing Schools to Support Teachers’ Ongoing Learning
Paul CobbVanderbilt University
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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
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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)
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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
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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
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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
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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
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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
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High-Quality Instruction
• Keep one eye on the mathematical horizon and the other on students’ current understandings, concerns, and interests(Ball, 1993)
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Measuring With a Ten Bar
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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]
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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].
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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.
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Measuring With a Ten Bar
• Measuring as a sequence of separate units• Measuring as the accumulation of distance
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Classroom Discourse
• Not sufficient to show how measured• Also have to explain why measured in a particular way• Measuring organizes distance into units
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Research Team
Paul Cobb Tom SmithErin Henrick Kara JacksonGlenn Colby Annie Garrison Lynsey Gibbons Sarah GreenKarin Katterfeld Chuck MunterRebecca Schmidt Jonee Wilson
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Instructional Quality Assessment
Year 1
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LMT – Year 1 and 2
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LMT – Year 1 and 2
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One District as an Illustrative Case
• Conjectured support structures
• The district’s improvement plan
• Analysis and feedback to the district
• Overall findings
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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
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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
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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
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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
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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
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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
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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
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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
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Findings: Teacher Networks
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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
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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
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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
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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
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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
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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
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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
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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)
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Conjecture: Brokers
• Participate at least peripherally in the activities of two or more groups• Can bridge between differing agendas for mathematics instruction
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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
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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
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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
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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
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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
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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)
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Summary
• Teacher networks• Time for collaboration• Access to instructional expertise
• Shared instructional vision• Brokers
• Mutual accountability• Leadership content knowledge
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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
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Policy Research
• The outcomes of specific policies
• The process by which particular policies are implemented• No position on what high-quality instruction looks like
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Mathematics Education
• Students’ and teachers’ learning• Classroom in an institutional vacuum
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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
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