paul cobb vanderbilt university icme 11, monterrey, mexico, july 2008
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The Challenges of Scale: Designing Learning Organizations for Instructional Improvement in Mathematics. Paul Cobb Vanderbilt University ICME 11, Monterrey, Mexico, July 2008. Purpose. - PowerPoint PPT PresentationTRANSCRIPT
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The Challenges of Scale: Designing Learning Organizations for Instructional Improvement in
Mathematics
Paul CobbVanderbilt University
ICME 11, Monterrey, Mexico, July 2008
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Purpose
• Illustrate a way of conducting research studies that aim to inform the ongoing improvement of mathematics teaching and learning at scale
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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
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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
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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 practice
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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
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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
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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
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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
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Transcending This Forced Choice
• 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 structures distance into units
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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
• Skill in pursuing a mathematical agenda by building on students’ contributions
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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
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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 for each school in mathematics
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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
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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
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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
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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
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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 Smith
Erin Henrick Kara JacksonChuck Munter Sarah
GreenJohn Murphy Karin
KatterfeldLynsey Gibbons Glenn
Colby
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One District as an Illustrative Case
• Conjectured support structures
• The district’s improvement plan
• Findings and feedback to the district
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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
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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
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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
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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
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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
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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
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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 knowing 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 • 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
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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
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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
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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
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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 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• Organize the conditions for
continuous learning of school and district staff(Stein & Nelson)
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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
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Conjecture: Leadership Content Knowledge
• Distributed across formal and informal leaders• Lead mathematics teachers• Accomplished teachers as informal
instructional leaders
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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
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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
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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
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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
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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
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Summary
• Teacher networks• Time for collaboration• Access to expertise
• Shared instructional vision• Brokers
• Mutual accountability• Leadership content knowledge
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Next Steps
• Fall/autumn 2008:• Document district plan• To what extent have they actually
acted on the basis of our feedback?
• January-March 2009:• Document the consequences of
any changes
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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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